# Fight Finance

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The expression 'cash is king' emphasizes the importance of which business decision?

The expression 'you have to spend money to make money' relates to which business decision?

Which of the following decisions relates to the current assets and current liabilities of the firm?

A stock is expected to pay its next dividend of $1 in one year. Future annual dividends are expected to grow by 2% pa. So the first dividend of$1 will be in one year, the year after that $1.02 (=1*(1+0.02)^1), and a year later$1.0404 (=1*(1+0.02)^2) and so on forever.

Its required total return is 10% pa. The total required return and growth rate of dividends are given as effective annual rates.

Calculate the current stock price.

A stock just paid a dividend of $1. Future annual dividends are expected to grow by 2% pa. The next dividend of$1.02 (=1*(1+0.02)^1) will be in one year, and the year after that the dividend will be $1.0404 (=1*(1+0.02)^2), and so on forever. Its required total return is 10% pa. The total required return and growth rate of dividends are given as effective annual rates. Calculate the current stock price. A stock is just about to pay a dividend of$1 tonight. Future annual dividends are expected to grow by 2% pa. The next dividend of $1 will be paid tonight, and the year after that the dividend will be$1.02 (=1*(1+0.02)^1), and a year later 1.0404 (=1*(1+0.04)^2) and so on forever.

Its required total return is 10% pa. The total required return and growth rate of dividends are given as effective annual rates.

Calculate the current stock price.

The following cash flows are expected:

• Constant perpetual yearly payments of $70, with the first payment in 2.5 years from now (first payment at t=2.5). • A single payment of$600 in 3 years and 9 months (t=3.75) from now.

What is the NPV of the cash flows if the discount rate is 10% given as an effective annual rate?

The following cash flows are expected:

• 10 yearly payments of $80, with the first payment in 6.5 years from now (first payment at t=6.5). • A single payment of$500 in 4 years and 3 months (t=4.25) from now.

What is the NPV of the cash flows if the discount rate is 10% given as an effective annual rate?

A residential investment property has an expected nominal total return of 6% pa and nominal capital return of 2.5% pa. Inflation is expected to be 2.5% pa.

All of the above are effective nominal rates and investors believe that they will stay the same in perpetuity.

What are the property's expected real total, capital and income returns?

The answer choices below are given in the same order.

A low-growth mature stock has an expected nominal total return of 6% pa and nominal capital return of 2% pa. Inflation is expected to be 3% pa.

All of the above are effective nominal rates and investors believe that they will stay the same in perpetuity.

What are the stock's expected real total, capital and income returns?

The answer choices below are given in the same order.

Which of the following statements is NOT correct?

Which of the following statements about cash in the form of notes and coins is NOT correct? Assume that inflation is positive.

Notes and coins:

How can a nominal cash flow be precisely converted into a real cash flow?

Total cash flows can be broken into income and capital cash flows.

What is the name given to the cash flow generated from selling shares at a higher price than they were bought?

The perpetuity with growth formula, also known as the dividend discount model (DDM) or Gordon growth model, is appropriate for valuing a company's shares. $P_0$ is the current share price, $C_1$ is next year's expected dividend, $r$ is the total required return and $g$ is the expected growth rate of the dividend.

$$P_0=\dfrac{C_1}{r-g}$$

The below graph shows the expected future price path of the company's shares. Which of the following statements about the graph is NOT correct?

If housing rents are constrained from growing more than the maximum target inflation rate, and houses can be priced as a perpetuity of growing net rental cash flows, then what is the implication for house prices, all things remaining equal? Select the most correct answer.

Background: Since 1990, many central banks across the world have become 'inflation targeters'. They have adopted a policy of trying to keep inflation in a predictable narrow range, with the hope of encouraging long-term lending to fund more investment and maintain higher GDP growth.

Australia's central bank, the Reserve Bank of Australia (RBA), has specifically stated their inflation target range is between 2 and 3% pa.

Some Australian residential property market commentators suggest that because rental costs comprise a large part of the Australian consumer price index (CPI), rent costs across the nation cannot significantly exceed the maximum inflation target range of 3% pa without the prices of other goods growing by less than the target range for long periods, which is unlikely.

You are promised 20 payments of $100, where the first payment is immediate (t=0) and the last is at the end of the 19th year (t=19). The effective annual discount rate is $r$. Which of the following equations does NOT give the correct present value of these 20 payments? Who is most in danger of being personally bankrupt? Assume that all of their businesses' assets are highly liquid and can therefore be sold immediately. An investor owns a whole level of an old office building which is currently worth$1 million. There are three mutually exclusive projects that can be started by the investor. The office building level can be:

• Rented out to a tenant for one year at $0.1m paid immediately, and then sold for$0.99m in one year.
• Refurbished into more modern commercial office rooms at a cost of $1m now, and then sold for$2.3m when the refurbishment is finished in one year.
• Converted into residential apartments at a cost of $2m now, and then sold for$3.4m when the conversion is finished in one year.

All of the development projects have the same risk so the required return of each is 10% pa. The table below shows the estimated cash flows and internal rates of returns (IRR's).

 Mutually Exclusive Projects Project Cash flownow ($) Cash flow inone year ($) IRR(% pa) Rent then sell as is -900,000 990,000 10 Refurbishment into modern offices -2,000,000 2,400,000 20 Conversion into residential apartments -3,000,000 3,400,000 13.33

Which project should the investor accept?

You have $100,000 in the bank. The bank pays interest at 10% pa, given as an effective annual rate. You wish to consume twice as much now (t=0) as in one year (t=1) and have nothing left in the bank at the end. How much can you consume at time zero and one? The answer choices are given in the same order. You have$100,000 in the bank. The bank pays interest at 10% pa, given as an effective annual rate.

You wish to consume half as much now (t=0) as in one year (t=1) and have nothing left in the bank at the end.

How much can you consume at time zero and one? The answer choices are given in the same order.

You are an equities analyst trying to value the equity of the Australian telecoms company Telstra, with ticker TLS. In Australia, listed companies like Telstra tend to pay dividends every 6 months. The payment around August is called the final dividend and the payment around February is called the interim dividend. Both occur annually.

• Today is mid-March 2015.
• TLS's last interim dividend of $0.15 was one month ago in mid-February 2015. • TLS's last final dividend of$0.15 was seven months ago in mid-August 2014.

Judging by TLS's dividend history and prospects, you estimate that the nominal dividend growth rate will be 1% pa. Assume that TLS's total nominal cost of equity is 6% pa. The dividends are nominal cash flows and the inflation rate is 2.5% pa. All rates are quoted as nominal effective annual rates. Assume that each month is exactly one twelfth (1/12) of a year, so you can ignore the number of days in each month.

Calculate the current TLS share price.

The expression 'my word is my bond' is often used in everyday language to make a serious promise.

Why do you think this expression uses the metaphor of a bond rather than a share?

Estimate the French bank Societe Generale's share price using a backward-looking price earnings (PE) multiples approach with the following assumptions and figures only. Note that EUR is the euro, the European monetary union's currency.

• The 4 major European banks Credit Agricole (ACA), Deutsche Bank AG (DBK), UniCredit (UCG) and Banco Santander (SAN) are comparable companies to Societe Generale (GLE);
• Societe Generale's (GLE's) historical earnings per share (EPS) is EUR 2.92;
• ACA's backward-looking PE ratio is 16.29 and historical EPS is EUR 0.84;
• DBK's backward-looking PE ratio is 25.01 and historical EPS is EUR 1.26;
• SAN's backward-looking PE ratio is 14.71 and historical EPS is EUR 0.47;
• UCG's backward-looking PE ratio is 15.78 and historical EPS is EUR 0.40;

Note: Figures sourced from Google Finance on 27 March 2015.

Risk-free government bonds that have coupon rates greater than their yields:

A 'fully amortising' loan can also be called a:

Which one of the below statements about effective rates and annualised percentage rates (APR's) is NOT correct?

Which of the following statements is NOT correct? Bond investors:

For an asset price to double every 10 years, what must be the expected future capital return, given as an effective annual rate?

A firm wishes to raise $10 million now. They will issue 6% pa semi-annual coupon bonds that will mature in 3 years and have a face value of$100 each. Bond yields are 5% pa, given as an APR compounding every 6 months, and the yield curve is flat.

How many bonds should the firm issue?

Which of the following statements about the capital and income returns of a 25 year fully amortising loan asset is correct?

Assume that the yield curve (which shows total returns over different maturities) is flat and is not expected to change.

Over the 25 years from issuance to maturity, a fully amortising loan's expected annual effective:

Which of the following statements about the capital and income returns of an interest-only loan is correct?

Assume that the yield curve (which shows total returns over different maturities) is flat and is not expected to change.

An interest-only loan's expected:

A firm pays out all of its earnings as dividends. Because of this, the firm has no real growth in earnings, dividends or stock price since there is no re-investment back into the firm to buy new assets and make higher earnings. The dividend discount model is suitable to value this company.

The firm's revenues and costs are expected to increase by inflation in the foreseeable future. The firm has no debt. It operates in the services industry and has few physical assets so there is negligible depreciation expense and negligible net working capital required.

Which of the following statements about this firm's PE ratio is NOT correct? The PE ratio should:

Note: The inverse of x is 1/x.

The saying "buy low, sell high" suggests that investors should make a:

Which of the following is NOT a synonym of 'required return'?

Total cash flows can be broken into income and capital cash flows. What is the name given to the income cash flow from owning shares?

Which of the following equations is NOT equal to the total return of an asset?

Let $p_0$ be the current price, $p_1$ the expected price in one year and $c_1$ the expected income in one year.

An asset's total expected return over the next year is given by:

$$r_\text{total} = \dfrac{c_1+p_1-p_0}{p_0}$$

Where $p_0$ is the current price, $c_1$ is the expected income in one year and $p_1$ is the expected price in one year. The total return can be split into the income return and the capital return.

Which of the following is the expected capital return?

A stock was bought for $8 and paid a dividend of$0.50 one year later (at t=1 year). Just after the dividend was paid, the stock price was $7 (at t=1 year). What were the total, capital and dividend returns given as effective annual rates? The choices are given in the same order: $r_\text{total}$, $r_\text{capital}$, $r_\text{dividend}$. A share was bought for$30 (at t=0) and paid its annual dividend of $6 one year later (at t=1). Just after the dividend was paid, the share price fell to$27 (at t=1). What were the total, capital and income returns given as effective annual rates?

The choices are given in the same order:

$r_\text{total}$ , $r_\text{capital}$ , $r_\text{dividend}$.

A fixed coupon bond was bought for $90 and paid its annual coupon of$3 one year later (at t=1 year). Just after the coupon was paid, the bond price was $92 (at t=1 year). What was the total return, capital return and income return? Calculate your answers as effective annual rates. The choices are given in the same order: $r_\text{total},r_\text{capital},r_\text{income}$. One and a half years ago Frank bought a house for$600,000. Now it's worth only $500,000, based on recent similar sales in the area. The expected total return on Frank's residential property is 7% pa. He rents his house out for$1,600 per month, paid in advance. Every 12 months he plans to increase the rental payments.

The present value of 12 months of rental payments is $18,617.27. The future value of 12 months of rental payments one year in the future is$19,920.48.

What is the expected annual rental yield of the property? Ignore the costs of renting such as maintenance, real estate agent fees and so on.

Imagine that the interest rate on your savings account was 1% per year and inflation was 2% per year.

After one year, would you be able to buy , exactly the as or than today with the money in this account?

When valuing assets using discounted cash flow (net present value) methods, it is important to consider inflation. To properly deal with inflation:

(I) Discount nominal cash flows by nominal discount rates.

(II) Discount nominal cash flows by real discount rates.

(III) Discount real cash flows by nominal discount rates.

(IV) Discount real cash flows by real discount rates.

Which of the above statements is or are correct?

In the 'Austin Powers' series of movies, the character Dr. Evil threatens to destroy the world unless the United Nations pays him a ransom (video 1, video 2). Dr. Evil makes the threat on two separate occasions:

• In 1969 he demands a ransom of $1 million (=10^6), and again; • In 1997 he demands a ransom of$100 billion (=10^11).

If Dr. Evil's demands are equivalent in real terms, in other words $1 million will buy the same basket of goods in 1969 as$100 billion would in 1997, what was the implied inflation rate over the 28 years from 1969 to 1997?

The answer choices below are given as effective annual rates:

A residential investment property has an expected nominal total return of 6% pa and nominal capital return of 3% pa.

Inflation is expected to be 2% pa. All rates are given as effective annual rates.

What are the property's expected real total, capital and income returns? The answer choices below are given in the same order.

The market expects the Reserve Bank of Australia (RBA) to increase the policy rate by 25 basis points at their next meeting.

Then unexpectedly, the RBA announce that they will increase the policy rate by 50 basis points due to high future GDP and inflation forecasts.

What do you expect to happen to Australia's exchange rate in the short term? The Australian dollar will:

The market expects the Reserve Bank of Australia (RBA) to increase the policy rate by 25 basis points at their next meeting.

As expected, the RBA increases the policy rate by 25 basis points.

What do you expect to happen to Australia's exchange rate in the short term? The Australian dollar will:

Investors expect the Reserve Bank of Australia (RBA) to decrease the overnight cash rate at their next meeting.

Then unexpectedly, the RBA announce that they will keep the policy rate unchanged.

What do you expect to happen to Australia's exchange rate in the short term? The Australian dollar is likely to:

Suppose the Australian cash rate is expected to be 8.15% pa and the US federal funds rate is expected to be 3.00% pa over the next 2 years, both given as nominal effective annual rates. The current exchange rate is at parity, so 1 USD = 1 AUD.

What is the implied 2 year forward foreign exchange rate?

In the below term structure of interest rates equation, all rates are effective annual yields and the numbers in subscript represent the years that the yields are measured over:

$$(1+r_{0-3})^3 = (1+r_{0-1})(1+r_{1-2})(1+r_{2-3})$$

Which of the following statements is NOT correct?

In the below term structure of interest rates equation, all rates are effective annual yields and the numbers in subscript represent the years that the yields are measured over:

$$(1+r_{0-3})^3 = (1+r_{0-1})(1+r_{1-2})(1+r_{2-3})$$

Which of the following statements is NOT correct?

A European company just issued two bonds, a

• 1 year zero coupon bond at a yield of 8% pa, and a
• 2 year zero coupon bond at a yield of 10% pa.

What is the company's forward rate over the second year (from t=1 to t=2)? Give your answer as an effective annual rate, which is how the above bond yields are quoted.

A European company just issued two bonds, a

• 2 year zero coupon bond at a yield of 8% pa, and a
• 3 year zero coupon bond at a yield of 10% pa.

What is the company's forward rate over the third year (from t=2 to t=3)? Give your answer as an effective annual rate, which is how the above bond yields are quoted.

A European company just issued two bonds, a

• 3 year zero coupon bond at a yield of 6% pa, and a
• 4 year zero coupon bond at a yield of 6.5% pa.

What is the company's forward rate over the fourth year (from t=3 to t=4)? Give your answer as an effective annual rate, which is how the above bond yields are quoted.

An Australian company just issued two bonds:

• A 6-month zero coupon bond at a yield of 6% pa, and
• A 12 month zero coupon bond at a yield of 7% pa.

What is the company's forward rate from 6 to 12 months? Give your answer as an APR compounding every 6 months, which is how the above bond yields are quoted.

An Australian company just issued two bonds:

• A 1 year zero coupon bond at a yield of 8% pa, and
• A 2 year zero coupon bond at a yield of 10% pa.

What is the forward rate on the company's debt from years 1 to 2? Give your answer as an APR compounding every 6 months, which is how the above bond yields are quoted.

An Australian company just issued two bonds:

• A 1 year zero coupon bond at a yield of 10% pa, and
• A 2 year zero coupon bond at a yield of 8% pa.

What is the forward rate on the company's debt from years 1 to 2? Give your answer as an APR compounding every 6 months, which is how the above bond yields are quoted.

Suppose you had $100 in a savings account and the interest rate was 2% per year. After 5 years, how much do you think you would have in the account if you left the money to grow? than$102, $102 or than$102?

Do you think that the following statement is or ? “Buying a single company stock usually provides a safer return than a stock mutual fund.”

Katya offers to pay you $10 at the end of every year for the next 5 years (t=1,2,3,4,5) if you pay her$50 now (t=0). You can borrow and lend from the bank at an interest rate of 10% pa, given as an effective annual rate.

Ignore credit risk.

Will you or Katya's deal?

The following equation is called the Dividend Discount Model (DDM), Gordon Growth Model or the perpetuity with growth formula: $$P_0 = \frac{ C_1 }{ r - g }$$

What is $g$? The value $g$ is the long term expected:

For a price of $13, Carla will sell you a share which will pay a dividend of$1 in one year and every year after that forever. The required return of the stock is 10% pa.

Would you like to Carla's share or politely ?

For a price of $6, Carlos will sell you a share which will pay a dividend of$1 in one year and every year after that forever. The required return of the stock is 10% pa.

Would you like to his share or politely ?

For a price of $102, Andrea will sell you a share which just paid a dividend of$10 yesterday, and is expected to pay dividends every year forever, growing at a rate of 5% pa.

So the next dividend will be $10(1+0.05)^1=10.50$ in one year from now, and the year after it will be $10(1+0.05)^2=11.025$ and so on.

The required return of the stock is 15% pa.

Would you like to the share or politely ?

For a price of $1040, Camille will sell you a share which just paid a dividend of$100, and is expected to pay dividends every year forever, growing at a rate of 5% pa.

So the next dividend will be $100(1+0.05)^1=105.00$, and the year after it will be $100(1+0.05)^2=110.25$ and so on.

The required return of the stock is 15% pa.

Would you like to the share or politely ?

For a price of $10.20 each, Renee will sell you 100 shares. Each share is expected to pay dividends in perpetuity, growing at a rate of 5% pa. The next dividend is one year away (t=1) and is expected to be$1 per share.

The required return of the stock is 15% pa.

Would you like to the shares or politely ?

For a price of $129, Joanne will sell you a share which is expected to pay a$30 dividend in one year, and a $10 dividend every year after that forever. So the stock's dividends will be$30 at t=1, $10 at t=2,$10 at t=3, and $10 forever onwards. The required return of the stock is 10% pa. Would you like to the share or politely ? For a price of$95, Sherylanne will sell you a share which is expected to pay its first dividend of $10 in 7 years (t=7), and will continue to pay the same$10 dividend every year after that forever.

The required return of the stock is 10% pa.

Would you like to the share or politely ?

For a price of $100, Vera will sell you a 2 year bond paying semi-annual coupons of 10% pa. The face value of the bond is$100. Other bonds with similar risk, maturity and coupon characteristics trade at a yield of 8% pa.

Would you like to her bond or politely ?

For a price of $100, Carol will sell you a 5 year bond paying semi-annual coupons of 16% pa. The face value of the bond is$100. Other bonds with similar risk, maturity and coupon characteristics trade at a yield of 12% pa.

Would you like to her bond or politely ?

For a price of $100, Rad will sell you a 5 year bond paying semi-annual coupons of 16% pa. The face value of the bond is$100. Other bonds with the same risk, maturity and coupon characteristics trade at a yield of 6% pa.

Would you like to the bond or politely ?

For a price of $100, Andrea will sell you a 2 year bond paying annual coupons of 10% pa. The face value of the bond is$100. Other bonds with the same risk, maturity and coupon characteristics trade at a yield of 6% pa.

Would you like to the bond or politely ?

For a price of $95, Nicole will sell you a 10 year bond paying semi-annual coupons of 8% pa. The face value of the bond is$100. Other bonds with the same risk, maturity and coupon characteristics trade at a yield of 8% pa.

Would you like to the bond or politely ?

A person is thinking about borrowing $100 from the bank at 7% pa and investing it in shares with an expected return of 10% pa. One year later the person will sell the shares and pay back the loan in full. Both the loan and the shares are fairly priced. What is the Net Present Value (NPV) of this one year investment? Note that you are asked to find the present value ($V_0$), not the value in one year ($V_1$). The US government recently announced that subsidies for fresh milk producers will be gradually phased out over the next year. Newspapers say that there are expectations of a 40% increase in the spot price of fresh milk over the next year. Option prices on fresh milk trading on the Chicago Mercantile Exchange (CME) reflect expectations of this 40% increase in spot prices over the next year. Similarly to the rest of the market, you believe that prices will rise by 40% over the next year. What option trades are likely to be profitable, or to be more specific, result in a positive Net Present Value (NPV)? Assume that: • Only the spot price is expected to increase and there is no change in expected volatility or other variables that affect option prices. • No taxes, transaction costs, information asymmetry, bid-ask spreads or other market frictions. Which one of the following will increase the Cash Flow From Assets in this year for a tax-paying firm, all else remaining constant? A residential investment property has an expected nominal total return of 8% pa and nominal capital return of 3% pa. Inflation is expected to be 2% pa. All rates are given as effective annual rates. What are the property's expected real total, capital and income returns? The answer choices below are given in the same order. A stock has a real expected total return of 7% pa and a real expected capital return of 2% pa. Inflation is expected to be 2% pa. All rates are given as effective annual rates. What is the nominal expected total return, capital return and dividend yield? The answers below are given in the same order. You are a banker about to grant a 2 year loan to a customer. The loan's principal and interest will be repaid in a single payment at maturity, sometimes called a zero-coupon loan, discount loan or bullet loan. You require a real return of 6% pa over the two years, given as an effective annual rate. Inflation is expected to be 2% this year and 4% next year, both given as effective annual rates. You judge that the customer can afford to pay back$1,000,000 in 2 years, given as a nominal cash flow. How much should you lend to her right now?

You're considering making an investment in a particular company. They have preference shares, ordinary shares, senior debt and junior debt.

Which is the safest investment? Which will give the highest returns?

A newly floated farming company is financed with senior bonds, junior bonds, cumulative non-voting preferred stock and common stock. The new company has no retained profits and due to floods it was unable to record any revenues this year, leading to a loss. The firm is not bankrupt yet since it still has substantial contributed equity (same as paid-up capital).

On which securities must it pay interest or dividend payments in this terrible financial year?

Which business structure or structures have the advantage of limited liability for equity investors?

What is the lowest and highest expected share price and expected return from owning shares in a company over a finite period of time?

Let the current share price be $p_0$, the expected future share price be $p_1$, the expected future dividend be $d_1$ and the expected return be $r$. Define the expected return as:

$r=\dfrac{p_1-p_0+d_1}{p_0}$

The answer choices are stated using inequalities. As an example, the first answer choice "(a) $0≤p<∞$ and $0≤r< 1$", states that the share price must be larger than or equal to zero and less than positive infinity, and that the return must be larger than or equal to zero and less than one.

Which of the following statements about book and market equity is NOT correct?

One year ago a pharmaceutical firm floated by selling its 1 million shares for $100 each. Its book and market values of equity were both$100m. Its debt totalled $50m. The required return on the firm's assets was 15%, equity 20% and debt 5% pa. In the year since then, the firm: • Earned net income of$29m.
• Paid dividends totaling $10m. • Discovered a valuable new drug that will lead to a massive 1,000 times increase in the firm's net income in 10 years after the research is commercialised. News of the discovery was publicly announced. The firm's systematic risk remains unchanged. Which of the following statements is NOT correct? All statements are about current figures, not figures one year ago. Hint: Book return on assets (ROA) and book return on equity (ROE) are ratios that accountants like to use to measure a business's past performance. $$\text{ROA}= \dfrac{\text{Net income}}{\text{Book value of assets}}$$ $$\text{ROE}= \dfrac{\text{Net income}}{\text{Book value of equity}}$$ The required return on assets $r_V$ is a return that financiers like to use to estimate a business's future required performance which compensates them for the firm's assets' risks. If the business were to achieve realised historical returns equal to its required returns, then investment into the business's assets would have been a zero-NPV decision, which is neither good nor bad but fair. $$r_\text{V, 0 to 1}= \dfrac{\text{Cash flow from assets}_\text{1}}{\text{Market value of assets}_\text{0}} = \dfrac{CFFA_\text{1}}{V_\text{0}}$$ Similarly for equity and debt. The below screenshot of Commonwealth Bank of Australia's (CBA) details were taken from the Google Finance website on 7 Nov 2014. Some information has been deliberately blanked out. What was CBA's market capitalisation of equity? The below screenshot of Microsoft's (MSFT) details were taken from the Google Finance website on 28 Nov 2014. Some information has been deliberately blanked out. What was MSFT's market capitalisation of equity? The investment decision primarily affects which part of a business? The working capital decision primarily affects which part of a business? The financing decision primarily affects which part of a business? Payout policy is most closely related to which part of a business? Business people make lots of important decisions. Which of the following is the most important long term decision? This annuity formula $\dfrac{C_1}{r}\left(1-\dfrac{1}{(1+r)^3} \right)$ is equivalent to which of the following formulas? Note the 3. In the below formulas, $C_t$ is a cash flow at time t. All of the cash flows are equal, but paid at different times. Your friend overheard that you need some cash and asks if you would like to borrow some money. She can lend you$5,000 now (t=0), and in return she wants you to pay her back $1,000 in two years (t=2) and every year after that for the next 5 years, so there will be 6 payments of$1,000 from t=2 to t=7 inclusive.

What is the net present value (NPV) of borrowing from your friend?

Assume that banks loan funds at interest rates of 10% pa, given as an effective annual rate.

Some countries' interest rates are so low that they're zero.

If interest rates are 0% pa and are expected to stay at that level for the foreseeable future, what is the most that you would be prepared to pay a bank now if it offered to pay you $10 at the end of every year for the next 5 years? In other words, what is the present value of five$10 payments at time 1, 2, 3, 4 and 5 if interest rates are 0% pa?

The first payment of a constant perpetual annual cash flow is received at time 5. Let this cash flow be $C_5$ and the required return be $r$.

So there will be equal annual cash flows at time 5, 6, 7 and so on forever, and all of the cash flows will be equal so $C_5 = C_6 = C_7 = ...$

When the perpetuity formula is used to value this stream of cash flows, it will give a value (V) at time:

The following equation is the Dividend Discount Model, also known as the 'Gordon Growth Model' or the 'Perpetuity with growth' equation.

$$P_{0} = \frac{C_1}{r_{\text{eff}} - g_{\text{eff}}}$$

What would you call the expression $C_1/P_0$?

A stock just paid its annual dividend of $9. The share price is$60. The required return of the stock is 10% pa as an effective annual rate.

What is the implied growth rate of the dividend per year?

The following equation is the Dividend Discount Model, also known as the 'Gordon Growth Model' or the 'Perpetuity with growth' equation.

$$P_0=\frac{d_1}{r-g}$$

A stock pays dividends annually. It just paid a dividend, but the next dividend ($d_1$) will be paid in one year.

According to the DDM, what is the correct formula for the expected price of the stock in 2.5 years?

Two years ago Fred bought a house for $300,000. Now it's worth$500,000, based on recent similar sales in the area.

Fred's residential property has an expected total return of 8% pa.

He rents his house out for $2,000 per month, paid in advance. Every 12 months he plans to increase the rental payments. The present value of 12 months of rental payments is$23,173.86.

The future value of 12 months of rental payments one year ahead is $25,027.77. What is the expected annual growth rate of the rental payments? In other words, by what percentage increase will Fred have to raise the monthly rent by each year to sustain the expected annual total return of 8%? Your friend is trying to find the net present value of a project. The project is expected to last for just one year with: • a negative cash flow of -$1 million initially (t=0), and
• a positive cash flow of $1.1 million in one year (t=1). The project has a total required return of 10% pa due to its moderate level of undiversifiable risk. Your friend is aware of the importance of opportunity costs and the time value of money, but he is unsure of how to find the NPV of the project. He knows that the opportunity cost of investing the$1m in the project is the expected gain from investing the money in shares instead. Like the project, shares also have an expected return of 10% since they have moderate undiversifiable risk. This opportunity cost is $0.1m $(=1m \times 10\%)$ which occurs in one year (t=1). He knows that the time value of money should be accounted for, and this can be done by finding the present value of the cash flows in one year. Your friend has listed a few different ways to find the NPV which are written down below. (I) $-1m + \dfrac{1.1m}{(1+0.1)^1}$ (II) $-1m + \dfrac{1.1m}{(1+0.1)^1} - \dfrac{1m}{(1+0.1)^1} \times 0.1$ (III) $-1m + \dfrac{1.1m}{(1+0.1)^1} - \dfrac{1.1m}{(1+0.1)^1} \times 0.1$ (IV) $-1m + 1.1m - \dfrac{1.1m}{(1+0.1)^1} \times 0.1$ (V) $-1m + 1.1m - 1.1m \times 0.1$ Which of the above calculations give the correct NPV? Select the most correct answer. A young lady is trying to decide if she should attend university or not. The young lady's parents say that she must attend university because otherwise all of her hard work studying and attending school during her childhood was a waste. What's the correct way to classify this item from a capital budgeting perspective when trying to decide whether to attend university? The hard work studying at school in her childhood should be classified as: A young lady is trying to decide if she should attend university. Her friends say that she should go to university because she is more likely to meet a clever young man than if she begins full time work straight away. What's the correct way to classify this item from a capital budgeting perspective when trying to find the Net Present Value of going to university rather than working? The opportunity to meet a desirable future spouse should be classified as: A man is thinking about taking a day off from his casual painting job to relax. He just woke up early in the morning and he's about to call his boss to say that he won't be coming in to work. But he's thinking about the hours that he could work today (in the future) which are: A man has taken a day off from his casual painting job to relax. It's the end of the day and he's thinking about the hours that he could have spent working (in the past) which are now: What is the net present value (NPV) of undertaking a full-time Australian undergraduate business degree as an Australian citizen? Only include the cash flows over the duration of the degree, ignore any benefits or costs of the degree after it's completed. Assume the following: • The degree takes 3 years to complete and all students pass all subjects. • There are 2 semesters per year and 4 subjects per semester. • University fees per subject per semester are$1,277, paid at the start of each semester. Fees are expected to stay constant for the next 3 years.
• There are 52 weeks per year.
• The first semester is just about to start (t=0). The first semester lasts for 19 weeks (t=0 to 19).
• The second semester starts immediately afterwards (t=19) and lasts for another 19 weeks (t=19 to 38).
• The summer holidays begin after the second semester ends and last for 14 weeks (t=38 to 52). Then the first semester begins the next year, and so on.
• Working full time at the grocery store instead of studying full-time pays $20/hr and you can work 35 hours per week. Wages are paid at the end of each week. • Full-time students can work full-time during the summer holiday at the grocery store for the same rate of$20/hr for 35 hours per week. Wages are paid at the end of each week.
• The discount rate is 9.8% pa. All rates and cash flows are real. Inflation is expected to be 3% pa. All rates are effective annual.

The NPV of costs from undertaking the university degree is:

Find Candys Corporation's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.

 Candys Corp Income Statement for year ending 30th June 2013 $m Sales 200 COGS 50 Operating expense 10 Depreciation 20 Interest expense 10 Income before tax 110 Tax at 30% 33 Net income 77  Candys Corp Balance Sheet as at 30th June 2013 2012$m $m Assets Current assets 220 180 PPE Cost 300 340 Accumul. depr. 60 40 Carrying amount 240 300 Total assets 460 480 Liabilities Current liabilities 175 190 Non-current liabilities 135 130 Owners' equity Retained earnings 50 60 Contributed equity 100 100 Total L and OE 460 480 Note: all figures are given in millions of dollars ($m).

Why is Capital Expenditure (CapEx) subtracted in the Cash Flow From Assets (CFFA) formula?

$$CFFA=NI+Depr-CapEx - \Delta NWC+IntExp$$

Cash Flow From Assets (CFFA) can be defined as:

A firm has forecast its Cash Flow From Assets (CFFA) for this year and management is worried that it is too low. Which one of the following actions will lead to a higher CFFA for this year (t=0 to 1)? Only consider cash flows this year. Do not consider cash flows after one year, or the change in the NPV of the firm. Consider each action in isolation.

A company increases the proportion of debt funding it uses to finance its assets by issuing bonds and using the cash to repurchase stock, leaving assets unchanged.

Ignoring the costs of financial distress, which of the following statements is NOT correct:

Which one of the following will decrease net income (NI) but increase cash flow from assets (CFFA) in this year for a tax-paying firm, all else remaining constant?

Remember:

$$NI = (Rev-COGS-FC-Depr-IntExp).(1-t_c )$$ $$CFFA=NI+Depr-CapEx - \Delta NWC+IntExp$$

Find Sidebar Corporation's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.

 Sidebar Corp Income Statement for year ending 30th June 2013 $m Sales 405 COGS 100 Depreciation 34 Rent expense 22 Interest expense 39 Taxable Income 210 Taxes at 30% 63 Net income 147  Sidebar Corp Balance Sheet as at 30th June 2013 2012$m $m Inventory 70 50 Trade debtors 11 16 Rent paid in advance 4 3 PPE 700 680 Total assets 785 749 Trade creditors 11 19 Bond liabilities 400 390 Contributed equity 220 220 Retained profits 154 120 Total L and OE 785 749 Note: All figures are given in millions of dollars ($m).

The cash flow from assets was:

Over the next year, the management of an unlevered company plans to:

• Achieve firm free cash flow (FFCF or CFFA) of $1m. • Pay dividends of$1.8m
• Complete a $1.3m share buy-back. • Spend$0.8m on new buildings without buying or selling any other fixed assets. This capital expenditure is included in the CFFA figure quoted above.

Assume that:

• All amounts are received and paid at the end of the year so you can ignore the time value of money.
• The firm has sufficient retained profits to pay the dividend and complete the buy back.
• The firm plans to run a very tight ship, with no excess cash above operating requirements currently or over the next year.

How much new equity financing will the company need? In other words, what is the value of new shares that will need to be issued?

Which one of the following will have no effect on net income (NI) but decrease cash flow from assets (CFFA or FFCF) in this year for a tax-paying firm, all else remaining constant?

Remember:

$$NI=(Rev-COGS-FC-Depr-IntExp).(1-t_c )$$ $$CFFA=NI+Depr-CapEx - ΔNWC+IntExp$$

Find Ching-A-Lings Corporation's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.

 Ching-A-Lings Corp Income Statement for year ending 30th June 2013 $m Sales 100 COGS 20 Depreciation 20 Rent expense 11 Interest expense 19 Taxable Income 30 Taxes at 30% 9 Net income 21  Ching-A-Lings Corp Balance Sheet as at 30th June 2013 2012$m $m Inventory 49 38 Trade debtors 14 2 Rent paid in advance 5 5 PPE 400 400 Total assets 468 445 Trade creditors 4 10 Bond liabilities 200 190 Contributed equity 145 145 Retained profits 119 100 Total L and OE 468 445 Note: All figures are given in millions of dollars ($m).

The cash flow from assets was:

Over the next year, the management of an unlevered company plans to:

• Make $5m in sales,$1.9m in net income and $2m in equity free cash flow (EFCF). • Pay dividends of$1m.
• Complete a $1.3m share buy-back. Assume that: • All amounts are received and paid at the end of the year so you can ignore the time value of money. • The firm has sufficient retained profits to legally pay the dividend and complete the buy back. • The firm plans to run a very tight ship, with no excess cash above operating requirements currently or over the next year. How much new equity financing will the company need? In other words, what is the value of new shares that will need to be issued? Read the following financial statements and calculate the firm's free cash flow over the 2014 financial year.  UBar Corp Income Statement for year ending 30th June 2014$m Sales 293 COGS 200 Rent expense 15 Gas expense 8 Depreciation 10 EBIT 60 Interest expense 0 Taxable income 60 Taxes 18 Net income 42
 UBar Corp Balance Sheet as at 30th June 2014 2013 $m$m Assets Cash 30 29 Accounts receivable 5 7 Pre-paid rent expense 1 0 Inventory 50 46 PPE 290 300 Total assets 376 382 Liabilities Trade payables 20 18 Accrued gas expense 3 2 Non-current liabilities 0 0 Contributed equity 212 212 Retained profits 136 150 Asset revaluation reserve 5 0 Total L and OE 376 382

Note: all figures are given in millions of dollars ($m). The firm's free cash flow over the 2014 financial year was: Find the cash flow from assets (CFFA) of the following project.  One Year Mining Project Data Project life 1 year Initial investment in building mine and equipment$9m Depreciation of mine and equipment over the year $8m Kilograms of gold mined at end of year 1,000 Sale price per kilogram$0.05m Variable cost per kilogram $0.03m Before-tax cost of closing mine at end of year$4m Tax rate 30%

Note 1: Due to the project, the firm also anticipates finding some rare diamonds which will give before-tax revenues of $1m at the end of the year. Note 2: The land that will be mined actually has thermal springs and a family of koalas that could be sold to an eco-tourist resort for an after-tax amount of$3m right now. However, if the mine goes ahead then this natural beauty will be destroyed.

Note 3: The mining equipment will have a book value of $1m at the end of the year for tax purposes. However, the equipment is expected to fetch$2.5m when it is sold.

Find the project's CFFA at time zero and one. Answers are given in millions of dollars ($m), with the first cash flow at time zero, and the second at time one. Issuing debt doesn't give away control of the firm because debt holders can't cast votes to determine the company's affairs, such as at the annual general meeting (AGM), and can't appoint directors to the board. or ? Companies must pay debt holders the interest and principal payments that they promise. But companies do not promise to pay dividends to share holders, dividends are only paid if the company can afford them. or ? Your friend just bought a house for$400,000. He financed it using a $320,000 mortgage loan and a deposit of$80,000.

In the context of residential housing and mortgages, the 'equity' tied up in the value of a person's house is the value of the house less the value of the mortgage. So the initial equity your friend has in his house is $80,000. Let this amount be E, let the value of the mortgage be D and the value of the house be V. So $V=D+E$. If house prices suddenly fall by 10%, what would be your friend's percentage change in equity (E)? Assume that the value of the mortgage is unchanged and that no income (rent) was received from the house during the short time over which house prices fell. Remember: $$r_{0\rightarrow1}=\frac{p_1-p_0+c_1}{p_0}$$ where $r_{0-1}$ is the return (percentage change) of an asset with price $p_0$ initially, $p_1$ one period later, and paying a cash flow of $c_1$ at time $t=1$. Your friend just bought a house for$1,000,000. He financed it using a $900,000 mortgage loan and a deposit of$100,000.

In the context of residential housing and mortgages, the 'equity' or 'net wealth' tied up in a house is the value of the house less the value of the mortgage loan. Assuming that your friend's only asset is his house, his net wealth is $100,000. If house prices suddenly fall by 15%, what would be your friend's percentage change in net wealth? Assume that: • No income (rent) was received from the house during the short time over which house prices fell. • Your friend will not declare bankruptcy, he will always pay off his debts. One year ago you bought$100,000 of shares partly funded using a margin loan. The margin loan size was $70,000 and the other$30,000 was your own wealth or 'equity' in the share assets.

The interest rate on the margin loan was 7.84% pa.

Over the year, the shares produced a dividend yield of 4% pa and a capital gain of 5% pa.

What was the total return on your wealth? Ignore taxes, assume that all cash flows (interest payments and dividends) were paid and received at the end of the year, and all rates above are effective annual rates.

Hint: Remember that wealth in this context is your equity (E) in the house asset (V = D+E) which is funded by the loan (D) and your deposit or equity (E).

Here are the Net Income (NI) and Cash Flow From Assets (CFFA) equations:

$$NI=(Rev-COGS-FC-Depr-IntExp).(1-t_c)$$

$$CFFA=NI+Depr-CapEx - \varDelta NWC+IntExp$$

What is the formula for calculating annual interest expense (IntExp) which is used in the equations above?

Select one of the following answers. Note that D is the value of debt which is constant through time, and $r_D$ is the cost of debt.

Interest expense (IntExp) is an important part of a company's income statement (or 'profit and loss' or 'statement of financial performance').

How does an accountant calculate the annual interest expense of a fixed-coupon bond that has a liquid secondary market? Select the most correct answer:

Annual interest expense is equal to:

Which one of the following will decrease net income (NI) but increase cash flow from assets (CFFA) in this year for a tax-paying firm, all else remaining constant?

Remember:

$$NI=(Rev-COGS-FC-Depr-IntExp).(1-t_c )$$ $$CFFA=NI+Depr-CapEx - ΔNWC+IntExp$$

A manufacturing company is considering a new project in the more risky services industry. The cash flows from assets (CFFA) are estimated for the new project, with interest expense excluded from the calculations. To get the levered value of the project, what should these unlevered cash flows be discounted by?

Assume that the manufacturing firm has a target debt-to-assets ratio that it sticks to.

A retail furniture company buys furniture wholesale and distributes it through its retail stores. The owner believes that she has some good ideas for making stylish new furniture. She is considering a project to buy a factory and employ workers to manufacture the new furniture she's designed. Furniture manufacturing has more systematic risk than furniture retailing.

Her furniture retailing firm's after-tax WACC is 20%. Furniture manufacturing firms have an after-tax WACC of 30%. Both firms are optimally geared. Assume a classical tax system.

Which method(s) will give the correct valuation of the new furniture-making project? Select the most correct answer.

Assume the following:

• Google had a 10% after-tax weighted average cost of capital (WACC) before it bought Motorola.
• Motorola had a 20% after-tax WACC before it merged with Google.
• Google and Motorola have the same level of gearing.
• Both companies operate in a classical tax system.

You are a manager at Motorola. You must value a project for making mobile phones. Which method(s) will give the correct valuation of the mobile phone manufacturing project? Select the most correct answer.

The mobile phone manufacturing project's:

There are many ways to calculate a firm's free cash flow (FFCF), also called cash flow from assets (CFFA). Some include the annual interest tax shield in the cash flow and some do not.

Which of the below FFCF formulas include the interest tax shield in the cash flow?

$$(1) \quad FFCF=NI + Depr - CapEx -ΔNWC + IntExp$$ $$(2) \quad FFCF=NI + Depr - CapEx -ΔNWC + IntExp.(1-t_c)$$ $$(3) \quad FFCF=EBIT.(1-t_c )+ Depr- CapEx -ΔNWC+IntExp.t_c$$ $$(4) \quad FFCF=EBIT.(1-t_c) + Depr- CapEx -ΔNWC$$ $$(5) \quad FFCF=EBITDA.(1-t_c )+Depr.t_c- CapEx -ΔNWC+IntExp.t_c$$ $$(6) \quad FFCF=EBITDA.(1-t_c )+Depr.t_c- CapEx -ΔNWC$$ $$(7) \quad FFCF=EBIT-Tax + Depr - CapEx -ΔNWC$$ $$(8) \quad FFCF=EBIT-Tax + Depr - CapEx -ΔNWC-IntExp.t_c$$ $$(9) \quad FFCF=EBITDA-Tax - CapEx -ΔNWC$$ $$(10) \quad FFCF=EBITDA-Tax - CapEx -ΔNWC-IntExp.t_c$$

The formulas for net income (NI also called earnings), EBIT and EBITDA are given below. Assume that depreciation and amortisation are both represented by 'Depr' and that 'FC' represents fixed costs such as rent.

$$NI=(Rev - COGS - Depr - FC - IntExp).(1-t_c )$$ $$EBIT=Rev - COGS - FC-Depr$$ $$EBITDA=Rev - COGS - FC$$ $$Tax =(Rev - COGS - Depr - FC - IntExp).t_c= \dfrac{NI.t_c}{1-t_c}$$

A method commonly seen in textbooks for calculating a levered firm's free cash flow (FFCF, or CFFA) is the following:

\begin{aligned} FFCF &= (Rev - COGS - Depr - FC - IntExp)(1-t_c) + \\ &\space\space\space+ Depr - CapEx -\Delta NWC + IntExp(1-t_c) \\ \end{aligned}
Does this annual FFCF or the annual interest tax shield?

One formula for calculating a levered firm's free cash flow (FFCF, or CFFA) is to use earnings before interest and tax (EBIT).

\begin{aligned} FFCF &= (EBIT)(1-t_c) + Depr - CapEx -\Delta NWC + IntExp.t_c \\ &= (Rev - COGS - Depr - FC)(1-t_c) + Depr - CapEx -\Delta NWC + IntExp.t_c \\ \end{aligned} \\
Does this annual FFCF or the annual interest tax shield?

One method for calculating a firm's free cash flow (FFCF, or CFFA) is to ignore interest expense. That is, pretend that interest expense $(IntExp)$ is zero:

\begin{aligned} FFCF &= (Rev - COGS - Depr - FC - IntExp)(1-t_c) + Depr - CapEx -\Delta NWC + IntExp \\ &= (Rev - COGS - Depr - FC - 0)(1-t_c) + Depr - CapEx -\Delta NWC - 0\\ \end{aligned}
Does this annual FFCF with zero interest expense or the annual interest tax shield?

One formula for calculating a levered firm's free cash flow (FFCF, or CFFA) is to use net operating profit after tax (NOPAT).

\begin{aligned} FFCF &= NOPAT + Depr - CapEx -\Delta NWC \\ &= (Rev - COGS - Depr - FC)(1-t_c) + Depr - CapEx -\Delta NWC \\ \end{aligned} \\
Does this annual FFCF or the annual interest tax shield?

There are many ways to calculate a firm's free cash flow (FFCF), also called cash flow from assets (CFFA).

One method is to use the following formulas to transform net income (NI) into FFCF including interest and depreciation tax shields:

$$FFCF=NI + Depr - CapEx -ΔNWC + IntExp$$

$$NI=(Rev - COGS - Depr - FC - IntExp).(1-t_c )$$

Another popular method is to use EBITDA rather than net income. EBITDA is defined as:

$$EBITDA=Rev - COGS - FC$$

One of the below formulas correctly calculates FFCF from EBITDA, including interest and depreciation tax shields, giving an identical answer to that above. Which formula is correct?

Which statement about risk, required return and capital structure is the most correct?

A company issues a large amount of bonds to raise money for new projects of similar risk to the company's existing projects. The net present value (NPV) of the new projects is positive but small. Assume a classical tax system. Which statement is NOT correct?

A firm is considering a new project of similar risk to the current risk of the firm. This project will expand its existing business. The cash flows of the project have been calculated assuming that there is no interest expense. In other words, the cash flows assume that the project is all-equity financed.

In fact the firm has a target debt-to-equity ratio of 1, so the project will be financed with 50% debt and 50% equity. To find the levered value of the firm's assets, what discount rate should be applied to the project's unlevered cash flows? Assume a classical tax system.

A firm has a debt-to-assets ratio of 50%. The firm then issues a large amount of equity to raise money for new projects of similar systematic risk to the company's existing projects. Assume a classical tax system. Which statement is correct?

Question 99  capital structure, interest tax shield, Miller and Modigliani, trade off theory of capital structure

A firm changes its capital structure by issuing a large amount of debt and using the funds to repurchase shares. Its assets are unchanged.

Assume that:

• The firm and individual investors can borrow at the same rate and have the same tax rates.
• The firm's debt and shares are fairly priced and the shares are repurchased at the market price, not at a premium.
• There are no market frictions relating to debt such as asymmetric information or transaction costs.
• Shareholders wealth is measured in terms of utiliity. Shareholders are wealth-maximising and risk-averse. They have a preferred level of overall leverage. Before the firm's capital restructure all shareholders were optimally levered.

According to Miller and Modigliani's theory, which statement is correct?

A firm has a debt-to-assets ratio of 50%. The firm then issues a large amount of debt to raise money for new projects of similar risk to the company's existing projects. Assume a classical tax system. Which statement is correct?

Question 121  capital structure, leverage, costs of financial distress, interest tax shield

Fill in the missing words in the following sentence:

All things remaining equal, as a firm's amount of debt funding falls, benefits of interest tax shields __________ and the costs of financial distress __________.

A fast-growing firm is suitable for valuation using a multi-stage growth model.

It's nominal unlevered cash flow from assets ($CFFA_U$) at the end of this year (t=1) is expected to be $1 million. After that it is expected to grow at a rate of: • 12% pa for the next two years (from t=1 to 3), • 5% over the fourth year (from t=3 to 4), and • -1% forever after that (from t=4 onwards). Note that this is a negative one percent growth rate. Assume that: • The nominal WACC after tax is 9.5% pa and is not expected to change. • The nominal WACC before tax is 10% pa and is not expected to change. • The firm has a target debt-to-equity ratio that it plans to maintain. • The inflation rate is 3% pa. • All rates are given as nominal effective annual rates. What is the levered value of this fast growing firm's assets? A firm plans to issue equity and use the cash raised to pay off its debt. No assets will be bought or sold. Ignore the costs of financial distress. Which of the following statements is NOT correct, all things remaining equal? Which of the following statements about standard statistical mathematics notation is NOT correct? The following table shows a sample of historical total returns of shares in two different companies A and B.  Stock Returns Total effective annual returns Year $r_A$ $r_B$ 2007 0.2 0.4 2008 0.04 -0.2 2009 -0.1 -0.3 2010 0.18 0.5 What is the historical sample covariance ($\hat{\sigma}_{A,B}$) and correlation ($\rho_{A,B}$) of stock A and B's total effective annual returns? Diversification in a portfolio of two assets works best when the correlation between their returns is: Stock A and B's returns have a correlation of 0.3. Which statement is NOT correct? All things remaining equal, the variance of a portfolio of two positively-weighted stocks rises as:  Portfolio Details Stock Expected return Standard deviation Correlation Dollars invested A 0.1 0.4 0.5 60 B 0.2 0.6 140 What is the expected return of the above portfolio?  Portfolio Details Stock Expected return Standard deviation Correlation $(\rho_{A,B})$ Dollars invested A 0.1 0.4 0.5 60 B 0.2 0.6 140 What is the standard deviation (not variance) of the above portfolio?  Portfolio Details Stock Expected return Standard deviation Covariance $(\sigma_{A,B})$ Beta Dollars invested A 0.2 0.4 0.12 0.5 40 B 0.3 0.8 1.5 80 What is the standard deviation (not variance) of the above portfolio? Note that the stocks' covariance is given, not correlation. You're the boss of an investment bank's equities research team. Your five analysts are each trying to find the expected total return over the next year of shares in a mining company. The mining firm: • Is regarded as a mature company since it's quite stable in size and was floated around 30 years ago. It is not a high-growth company; • Share price is very sensitive to changes in the price of the market portfolio, economic growth, the exchange rate and commodities prices. Due to this, its standard deviation of total returns is much higher than that of the market index; • Experienced tough times in the last 10 years due to unexpected falls in commodity prices. • Shares are traded in an active liquid market. Your team of analysts present their findings, and everyone has different views. While there's no definitive true answer, who's calculation of the expected total return is the most plausible? Assume that: • The analysts' source data is correct and true, but their inferences might be wrong; • All returns and yields are given as effective annual nominal rates. Two risky stocks A and B comprise an equal-weighted portfolio. The correlation between the stocks' returns is 70%. If the variance of stock A increases but the: • Prices and expected returns of each stock stays the same, • Variance of stock B's returns stays the same, • Correlation of returns between the stocks stays the same. Which of the following statements is NOT correct? All things remaining equal, the higher the correlation of returns between two stocks: Which of the following statements about short-selling is NOT true? An investor wants to make a portfolio of two stocks A and B with a target expected portfolio return of 6% pa. • Stock A has an expected return of 5% pa. • Stock B has an expected return of 10% pa. What portfolio weights should the investor have in stocks A and B respectively? An investor wants to make a portfolio of two stocks A and B with a target expected portfolio return of 16% pa. • Stock A has an expected return of 8% pa. • Stock B has an expected return of 12% pa. What portfolio weights should the investor have in stocks A and B respectively? An investor wants to make a portfolio of two stocks A and B with a target expected portfolio return of 12% pa. • Stock A has an expected return of 10% pa and a standard deviation of 20% pa. • Stock B has an expected return of 15% pa and a standard deviation of 30% pa. The correlation coefficient between stock A and B's expected returns is 70%. What will be the annual standard deviation of the portfolio with this 12% pa target return? What is the covariance of a variable X with itself? The cov(X, X) or $\sigma_{X,X}$ equals: What is the correlation of a variable X with itself? The corr(X, X) or $\rho_{X,X}$ equals: What is the covariance of a variable X with a constant C? The cov(X, C) or $\sigma_{X,C}$ equals: What is the correlation of a variable X with a constant C? The corr(X, C) or $\rho_{X,C}$ equals: The standard deviation and variance of a stock's annual returns are calculated over a number of years. The units of the returns are percent per annum $(\% pa)$. What are the units of the standard deviation $(\sigma)$ and variance $(\sigma^2)$ of returns respectively? Hint: Visit Wikipedia to understand the difference between percentage points $(\text{pp})$ and percent $(\%)$. The covariance and correlation of two stocks X and Y's annual returns are calculated over a number of years. The units of the returns are in percent per annum $(\% pa)$. What are the units of the covariance $(\sigma_{X,Y})$ and correlation $(\rho_{X,Y})$ of returns respectively? Hint: Visit Wikipedia to understand the difference between percentage points $(\text{pp})$ and percent $(\%)$. Let the variance of returns for a share per month be $\sigma_\text{monthly}^2$. What is the formula for the variance of the share's returns per year $(\sigma_\text{yearly}^2)$? Assume that returns are independently and identically distributed (iid) so they have zero auto correlation, meaning that if the return was higher than average today, it does not indicate that the return tomorrow will be higher or lower than average. Let the standard deviation of returns for a share per month be $\sigma_\text{monthly}$. What is the formula for the standard deviation of the share's returns per year $(\sigma_\text{yearly})$? Assume that returns are independently and identically distributed (iid) so they have zero auto correlation, meaning that if the return was higher than average today, it does not indicate that the return tomorrow will be higher or lower than average. Diversification is achieved by investing in a large amount of stocks. What type of risk is reduced by diversification? According to the theory of the Capital Asset Pricing Model (CAPM), total variance can be broken into two components, systematic variance and idiosyncratic variance. Which of the following events would be considered the most diversifiable according to the theory of the CAPM? According to the theory of the Capital Asset Pricing Model (CAPM), total risk can be broken into two components, systematic risk and idiosyncratic risk. Which of the following events would be considered a systematic, undiversifiable event according to the theory of the CAPM? Treasury bonds currently have a return of 5% pa. A stock has a beta of 0.5 and the market return is 10% pa. What is the expected return of the stock? A fairly priced stock has an expected return equal to the market's. Treasury bonds yield 5% pa and the market portfolio's expected return is 10% pa. What is the stock's beta? A stock has a beta of 0.5. Its next dividend is expected to be$3, paid one year from now. Dividends are expected to be paid annually and grow by 2% pa forever. Treasury bonds yield 5% pa and the market portfolio's expected return is 10% pa. All returns are effective annual rates.

What is the price of the stock now?

The security market line (SML) shows the relationship between beta and expected return.

Investment projects that plot on the SML would have:

The security market line (SML) shows the relationship between beta and expected return.

Investment projects that plot above the SML would have:

 Portfolio Details Stock Expected return Standard deviation Correlation Beta Dollars invested A 0.2 0.4 0.12 0.5 40 B 0.3 0.8 1.5 80

What is the beta of the above portfolio?

Stock A has a beta of 0.5 and stock B has a beta of 1. Which statement is NOT correct?

Which statement is the most correct?

Which statement(s) are correct?

(i) All stocks that plot on the Security Market Line (SML) are fairly priced.

(ii) All stocks that plot above the Security Market Line (SML) are overpriced.

(iii) All fairly priced stocks that plot on the Capital Market Line (CML) have zero idiosyncratic risk.

Select the most correct response:

A stock's correlation with the market portfolio increases while its total risk is unchanged. What will happen to the stock's expected return and systematic risk?

A firm changes its capital structure by issuing a large amount of debt and using the funds to repurchase shares. Its assets are unchanged. Ignore interest tax shields.

According to the Capital Asset Pricing Model (CAPM), which statement is correct?

A firm changes its capital structure by issuing a large amount of equity and using the funds to repay debt. Its assets are unchanged. Ignore interest tax shields.

According to the Capital Asset Pricing Model (CAPM), which statement is correct?

The total return of any asset can be broken down in different ways. One possible way is to use the dividend discount model (or Gordon growth model):

$$p_0 = \frac{c_1}{r_\text{total}-r_\text{capital}}$$

Which, since $c_1/p_0$ is the income return ($r_\text{income}$), can be expressed as:

$$r_\text{total}=r_\text{income}+r_\text{capital}$$

So the total return of an asset is the income component plus the capital or price growth component.

Another way to break up total return is to use the Capital Asset Pricing Model:

$$r_\text{total}=r_\text{f}+β(r_\text{m}- r_\text{f})$$

$$r_\text{total}=r_\text{time value}+r_\text{risk premium}$$

So the risk free rate is the time value of money and the term $β(r_\text{m}- r_\text{f})$ is the compensation for taking on systematic risk.

Using the above theory and your general knowledge, which of the below equations, if any, are correct?

(I) $r_\text{income}=r_\text{time value}$

(II) $r_\text{income}=r_\text{risk premium}$

(III) $r_\text{capital}=r_\text{time value}$

(IV) $r_\text{capital}=r_\text{risk premium}$

(V) $r_\text{income}+r_\text{capital}=r_\text{time value}+r_\text{risk premium}$

Which of the equations are correct?

The CAPM can be used to find a business's expected opportunity cost of capital:

$$r_i=r_f+β_i (r_m-r_f)$$

What should be used as the risk free rate $r_f$?

You just bought a house worth $1,000,000. You financed it with an$800,000 mortgage loan and a deposit of $200,000. You estimate that: • The house has a beta of 1; • The mortgage loan has a beta of 0.2. What is the beta of the equity (the$200,000 deposit) that you have in your house?

Also, if the risk free rate is 5% pa and the market portfolio's return is 10% pa, what is the expected return on equity in your house? Ignore taxes, assume that all cash flows (interest payments and rent) were paid and received at the end of the year, and all rates are effective annual rates.

A firm's WACC before tax would decrease due to:

A firm can issue 5 year annual coupon bonds at a yield of 8% pa and a coupon rate of 12% pa.

The beta of its levered equity is 1. Five year government bonds yield 5% pa with a coupon rate of 6% pa. The market's expected dividend return is 4% pa and its expected capital return is 6% pa.

The firm's debt-to-equity ratio is 2:1. The corporate tax rate is 30%.

What is the firm's after-tax WACC? Assume a classical tax system.

Which of the following statements about the weighted average cost of capital (WACC) is NOT correct?

There are many different ways to value a firm's assets. Which of the following will NOT give the correct market value of a levered firm's assets $(V_L)$? Assume that:

• The firm is financed by listed common stock and vanilla annual fixed coupon bonds, which are both traded in a liquid market.
• The bonds' yield is equal to the coupon rate, so the bonds are issued at par. The yield curve is flat and yields are not expected to change. When bonds mature they will be rolled over by issuing the same number of new bonds with the same expected yield and coupon rate, and so on forever.
• Tax rates on the dividends and capital gains received by investors are equal, and capital gains tax is paid every year, even on unrealised gains regardless of when the asset is sold.
• There is no re-investment of the firm's cash back into the business. All of the firm's excess cash flow is paid out as dividends so real growth is zero.
• The firm operates in a mature industry with zero real growth.
• All cash flows and rates in the below equations are real (not nominal) and are expected to be stable forever. Therefore the perpetuity equation with no growth is suitable for valuation.

Where:

$$r_\text{WACC before tax} = r_D.\frac{D}{V_L} + r_{EL}.\frac{E_L}{V_L} = \text{Weighted average cost of capital before tax}$$ $$r_\text{WACC after tax} = r_D.(1-t_c).\frac{D}{V_L} + r_{EL}.\frac{E_L}{V_L} = \text{Weighted average cost of capital after tax}$$ $$NI_L=(Rev-COGS-FC-Depr-\mathbf{IntExp}).(1-t_c) = \text{Net Income Levered}$$ $$CFFA_L=NI_L+Depr-CapEx - \varDelta NWC+\mathbf{IntExp} = \text{Cash Flow From Assets Levered}$$ $$NI_U=(Rev-COGS-FC-Depr).(1-t_c) = \text{Net Income Unlevered}$$ $$CFFA_U=NI_U+Depr-CapEx - \varDelta NWC= \text{Cash Flow From Assets Unlevered}$$

 Project Data Project life 1 year Initial investment in equipment $8m Depreciation of equipment per year$8m Expected sale price of equipment at end of project 0 Unit sales per year 4m Sale price per unit $10 Variable cost per unit$5 Fixed costs per year, paid at the end of each year $2m Interest expense in first year (at t=1)$0.562m Corporate tax rate 30% Government treasury bond yield 5% Bank loan debt yield 9% Market portfolio return 10% Covariance of levered equity returns with market 0.32 Variance of market portfolio returns 0.16 Firm's and project's debt-to-equity ratio 50%

Notes

1. Due to the project, current assets will increase by $6m now (t=0) and fall by$6m at the end (t=1). Current liabilities will not be affected.

Assumptions

• The debt-to-equity ratio will be kept constant throughout the life of the project. The amount of interest expense at the end of each period has been correctly calculated to maintain this constant debt-to-equity ratio.
• Millions are represented by 'm'.
• All cash flows occur at the start or end of the year as appropriate, not in the middle or throughout the year.
• All rates and cash flows are real. The inflation rate is 2% pa. All rates are given as effective annual rates.
• The project is undertaken by a firm, not an individual.

What is the net present value (NPV) of the project?

Jan asks you for a loan. He wants $100 now and offers to pay you back$120 in 1 year. You can borrow and lend from the bank at an interest rate of 10% pa, given as an effective annual rate.

Ignore credit risk. Remember:

$$V_0 = \frac{V_t}{(1+r_\text{eff})^t}$$

Will you or Jan's deal?

A company selling charting and technical analysis software claims that independent academic studies have shown that its software makes significantly positive abnormal returns. Assuming the claim is true, which statement(s) are correct?

(I) Weak form market efficiency is broken.

(II) Semi-strong form market efficiency is broken.

(III) Strong form market efficiency is broken.

(IV) The asset pricing model used to measure the abnormal returns (such as the CAPM) had mis-specification error so the returns may not be abnormal but rather fair for the level of risk.

Select the most correct response:

Your friend claims that by reading 'The Economist' magazine's economic news articles, she can identify shares that will have positive abnormal expected returns over the next 2 years. Assuming that her claim is true, which statement(s) are correct?

(i) Weak form market efficiency is broken.

(ii) Semi-strong form market efficiency is broken.

(iii) Strong form market efficiency is broken.

(iv) The asset pricing model used to measure the abnormal returns (such as the CAPM) is either wrong (mis-specification error) or is measured using the wrong inputs (data errors) so the returns may not be abnormal but rather fair for the level of risk.

Select the most correct response:

Select the most correct statement from the following.

'Chartists', also known as 'technical traders', believe that:

Fundamentalists who analyse company financial reports and news announcements (but who don't have inside information) will make positive abnormal returns if:

The theory of fixed interest bond pricing is an application of the theory of Net Present Value (NPV). Also, a 'fairly priced' asset is not over- or under-priced. Buying or selling a fairly priced asset has an NPV of zero.

Considering this, which of the following statements is NOT correct?

The theory of fixed interest bond pricing is an application of the theory of Net Present Value (NPV). Also, a 'fairly priced' asset is not over- or under-priced. Buying or selling a fairly priced asset has an NPV of zero.

Considering this, which of the following statements is NOT correct?

Economic statistics released this morning were a surprise: they show a strong chance of consumer price inflation (CPI) reaching 5% pa over the next 2 years.

This is much higher than the previous forecast of 3% pa.

A vanilla fixed-coupon 2-year risk-free government bond was issued at par this morning, just before the economic news was released.

What is the expected change in bond price after the economic news this morning, and in the next 2 years? Assume that:

• Inflation remains at 5% over the next 2 years.
• Investors demand a constant real bond yield.
• The bond price falls by the (after-tax) value of the coupon the night before the ex-coupon date, as in real life.

A man inherits $500,000 worth of shares. He believes that by learning the secrets of trading, keeping up with the financial news and doing complex trend analysis with charts that he can quit his job and become a self-employed day trader in the equities markets. What is the expected gain from doing this over the first year? Measure the net gain in wealth received at the end of this first year due to the decision to become a day trader. Assume the following: • He earns$60,000 pa in his current job, paid in a lump sum at the end of each year.
• He enjoys examining share price graphs and day trading just as much as he enjoys his current job.
• Stock markets are weak form and semi-strong form efficient.
• He has no inside information.
• He makes 1 trade every day and there are 250 trading days in the year. Trading costs are $20 per trade. His broker invoices him for the trading costs at the end of the year. • The shares that he currently owns and the shares that he intends to trade have the same level of systematic risk as the market portfolio. • The market portfolio's expected return is 10% pa. Measure the net gain over the first year as an expected wealth increase at the end of the year. A managed fund charges fees based on the amount of money that you keep with them. The fee is 2% of the start-of-year amount, but it is paid at the end of every year. This fee is charged regardless of whether the fund makes gains or losses on your money. The fund offers to invest your money in shares which have an expected return of 10% pa before fees. You are thinking of investing$100,000 in the fund and keeping it there for 40 years when you plan to retire.

What is the Net Present Value (NPV) of investing your money in the fund? Note that the question is not asking how much money you will have in 40 years, it is asking: what is the NPV of investing in the fund? Assume that:

• The fund has no private information.
• Markets are weak and semi-strong form efficient.
• The fund's transaction costs are negligible.
• The cost and trouble of investing your money in shares by yourself, without the managed fund, is negligible.

A residential real estate investor believes that house prices will grow at a rate of 5% pa and that rents will grow by 2% pa forever.

All rates are given as nominal effective annual returns. Assume that:

• His forecast is true.
• Real estate is and always will be fairly priced and the capital asset pricing model (CAPM) is true.
• Ignore all costs such as taxes, agent fees, maintenance and so on.
• All rental income cash flow is paid out to the owner, so there is no re-investment and therefore no additions or improvements made to the property.
• The non-monetary benefits of owning real estate and renting remain constant.

Which one of the following statements is NOT correct? Over time:

A company advertises an investment costing $1,000 which they say is underpriced. They say that it has an expected total return of 15% pa, but a required return of only 10% pa. Assume that there are no dividend payments so the entire 15% total return is all capital return. Assuming that the company's statements are correct, what is the NPV of buying the investment if the 15% return lasts for the next 100 years (t=0 to 100), then reverts to 10% pa after that time? Also, what is the NPV of the investment if the 15% return lasts forever? In both cases, assume that the required return of 10% remains constant. All returns are given as effective annual rates. The answer choices below are given in the same order (15% for 100 years, and 15% forever): The following is the Dividend Discount Model (DDM) used to price stocks: $$P_0 = \frac{d_1}{r-g}$$ Assume that the assumptions of the DDM hold and that the time period is measured in years. Which of the following is equal to the expected dividend in 3 years, $d_3$? The following equation is the Dividend Discount Model, also known as the 'Gordon Growth Model' or the 'Perpetuity with growth' equation. $$p_0=\frac{d_1}{r_\text{eff}-g_\text{eff}}$$ Which expression is NOT equal to the expected capital return? Which of the following investable assets are NOT suitable for valuation using PE multiples techniques? Which of the following investable assets are NOT suitable for valuation using PE multiples techniques? An 'interest payment' is the same thing as a 'coupon payment'. or ? An 'interest rate' is the same thing as a 'yield'. or ? An 'interest only' loan can also be called a: Which of the following statements is NOT correct? Lenders: Which of the following statements about effective rates and annualised percentage rates (APR's) is NOT correct? Bonds A and B are issued by the same company. They have the same face value, maturity, seniority and coupon payment frequency. The only difference is that bond A has a 5% coupon rate, while bond B has a 10% coupon rate. The yield curve is flat, which means that yields are expected to stay the same. Which of the following statements will be true about their prices? Bonds A and B are issued by the same Australian company. Both bonds yield 7% pa, and they have the same face value ($100), maturity, seniority, and payment frequency.

The only difference is that bond A pays coupons of 10% pa and bond B pays coupons of 5% pa. Which of the following statements is true about the bonds' prices?

Bonds X and Y are issued by the same company. Both bonds yield 10% pa, and they have the same face value ($100), maturity, seniority, and payment frequency. The only difference is that bond X pays coupons of 6% pa and bond Y pays coupons of 8% pa. Which of the following statements is true? The average weekly earnings of an Australian adult worker before tax was$1,542.40 per week in November 2014 according to the Australian Bureau of Statistics. Therefore average annual earnings before tax were $80,204.80 assuming 52 weeks per year. Personal income tax rates published by the Australian Tax Office are reproduced for the 2014-2015 financial year in the table below: Taxable income Tax on this income 0 –$18,200 Nil
$18,201 –$37,000 19c for each $1 over$18,200
$37,001 –$80,000 $3,572 plus 32.5c for each$1 over $37,000$80,001 – $180,000$17,547 plus 37c for each $1 over$80,000
$180,001 and over$54,547 plus 45c for each $1 over$180,000

The above rates do not include the Medicare levy of 2%. Exclude the Medicare levy from your calculations

How much personal income tax would you have to pay per year if you earned $80,204.80 per annum before-tax? A small private company has a single shareholder. This year the firm earned a$100 profit before tax. All of the firm's after tax profits will be paid out as dividends to the owner.

The corporate tax rate is 30% and the sole shareholder's personal marginal tax rate is 45%.

The Australian imputation tax system applies because the company generates all of its income in Australia and pays corporate tax to the Australian Tax Office. Therefore all of the company's dividends are fully franked. The sole shareholder is an Australian for tax purposes and can therefore use the franking credits to offset his personal income tax liability.

What will be the personal tax payable by the shareholder and the corporate tax payable by the company?

Question 449  personal tax on dividends, classical tax system

A small private company has a single shareholder. This year the firm earned a $100 profit before tax. All of the firm's after tax profits will be paid out as dividends to the owner. The corporate tax rate is 30% and the sole shareholder's personal marginal tax rate is 45%. The United States' classical tax system applies because the company generates all of its income in the US and pays corporate tax to the Internal Revenue Service. The shareholder is also an American for tax purposes. What will be the personal tax payable by the shareholder and the corporate tax payable by the company? A firm pays a fully franked cash dividend of$100 to one of its Australian shareholders who has a personal marginal tax rate of 15%. The corporate tax rate is 30%.

What will be the shareholder's personal tax payable due to the dividend payment?

A company announces that it will pay a dividend, as the market expected. The company's shares trade on the stock exchange which is open from 10am in the morning to 4pm in the afternoon each weekday. When would the share price be expected to fall by the amount of the dividend? Ignore taxes.

The share price is expected to fall during the:

Due to floods overseas, there is a cut in the supply of the mineral iron ore and its price increases dramatically. An Australian iron ore mining company therefore expects a large but temporary increase in its profit and cash flows. The mining company does not have any positive NPV projects to begin, so what should it do? Select the most correct answer.

Currently, a mining company has a share price of $6 and pays constant annual dividends of$0.50. The next dividend will be paid in 1 year. Suddenly and unexpectedly the mining company announces that due to higher than expected profits, all of these windfall profits will be paid as a special dividend of $0.30 in 1 year. If investors believe that the windfall profits and dividend is a one-off event, what will be the new share price? If investors believe that the additional dividend is actually permanent and will continue to be paid, what will be the new share price? Assume that the required return on equity is unchanged. Choose from the following, where the first share price includes the one-off increase in earnings and dividends for the first year only $(P_\text{0 one-off})$ , and the second assumes that the increase is permanent $(P_\text{0 permanent})$: Note: When a firm makes excess profits they sometimes pay them out as special dividends. Special dividends are just like ordinary dividends but they are one-off and investors do not expect them to continue, unlike ordinary dividends which are expected to persist. A pharmaceutical firm has just discovered a valuable new drug. So far the news has been kept a secret. The net present value of making and commercialising the drug is$200 million, but $600 million of bonds will need to be issued to fund the project and buy the necessary plant and equipment. The firm will release the news of the discovery and bond raising to shareholders simultaneously in the same announcement. The bonds will be issued shortly after. Once the announcement is made and the bonds are issued, what is the expected increase in the value of the firm's assets (ΔV), market capitalisation of debt (ΔD) and market cap of equity (ΔE)? The triangle symbol is the Greek letter capital delta which means change or increase in mathematics. Ignore the benefit of interest tax shields from having more debt. Remember: $ΔV = ΔD+ΔE$ A mining firm has just discovered a new mine. So far the news has been kept a secret. The net present value of digging the mine and selling the minerals is$250 million, but $500 million of new equity and$300 million of new bonds will need to be issued to fund the project and buy the necessary plant and equipment.

The firm will release the news of the discovery and equity and bond raising to shareholders simultaneously in the same announcement. The shares and bonds will be issued shortly after.

Once the announcement is made and the new shares and bonds are issued, what is the expected increase in the value of the firm's assets $(\Delta V)$, market capitalisation of debt $(\Delta D)$ and market cap of equity $(\Delta E)$? Assume that markets are semi-strong form efficient.

The triangle symbol $\Delta$ is the Greek letter capital delta which means change or increase in mathematics.

Ignore the benefit of interest tax shields from having more debt.

Remember: $\Delta V = \Delta D+ \Delta E$

Question 513  stock split, reverse stock split, stock dividend, bonus issue, rights issue

Which of the following statements is NOT correct?

A company's share price fell by 20% and its number of shares rose by 25%. Assume that there are no taxes, no signalling effects and no transaction costs.

Which one of the following corporate events may have happened?

A company conducts a 4 for 3 stock split. What is the percentage change in the stock price and the number of shares outstanding? The answers are given in the same order.

A company conducts a 1 for 5 rights issue at a subscription price of $7 when the pre-announcement stock price was$10. What is the percentage change in the stock price and the number of shares outstanding? The answers are given in the same order. Ignore all taxes, transaction costs and signalling effects.

In mid 2009 the listed mining company Rio Tinto announced a 21-for-40 renounceable rights issue. Below is the chronology of events:

• 04/06/2009. Share price opens at $69.00 and closes at$66.90.

• 05/06/2009. 21-for-40 rights issue announced at a subscription price of $28.29. • 16/06/2009. Last day that shares trade cum-rights. Share price opens at$76.40 and closes at $75.50. • 17/06/2009. Shares trade ex-rights. Rights trading commences. All things remaining equal, what would you expect Rio Tinto's stock price to open at on the first day that it trades ex-rights (17/6/2009)? Ignore the time value of money since time is negligibly short. Also ignore taxes. In late 2003 the listed bank ANZ announced a 2-for-11 rights issue to fund the takeover of New Zealand bank NBNZ. Below is the chronology of events: • 23/10/2003. Share price closes at$18.30.

• 24/10/2003. 2-for-11 rights issue announced at a subscription price of $13. The proceeds of the rights issue will be used to acquire New Zealand bank NBNZ. Trading halt announced in morning before market opens. • 28/10/2003. Trading halt lifted. Last (and only) day that shares trade cum-rights. Share price opens at$18.00 and closes at $18.14. • 29/10/2003. Shares trade ex-rights. All things remaining equal, what would you expect ANZ's stock price to open at on the first day that it trades ex-rights (29/10/2003)? Ignore the time value of money since time is negligibly short. Also ignore taxes. A fairly priced unlevered firm plans to pay a dividend of$1 next year (t=1) which is expected to grow by 3% pa every year after that. The firm's required return on equity is 8% pa.

The firm is thinking about reducing its future dividend payments by 10% so that it can use the extra cash to invest in more projects which are expected to return 8% pa, and have the same risk as the existing projects. Therefore, next year's dividend will be $0.90. What will be the stock's new annual capital return (proportional increase in price per year) if the change in payout policy goes ahead? Assume that payout policy is irrelevant to firm value and that all rates are effective annual rates. Is it possible for all countries' exchange rates to appreciate by 5% in the same year? or ? When someone says that they're "buying American dollars" (USD), what type of asset are they probably buying? They're probably buying: An American wishes to convert USD 1 million to Australian dollars (AUD). The exchange rate is 0.8 USD per AUD. How much is the USD 1 million worth in AUD? An Indonesian lady wishes to convert 1 million Indonesian rupiah (IDR) to Australian dollars (AUD). Exchange rates are 13,125 IDR per USD and 0.79 USD per AUD. How many AUD is the IDR 1 million worth? If the AUD appreciates against the USD, the American terms quote of the AUD will or ? If the USD appreciates against the AUD, the American terms quote of the AUD will or ? If the current AUD exchange rate is USD 0.9686 = AUD 1, what is the European terms quote of the AUD against the USD? If the AUD appreciates against the USD, the European terms quote of the AUD will or ? If the USD appreciates against the AUD, the European terms quote of the AUD will or ? How is the AUD normally quoted in Australia? Using or terms? Investors expect the Reserve Bank of Australia (RBA) to keep the policy rate steady at their next meeting. Then unexpectedly, the RBA announce that they will increase the policy rate by 25 basis points due to fears that the economy is growing too fast and that inflation will be above their target rate of 2 to 3 per cent. What do you expect to happen to Australia's exchange rate in the short term? The Australian dollar is likely to: In the 1997 Asian financial crisis many countries' exchange rates depreciated rapidly against the US dollar (USD). The Thai, Indonesian, Malaysian, Korean and Filipino currencies were severely affected. The below graph shows these Asian countries' currencies in USD per one unit of their currency, indexed to 100 in June 1997. Of the statements below, which is NOT correct? The Asian countries': The Chinese government attempts to fix its exchange rate against the US dollar and at the same time use monetary policy to fix its interest rate at a set level. To be able to fix its exchange rate and interest rate in this way, what does the Chinese government actually do? 1. Adopts capital controls to prevent financial arbitrage by private firms and individuals. 2. Adopts the same interest rate (monetary policy) as the United States. 3. Fixes inflation so that the domestic real interest rate is equal to the United States' real interest rate. Which of the above statements is or are true? For a bond that pays fixed semi-annual coupons, how is the annual coupon rate defined, and how is the bond's annual income yield from time 0 to 1 defined mathematically? Let: $P_0$ be the bond price now, $F_T$ be the bond's face value, $T$ be the bond's maturity in years, $r_\text{total}$ be the bond's total yield, $r_\text{income}$ be the bond's income yield, $r_\text{capital}$ be the bond's capital yield, and $C_t$ be the bond's coupon at time t in years. So $C_{0.5}$ is the coupon in 6 months, $C_1$ is the coupon in 1 year, and so on. Three important classes of investable risky assets are: • Corporate debt which has low total risk, • Real estate which has medium total risk, • Equity which has high total risk. Assume that the correlation between total returns on: • Corporate debt and real estate is 0.1, • Corporate debt and equity is 0.1, • Real estate and equity is 0.5. You are considering investing all of your wealth in one or more of these asset classes. Which portfolio will give the lowest total risk? You are restricted from shorting any of these assets. Disregard returns and the risk-return trade-off, pretend that you are only concerned with minimising risk. The accounting identity states that the book value of a company's assets (A) equals its liabilities (L) plus owners equity (OE), so A = L + OE. The finance version states that the market value of a company's assets (V) equals the market value of its debt (D) plus equity (E), so V = D + E. Therefore a business's assets can be seen as a portfolio of the debt and equity that fund the assets. Let $\sigma_\text{V total}^2$ be the total variance of returns on assets, $\sigma_\text{V syst}^2$ be the systematic variance of returns on assets, and $\sigma_\text{V idio}^2$ be the idiosyncratic variance of returns on assets, and $\rho_\text{D idio, E idio}$ be the correlation between the idiosyncratic returns on debt and equity. Which of the following equations is NOT correct? Bonds X and Y are issued by the same US company. Both bonds yield 10% pa, and they have the same face value ($100), maturity, seniority, and payment frequency.

The only difference is that bond X and Y's coupon rates are 8 and 12% pa respectively. Which of the following statements is true?

Which of the following statements about risk free government bonds is NOT correct?

Hint: Total return can be broken into income and capital returns as follows:

\begin{aligned} r_\text{total} &= \frac{c_1}{p_0} + \frac{p_1-p_0}{p_0} \\ &= r_\text{income} + r_\text{capital} \end{aligned}

The capital return is the growth rate of the price.
The income return is the periodic cash flow. For a bond this is the coupon payment.

Bonds X and Y are issued by different companies, but they both pay a semi-annual coupon of 10% pa and they have the same face value ($100) and maturity (3 years). The only difference is that bond X and Y's yields are 8 and 12% pa respectively. Which of the following statements is true? Bonds X and Y are issued by different companies, but they both pay a semi-annual coupon of 10% pa and they have the same face value ($100), maturity (3 years) and yield (10%) as each other.

Which of the following statements is true?

Which one of the following bonds is trading at a discount?

Which one of the following bonds is trading at par?

The coupon rate of a fixed annual-coupon bond is constant (always the same).

What can you say about the income return ($r_\text{income}$) of a fixed annual coupon bond? Remember that:

$$r_\text{total} = r_\text{income} + r_\text{capital}$$

$$r_\text{total, 0 to 1} = \frac{c_1}{p_0} + \frac{p_1-p_0}{p_0}$$

Assume that there is no change in the bond's total annual yield to maturity from when it is issued to when it matures.

Select the most correct statement.

From its date of issue until maturity, the income return of a fixed annual coupon:

Bonds X and Y are issued by the same US company. Both bonds yield 6% pa, and they have the same face value ($100), maturity, seniority, and payment frequency. The only difference is that bond X pays coupons of 8% pa and bond Y pays coupons of 12% pa. Which of the following statements is true? Below are some statements about loans and bonds. The first descriptive sentence is correct. But one of the second sentences about the loans' or bonds' prices is not correct. Which statement is NOT correct? Assume that interest rates are positive. Note that coupons or interest payments are the periodic payments made throughout a bond or loan's life. The face or par value of a bond or loan is the amount paid at the end when the debt matures. A young lady is trying to decide if she should attend university or begin working straight away in her home town. The young lady's grandma says that she should not go to university because she is less likely to marry the local village boy whom she likes because she will spend less time with him if she attends university. What's the correct way to classify this item from a capital budgeting perspective when trying to decide whether to attend university? The cost of not marrying the local village boy should be classified as: A stock's standard deviation of returns is expected to be: • 0.09 per month for the first 5 months; • 0.14 per month for the next 7 months. What is the expected standard deviation of the stock per year $(\sigma_\text{annual})$? Assume that returns are independently and identically distributed (iid) and therefore have zero auto-correlation. An 'interest rate' is the same thing as a 'coupon rate'. or ? Which of the below statements about effective rates and annualised percentage rates (APR's) is NOT correct? Which of the following statements is NOT correct? Borrowers: Which of the following statements is NOT equivalent to the yield on debt? Assume that the debt being referred to is fairly priced, but do not assume that it's priced at par. One of Miller and Modigliani's (M&M's) important insights is that a firm's managers should not try to achieve a particular level of leverage or interest tax shields under certain assumptions. So the firm's capital structure is irrelevant. This is because investors can make their own personal leverage and interest tax shields, so there's no need for managers to try to make corporate leverage and interest tax shields. This is true under the assumptions of equal tax rates, interest rates and debt availability for the person and the corporation, no transaction costs and symmetric information. This principal of 'home-made' or 'do-it-yourself' leverage can also be applied to other topics. Read the following statements to decide which are true: (I) Payout policy: a firm's managers should not try to achieve a particular pattern of equity payout. (II) Agency costs: a firm's managers should not try to minimise agency costs. (III) Diversification: a firm's managers should not try to diversify across industries. (IV) Shareholder wealth: a firm's managers should not try to maximise shareholders' wealth. Which of the above statement(s) are true? If a project's net present value (NPV) is zero, then its internal rate of return (IRR) will be: A three year project's NPV is negative. The cash flows of the project include a negative cash flow at the very start and positive cash flows over its short life. The required return of the project is 10% pa. Select the most correct statement. What is the Internal Rate of Return (IRR) of the project detailed in the table below? Assume that the cash flows shown in the table are paid all at once at the given point in time. All answers are given as effective annual rates.  Project Cash Flows Time (yrs) Cash flow ($) 0 -100 1 0 2 121

A project has an internal rate of return (IRR) which is greater than its required return. Select the most correct statement.

A project's net present value (NPV) is negative. Select the most correct statement.

A project's NPV is positive. Select the most correct statement:

A project has the following cash flows:

 Project Cash Flows Time (yrs) Cash flow ($) 0 -400 1 0 2 500 The required return on the project is 10%, given as an effective annual rate. What is the Internal Rate of Return (IRR) of this project? The following choices are effective annual rates. Assume that the cash flows shown in the table are paid all at once at the given point in time. A project's Profitability Index (PI) is less than 1. Select the most correct statement: Question 218 NPV, IRR, profitability index, average accounting return Which of the following statements is NOT correct? A firm is considering a business project which costs$11m now and is expected to pay a constant $1m at the end of every year forever. Assume that the initial$11m cost is funded using the firm's existing cash so no new equity or debt will be raised. The cost of capital is 10% pa.

Which of the following statements about net present value (NPV), internal rate of return (IRR) and payback period is NOT correct?

A firm is considering a business project which costs $10m now and is expected to pay a single cash flow of$12.1m in two years.

Assume that the initial $10m cost is funded using the firm's existing cash so no new equity or debt will be raised. The cost of capital is 10% pa. Which of the following statements about net present value (NPV), internal rate of return (IRR) and payback period is NOT correct? The below graph shows a project's net present value (NPV) against its annual discount rate. For what discount rate or range of discount rates would you accept and commence the project? All answer choices are given as approximations from reading off the graph. The below graph shows a project's net present value (NPV) against its annual discount rate. Which of the following statements is NOT correct? For an asset price to triple every 5 years, what must be the expected future capital return, given as an effective annual rate? A firm's weighted average cost of capital before tax ($r_\text{WACC before tax}$) would increase due to: A firm can issue 3 year annual coupon bonds at a yield of 10% pa and a coupon rate of 8% pa. The beta of its levered equity is 2. The market's expected return is 10% pa and 3 year government bonds yield 6% pa with a coupon rate of 4% pa. The market value of equity is$1 million and the market value of debt is $1 million. The corporate tax rate is 30%. What is the firm's after-tax WACC? Assume a classical tax system. Which of the following discount rates should be the highest for a levered company? Ignore the costs of financial distress. In the so called 'Swiss Loans Affair' of the 1980's, Australian banks offered loans denominated in Swiss Francs to Australian farmers at interest rates as low as 4% pa. This was far lower than interest rates on Australian Dollar loans which were above 10% due to very high inflation in Australia at the time. In the late-1980's there was a large depreciation in the Australian Dollar. The Australian Dollar nearly halved in value against the Swiss Franc. Many Australian farmers went bankrupt since they couldn't afford the interest payments on the Swiss Franc loans because the Australian Dollar value of those payments nearly doubled. The farmers accused the banks of promoting Swiss Franc loans without making them aware of the risks. What fundamental principal of finance did the Australian farmers (and the bankers) fail to understand? Question 245 foreign exchange rate, monetary policy, foreign exchange rate direct quote, no explanation Investors expect Australia's central bank, the RBA, to leave the policy rate unchanged at their next meeting. Then unexpectedly, the policy rate is reduced due to fears that Australia's GDP growth is slowing. What do you expect to happen to Australia's exchange rate? Direct and indirect quotes are given from the perspective of an Australian. The Australian dollar will: The market expects the Reserve Bank of Australia (RBA) to decrease the policy rate by 25 basis points at their next meeting. Then unexpectedly, the RBA announce that they will decrease the policy rate by 50 basis points due to fears of a recession and deflation. What do you expect to happen to Australia's exchange rate? The Australian dollar will: A three year bond has a face value of$100, a yield of 10% and a fixed coupon rate of 5%, paid semi-annually. What is its price?

A two year Government bond has a face value of $100, a yield of 2.5% pa and a fixed coupon rate of 0.5% pa, paid semi-annually. What is its price? A bond maturing in 10 years has a coupon rate of 4% pa, paid semi-annually. The bond's yield is currently 6% pa. The face value of the bond is$100. What is its price?

A three year bond has a face value of $100, a yield of 6% and a fixed coupon rate of 12%, paid semi-annually. What is its price? A four year bond has a face value of$100, a yield of 6% and a fixed coupon rate of 12%, paid semi-annually. What is its price?

A firm wishes to raise $20 million now. They will issue 8% pa semi-annual coupon bonds that will mature in 5 years and have a face value of$100 each. Bond yields are 6% pa, given as an APR compounding every 6 months, and the yield curve is flat.

How many bonds should the firm issue?

A five year bond has a face value of $100, a yield of 12% and a fixed coupon rate of 6%, paid semi-annually. What is the bond's price? A firm wishes to raise$8 million now. They will issue 7% pa semi-annual coupon bonds that will mature in 10 years and have a face value of $100 each. Bond yields are 10% pa, given as an APR compounding every 6 months, and the yield curve is flat. How many bonds should the firm issue? An investor bought two fixed-coupon bonds issued by the same company, a zero-coupon bond and a 7% pa semi-annual coupon bond. Both bonds have a face value of$1,000, mature in 10 years, and had a yield at the time of purchase of 8% pa.

A few years later, yields fell to 6% pa. Which of the following statements is correct? Note that a capital gain is an increase in price.

A firm wishes to raise $10 million now. They will issue 6% pa semi-annual coupon bonds that will mature in 8 years and have a face value of$1,000 each. Bond yields are 10% pa, given as an APR compounding every 6 months, and the yield curve is flat.

How many bonds should the firm issue?

A four year bond has a face value of $100, a yield of 9% and a fixed coupon rate of 6%, paid semi-annually. What is its price? In these tough economic times, central banks around the world have cut interest rates so low that they are practically zero. In some countries, government bond yields are also very close to zero. A three year government bond with a face value of$100 and a coupon rate of 2% pa paid semi-annually was just issued at a yield of 0%. What is the price of the bond?

A 30 year Japanese government bond was just issued at par with a yield of 1.7% pa. The fixed coupon payments are semi-annual. The bond has a face value of $100. Six months later, just after the first coupon is paid, the yield of the bond increases to 2% pa. What is the bond's new price? A 10 year Australian government bond was just issued at par with a yield of 3.9% pa. The fixed coupon payments are semi-annual. The bond has a face value of$1,000.

Six months later, just after the first coupon is paid, the yield of the bond decreases to 3.65% pa. What is the bond's new price?

Calculate the price of a newly issued ten year bond with a face value of $100, a yield of 8% pa and a fixed coupon rate of 6% pa, paid annually. So there's only one coupon per year, paid in arrears every year. Calculate the price of a newly issued ten year bond with a face value of$100, a yield of 8% pa and a fixed coupon rate of 6% pa, paid semi-annually. So there are two coupons per year, paid in arrears every six months.

An investor bought a 20 year 5% pa fixed coupon government bond priced at par. The face value is $100. Coupons are paid semi-annually and the next one is in 6 months. Six months later, just after the coupon at that time was paid, yields suddenly and unexpectedly rose to 5.5% pa. Note that all yields above are given as APR's compounding semi-annually. What was the bond investors' historical total return over that first 6 month period, given as an effective semi-annual rate? Government bonds currently have a return of 5% pa. A stock has an expected return of 6% pa and the market return is 7% pa. What is the beta of the stock? The following equation is the Dividend Discount Model, also known as the 'Gordon Growth Model' or the 'Perpetuity with growth' equation. $$p_{0} = \frac{c_1}{r_{\text{eff}} - g_{\text{eff}}}$$ What is the discount rate '$r_\text{eff}$' in this equation? A share was bought for$20 (at t=0) and paid its annual dividend of $3 one year later (at t=1). Just after the dividend was paid, the share price was$16 (at t=1). What was the total return, capital return and income return? Calculate your answers as effective annual rates.

The choices are given in the same order: $r_\text{total},r_\text{capital},r_\text{income}$.

When using the dividend discount model to price a stock:

$$p_{0} = \frac{d_1}{r - g}$$

The growth rate of dividends (g):

The following equation is the Dividend Discount Model, also known as the 'Gordon Growth Model' or the 'Perpetuity with growth' equation.

$$p_0 = \frac{d_1}{r - g}$$

Which expression is NOT equal to the expected dividend yield?

A share was bought for $10 (at t=0) and paid its annual dividend of$0.50 one year later (at t=1). Just after the dividend was paid, the share price was $11 (at t=1). What was the total return, capital return and income return? Calculate your answers as effective annual rates. The choices are given in the same order: $r_\text{total}$, $r_\text{capital}$, $r_\text{dividend}$. The following is the Dividend Discount Model used to price stocks: $$p_0=\frac{d_1}{r-g}$$ Which of the following statements about the Dividend Discount Model is NOT correct? The following is the Dividend Discount Model used to price stocks: $$p_0=\frac{d_1}{r-g}$$ All rates are effective annual rates and the cash flows ($d_1$) are received every year. Note that the r and g terms in the above DDM could also be labelled as below: $$r = r_{\text{total, 0}\rightarrow\text{1yr, eff 1yr}}$$ $$g = r_{\text{capital, 0}\rightarrow\text{1yr, eff 1yr}}$$ Which of the following statements is NOT correct? The following is the Dividend Discount Model (DDM) used to price stocks: $$P_0=\dfrac{C_1}{r-g}$$ If the assumptions of the DDM hold, which one of the following statements is NOT correct? The long term expected: A bank grants a borrower an interest-only residential mortgage loan with a very large 50% deposit and a nominal interest rate of 6% that is not expected to change. Assume that inflation is expected to be a constant 2% pa over the life of the loan. Ignore credit risk. From the bank's point of view, what is the long term expected nominal capital return of the loan asset? If the current AUD exchange rate is USD 0.9686 = AUD 1, what is the American terms quote of the AUD against the USD? Investors expect Australia's central bank, the RBA, to reduce the policy rate at their next meeting due to fears that the economy is slowing. Then unexpectedly, the policy rate is actually kept unchanged. What do you expect to happen to Australia's exchange rate? A levered company's required return on debt is always less than its required return on equity. or ? Interest expense on debt is tax-deductible, but dividend payments on equity are not. or ? The "interest expense" on a company's annual income statement is equal to the cash interest payments (but not principal payments) made to debt holders during the year. or ? A firm has a debt-to-equity ratio of 25%. What is its debt-to-assets ratio? A firm has a debt-to-equity ratio of 60%. What is its debt-to-assets ratio? A credit card offers an interest rate of 18% pa, compounding monthly. Find the effective monthly rate, effective annual rate and the effective daily rate. Assume that there are 365 days in a year. All answers are given in the same order: $$r_\text{eff monthly} , r_\text{eff yearly} , r_\text{eff daily}$$ What is the NPV of the following series of cash flows when the discount rate is 10% given as an effective annual rate? The first payment of$90 is in 3 years, followed by payments every 6 months in perpetuity after that which shrink by 3% every 6 months. That is, the growth rate every 6 months is actually negative 3%, given as an effective 6 month rate. So the payment at $t=3.5$ years will be $90(1-0.03)^1=87.3$, and so on.

A bathroom and plumbing supplies shop offers credit to its customers. Customers are given 60 days to pay for their goods, but if they pay within 7 days they will get a 2% discount.

What is the effective interest rate implicit in the discount being offered? Assume 365 days in a year and that all customers pay on either the 7th day or the 60th day. All rates given in this question are effective annual rates.

Estimate Microsoft's (MSFT) share price using a price earnings (PE) multiples approach with the following assumptions and figures only:

• Apple, Google and Microsoft are comparable companies,
• Apple's (AAPL) share price is $526.24 and historical EPS is$40.32.
• Google's (GOOG) share price is $1,215.65 and historical EPS is$36.23.
• Micrsoft's (MSFT) historical earnings per share (EPS) is $2.71. Source: Google Finance 28 Feb 2014. Estimate the US bank JP Morgan's share price using a price earnings (PE) multiples approach with the following assumptions and figures only: • The major US banks JP Morgan Chase (JPM), Citi Group (C) and Wells Fargo (WFC) are comparable companies; • JP Morgan Chase's historical earnings per share (EPS) is$4.37;
• Citi Group's share price is $50.05 and historical EPS is$4.26;
• Wells Fargo's share price is $48.98 and historical EPS is$3.89.

Note: Figures sourced from Google Finance on 24 March 2014.

Which firms tend to have low forward-looking price-earnings (PE) ratios?

Only consider firms with positive earnings, disregard firms with negative earnings and therefore negative PE ratios.

Estimate the Chinese bank ICBC's share price using a backward-looking price earnings (PE) multiples approach with the following assumptions and figures only. Note that the renminbi (RMB) is the Chinese currency, also known as the yuan (CNY).

• The 4 major Chinese banks ICBC, China Construction Bank (CCB), Bank of China (BOC) and Agricultural Bank of China (ABC) are comparable companies;
• ICBC 's historical earnings per share (EPS) is RMB 0.74;
• CCB's backward-looking PE ratio is 4.59;
• BOC 's backward-looking PE ratio is 4.78;
• ABC's backward-looking PE ratio is also 4.78;

Note: Figures sourced from Google Finance on 25 March 2014. Share prices are from the Shanghai stock exchange.

Which firms tend to have high forward-looking price-earnings (PE) ratios?

Which firms tend to have low forward-looking price-earnings (PE) ratios? Only consider firms with positive PE ratios.

Private equity firms are known to buy medium sized private companies operating in the same industry, merge them together into a larger company, and then sell it off in a public float (initial public offering, IPO).

If medium-sized private companies trade at PE ratios of 5 and larger listed companies trade at PE ratios of 15, what return can be achieved from this strategy?

Assume that:

• The medium-sized companies can be bought, merged and sold in an IPO instantaneously.
• There are no costs of finding, valuing, merging and restructuring the medium sized companies. Also, there is no competition to buy the medium-sized companies from other private equity firms.
• The large merged firm's earnings are the sum of the medium firms' earnings.
• The only reason for the difference in medium and large firm's PE ratios is due to the illiquidity of the medium firms' shares.
• Return is defined as: $r_{0→1} = (p_1-p_0+c_1)/p_0$ , where time zero is just before the merger and time one is just after.

Find the cash flow from assets (CFFA) of the following project.

 Project Data Project life 2 years Initial investment in equipment $8m Depreciation of equipment per year for tax purposes$3m Unit sales per year 10m Sale price per unit $9 Variable cost per unit$4 Fixed costs per year, paid at the end of each year $2m Tax rate 30% Note 1: Due to the project, the firm will have to purchase$40m of inventory initially (at t=0). Half of this inventory will be sold at t=1 and the other half at t=2.

Note 2: The equipment will have a book value of $2m at the end of the project for tax purposes. However, the equipment is expected to fetch$1m when it is sold. Assume that the full capital loss is tax-deductible and taxed at the full corporate tax rate.

Note 3: The project will be fully funded by equity which investors will expect to pay dividends totaling $10m at the end of each year. Find the project's CFFA at time zero, one and two. Answers are given in millions of dollars ($m).

What is the NPV of the following series of cash flows when the discount rate is 5% given as an effective annual rate?

The first payment of $10 is in 4 years, followed by payments every 6 months forever after that which shrink by 2% every 6 months. That is, the growth rate every 6 months is actually negative 2%, given as an effective 6 month rate. So the payment at $t=4.5$ years will be $10(1-0.02)^1=9.80$, and so on. A stock pays annual dividends which are expected to continue forever. It just paid a dividend of$10. The growth rate in the dividend is 2% pa. You estimate that the stock's required return is 10% pa. Both the discount rate and growth rate are given as effective annual rates. Using the dividend discount model, what will be the share price?

A stock is expected to pay the following dividends:

 Cash Flows of a Stock Time (yrs) 0 1 2 3 4 ... Dividend ($) 0.00 1.00 1.05 1.10 1.15 ... After year 4, the annual dividend will grow in perpetuity at 5% pa, so; • the dividend at t=5 will be$1.15(1+0.05),
• the dividend at t=6 will be $1.15(1+0.05)^2, and so on. The required return on the stock is 10% pa. Both the growth rate and required return are given as effective annual rates. What is the current price of the stock? A stock is expected to pay the following dividends:  Cash Flows of a Stock Time (yrs) 0 1 2 3 4 ... Dividend ($) 0.00 1.00 1.05 1.10 1.15 ...

After year 4, the annual dividend will grow in perpetuity at 5% pa, so;

• the dividend at t=5 will be $1.15(1+0.05), • the dividend at t=6 will be$1.15(1+0.05)^2, and so on.

The required return on the stock is 10% pa. Both the growth rate and required return are given as effective annual rates.

What will be the price of the stock in three and a half years (t = 3.5)?

Most listed Australian companies pay dividends twice per year, the 'interim' and 'final' dividends, which are roughly 6 months apart.

You are an equities analyst trying to value the company BHP. You decide to use the Dividend Discount Model (DDM) as a starting point, so you study BHP's dividend history and you find that BHP tends to pay the same interim and final dividend each year, and that both grow by the same rate.

You expect BHP will pay a $0.55 interim dividend in six months and a$0.55 final dividend in one year. You expect each to grow by 4% next year and forever, so the interim and final dividends next year will be $0.572 each, and so on in perpetuity. Assume BHP's cost of equity is 8% pa. All rates are quoted as nominal effective rates. The dividends are nominal cash flows and the inflation rate is 2.5% pa. What is the current price of a BHP share? A stock pays semi-annual dividends. It just paid a dividend of$10. The growth rate in the dividend is 1% every 6 months, given as an effective 6 month rate. You estimate that the stock's required return is 21% pa, as an effective annual rate.

Using the dividend discount model, what will be the share price?

A stock is expected to pay the following dividends:

 Cash Flows of a Stock Time (yrs) 0 1 2 3 4 ... Dividend ($) 0.00 1.15 1.10 1.05 1.00 ... After year 4, the annual dividend will grow in perpetuity at -5% pa. Note that this is a negative growth rate, so the dividend will actually shrink. So, • the dividend at t=5 will be $1(1-0.05) = 0.95$, • the dividend at t=6 will be $1(1-0.05)^2 = 0.9025$, and so on. The required return on the stock is 10% pa. Both the growth rate and required return are given as effective annual rates. What is the current price of the stock? A stock is expected to pay the following dividends:  Cash Flows of a Stock Time (yrs) 0 1 2 3 4 ... Dividend ($) 0.00 1.15 1.10 1.05 1.00 ...

After year 4, the annual dividend will grow in perpetuity at -5% pa. Note that this is a negative growth rate, so the dividend will actually shrink. So,

• the dividend at t=5 will be $1(1-0.05) = 0.95$,
• the dividend at t=6 will be $1(1-0.05)^2 = 0.9025$, and so on.

The required return on the stock is 10% pa. Both the growth rate and required return are given as effective annual rates.

What will be the price of the stock in four and a half years (t = 4.5)?

A share just paid its semi-annual dividend of $10. The dividend is expected to grow at 2% every 6 months forever. This 2% growth rate is an effective 6 month rate. Therefore the next dividend will be$10.20 in six months. The required return of the stock is 10% pa, given as an effective annual rate.

What is the price of the share now?

A share just paid its semi-annual dividend of $10. The dividend is expected to grow at 2% every 6 months forever. This 2% growth rate is an effective 6 month rate. Therefore the next dividend will be$10.20 in six months. The required return of the stock 10% pa, given as an effective annual rate.

What is the price of the share now?

For certain shares, the forward-looking Price-Earnings Ratio ($P_0/EPS_1$) is equal to the inverse of the share's total expected return ($1/r_\text{total}$).

For what shares is this true?

Assume:

• The general accounting definition of 'payout ratio' which is dividends per share (DPS) divided by earnings per share (EPS).
• All cash flows, earnings and rates are real.

A stock pays annual dividends. It just paid a dividend of $3. The growth rate in the dividend is 4% pa. You estimate that the stock's required return is 10% pa. Both the discount rate and growth rate are given as effective annual rates. Using the dividend discount model, what will be the share price? A stock is expected to pay the following dividends:  Cash Flows of a Stock Time (yrs) 0 1 2 3 4 ... Dividend ($) 8 8 8 20 8 ...

After year 4, the dividend will grow in perpetuity at 4% pa. The required return on the stock is 10% pa. Both the growth rate and required return are given as effective annual rates.

What is the current price of the stock?

A stock is expected to pay the following dividends:

 Cash Flows of a Stock Time (yrs) 0 1 2 3 4 ... Dividend ($) 8 8 8 20 8 ... After year 4, the dividend will grow in perpetuity at 4% pa. The required return on the stock is 10% pa. Both the growth rate and required return are given as effective annual rates. What will be the price of the stock in 5 years (t = 5), just after the dividend at that time has been paid? A stock pays annual dividends. It just paid a dividend of$5. The growth rate in the dividend is 1% pa. You estimate that the stock's required return is 8% pa. Both the discount rate and growth rate are given as effective annual rates.

Using the dividend discount model, what will be the share price?

A stock is expected to pay the following dividends:

 Cash Flows of a Stock Time (yrs) 0 1 2 3 4 ... Dividend ($) 2 2 2 10 3 ... After year 4, the dividend will grow in perpetuity at 4% pa. The required return on the stock is 10% pa. Both the growth rate and required return are given as effective annual rates. What is the current price of the stock? A stock is expected to pay the following dividends:  Cash Flows of a Stock Time (yrs) 0 1 2 3 4 ... Dividend ($) 2 2 2 10 3 ...

After year 4, the dividend will grow in perpetuity at 4% pa. The required return on the stock is 10% pa. Both the growth rate and required return are given as effective annual rates.

What will be the price of the stock in 5 years (t = 5), just after the dividend at that time has been paid?

A share pays annual dividends. It just paid a dividend of $2. The growth rate in the dividend is 3% pa. You estimate that the stock's required return is 8% pa. Both the discount rate and growth rate are given as effective annual rates. Using the dividend discount model, what is the share price? A stock is expected to pay the following dividends:  Cash Flows of a Stock Time (yrs) 0 1 2 3 4 ... Dividend ($) 0 6 12 18 20 ...

After year 4, the dividend will grow in perpetuity at 5% pa. The required return of the stock is 10% pa. Both the growth rate and required return are given as effective annual rates.

What is the current price of the stock?

A stock is expected to pay the following dividends:

 Cash Flows of a Stock Time (yrs) 0 1 2 3 4 ... Dividend ($) 0 6 12 18 20 ... After year 4, the dividend will grow in perpetuity at 5% pa. The required return of the stock is 10% pa. Both the growth rate and required return are given as effective annual rates. What will be the price of the stock in 7 years (t = 7), just after the dividend at that time has been paid? A stock is expected to pay a dividend of$15 in one year (t=1), then $25 for 9 years after that (payments at t=2 ,3,...10), and on the 11th year (t=11) the dividend will be 2% less than at t=10, and will continue to shrink at the same rate every year after that forever. The required return of the stock is 10%. All rates are effective annual rates. What is the price of the stock now? A share just paid its semi-annual dividend of$5. The dividend is expected to grow at 1% every 6 months forever. This 1% growth rate is an effective 6 month rate.

Therefore the next dividend will be $5.05 in six months. The required return of the stock 8% pa, given as an effective annual rate. What is the price of the share now? A company's shares just paid their annual dividend of$2 each.

The stock price is now $40 (just after the dividend payment). The annual dividend is expected to grow by 3% every year forever. The assumptions of the dividend discount model are valid for this company. What do you expect the effective annual dividend yield to be in 3 years (dividend yield from t=3 to t=4)? You own an apartment which you rent out as an investment property. What is the price of the apartment using discounted cash flow (DCF, same as NPV) valuation? Assume that: • You just signed a contract to rent the apartment out to a tenant for the next 12 months at$2,000 per month, payable in advance (at the start of the month, t=0). The tenant is just about to pay you the first $2,000 payment. • The contract states that monthly rental payments are fixed for 12 months. After the contract ends, you plan to sign another contract but with rental payment increases of 3%. You intend to do this every year. So rental payments will increase at the start of the 13th month (t=12) to be$2,060 (=2,000(1+0.03)), and then they will be constant for the next 12 months.
Rental payments will increase again at the start of the 25th month (t=24) to be $2,121.80 (=2,000(1+0.03)2), and then they will be constant for the next 12 months until the next year, and so on. • The required return of the apartment is 8.732% pa, given as an effective annual rate. • Ignore all taxes, maintenance, real estate agent, council and strata fees, periods of vacancy and other costs. Assume that the apartment will last forever and so will the rental payments. In the dividend discount model: $$P_0 = \dfrac{C_1}{r-g}$$ The return $r$ is supposed to be the: In the dividend discount model: $$P_0= \frac{d_1}{r-g}$$ The pronumeral $g$ is supposed to be the: The following equation is the Dividend Discount Model, also known as the 'Gordon Growth Model' or the 'Perpetuity with growth' equation. $$p_0= \frac{c_1}{r-g}$$ Which expression is equal to the expected dividend return? When using the dividend discount model, care must be taken to avoid using a nominal dividend growth rate that exceeds the country's nominal GDP growth rate. Otherwise the firm is forecast to take over the country since it grows faster than the average business forever. Suppose a firm's nominal dividend grows at 10% pa forever, and nominal GDP growth is 5% pa forever. The firm's total dividends are currently$1 billion (t=0). The country's GDP is currently $1,000 billion (t=0). In approximately how many years will the company's total dividends be as large as the country's GDP? Stocks in the United States usually pay quarterly dividends. For example, the retailer Wal-Mart Stores paid a$0.47 dividend every quarter over the 2013 calendar year and plans to pay a $0.48 dividend every quarter over the 2014 calendar year. Using the dividend discount model and net present value techniques, calculate the stock price of Wal-Mart Stores assuming that: • The time now is the beginning of January 2014. The next dividend of$0.48 will be received in 3 months (end of March 2014), with another 3 quarterly payments of $0.48 after this (end of June, September and December 2014). • The quarterly dividend will increase by 2% every year, but each quarterly dividend over the year will be equal. So each quarterly dividend paid in 2015 will be$0.4896 ($=0.48×(1+0.02)^1$), with the first at the end of March 2015 and the last at the end of December 2015. In 2016 each quarterly dividend will be $0.499392 ($=0.48×(1+0.02)^2$), with the first at the end of March 2016 and the last at the end of December 2016, and so on forever. • The total required return on equity is 6% pa. • The required return and growth rate are given as effective annual rates. • All cash flows and rates are nominal. Inflation is 3% pa. • Dividend payment dates and ex-dividend dates are at the same time. • Remember that there are 4 quarters in a year and 3 months in a quarter. What is the current stock price? Three years ago Frederika bought a house for$400,000.

Now it's worth $600,000, based on recent similar sales in the area. Frederika's residential property has an expected total return of 7% pa. She rents her house out for$2,500 per month, paid in advance. Every 12 months she plans to increase the rental payments.

The present value of 12 months of rental payments is $29,089.48. The future value of 12 months of rental payments one year ahead is$31,125.74.

What is the expected annual capital yield of the property?

Stocks in the United States usually pay quarterly dividends. For example, the software giant Microsoft paid a $0.23 dividend every quarter over the 2013 financial year and plans to pay a$0.28 dividend every quarter over the 2014 financial year.

Using the dividend discount model and net present value techniques, calculate the stock price of Microsoft assuming that:

• The time now is the beginning of July 2014. The next dividend of $0.28 will be received in 3 months (end of September 2014), with another 3 quarterly payments of$0.28 after this (end of December 2014, March 2015 and June 2015).
• The quarterly dividend will increase by 2.5% every year, but each quarterly dividend over the year will be equal. So each quarterly dividend paid in the financial year beginning in September 2015 will be $0.287 $(=0.28×(1+0.025)^1)$, with the last at the end of June 2016. In the next financial year beginning in September 2016 each quarterly dividend will be$0.294175 $(=0.28×(1+0.025)^2)$, with the last at the end of June 2017, and so on forever.
• The total required return on equity is 6% pa.
• The required return and growth rate are given as effective annual rates.
• Dividend payment dates and ex-dividend dates are at the same time.
• Remember that there are 4 quarters in a year and 3 months in a quarter.

What is the current stock price?

The perpetuity with growth formula is:

$$P_0= \dfrac{C_1}{r-g}$$

Which of the following is NOT equal to the total required return (r)?

A managed fund charges fees based on the amount of money that you keep with them. The fee is 2% of the end-of-year amount, paid at the end of every year.

This fee is charged regardless of whether the fund makes gains or losses on your money.

The fund offers to invest your money in shares which have an expected return of 10% pa before fees.

You are thinking of investing $100,000 in the fund and keeping it there for 40 years when you plan to retire. How much money do you expect to have in the fund in 40 years? Also, what is the future value of the fees that the fund expects to earn from you? Give both amounts as future values in 40 years. Assume that: • The fund has no private information. • Markets are weak and semi-strong form efficient. • The fund's transaction costs are negligible. • The cost and trouble of investing your money in shares by yourself, without the managed fund, is negligible. • The fund invests its fees in the same companies as it invests your funds in, but with no fees. The below answer choices list your expected wealth in 40 years and then the fund's expected wealth in 40 years. A fairly valued share's current price is$4 and it has a total required return of 30%. Dividends are paid annually and next year's dividend is expected to be $1. After that, dividends are expected to grow by 5% pa in perpetuity. All rates are effective annual returns. What is the expected dividend income paid at the end of the second year (t=2) and what is the expected capital gain from just after the first dividend (t=1) to just after the second dividend (t=2)? The answers are given in the same order, the dividend and then the capital gain. The perpetuity with growth equation is: $$P_0=\dfrac{C_1}{r-g}$$ Which of the following is NOT equal to the expected capital return as an effective annual rate? Discounted cash flow (DCF) valuation prices assets by finding the present value of the asset's future cash flows. The single cash flow, annuity, and perpetuity equations are very useful for this. Which of the following equations is the 'perpetuity with growth' equation? Two companies BigDiv and ZeroDiv are exactly the same except for their dividend payouts. BigDiv pays large dividends and ZeroDiv doesn't pay any dividends. Currently the two firms have the same earnings, assets, number of shares, share price, expected total return and risk. Assume a perfect world with no taxes, no transaction costs, no asymmetric information and that all assets including business projects are fairly priced and therefore zero-NPV. All things remaining equal, which of the following statements is NOT correct? A stock will pay you a dividend of$10 tonight if you buy it today. Thereafter the annual dividend is expected to grow by 5% pa, so the next dividend after the $10 one tonight will be$10.50 in one year, then in two years it will be $11.025 and so on. The stock's required return is 10% pa. What is the stock price today and what do you expect the stock price to be tomorrow, approximately? A share currently worth$100 is expected to pay a constant dividend of $4 for the next 5 years with the first dividend in one year (t=1) and the last in 5 years (t=5). The total required return is 10% pa. What do you expected the share price to be in 5 years, just after the dividend at that time has been paid? You want to buy an apartment priced at$300,000. You have saved a deposit of $30,000. The bank has agreed to lend you the$270,000 as a fully amortising loan with a term of 25 years. The interest rate is 12% pa and is not expected to change.

What will be your monthly payments? Remember that mortgage loan payments are paid in arrears (at the end of the month).

Your friend wants to borrow $1,000 and offers to pay you back$100 in 6 months, with more $100 payments at the end of every month for another 11 months. So there will be twelve$100 payments in total. She says that 12 payments of $100 equals$1,200 so she's being generous.

If interest rates are 12% pa, given as an APR compounding monthly, what is the Net Present Value (NPV) of your friend's deal?

A European bond paying annual coupons of 6% offers a yield of 10% pa.

Convert the yield into an effective monthly rate, an effective annual rate and an effective daily rate. Assume that there are 365 days in a year.

All answers are given in the same order:

$$r_\text{eff, monthly} , r_\text{eff, yearly} , r_\text{eff, daily}$$

You want to buy an apartment worth $500,000. You have saved a deposit of$50,000. The bank has agreed to lend you the $450,000 as a fully amortising mortgage loan with a term of 25 years. The interest rate is 6% pa and is not expected to change. What will be your monthly payments? You want to buy an apartment worth$400,000. You have saved a deposit of $80,000. The bank has agreed to lend you the$320,000 as a fully amortising mortgage loan with a term of 30 years. The interest rate is 6% pa and is not expected to change. What will be your monthly payments?

You want to buy an apartment priced at $500,000. You have saved a deposit of$50,000. The bank has agreed to lend you the $450,000 as a fully amortising loan with a term of 30 years. The interest rate is 6% pa and is not expected to change. What will be your monthly payments? You just signed up for a 30 year fully amortising mortgage loan with monthly payments of$2,000 per month. The interest rate is 9% pa which is not expected to change.

How much did you borrow? After 5 years, how much will be owing on the mortgage? The interest rate is still 9% and is not expected to change.

You just signed up for a 30 year fully amortising mortgage with monthly payments of $1,000 per month. The interest rate is 6% pa which is not expected to change. How much did you borrow? After 20 years, how much will be owing on the mortgage? The interest rate is still 6% and is not expected to change. You just signed up for a 30 year fully amortising mortgage loan with monthly payments of$1,500 per month. The interest rate is 9% pa which is not expected to change.

How much did you borrow? After 10 years, how much will be owing on the mortgage? The interest rate is still 9% and is not expected to change.

You just agreed to a 30 year fully amortising mortgage loan with monthly payments of $2,500. The interest rate is 9% pa which is not expected to change. How much did you borrow? After 10 years, how much will be owing on the mortgage? The interest rate is still 9% and is not expected to change. The below choices are given in the same order. You want to buy a house priced at$400,000. You have saved a deposit of $40,000. The bank has agreed to lend you$360,000 as a fully amortising loan with a term of 30 years. The interest rate is 8% pa payable monthly and is not expected to change.

What will be your monthly payments?

The required return of a project is 10%, given as an effective annual rate. Assume that the cash flows shown in the table are paid all at once at the given point in time.

What is the Net Present Value (NPV) of the project?

 Project Cash Flows Time (yrs) Cash flow ($) 0 -100 1 0 2 121 The phone company Telstra have 2 mobile service plans on offer which both have the same amount of phone call, text message and internet data credit. Both plans have a contract length of 24 months and the monthly cost is payable in advance. The only difference between the two plans is that one is a: • 'Bring Your Own' (BYO) mobile service plan, costing$50 per month. There is no phone included in this plan. The other plan is a:
• 'Bundled' mobile service plan that comes with the latest smart phone, costing $71 per month. This plan includes the latest smart phone. Neither plan has any additional payments at the start or end. The only difference between the plans is the phone, so what is the implied cost of the phone as a present value? Assume that the discount rate is 2% per month given as an effective monthly rate, the same high interest rate on credit cards. A project to build a toll bridge will take two years to complete, costing three payments of$100 million at the start of each year for the next three years, that is at t=0, 1 and 2.

After completion, the toll bridge will yield a constant $50 million at the end of each year for the next 10 years. So the first payment will be at t=3 and the last at t=12. After the last payment at t=12, the bridge will be given to the government. The required return of the project is 21% pa given as an effective annual nominal rate. All cash flows are real and the expected inflation rate is 10% pa given as an effective annual rate. Ignore taxes. The Net Present Value is: The required return of a project is 10%, given as an effective annual rate. Assume that the cash flows shown in the table are paid all at once at the given point in time. What is the Net Present Value (NPV) of the project?  Project Cash Flows Time (yrs) Cash flow ($) 0 -100 1 11 2 121

In Australia, domestic university students are allowed to buy concession tickets for the bus, train and ferry which sell at a discount of 50% to full-price tickets.

The Australian Government do not allow international university students to buy concession tickets, they have to pay the full price.

Some international students see this as unfair and they are willing to pay for fake university identification cards which have the concession sticker.

What is the most that an international student would be willing to pay for a fake identification card?

Assume that international students:

• consider buying their fake card on the morning of the first day of university from their neighbour, just before they leave to take the train into university.
• buy their weekly train tickets on the morning of the first day of each week.
• ride the train to university and back home again every day seven days per week until summer holidays 40 weeks from now. The concession card only lasts for those 40 weeks. Assume that there are 52 weeks in the year for the purpose of interest rate conversion.
• a single full-priced one-way train ride costs $5. • have a discount rate of 11% pa, given as an effective annual rate. Approach this question from a purely financial view point, ignoring the illegality, embarrassment and the morality of committing fraud. The following cash flows are expected: • 10 yearly payments of$60, with the first payment in 3 years from now (first payment at t=3).
• 1 payment of $400 in 5 years and 6 months (t=5.5) from now. What is the NPV of the cash flows if the discount rate is 10% given as an effective annual rate? A text book publisher is thinking of asking some teachers to write a new textbook at a cost of$100,000, payable now. The book would be written, printed and ready to sell to students in 2 years. It will be ready just before semester begins.

A cash flow of $100 would be made from each book sold, after all costs such as printing and delivery. There are 600 students per semester. Assume that every student buys a new text book. Remember that there are 2 semesters per year and students buy text books at the beginning of the semester. Assume that text book publishers will sell the books at the same price forever and that the number of students is constant. If the discount rate is 8% pa, given as an effective annual rate, what is the NPV of the project? A student just won the lottery. She won$1 million in cash after tax. She is trying to calculate how much she can spend per month for the rest of her life. She assumes that she will live for another 60 years. She wants to withdraw equal amounts at the beginning of every month, starting right now.

All of the cash is currently sitting in a bank account which pays interest at a rate of 6% pa, given as an APR compounding per month. On her last withdrawal, she intends to have nothing left in her bank account. How much can she withdraw at the beginning of each month?

The following cash flows are expected:

• 10 yearly payments of $80, with the first payment in 3 years from now (first payment at t=3). • 1 payment of$600 in 5 years and 6 months (t=5.5) from now.

What is the NPV of the cash flows if the discount rate is 10% given as an effective annual rate?

Harvey Norman the large retailer often runs sales advertising 2 years interest free when you purchase its products. This offer can be seen as a free personal loan from Harvey Norman to its customers.

Assume that banks charge an interest rate on personal loans of 12% pa given as an APR compounding per month. This is the interest rate that Harvey Norman deserves on the 2 year loan it extends to its customers. Therefore Harvey Norman must implicitly include the cost of this loan in the advertised sale price of its goods.

If you were a customer buying from Harvey Norman, and you were paying immediately, not in 2 years, what is the minimum percentage discount to the advertised sale price that you would insist on? (Hint: if it makes it easier, assume that you’re buying a product with an advertised price of $100). A stock is expected to pay the following dividends:  Cash Flows of a Stock Time (yrs) 0 1 2 3 4 ... Dividend ($) 0 6 12 18 20 ...

After year 4, the dividend will grow in perpetuity at 5% pa. The required return of the stock is 10% pa. Both the growth rate and required return are given as effective annual rates.

If all of the dividends since time period zero were deposited into a bank account yielding 8% pa as an effective annual rate, how much money will be in the bank account in 2.5 years (in other words, at t=2.5)?

A very low-risk stock just paid its semi-annual dividend of $0.14, as it has for the last 5 years. You conservatively estimate that from now on the dividend will fall at a rate of 1% every 6 months. If the stock currently sells for$3 per share, what must be its required total return as an effective annual rate?

If risk free government bonds are trading at a yield of 4% pa, given as an effective annual rate, would you consider buying or selling the stock?

The stock's required total return is:

Examine the following graph which shows stocks' betas $(\beta)$ and expected returns $(\mu)$:

Assume that the CAPM holds and that future expectations of stocks' returns and betas are correctly measured. Which statement is NOT correct?

Your neighbour asks you for a loan of $100 and offers to pay you back$120 in one year.

You don't actually have any money right now, but you can borrow and lend from the bank at a rate of 10% pa. Rates are given as effective annual rates.

Assume that your neighbour will definitely pay you back. Ignore interest tax shields and transaction costs.

The Net Present Value (NPV) of lending to your neighbour is $9.09. Describe what you would do to actually receive a$9.09 cash flow right now with zero net cash flows in the future.

You have $100,000 in the bank. The bank pays interest at 10% pa, given as an effective annual rate. You wish to consume an equal amount now (t=0) and in one year (t=1) and have nothing left in the bank at the end. How much can you consume at each time? You have$100,000 in the bank. The bank pays interest at 10% pa, given as an effective annual rate.

You wish to consume an equal amount now (t=0), in one year (t=1) and in two years (t=2), and still have $50,000 in the bank after that (t=2). How much can you consume at each time? You just started work at your new job which pays$48,000 per year.

The human resources department have given you the option of being paid at the end of every week or every month.

Assume that there are 4 weeks per month, 12 months per year and 48 weeks per year.

Bank interest rates are 12% pa given as an APR compounding per month.

What is the dollar gain over one year, as a net present value, of being paid every week rather than every month?

Your poor friend asks to borrow some money from you. He would like $1,000 now (t=0) and every year for the next 5 years, so there will be 6 payments of$1,000 from t=0 to t=5 inclusive. In return he will pay you $10,000 in seven years from now (t=7). What is the net present value (NPV) of lending to your friend? Assume that your friend will definitely pay you back so the loan is risk-free, and that the yield on risk-free government debt is 10% pa, given as an effective annual rate. A levered firm has zero-coupon bonds which mature in one year and have a combined face value of$9.9m.

Investors are risk-neutral and therefore all debt and equity holders demand the same required return of 10% pa.

In one year the firm's assets will be worth:

• $13.2m with probability 0.5 in the good state of the world, or •$6.6m with probability 0.5 in the bad state of the world.

A new project presents itself which requires an investment of $2m and will provide a certain cash flow of$3.3m in one year.

The firm doesn't have any excess cash to make the initial $2m investment, but the funds can be raised from shareholders through a fairly priced rights issue. Ignore all transaction costs. Should shareholders vote to proceed with the project and equity raising? What will be the gain in shareholder wealth if they decide to proceed? The boss of WorkingForTheManCorp has a wicked (and unethical) idea. He plans to pay his poor workers one week late so that he can get more interest on his cash in the bank. Every week he is supposed to pay his 1,000 employees$1,000 each. So $1 million is paid to employees every week. The boss was just about to pay his employees today, until he thought of this idea so he will actually pay them one week (7 days) later for the work they did last week and every week in the future, forever. Bank interest rates are 10% pa, given as a real effective annual rate. So $r_\text{eff annual, real} = 0.1$ and the real effective weekly rate is therefore $r_\text{eff weekly, real} = (1+0.1)^{1/52}-1 = 0.001834569$ All rates and cash flows are real, the inflation rate is 3% pa and there are 52 weeks per year. The boss will always pay wages one week late. The business will operate forever with constant real wages and the same number of employees. What is the net present value (NPV) of the boss's decision to pay later? What type of present value equation is best suited to value a residential house investment property that is expected to pay constant rental payments forever? Note that 'constant' has the same meaning as 'level' in this context. A business project is expected to cost$100 now (t=0), then pay $10 at the end of the third (t=3), fourth, fifth and sixth years, and then grow by 5% pa every year forever. So the cash flow will be$10.5 at the end of the seventh year (t=7), then $11.025 at the end of the eighth year (t=8) and so on perpetually. The total required return is 10℅ pa. Which of the following formulas will NOT give the correct net present value of the project? An investor owns an empty block of land that has local government approval to be developed into a petrol station, car wash or car park. The council will only allow a single development so the projects are mutually exclusive. All of the development projects have the same risk and the required return of each is 10% pa. Each project has an immediate cost and once construction is finished in one year the land and development will be sold. The table below shows the estimated costs payable now, expected sale prices in one year and the internal rates of returns (IRR's).  Mutually Exclusive Projects Project Costnow ($) Sale price inone year ($) IRR(% pa) Petrol station 9,000,000 11,000,000 22.22 Car wash 800,000 1,100,000 37.50 Car park 70,000 110,000 57.14 Which project should the investor accept? On his 20th birthday, a man makes a resolution. He will deposit$30 into a bank account at the end of every month starting from now, which is the start of the month. So the first payment will be in one month. He will write in his will that when he dies the money in the account should be given to charity.

The bank account pays interest at 6% pa compounding monthly, which is not expected to change.

If the man lives for another 60 years, how much money will be in the bank account if he dies just after making his last (720th) payment?

There are many ways to write the ordinary annuity formula.

Which of the following is NOT equal to the ordinary annuity formula?

A company has:

• 10 million common shares outstanding, each trading at a price of $90. • 1 million preferred shares which have a face (or par) value of$100 and pay a constant dividend of 9% of par. They currently trade at a price of $120 each. • Debentures that have a total face value of$60,000,000 and a yield to maturity of 6% per annum. They are publicly traded and their market price is equal to 90% of their face value.
• The risk-free rate is 5% and the market return is 10%.
• Market analysts estimate that the company's common stock has a beta of 1.2. The corporate tax rate is 30%.

What is the company's after-tax Weighted Average Cost of Capital (WACC)? Assume a classical tax system.

A project has the following cash flows. Normally cash flows are assumed to happen at the given time. But here, assume that the cash flows are received smoothly over the year. So the $250 at time 2 is actually earned smoothly from t=1 to t=2:  Project Cash Flows Time (yrs) Cash flow ($) 0 -400 1 200 2 250

What is the payback period of the project in years?

A project has the following cash flows. Normally cash flows are assumed to happen at the given time. But here, assume that the cash flows are received smoothly over the year. So the $105 at time 2 is actually earned smoothly from t=1 to t=2:  Project Cash Flows Time (yrs) Cash flow ($) 0 -90 1 30 2 105

What is the payback period of the project in years?

Which of the following companies is most suitable for valuation using PE multiples techniques?

Which of the following investable assets is the LEAST suitable for valuation using PE multiples techniques?

A mature firm has constant expected future earnings and dividends. Both amounts are equal. So earnings and dividends are expected to be equal and unchanging.

Which of the following statements is NOT correct?

Details of two different types of light bulbs are given below:

• Low-energy light bulbs cost $3.50, have a life of nine years, and use about$1.60 of electricity a year, paid at the end of each year.
• Conventional light bulbs cost only $0.50, but last only about a year and use about$6.60 of energy a year, paid at the end of each year.

The real discount rate is 5%, given as an effective annual rate. Assume that all cash flows are real. The inflation rate is 3% given as an effective annual rate.

Find the Equivalent Annual Cost (EAC) of the low-energy and conventional light bulbs. The below choices are listed in that order.

An industrial chicken farmer grows chickens for their meat. Chickens:

1. Cost $0.50 each to buy as chicks. They are bought on the day they’re born, at t=0. 2. Grow at a rate of$0.70 worth of meat per chicken per week for the first 6 weeks (t=0 to t=6).
3. Grow at a rate of $0.40 worth of meat per chicken per week for the next 4 weeks (t=6 to t=10) since they’re older and grow more slowly. 4. Feed costs are$0.30 per chicken per week for their whole life. Chicken feed is bought and fed to the chickens once per week at the beginning of the week. So the first amount of feed bought for a chicken at t=0 costs $0.30, and so on. 5. Can be slaughtered (killed for their meat) and sold at no cost at the end of the week. The price received for the chicken is their total value of meat (note that the chicken grows fast then slow, see above). The required return of the chicken farm is 0.5% given as an effective weekly rate. Ignore taxes and the fixed costs of the factory. Ignore the chicken’s welfare and other environmental and ethical concerns. Find the equivalent weekly cash flow of slaughtering a chicken at 6 weeks and at 10 weeks so the farmer can figure out the best time to slaughter his chickens. The choices below are given in the same order, 6 and 10 weeks. You're advising your superstar client 40-cent who is weighing up buying a private jet or a luxury yacht. 40-cent is just as happy with either, but he wants to go with the more cost-effective option. These are the cash flows of the two options: • The private jet can be bought for$6m now, which will cost $12,000 per month in fuel, piloting and airport costs, payable at the end of each month. The jet will last for 12 years. • Or the luxury yacht can be bought for$4m now, which will cost $20,000 per month in fuel, crew and berthing costs, payable at the end of each month. The yacht will last for 20 years. What's unusual about 40-cent is that he is so famous that he will actually be able to sell his jet or yacht for the same price as it was bought since the next generation of superstar musicians will buy it from him as a status symbol. Bank interest rates are 10% pa, given as an effective annual rate. You can assume that 40-cent will live for another 60 years and that when the jet or yacht's life is at an end, he will buy a new one with the same details as above. Would you advise 40-cent to buy the or the ? Note that the effective monthly rate is $r_\text{eff monthly}=(1+0.1)^{1/12}-1=0.00797414$ You're about to buy a car. These are the cash flows of the two different cars that you can buy: • You can buy an old car for$5,000 now, for which you will have to buy $90 of fuel at the end of each week from the date of purchase. The old car will last for 3 years, at which point you will sell the old car for$500.
• Or you can buy a new car for $14,000 now for which you will have to buy$50 of fuel at the end of each week from the date of purchase. The new car will last for 4 years, at which point you will sell the new car for $1,000. Bank interest rates are 10% pa, given as an effective annual rate. Assume that there are exactly 52 weeks in a year. Ignore taxes and environmental and pollution factors. Should you buy the or the ? You really want to go on a back packing trip to Europe when you finish university. Currently you have$1,500 in the bank. Bank interest rates are 8% pa, given as an APR compounding per month. If the holiday will cost $2,000, how long will it take for your bank account to reach that amount? You're trying to save enough money to buy your first car which costs$2,500. You can save $100 at the end of each month starting from now. You currently have no money at all. You just opened a bank account with an interest rate of 6% pa payable monthly. How many months will it take to save enough money to buy the car? Assume that the price of the car will stay the same over time. You just signed up for a 30 year fully amortising mortgage loan with monthly payments of$1,500 per month. The interest rate is 9% pa which is not expected to change.

To your surprise, you can actually afford to pay $2,000 per month and your mortgage allows early repayments without fees. If you maintain these higher monthly payments, how long will it take to pay off your mortgage? You want to buy an apartment priced at$300,000. You have saved a deposit of $30,000. The bank has agreed to lend you the$270,000 as an interest only loan with a term of 25 years. The interest rate is 12% pa and is not expected to change.

What will be your monthly payments? Remember that mortgage payments are paid in arrears (at the end of the month).

You just signed up for a 30 year interest-only mortgage with monthly payments of $3,000 per month. The interest rate is 6% pa which is not expected to change. How much did you borrow? After 15 years, just after the 180th payment at that time, how much will be owing on the mortgage? The interest rate is still 6% and is not expected to change. Remember that the mortgage is interest-only and that mortgage payments are paid in arrears (at the end of the month). You just borrowed$400,000 in the form of a 25 year interest-only mortgage with monthly payments of $3,000 per month. The interest rate is 9% pa which is not expected to change. You actually plan to pay more than the required interest payment. You plan to pay$3,300 in mortgage payments every month, which your mortgage lender allows. These extra payments will reduce the principal and the minimum interest payment required each month.

At the maturity of the mortgage, what will be the principal? That is, after the last (300th) interest payment of $3,300 in 25 years, how much will be owing on the mortgage? You want to buy an apartment worth$300,000. You have saved a deposit of $60,000. The bank has agreed to lend you$240,000 as an interest only mortgage loan with a term of 30 years. The interest rate is 6% pa and is not expected to change. What will be your monthly payments?

You want to buy an apartment priced at $500,000. You have saved a deposit of$50,000. The bank has agreed to lend you the $450,000 as an interest only loan with a term of 30 years. The interest rate is 6% pa and is not expected to change. What will be your monthly payments? A prospective home buyer can afford to pay$2,000 per month in mortgage loan repayments. The central bank recently lowered its policy rate by 0.25%, and residential home lenders cut their mortgage loan rates from 4.74% to 4.49%.

How much more can the prospective home buyer borrow now that interest rates are 4.49% rather than 4.74%? Give your answer as a proportional increase over the original amount he could borrow ($V_\text{before}$), so:

$$\text{Proportional increase} = \frac{V_\text{after}-V_\text{before}}{V_\text{before}}$$

Assume that:

• Interest rates are expected to be constant over the life of the loan.

• Loans are interest-only and have a life of 30 years.

• Mortgage loan payments are made every month in arrears and all interest rates are given as annualised percentage rates compounding per month.

In Australia in the 1980's, inflation was around 8% pa, and residential mortgage loan interest rates were around 14%.

In 2013, inflation was around 2.5% pa, and residential mortgage loan interest rates were around 4.5%.

If a person can afford constant mortgage loan payments of $2,000 per month, how much more can they borrow when interest rates are 4.5% pa compared with 14.0% pa? Give your answer as a proportional increase over the amount you could borrow when interest rates were high $(V_\text{high rates})$, so: $$\text{Proportional increase} = \dfrac{V_\text{low rates}-V_\text{high rates}}{V_\text{high rates}}$$ Assume that: • Interest rates are expected to be constant over the life of the loan. • Loans are interest-only and have a life of 30 years. • Mortgage loan payments are made every month in arrears and all interest rates are given as annualised percentage rates (APR's) compounding per month. Many Australian home loans that are interest-only actually require payments to be made on a fully amortising basis after a number of years. You decide to borrow$600,000 from the bank at an interest rate of 4.25% pa for 25 years. The payments will be interest-only for the first 10 years (t=0 to 10 years), then they will have to be paid on a fully amortising basis for the last 15 years (t=10 to 25 years).

Assuming that interest rates will remain constant, what will be your monthly payments for the next 10 years from now, and then the next 15 years after that? The answer options are given in the same order.

A firm pays a fully franked cash dividend of $70 to one of its Australian shareholders who has a personal marginal tax rate of 45%. The corporate tax rate is 30%. What will be the shareholder's personal tax payable due to the dividend payment? A company has: • 50 million shares outstanding. • The market price of one share is currently$6.
• The risk-free rate is 5% and the market return is 10%.
• Market analysts believe that the company's ordinary shares have a beta of 2.
• The company has 1 million preferred stock which have a face (or par) value of $100 and pay a constant dividend of 10% of par. They currently trade for$80 each.
• The company's debentures are publicly traded and their market price is equal to 90% of their face value.
• The debentures have a total face value of $60,000,000 and the current yield to maturity of corporate debentures is 10% per annum. The corporate tax rate is 30%. What is the company's after-tax weighted average cost of capital (WACC)? Assume a classical tax system. A company has: • 140 million shares outstanding. • The market price of one share is currently$2.
• The company's debentures are publicly traded and their market price is equal to 93% of the face value.
• The debentures have a total face value of $50,000,000 and the current yield to maturity of corporate debentures is 12% per annum. • The risk-free rate is 8.50% and the market return is 13.7%. • Market analysts estimated that the company's stock has a beta of 0.90. • The corporate tax rate is 30%. What is the company's after-tax weighted average cost of capital (WACC) in a classical tax system? A company has: • 100 million ordinary shares outstanding which are trading at a price of$5 each. Market analysts estimated that the company's ordinary stock has a beta of 1.5. The risk-free rate is 5% and the market return is 10%.
• 1 million preferred shares which have a face (or par) value of $100 and pay a constant annual dividend of 9% of par. The next dividend will be paid in one year. Assume that all preference dividends will be paid when promised. They currently trade at a price of$90 each.
• Debentures that have a total face value of $200 million and a yield to maturity of 6% per annum. They are publicly traded and their market price is equal to 110% of their face value. The corporate tax rate is 30%. All returns and yields are given as effective annual rates. What is the company's after-tax Weighted Average Cost of Capital (WACC)? Assume a classical tax system. Calculate the effective annual rates of the following three APR's: • A credit card offering an interest rate of 18% pa, compounding monthly. • A bond offering a yield of 6% pa, compounding semi-annually. • An annual dividend-paying stock offering a return of 10% pa compounding annually. All answers are given in the same order: $r_\text{credit card, eff yrly}$, $r_\text{bond, eff yrly}$, $r_\text{stock, eff yrly}$ Your credit card shows a$600 debt liability. The interest rate is 24% pa, payable monthly. You can't pay any of the debt off, except in 6 months when it's your birthday and you'll receive $50 which you'll use to pay off the credit card. If that is your only repayment, how much will the credit card debt liability be one year from now? A three year corporate bond yields 12% pa with a coupon rate of 10% pa, paid semi-annually. Find the effective six month yield, effective annual yield and the effective daily yield. Assume that each month has 30 days and that there are 360 days in a year. All answers are given in the same order: $r_\text{eff semi-annual}$, $r_\text{eff yearly}$, $r_\text{eff daily}$. A 2 year government bond yields 5% pa with a coupon rate of 6% pa, paid semi-annually. Find the effective six month rate, effective annual rate and the effective daily rate. Assume that each month has 30 days and that there are 360 days in a year. All answers are given in the same order: $r_\text{eff semi-annual}$, $r_\text{eff yrly}$, $r_\text{eff daily}$. A 2 year corporate bond yields 3% pa with a coupon rate of 5% pa, paid semi-annually. Find the effective monthly rate, effective six month rate, and effective annual rate. $r_\text{eff monthly}$, $r_\text{eff 6 month}$, $r_\text{eff annual}$. You're trying to save enough money for a deposit to buy a house. You want to buy a house worth$400,000 and the bank requires a 20% deposit ($80,000) before it will give you a loan for the other$320,000 that you need.

You currently have no savings, but you just started working and can save $2,000 per month, with the first payment in one month from now. Bank interest rates on savings accounts are 4.8% pa with interest paid monthly and interest rates are not expected to change. How long will it take to save the$80,000 deposit? Round your answer up to the nearest month.

Government bonds currently have a return of 5%. A stock has a beta of 2 and the market return is 7%. What is the expected return of the stock?

Assume that there exists a perfect world with no transaction costs, no asymmetric information, no taxes, no agency costs, equal borrowing rates for corporations and individual investors, the ability to short the risk free asset, semi-strong form efficient markets, the CAPM holds, investors are rational and risk-averse and there are no other market frictions.

For a firm operating in this perfect world, which statement(s) are correct?

(i) When a firm changes its capital structure and/or payout policy, share holders' wealth is unaffected.

(ii) When the idiosyncratic risk of a firm's assets increases, share holders do not expect higher returns.

(iii) When the systematic risk of a firm's assets increases, share holders do not expect higher returns.

Select the most correct response:

A fairly priced stock has an expected return of 15% pa. Treasury bonds yield 5% pa and the market portfolio's expected return is 10% pa. What is the beta of the stock?

A fairly priced stock has a beta that is the same as the market portfolio's beta. Treasury bonds yield 5% pa and the market portfolio's expected return is 10% pa. What is the expected return of the stock?

Which of the following statements is NOT correct?

High risk firms in danger of bankruptcy tend to have:

Question 472  quick ratio, accounting ratio

A firm has current assets totaling $1.5b of which cash is$0.25b and inventories is $0.5b. Current liabilities total$2b of which accounts payable is $1b. What is the firm's quick ratio, also known as the acid test ratio? High risk firms in danger of bankruptcy tend to have: A project to build a toll road will take 3 years to complete, costing three payments of$50 million, paid at the start of each year (at times 0, 1, and 2).

After completion, the toll road will yield a constant $10 million at the end of each year forever with no costs. So the first payment will be at t=4. The required return of the project is 10% pa given as an effective nominal rate. All cash flows are nominal. What is the payback period? The required return of a project is 10%, given as an effective annual rate. What is the payback period of the project in years? Assume that the cash flows shown in the table are received smoothly over the year. So the$121 at time 2 is actually earned smoothly from t=1 to t=2.

 Project Cash Flows Time (yrs) Cash flow ($) 0 -100 1 11 2 121 A project has the following cash flows:  Project Cash Flows Time (yrs) Cash flow ($) 0 -400 1 0 2 500

What is the payback period of the project in years?

Normally cash flows are assumed to happen at the given time. But here, assume that the cash flows are received smoothly over the year. So the $500 at time 2 is actually earned smoothly from t=1 to t=2. A firm has 1 million shares which trade at a price of$30 each. The firm is expected to announce earnings of $3 million at the end of the year and pay an annual dividend of$1.50 per share.

What is the firm's (forward looking) price/earnings (PE) ratio?

A firm has 2m shares and a market capitalisation of equity of $30m. The firm just announced earnings of$5m and paid an annual dividend of $0.75 per share. What is the firm's (backward looking) price/earnings (PE) ratio? The below screenshot of Microsoft's (MSFT) details were taken from the Google Finance website on 28 Nov 2014. Some information has been deliberately blanked out. What was MSFT's backwards-looking price-earnings ratio? The below screenshot of Commonwealth Bank of Australia's (CBA) details were taken from the Google Finance website on 7 Nov 2014. Some information has been deliberately blanked out. What was CBA's backwards-looking price-earnings ratio? You just entered into a fully amortising home loan with a principal of$600,000, a variable interest rate of 4.25% pa and a term of 25 years.

Immediately after settling the loan, the variable interest rate suddenly falls to 4% pa! You can't believe your luck. Despite this, you plan to continue paying the same home loan payments as you did before. How long will it now take to pay off your home loan?

Assume that the lower interest rate was granted immediately and that rates were and are now again expected to remain constant. Round your answer up to the nearest whole month.

There are a number of ways that assets can be depreciated. Generally the government's tax office stipulates a certain method.

But if it didn't, what would be the ideal way to depreciate an asset from the perspective of a businesses owner?

A 180-day Bank Accepted Bill has a face value of $1,000,000. The interest rate is 8% pa and there are 365 days in the year. What will be its price? A 90-day Bank Accepted Bill (BAB) has a face value of$1,000,000. The simple interest rate is 10% pa and there are 365 days in the year. What will be its price?

A 30-day Bank Accepted Bill has a face value of $1,000,000. The interest rate is 8% pa and there are 365 days in the year. What will be its price? A 90-day Bank Accepted Bill has a face value of$1,000,000. The interest rate is 6% pa and there are 365 days in the year. What is its price?

A 60-day Bank Accepted Bill has a face value of $1,000,000. The interest rate is 8% pa and there are 365 days in the year. What will be its price? A 30-day Bank Accepted Bill has a face value of$1,000,000. The interest rate is 2.5% pa and there are 365 days in the year. What will be its price?

On 27/09/13, three month Swiss government bills traded at a yield of -0.2%, given as a simple annual yield. That is, interest rates were negative.

If the face value of one of these 90 day bills is CHF1,000,000 (CHF represents Swiss Francs, the Swiss currency), what is the price of one of these bills?

A wholesale glass importer offers credit to its customers. Customers are given 30 days to pay for their goods, but if they pay within 5 days they will get a 1% discount.

What is the effective interest rate implicit in the discount being offered? Assume 365 days in a year and that all customers pay on either the 5th day or the 30th day. All rates given below are effective annual rates.

A wholesale horticulture nursery offers credit to its customers.

Customers are given 60 days to pay for their goods, but if they pay immediately they will get a 3% discount.

What is the effective interest rate implicit in the discount being offered? Assume 365 days in a year and that all customers pay either immediately or on the 60th day. All rates given below are effective annual rates.

A wholesale building supplies business offers credit to its customers. Customers are given 60 days to pay for their goods, but if they pay within 7 days they will get a 2% discount.

What is the effective interest rate implicit in the discount being offered?

Assume 365 days in a year and that all customers pay on either the 7th day or the 60th day. All rates given below are effective annual rates.

A wholesale shop offers credit to its customers. The customers are given 21 days to pay for their goods. But if they pay straight away (now) they get a 1% discount.

What is the effective interest rate given to customers who pay in 21 days? All rates given below are effective annual rates. Assume 365 days in a year.

A wholesale vitamin supplements store offers credit to its customers. Customers are given 30 days to pay for their goods, but if they pay within 5 days they will get a 1% discount.

What is the effective interest rate implicit in the discount being offered? Assume 365 days in a year and that all customers pay on either the 5th day or the 30th day. All of the below answer choices are given as effective annual interest rates.

A wholesale store offers credit to its customers. Customers are given 60 days to pay for their goods, but if they pay immediately they will get a 1.5% discount.

What is the effective interest rate implicit in the discount being offered? Assume 365 days in a year and that all customers pay either immediately or the 60th day. All of the below answer choices are given as effective annual interest rates.

A furniture distributor offers credit to its customers. Customers are given 25 days to pay for their goods, but if they pay immediately they will get a 1% discount.

What is the effective interest rate implicit in the discount being offered? Assume 365 days in a year and that all customers pay either immediately or on the 25th day. All rates given below are effective annual rates.

You just bought $100,000 worth of inventory from a wholesale supplier. You are given the option of paying within 5 days and receiving a 2% discount, or paying the full price within 60 days. You actually don't have the cash to pay within 5 days, but you could borrow it from the bank (as an overdraft) at 10% pa, given as an effective annual rate. In 60 days you will have enough money to pay the full cost without having to borrow from the bank. What is the implicit interest rate charged by the wholesale supplier, given as an effective annual rate? Also, should you borrow from the bank in 5 days to pay the supplier and receive the discount? Or just pay the full price on the last possible date? Assume that there are 365 days per year. The 'option price' in an option contract is paid at the start when the option contract is agreed to. or ? The 'futures price' in a futures contract is paid at the start when the futures contract is agreed to. or ? The 'option strike price' in an option contract, also known as the exercise price, is paid at the start when the option contract is agreed to. or ? The 'initial margin', also known as the performance bond in a futures contract, is paid at the start when the futures contract is agreed to. or ? In the Merton model of corporate debt, buying a levered company's debt is equivalent to buying risk free government bonds and: In the Merton model of corporate debt, buying a levered company's shares is equivalent to: In the Merton model of corporate debt, buying a levered company's debt is equivalent to buying the company's assets and: A risky firm will last for one period only (t=0 to 1), then it will be liquidated. So it's assets will be sold and the debt holders and equity holders will be paid out in that order. The firm has the following quantities: $V$ = Market value of assets. $E$ = Market value of (levered) equity. $D$ = Market value of zero coupon bonds. $F_1$ = Total face value of zero coupon bonds which is promised to be paid in one year. The levered equity graph above contains bold labels a to e. Which of the following statements about those labels is NOT correct? A risky firm will last for one period only (t=0 to 1), then it will be liquidated. So it's assets will be sold and the debt holders and equity holders will be paid out in that order. The firm has the following quantities: $V$ = Market value of assets. $E$ = Market value of (levered) equity. $D$ = Market value of zero coupon bonds. $F_1$ = Total face value of zero coupon bonds which is promised to be paid in one year. The risky corporate debt graph above contains bold labels a to e. Which of the following statements about those labels is NOT correct? A risky firm will last for one period only (t=0 to 1), then it will be liquidated. So it's assets will be sold and the debt holders and equity holders will be paid out in that order. The firm has the following quantities: $V$ = Market value of assets. $E$ = Market value of (levered) equity. $D$ = Market value of zero coupon bonds. $F_1$ = Total face value of zero coupon bonds which is promised to be paid in one year. What is the payoff to equity holders at maturity, assuming that they keep their shares until maturity? A risky firm will last for one period only (t=0 to 1), then it will be liquidated. So it's assets will be sold and the debt holders and equity holders will be paid out in that order. The firm has the following quantities: $V$ = Market value of assets. $E$ = Market value of (levered) equity. $D$ = Market value of zero coupon bonds. $F_1$ = Total face value of zero coupon bonds which is promised to be paid in one year. What is the payoff to debt holders at maturity, assuming that they keep their debt until maturity? Acquirer firm plans to launch a takeover of Target firm. The deal is expected to create a present value of synergies totaling$105 million. A cash offer will be made that pays the fair price for the target's shares plus 75% of the total synergy value. The cash will be paid out of the firm's cash holdings, no new debt or equity will be raised.

 Firms Involved in the Takeover Acquirer Target Assets ($m) 6,000 700 Debt ($m) 4,800 400 Share price ($) 40 20 Number of shares (m) 30 15 Ignore transaction costs and fees. Assume that the firms' debt and equity are fairly priced, and that each firms' debts' risk, yield and values remain constant. The acquisition is planned to occur immediately, so ignore the time value of money. Calculate the merged firm's share price and total number of shares after the takeover has been completed. Acquirer firm plans to launch a takeover of Target firm. The deal is expected to create a present value of synergies totaling$105 million. A scrip offer will be made that pays the fair price for the target's shares plus 75% of the total synergy value.

 Firms Involved in the Takeover Acquirer Target Assets ($m) 6,000 700 Debt ($m) 4,800 400 Share price ($) 40 20 Number of shares (m) 30 15 Ignore transaction costs and fees. Assume that the firms' debt and equity are fairly priced, and that each firms' debts' risk, yield and values remain constant. The acquisition is planned to occur immediately, so ignore the time value of money. Calculate the merged firm's share price and total number of shares after the takeover has been completed. Acquirer firm plans to launch a takeover of Target firm. The firms operate in different industries and the CEO's rationale for the merger is to increase diversification and thereby decrease risk. The deal is not expected to create any synergies. An 80% scrip and 20% cash offer will be made that pays the fair price for the target's shares. The cash will be paid out of the firms' cash holdings, no new debt or equity will be raised.  Firms Involved in the Takeover Acquirer Target Assets ($m) 6,000 700 Debt ($m) 4,800 400 Share price ($) 40 20 Number of shares (m) 30 15

Ignore transaction costs and fees. Assume that the firms' debt and equity are fairly priced, and that each firms' debts' risk, yield and values remain constant. The acquisition is planned to occur immediately, so ignore the time value of money.

Calculate the merged firm's share price and total number of shares after the takeover has been completed.

Acquirer firm plans to launch a takeover of Target firm. The deal is expected to create a present value of synergies totaling $105 million. A 40% scrip and 60% cash offer will be made that pays the fair price for the target's shares plus 75% of the total synergy value. The cash will be paid out of the firm's cash holdings, no new debt or equity will be raised.  Firms Involved in the Takeover Acquirer Target Assets ($m) 6,000 700 Debt ($m) 4,800 400 Share price ($) 40 20 Number of shares (m) 30 15

Ignore transaction costs and fees. Assume that the firms' debt and equity are fairly priced, and that each firms' debts' risk, yield and values remain constant. The acquisition is planned to occur immediately, so ignore the time value of money.

Calculate the merged firm's share price and total number of shares after the takeover has been completed.

Acquirer firm plans to launch a takeover of Target firm. The deal is expected to create a present value of synergies totaling $2 million. A cash offer will be made that pays the fair price for the target's shares plus 70% of the total synergy value. The cash will be paid out of the firm's cash holdings, no new debt or equity will be raised.  Firms Involved in the Takeover Acquirer Target Assets ($m) 60 10 Debt ($m) 20 2 Share price ($) 10 8 Number of shares (m) 4 1

Ignore transaction costs and fees. Assume that the firms' debt and equity are fairly priced, and that each firms' debts' risk, yield and values remain constant. The acquisition is planned to occur immediately, so ignore the time value of money.

Calculate the merged firm's share price and total number of shares after the takeover has been completed.

Acquirer firm plans to launch a takeover of Target firm. The deal is expected to create a present value of synergies totaling $2 million. A scrip offer will be made that pays the fair price for the target's shares plus 70% of the total synergy value.  Firms Involved in the Takeover Acquirer Target Assets ($m) 60 10 Debt ($m) 20 2 Share price ($) 10 8 Number of shares (m) 4 1

Ignore transaction costs and fees. Assume that the firms' debt and equity are fairly priced, and that each firms' debts' risk, yield and values remain constant. The acquisition is planned to occur immediately, so ignore the time value of money.

Calculate the merged firm's share price and total number of shares after the takeover has been completed.

Acquirer firm plans to launch a takeover of Target firm. The deal is expected to create a present value of synergies totaling $0.5 million, but investment bank fees and integration costs with a present value of$1.5 million is expected. A 10% cash and 90% scrip offer will be made that pays the fair price for the target's shares only. Assume that the Target and Acquirer agree to the deal. The cash will be paid out of the firms' cash holdings, no new debt or equity will be raised.

 Firms Involved in the Takeover Acquirer Target Assets ($m) 60 10 Debt ($m) 20 2 Share price ($) 10 8 Number of shares (m) 4 1 Assume that the firms' debt and equity are fairly priced, and that each firms' debts' risk, yield and values remain constant. The acquisition is planned to occur immediately, so ignore the time value of money. Calculate the merged firm's share price and total number of shares after the takeover has been completed. In a takeover deal where the offer is 100% cash, the merged firm's number of shares will be equal to the acquirer firm's original number of shares. or ? In a takeover deal where the offer is 100% scrip (shares), the merged firm's number of shares will be equal to the acquirer firm's original number of shares. or ? In a takeover deal where the offer is 100% scrip (shares), the merged firm's number of shares will be equal to the sum of the acquirer and target firms' original number of shares. or ? A company runs a number of slaughterhouses which supply hamburger meat to McDonalds. The company is afraid that live cattle prices will increase over the next year, even though there is widespread belief in the market that they will be stable. What can the company do to hedge against the risk of increasing live cattle prices? Which statement(s) are correct? (i) buy call options on live cattle. (ii) buy put options on live cattle. (iii) sell call options on live cattle. Select the most correct response: Below are 4 option graphs. Note that the y-axis is payoff at maturity (T). What options do they depict? List them in the order that they are numbered. You have just sold an 'in the money' 6 month European put option on the mining company BHP at an exercise price of$40 for a premium of $3. Which of the following statements best describes your situation? Below are 4 option graphs. Note that the y-axis is payoff at maturity (T). What options do they depict? List them in the order that they are numbered You operate a cattle farm that supplies hamburger meat to the big fast food chains. You buy a lot of grain to feed your cattle, and you sell the fully grown cattle on the livestock market. You're afraid of adverse movements in grain and livestock prices. What options should you buy to hedge your exposures in the grain and cattle livestock markets? Select the most correct response: All things remaining equal, according to the capital asset pricing model, if the systematic variance of an asset increases, its required return will increase and its price will decrease. If the idiosyncratic variance of an asset increases, its price will be unchanged. What is the relationship between the price of a call or put option and the total, systematic and idiosyncratic variance of the underlying asset that the option is based on? Select the most correct answer. Call and put option prices increase when the: Which one of the following is NOT usually considered an 'investable' asset for long-term wealth creation? You believe that the price of a share will fall significantly very soon, but the rest of the market does not. The market thinks that the share price will remain the same. Assuming that your prediction will soon be true, which of the following trades is a bad idea? In other words, which trade will NOT make money or prevent losses? Which option position has the possibility of unlimited potential losses? Which of the following is the least useful method or model to calculate the value of a real option in a project? A moped is a bicycle with pedals and a little motor that can be switched on to assist the rider. Mopeds offer the rider: Some financially minded people insist on a prenuptial agreement before committing to marry their partner. This agreement states how the couple's assets should be divided in case they divorce. Prenuptial agreements are designed to give the richer partner more of the couples' assets if they divorce, thus maximising the richer partner's: An expansion option is best modeled as a or option? An abandonment option is best modeled as a or option? A timing option is best modeled as a or option? According to option theory, it's rational for students to submit their assignments as or as possible? Details of two different types of desserts or edible treats are given below: • High-sugar treats like candy, chocolate and ice cream make a person very happy. High sugar treats are cheap at only$2 per day.
• Low-sugar treats like nuts, cheese and fruit make a person equally happy if these foods are of high quality. Low sugar treats are more expensive at $4 per day. The advantage of low-sugar treats is that a person only needs to pay the dentist$2,000 for fillings and root canal therapy once every 15 years. Whereas with high-sugar treats, that treatment needs to be done every 5 years.

The real discount rate is 10%, given as an effective annual rate. Assume that there are 365 days in every year and that all cash flows are real. The inflation rate is 3% given as an effective annual rate.

Find the equivalent annual cash flow (EAC) of the high-sugar treats and low-sugar treats, including dental costs. The below choices are listed in that order.

Ignore the pain of dental therapy, personal preferences and other factors.

You own a nice suit which you wear once per week on nights out. You bought it one year ago for $600. In your experience, suits used once per week last for 6 years. So you expect yours to last for another 5 years. Your younger brother said that retro is back in style so he wants to wants to borrow your suit once a week when he goes out. With the increased use, your suit will only last for another 4 years rather than 5. What is the present value of the cost of letting your brother use your current suit for the next 4 years? Assume: that bank interest rates are 10% pa, given as an effective annual rate; you will buy a new suit when your current one wears out and your brother will not use the new one; your brother will only use your current suit so he will only use it for the next four years; and the price of a new suit never changes. You just bought a nice dress which you plan to wear once per month on nights out. You bought it a moment ago for$600 (at t=0). In your experience, dresses used once per month last for 6 years.

Your younger sister is a student with no money and wants to borrow your dress once a month when she hits the town. With the increased use, your dress will only last for another 3 years rather than 6.

What is the present value of the cost of letting your sister use your current dress for the next 3 years?

Assume: that bank interest rates are 10% pa, given as an effective annual rate; you will buy a new dress when your current one wears out; your sister will only use the current dress, not the next one that you will buy; and the price of a new dress never changes.

Carlos and Edwin are brothers and they both love Holden Commodore cars.

Carlos likes to buy the latest Holden Commodore car for $40,000 every 4 years as soon as the new model is released. As soon as he buys the new car, he sells the old one on the second hand car market for$20,000. Carlos never has to bother with paying for repairs since his cars are brand new.

Edwin also likes Commodores, but prefers to buy 4-year old cars for $20,000 and keep them for 11 years until the end of their life (new ones last for 15 years in total but the 4-year old ones only last for another 11 years). Then he sells the old car for$2,000 and buys another 4-year old second hand car, and so on.

Every time Edwin buys a second hand 4 year old car he immediately has to spend $1,000 on repairs, and then$1,000 every year after that for the next 10 years. So there are 11 payments in total from when the second hand car is bought at t=0 to the last payment at t=10. One year later (t=11) the old car is at the end of its total 15 year life and can be scrapped for $2,000. Assuming that Carlos and Edwin maintain their love of Commodores and keep up their habits of buying new ones and second hand ones respectively, how much larger is Carlos' equivalent annual cost of car ownership compared with Edwin's? The real discount rate is 10% pa. All cash flows are real and are expected to remain constant. Inflation is forecast to be 3% pa. All rates are effective annual. Ignore capital gains tax and tax savings from depreciation since cars are tax-exempt for individuals. You own some nice shoes which you use once per week on date nights. You bought them 2 years ago for$500. In your experience, shoes used once per week last for 6 years. So you expect yours to last for another 4 years.

Your younger sister said that she wants to borrow your shoes once per week. With the increased use, your shoes will only last for another 2 years rather than 4.

What is the present value of the cost of letting your sister use your current shoes for the next 2 years?

Assume: that bank interest rates are 10% pa, given as an effective annual rate; you will buy a new pair of shoes when your current pair wears out and your sister will not use the new ones; your sister will only use your current shoes so she will only use it for the next 2 years; and the price of new shoes never changes.

A low-quality second-hand car can be bought now for $1,000 and will last for 1 year before it will be scrapped for nothing. A high-quality second-hand car can be bought now for$4,900 and it will last for 5 years before it will be scrapped for nothing.

What is the equivalent annual cost of each car? Assume a discount rate of 10% pa, given as an effective annual rate.

The answer choices are given as the equivalent annual cost of the low-quality car and then the high quality car.

An Apple iPhone 6 smart phone can be bought now for $999. An Android Kogan Agora 4G+ smart phone can be bought now for$240.

If the Kogan phone lasts for one year, approximately how long must the Apple phone last for to have the same equivalent annual cost?

Assume that both phones have equivalent features besides their lifetimes, that both are worthless once they've outlasted their life, the discount rate is 10% pa given as an effective annual rate, and there are no extra costs or benefits from either phone.

Find Trademark Corporation's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.

 Trademark Corp Income Statement for year ending 30th June 2013 $m Sales 100 COGS 25 Operating expense 5 Depreciation 20 Interest expense 20 Income before tax 30 Tax at 30% 9 Net income 21  Trademark Corp Balance Sheet as at 30th June 2013 2012$m $m Assets Current assets 120 80 PPE Cost 150 140 Accumul. depr. 60 40 Carrying amount 90 100 Total assets 210 180 Liabilities Current liabilities 75 65 Non-current liabilities 75 55 Owners' equity Retained earnings 10 10 Contributed equity 50 50 Total L and OE 210 180 Note: all figures are given in millions of dollars ($m).

Find UniBar Corp's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.

 UniBar Corp Income Statement for year ending 30th June 2013 $m Sales 80 COGS 40 Operating expense 15 Depreciation 10 Interest expense 5 Income before tax 10 Tax at 30% 3 Net income 7  UniBar Corp Balance Sheet as at 30th June 2013 2012$m \$m Assets Current assets 120 90 PPE Cost 360