# Fight Finance

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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 Profitability Index (PI) of the project?

 Project Cash Flows Time (yrs) Cash flow ($) 0 -100 1 0 2 121 A project has the following cash flows:  Project Cash Flows Time (yrs) Cash flow ($) 0 -400 1 200 2 250

What is the Profitability Index (PI) of the project? Assume that the cash flows shown in the table are paid all at once at the given point in time. The required return is 10% pa, given as an effective annual rate.

A project's Profitability Index (PI) is less than 1. Select the most correct statement:

A project has the following cash flows:

 Project Cash Flows Time (yrs) Cash flow ($) 0 -90 1 30 2 105 The required return of a project is 10%, given as an effective annual rate. Assume that the cash flows shown in the table are paid all at once at the given point in time. What is the Profitability Index (PI) of the project? The required return of a project is 10%, given as an effective annual rate. Assume that the cash flows shown in the table are paid all at once at the given point in time. What is the Net Present Value (NPV) of the project?  Project Cash Flows Time (yrs) Cash flow ($) 0 -100 1 0 2 121

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 If a project's net present value (NPV) is zero, then its internal rate of return (IRR) will be: The required return of a building 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. The building firm is just about to start the project and the client has signed the contract. Initially the firm will pay$100 to the sub-contractors to carry out the work and then will receive an $11 payment from the client in one year and$121 when the project is finished in 2 years. Ignore credit risk.

But the building company is considering selling the project to a competitor at different points in time and is pondering the minimum price that they should sell it for.

 Project Cash Flows Time (yrs) Cash flow ($) 0 -100 1 11 2 121 Which of the below statements is NOT correct? The project is worth: 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. The below graph shows a project's net present value (NPV) against its annual discount rate. Which of the following statements is NOT correct? 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 (t=1).

How much can you consume at each time?

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.

How many years will it take for an asset's price to double if the price grows by 10% pa?

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.

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.

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?

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?

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

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?

For an asset price to triple every 5 years, what must be the expected future capital return, given as an effective annual rate?

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?

You currently have $100 in the bank which pays a 10% pa interest rate. Oranges currently cost$1 each at the shop and inflation is 5% pa which is the expected growth rate in the orange price.

This information is summarised in the table below, with some parts missing that correspond to the answer options. All rates are given as effective annual rates. Note that when payments are not specified as real, as in this question, they're conventionally assumed to be nominal.

 Wealth in Dollars and Oranges Time (year) Bank account wealth ($) Orange price ($) Wealth in oranges 0 100 1 100 1 110 1.05 (a) 2 (b) (c) (d)

Which of the following statements is NOT correct? Your:

Which of the following statements about inflation is NOT correct?

What is the present value of a nominal payment of $1,000 in 4 years? The nominal discount rate is 8% pa and the inflation rate is 2% pa. 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. 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? There are many ways to write the ordinary annuity formula. Which of the following is NOT equal to the ordinary annuity formula? 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. 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 and last at t=12).
• 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? 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.

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:

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?

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?

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 ?

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:

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 ?

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?

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 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?

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?

In the dividend discount model:

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

The return $r$ is supposed to be the:

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%? 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? 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)?

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. 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. 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.

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.

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

An 'interest payment' is the same thing as a 'coupon payment'. or ?

An 'interest rate' is the same thing as a 'coupon rate'. or ?

An 'interest rate' is the same thing as a 'yield'. or ?

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.

An 'interest only' loan can also be called a:

Which of the following statements is NOT correct? Borrowers:

Which of the following statements is NOT correct? Lenders:

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

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

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:

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

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:

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

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:

$r_\text{credit card, eff yrly}$, $r_\text{bond, eff yrly}$, $r_\text{stock, eff yrly}$

A home loan company advertises an interest rate of 6% pa, payable monthly. Which of the following statements about the interest rate is NOT correct? All rates are given to four decimal places.

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? 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).

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 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 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 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 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? 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. 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?

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?

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 fixed coupon rate of 12% pa, paid semi-annually. The bond's yield is currently 6% pa. The face value is$100. What is its price?

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

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 10 year bond has a face value of$100, a yield of 6% pa and a fixed coupon rate of 8% pa, paid semi-annually. What is its price?

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 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.

An Australian company just issued two bonds paying semi-annual coupons:

• 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.

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 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 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 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? 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).

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 $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 two year Government bond has a face value of $100, a yield of 0.5% and a fixed coupon rate of 0.5%, 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 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?

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?

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

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.

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 $m Cash 0 0 Inventory 70 50 Trade debtors 11 16 Rent paid in advance 4 3 PPE 700 680 Total assets 785 749 Trade creditors 11 19 Bond liabilities 400 390 Contributed equity 220 220 Retained profits 154 120 Total L and OE 785 749 Note: All figures are given in millions of dollars ($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 ($m). The firm's free cash flow over the 2014 financial year was: Find UniBar Corp's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.  UniBar Corp Income Statement for year ending 30th June 2013$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 360 320 Accumul. depr. 40 30 Carrying amount 320 290 Total assets 440 380 Liabilities Current liabilities 110 60 Non-current liabilities 190 180 Owners' equity Retained earnings 95 95 Contributed equity 45 45 Total L and OE 440 380

Note: all figures are given in millions of dollars ($m). Find Piano Bar's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.  Piano Bar Income Statement for year ending 30th June 2013$m Sales 310 COGS 185 Operating expense 20 Depreciation 15 Interest expense 10 Income before tax 80 Tax at 30% 24 Net income 56
 Piano Bar Balance Sheet as at 30th June 2013 2012 $m$m Assets Current assets 240 230 PPE Cost 420 400 Accumul. depr. 50 35 Carrying amount 370 365 Total assets 610 595 Liabilities Current liabilities 180 190 Non-current liabilities 290 265 Owners' equity Retained earnings 90 90 Contributed equity 50 50 Total L and OE 610 595

Note: all figures are given in millions of dollars ($m). Find World Bar's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.  World Bar Income Statement for year ending 30th June 2013$m Sales 300 COGS 150 Operating expense 50 Depreciation 40 Interest expense 10 Taxable income 50 Tax at 30% 15 Net income 35
 World Bar Balance Sheet as at 30th June 2013 2012 $m$m Assets Current assets 200 230 PPE Cost 400 400 Accumul. depr. 75 35 Carrying amount 325 365 Total assets 525 595 Liabilities Current liabilities 150 205 Non-current liabilities 235 250 Owners' equity Retained earnings 100 100 Contributed equity 40 40 Total L and OE 525 595

Note: all figures above and below are given in millions of dollars ($m). 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: Find the cash flow from assets (CFFA) of the following project.  Project Data Project life 2 years Initial investment in equipment$6m Depreciation of equipment per year for tax purposes $1m Unit sales per year 4m Sale price per unit$8 Variable cost per unit $3 Fixed costs per year, paid at the end of each year$1.5m Tax rate 30%

Note 1: The equipment will have a book value of $4m at the end of the project for tax purposes. However, the equipment is expected to fetch$0.9 million when it is sold at t=2.

Note 2: Due to the project, the firm will have to purchase $0.8m of inventory initially, which it will sell at t=1. The firm will buy another$0.8m at t=1 and sell it all again at t=2 with zero inventory left. The project will have no effect on the firm's current liabilities.

Find the project's CFFA at time zero, one and two. Answers are given in millions of dollars ($m). Convert a 10% continuously compounded annual rate $(r_\text{cc annual})$ into an effective annual rate $(r_\text{eff annual})$. The equivalent effective annual rate is: Which of the following interest rate quotes is NOT equivalent to a 10% effective annual rate of return? Assume that each year has 12 months, each month has 30 days, each day has 24 hours, each hour has 60 minutes and each minute has 60 seconds. APR stands for Annualised Percentage Rate. An effective monthly return of 1% $(r_\text{eff monthly})$ is equivalent to an effective annual return $(r_\text{eff annual})$ of: Which of the following quantities is commonly assumed to be normally distributed? If a stock's future expected effective annual returns are log-normally distributed, what will be bigger, the stock's or effective annual return? Or would you expect them to be ? A$100 stock has a continuously compounded expected total return of 10% pa. Its dividend yield is 2% pa with continuous compounding. What do you expect its price to be in 2.5 years?

A continuously compounded semi-annual return of 5% $(r_\text{cc 6mth})$ is equivalent to a continuously compounded annual return $(r_\text{cc annual})$ of:

A stock has an arithmetic average continuously compounded return (AALGDR) of 10% pa, a standard deviation of continuously compounded returns (SDLGDR) of 80% pa and current stock price of $1. Assume that stock prices are log-normally distributed. In 5 years, what do you expect the mean and median prices to be? The answer options are given in the same order. 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 interest and principal payments to debt-holders. They're compulsory. But companies are not forced to pay dividends to share holders. 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.

Which one of the following will increase the Cash Flow From Assets in this year for a tax-paying firm, all else remaining constant?

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 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:

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?

A firm has a debt-to-equity ratio of 60%. What is its debt-to-assets ratio?

In the home loan market, the acronym LVR stands for Loan to Valuation Ratio. If you bought a house worth one million dollars, partly funded by an $800,000 home loan, then your LVR was 80%. The LVR is equivalent to which of the following ratios? Use the below information to value a levered company with constant annual perpetual cash flows from assets. The next cash flow will be generated in one year from now, so a perpetuity can be used to value this firm. Both the operating and firm free cash flows are constant (but not equal to each other).  Data on a Levered Firm with Perpetual Cash Flows Item abbreviation Value Item full name $\text{OFCF}$$48.5m Operating free cash flow $\text{FFCF or CFFA}$ $50m Firm free cash flow or cash flow from assets $g$ 0% pa Growth rate of OFCF and FFCF $\text{WACC}_\text{BeforeTax}$ 10% pa Weighted average cost of capital before tax $\text{WACC}_\text{AfterTax}$ 9.7% pa Weighted average cost of capital after tax $r_\text{D}$ 5% pa Cost of debt $r_\text{EL}$ 11.25% pa Cost of levered equity $D/V_L$ 20% pa Debt to assets ratio, where the asset value includes tax shields $t_c$ 30% Corporate tax rate What is the value of the levered firm including interest tax shields? To value a business's assets, the free cash flow of the firm (FCFF, also called CFFA) needs to be calculated. This requires figures from the firm's income statement and balance sheet. For what figures is the income statement needed? Note that the income statement is sometimes also called the profit and loss, P&L, or statement of financial performance. 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 market risk to the company's existing projects. Assume a classical tax system. Which statement is correct? A firm's weighted average cost of capital before tax ($r_\text{WACC before tax}$) would increase due to: 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? When someone says that they're "buying American dollars" (USD), what type of asset are they probably buying? They're probably buying: Australians usually quote the Australian dollar in USD per 1 AUD. For example, in October 2015 the Australian dollar was quoted as 0.72 USD per AUD. Is this an or terms quote? Chinese people usually quote the Chinese Yuan or Renminbi in RMB per 1 USD. For example, in October 2015 the Chinese Renminbi was 6.35 RMB per USD. Is this an or terms quote? If the current AUD exchange rate is USD 0.9686 = AUD 1, what is the European terms quote of the AUD against the USD? 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 Australian cash rate is expected to be 2% pa over the next one year, while the Japanese cash rate is expected to be 0% pa, both given as nominal effective annual rates. The current exchange rate is 100 JPY per AUD. What is the implied 1 year forward foreign exchange rate? 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? Is it possible for all countries' exchange rates to appreciate by 5% in the same year, including the USD? or ? If the USD appreciates against the AUD, the American terms quote of the AUD will or ? If the AUD appreciates against the USD, the European terms quote of the AUD will or ? How is the AUD normally quoted in Australia? Using or terms? 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: 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? Vietnamese people usually quote the Vietnamese Dong in VND per 1 USD. For example, in October 2015 the Vietnamese Dong was 22,300 VND per USD. Is this an or terms quote? If the Reserve Bank of Australia is expected to keep its interbank overnight cash rate at 2% pa while the US Federal Reserve is expected to keep its federal funds rate at 0% pa over the next year, is the AUD is expected to , , or remain against the USD over the next year? Which of the following FX quotes (current in October 2015) is given in American terms? The Australian dollar's value was: • 1.4875 USD per AUD on 31 August 1974. • 0.4890 USD per AUD on 31 March 2001. Did the Australian dollar or against the US dollar between these dates? The Australian cash rate is expected to be 2% pa over the next one year, while the US cash rate is expected to be 0% pa, both given as nominal effective annual rates. The current exchange rate is 0.73 USD per AUD. What is the implied 1 year USD per AUD forward foreign exchange rate? Suppose the yield curve in the USA and Germany is flat and the: • USD federal funds rate at the Federal Reserve is 1% pa; • EUR deposit facility at the European Central Bank is -0.4% pa (note the negative sign); • Spot EUR exchange rate is 1 USD per EUR; • One year forward EUR exchange rate is 1.011 USD per EUR. You suspect that there’s an arbitrage opportunity. Which one of the following statements about the potential arbitrage opportunity is NOT correct? If the Australian dollar quote of 0.8 USD per AUD suddenly falls to 0.7 USD per AUD, has the Australian dollar or against the US dollar? In the ‘Nixon Shock’ on August 15, 1971, the United States government: Question 882 Asian currency crisis, foreign exchange rate, original sin, no explanation In the 1997 Asian currency crisis, the businesses most vulnerable to bankruptcy were those that: A Brazilian lady wishes to convert 1 million Brazilian Real (BRL) into Chinese Renminbi (RMB, also called the Yuan or CNY). The exchange rate is 3.42 BRL per USD and 6.27 RMB per USD. How much is the BRL 1 million worth in RMB? The market expects the Reserve Bank of Australia (RBA) to increase the policy rate by 25 basis points at their next meeting. The current exchange rate is 0.8 USD per AUD. Then unexpectedly, the RBA announce that they will increase the policy rate by 50 basis points due to increased fears of inflation. What do you expect to happen to Australia's exchange rate on the day when the surprise announcement is made? The Australian dollar is likely to suddenly: Under the Bretton Woods System (1944 to 1971), currencies were priced relative to: A Malaysian man wishes to convert 1 million Malaysian Ringgit (MYR) into Indian Rupees (IND). The exchange rate is 4.2 MYR per USD and 71 IND per USD. How much is the MYR 1 million worth in IND? Suppose the current Australian exchange rate is 0.8 USD per AUD. If you think that the AUD will appreciate against the USD, contrary to the rest of the market, how could you profit? Right now you should: Suppose the market expects the Reserve Bank of Australia (RBA) to increase the policy rate by 25 basis points at their next meeting. The current exchange rate is 0.8 USD per AUD. Then unexpectedly, the RBA announce that they will leave the policy rate unchanged due to increasing unemployment and fears of a potential recession. What do you expect to happen to Australia's exchange rate on the day when the surprise announcement is made? The Australian dollar is likely to: 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. 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. 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 $r_\text{eff monthly}=(1+0.1)^{1/12}-1=0.00797414$ 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'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 ?

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?

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 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?

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 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 firm's WACC before tax would decrease due to:

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

One year ago you bought a $1,000,000 house partly funded using a mortgage loan. The loan size was$800,000 and the other $200,000 was your wealth or 'equity' in the house asset. The interest rate on the home loan was 4% pa. Over the year, the house produced a net rental yield of 2% pa and a capital gain of 2.5% pa. Assuming that all cash flows (interest payments and net rental payments) were paid and received at the end of the year, and all rates are given as effective annual rates, what was the total return on your wealth over the past year? 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). 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. Which of the following statements about standard statistical mathematics notation is NOT correct? Diversification in a portfolio of two assets works best when the correlation between their returns is: All things remaining equal, the variance of a portfolio of two positively-weighted stocks rises as:  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? 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? 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 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 correlation of a variable X with itself? The corr(X, X) or $\rho_{X,X}$ equals: What is the correlation of a variable X with a constant C? The corr(X, C) or $\rho_{X,C}$ equals:  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. Find the sample standard deviation of returns using the data in the table:  Stock Returns Year Return pa 2008 0.3 2009 0.02 2010 -0.2 2011 0.4 The returns above and standard deviations below are given in decimal form. 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. Which of the following statements about an asset’s standard deviation of returns is NOT correct? All other things remaining equal, the higher the asset’s standard deviation of returns: The capital market line (CML) is shown in the graph below. The total standard deviation is denoted by σ and the expected return is μ. Assume that markets are efficient so all assets are fairly priced. Which of the below statements is NOT correct? Which of the following assets would you expect to have the highest required rate of return? All values are current market values.  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? What is the covariance of a variable X with a constant C? The cov(X, C) or $\sigma_{X,C}$ equals: 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 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 owns a portfolio with: • 80% invested in stock A; and • 20% invested in stock B. Today there was a: • 10% rise in stock A's price; and • No change in stock B's price. No dividends were paid on either stock. What was the total historical portfolio return on this day? All returns above and answer options below are given as effective daily rates.  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? 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 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? 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? The security market line (SML) shows the relationship between beta and expected return. Investment projects that plot above the SML would have: 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? 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? Assets A, B, M and $r_f$ are shown on the graphs above. Asset M is the market portfolio and $r_f$ is the risk free yield on government bonds. Which of the below statements is NOT correct? Assets A, B, M and $r_f$ are shown on the graphs above. Asset M is the market portfolio and $r_f$ is the risk free yield on government bonds. Assume that investors can borrow and lend at the risk free rate. Which of the below statements is NOT correct? A stock has a beta of 1.5. The market's expected total return is 10% pa and the risk free rate is 5% pa, both given as effective annual rates. What do you think will be the stock's expected return over the next year, given as an effective annual rate? A stock has a beta of 1.5. The market's expected total return is 10% pa and the risk free rate is 5% pa, both given as effective annual rates. In the last 5 minutes, bad economic news was released showing a higher chance of recession. Over this time the share market fell by 1%. The risk free rate was unchanged. What do you think was the stock's historical return over the last 5 minutes, given as an effective 5 minute rate? A stock has a beta of 1.5. The market's expected total return is 10% pa and the risk free rate is 5% pa, both given as effective annual rates. Over the last year, bad economic news was released showing a higher chance of recession. Over this time the share market fell by 1%. So $r_{m} = (P_{0} - P_{-1})/P_{-1} = -0.01$, where the current time is zero and one year ago is time -1. The risk free rate was unchanged. What do you think was the stock's historical return over the last year, given as an effective annual rate? Select the most correct statement from the following. 'Chartists', also known as 'technical traders', believe that: 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: 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 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: Question 625 dividend re-investment plan, capital raising Which of the following statements about dividend re-investment plans (DRP's) is NOT correct? 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. 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.

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.

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 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.

A company conducts a 2 for 3 rights issue at a subscription price of $8 when the pre-announcement stock price was$9. Assume that all investors use their rights to buy those extra shares.

What is the percentage increase in the stock price and the number of shares outstanding? The answers are given in the same order.

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 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?

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.

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.

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?

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).

In 2014 the median starting salaries of male and female Australian bachelor degree accounting graduates aged less than 25 years in their first full-time industry job was $50,000 before tax, according to Graduate Careers Australia. See page 9 of this report. 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 $50,000 per annum before-tax? 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 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 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: $\Delta V = \Delta D+ \Delta E$

A firm wishes to raise $30 million now. The firm's current market value of equity is$60m and the market price per share is $20. They estimate that they'll be able to issue shares in a rights issue at a subscription price of$15. Ignore the time value of money and assume that all shareholders exercise their rights. Which of the following statements is NOT correct?

Stock A and B's returns have a correlation of 0.3. Which statement is NOT correct?

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:

Use the below information to value a levered company with constant annual perpetual cash flows from assets. The next cash flow will be generated in one year from now, so a perpetuity can be used to value this firm. Both the operating and firm free cash flows are constant (but not equal to each other).

 Data on a Levered Firm with Perpetual Cash Flows Item abbreviation Value Item full name $\text{OFCF}$ $100m Operating free cash flow $\text{FFCF or CFFA}$$112m Firm free cash flow or cash flow from assets (includes interest tax shields) $g$ 0% pa Growth rate of OFCF and FFCF $\text{WACC}_\text{BeforeTax}$ 7% pa Weighted average cost of capital before tax $\text{WACC}_\text{AfterTax}$ 6.25% pa Weighted average cost of capital after tax $r_\text{D}$ 5% pa Cost of debt $r_\text{EL}$ 9% pa Cost of levered equity $D/V_L$ 50% pa Debt to assets ratio, where the asset value includes tax shields $t_c$ 30% Corporate tax rate

What is the value of the levered firm including interest tax shields?

What creates interest tax shields for a company?

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.

Interest expense on debt is tax-deductible, but dividend payments on equity are not. or ?

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? The security market line (SML) shows the relationship between beta and expected return. Investment projects that plot on the SML would have: 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? A stock's required total return will increase when its: The equations for Net Income (NI, also known as Earnings or Net Profit After Tax) and Cash Flow From Assets (CFFA, also known as Free Cash Flow to the Firm) per year are: $$NI=(Rev-COGS-FC-Depr-IntExp).(1-t_c)$$ $$CFFA=NI+Depr-CapEx - \varDelta NWC+IntExp$$ For a firm with debt, what is the amount of the interest tax shield per year? Unrestricted negative gearing is allowed in Australia, New Zealand and Japan. Negative gearing laws allow income losses on investment properties to be deducted from a tax-payer's pre-tax personal income. Negatively geared investors benefit from this tax advantage. They also hope to benefit from capital gains which exceed the income losses. For example, a property investor buys an apartment funded by an interest only mortgage loan. Interest expense is$2,000 per month. The rental payments received from the tenant living on the property are $1,500 per month. The investor can deduct this income loss of$500 per month from his pre-tax personal income. If his personal marginal tax rate is 46.5%, this saves $232.5 per month in personal income tax. The advantage of negative gearing is an example of the benefits of: You deposit money into a bank account. Which of the following statements about this deposit is NOT correct? A semi-annual coupon bond has a yield of 3% pa. Which of the following statements about the yield is NOT correct? All rates are given to four decimal places. 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?

How much more can you borrow using an interest-only loan compared to a 25-year fully amortising loan if interest rates are 6% pa compounding per month and are not expected to change? If it makes it easier, assume that you can afford to pay $2,000 per month on either loan. Express your answer as a proportional increase using the following formula: $$\text{Proportional Increase} = \dfrac{V_\text{0,interest only}}{V_\text{0,fully amortising}} - 1$$ A 'fully amortising' loan can also be called a: 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):

A company advertises an investment costing $1,000 which they say is under priced. They say that it has an expected total return of 15% pa, but a required return of only 10% pa. Of the 15% pa total expected return, the dividend yield is expected to be 4% pa and the capital yield 11% pa. Assume that the company's statements are correct. What is the NPV of buying the investment if the 15% total return lasts for the next 100 years (t=0 to 100), then reverts to 10% 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, the dividends can only be re-invested at 10% pa and 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): 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: For an asset price to double every 10 years, what must be the expected future capital return, given as an effective annual rate? In February 2020, the RBA cash rate was 0.75% pa and the Australian CPI inflation rate was 1.8% pa. You currently have$100 in the bank which pays a 0.75% pa interest rate.

Apples currently cost $1 each at the shop and inflation is 1.8% pa which is the expected growth rate in the apple price. This information is summarised in the table below, with some parts missing that correspond to the answer options. All rates are given as effective annual rates. Note that when payments are not specified as real, as in this question, they're conventionally assumed to be nominal.  Wealth in Dollars and Apples Time (year) Bank account wealth ($) Apple price ($) Wealth in apples 0 100 1 100 1 100.75 1.018 (a) 2 (b) (c) (d) Which of the following statements is NOT correct? Your: How can a nominal cash flow be precisely converted into a real cash flow? What is the present value of a real payment of$500 in 2 years? The nominal discount rate is 7% pa and the inflation rate is 4% pa.

On his 20th birthday, a man makes a resolution. He will put $30 cash under his bed at the end of every month starting from today. His birthday today is the first day of the month. So the first addition to his cash stash will be in one month. He will write in his will that when he dies the cash under the bed should be given to charity. If the man lives for another 60 years, how much money will be under his bed if he dies just after making his last (720th) addition? Also, what will be the real value of that cash in today's prices if inflation is expected to 2.5% pa? Assume that the inflation rate is an effective annual rate and is not expected to change. The answers are given in the same order, the amount of money under his bed in 60 years, and the real value of that money in today's prices. If the nominal gold price is expected to increase at the same rate as inflation which is 3% pa, which of the following statements is NOT correct? 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. 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 expression 'you have to spend money to make money' relates to which business decision? The sayings "Don't cry over spilt milk", "Don't regret the things that you can't change" and "What's done is done" are most closely related to which financial concept? If a variable, say X, is normally distributed with mean $\mu$ and variance $\sigma^2$ then mathematicians write $X \sim \mathcal{N}(\mu, \sigma^2)$. If a variable, say Y, is log-normally distributed and the underlying normal distribution has mean $\mu$ and variance $\sigma^2$ then mathematicians write $Y \sim \mathbf{ln} \mathcal{N}(\mu, \sigma^2)$. The below three graphs show probability density functions (PDF) of three different random variables Red, Green and Blue. Select the most correct statement: If a stock's future expected continuously compounded annual returns are normally distributed, what will be bigger, the stock's or continuously compounded annual return? Or would you expect them to be ? If a stock's expected future prices are log-normally distributed, what will be bigger, the stock's or future price? Or would you expect them to be ? Question 908 effective rate, return types, gross discrete return, return distribution, price gains and returns over time For an asset's price to double from say$1 to $2 in one year, what must its gross discrete return (GDR) be? If the price now is $P_0$ and the price in one year is $P_1$ then the gross discrete return over the next year is: $$\text{GDR}_\text{annual} = \dfrac{P_1}{P_0}$$ 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?

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?