Fight Finance

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.

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.

You are a banker about to grant a 2 year loan to a customer. The loan's principal and interest will be repaid in a single payment at maturity, sometimes called a zero-coupon loan, discount loan or bullet loan.

You require a real return of 6% pa over the two years, given as an effective annual rate. Inflation is expected to be 2% this year and 4% next year, both given as effective annual rates.

You judge that the customer can afford to pay back $1,000,000 in 2 years, given as a nominal cash flow. How much should you lend to her right now?

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

Which is the safest investment? Which has the highest expected returns?

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

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

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

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

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

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

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

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

One year ago a pharmaceutical firm floated by selling its 1 million shares for $100 each. Its book and market values of equity were both $100m. Its debt totalled $50m. The required return on the firm's assets was 15%, equity 20% and debt 5% pa.

In the year since then, the firm:

• Earned net income of $29m.
• Paid dividends totaling $10m.
• Discovered a valuable new drug that will lead to a massive 1,000 times increase in the firm's net income in 10 years after the research is commercialised. News of the discovery was publicly announced. The firm's systematic risk remains unchanged.

Which of the following statements is NOT correct? All statements are about current figures, not figures one year ago.

Hint: Book return on assets (ROA) and book return on equity (ROE) are ratios that accountants like to use to measure a business's past performance.

###\text{ROA}= \dfrac{\text{Net income}}{\text{Book value of assets}}###

###\text{ROE}= \dfrac{\text{Net income}}{\text{Book value of equity}}###

The required return on assets ##r_V## is a return that financiers like to use to estimate a business's future required performance which compensates them for the firm's assets' risks. If the business were to achieve realised historical returns equal to its required returns, then investment into the business's assets would have been a zero-NPV decision, which is neither good nor bad but fair.

###r_\text{V, 0 to 1}= \dfrac{\text{Cash flow from assets}_\text{1}}{\text{Market value of assets}_\text{0}} = \dfrac{CFFA_\text{1}}{V_\text{0}}###

Similarly for equity and debt.

The below screenshot of Commonwealth Bank of Australia's (CBA) details were taken from the Google Finance website on 7 Nov 2014. Some information has been deliberately blanked out.

What was CBA's market capitalisation of equity?

The below screenshot of Microsoft's (MSFT) details were taken from the Google Finance website on 28 Nov 2014. Some information has been deliberately blanked out.

What was MSFT's market capitalisation of equity?

The investment decision primarily affects which part of a business?

The working capital decision primarily affects which part of a business?

The financing decision primarily affects which part of a business?

Payout policy is most closely related to which part of a business?

Business people make lots of important decisions. Which of the following is the most important long term decision?

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.

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.

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

If interest rates are 0% pa and are expected to stay at that level for the foreseeable future, what is the most that you would be prepared to pay a bank now if it offered to pay you $10 at the end of every year for the next 5 years?

In other words, what is the present value of five $10 payments at time 1, 2, 3, 4 and 5 if interest rates are 0% pa?

The 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:

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

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

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

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

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

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

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

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

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

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

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

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

Two years ago Fred bought a house for $300,000.

Now it's worth $500,000, based on recent similar sales in the area.

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

He rents his house out for $2,000 per month, paid in advance. Every 12 months he plans to increase the rental payments.

The present value of 12 months of rental payments is $23,173.86.

The future value of 12 months of rental payments one year ahead is $25,027.77.

What is the expected annual growth rate of the rental payments? In other words, by what percentage increase will Fred have to raise the monthly rent by each year to sustain the expected annual total return of 8%?

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 is expected to pay the following dividends:

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?

The following is the Dividend Discount Model (DDM) used to price stocks:

Assume that the assumptions of the DDM hold and that the time period is measured in years.

Which of the following is equal to the expected dividend in 3 years, ## d_3 ##?

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

###p_0=\frac{d_1}{r_\text{eff}-g_\text{eff}}###

Which expression is NOT equal to the expected capital return?

A stock pays semi-annual dividends. It just paid a dividend of $10. The growth rate in the dividend is 1% every 6 months, given as an effective 6 month rate. You estimate that the stock's required return is 21% pa, as an effective annual rate.

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

You own an apartment which you rent out as an investment property.

What is the price of the apartment using discounted cash flow (DCF, same as NPV) valuation?

Assume that:

• You just signed a contract to rent the apartment out to a tenant for the next 12 months at $2,000 per month, payable in advance (at the start of the month, t=0). The tenant is just about to pay you the first $2,000 payment.
• The contract states that monthly rental payments are fixed for 12 months. After the contract ends, you plan to sign another contract but with rental payment increases of 3%. You intend to do this every year.
  So rental payments will increase at the start of the 13th month (t=12) to be $2,060 (=2,000(1+0.03)), and then they will be constant for the next 12 months.
  Rental payments will increase again at the start of the 25th month (t=24) to be $2,121.80 (=2,000(1+0.03)²), and then they will be constant for the next 12 months until the next year, and so on.
• The required return of the apartment is 8.732% pa, given as an effective annual rate.
• Ignore all taxes, maintenance, real estate agent, council and strata fees, periods of vacancy and other costs. Assume that the apartment will last forever and so will the rental payments.

The boss of WorkingForTheManCorp has a wicked (and unethical) idea. He plans to pay his poor workers one week late so that he can get more interest on his cash in the bank.

Every week he is supposed to pay his 1,000 employees $1,000 each. So $1 million is paid to employees every week.

The boss was just about to pay his employees today, until he thought of this idea so he will actually pay them one week (7 days) later for the work they did last week and every week in the future, forever.

Bank interest rates are 10% pa, given as a real effective annual rate. So ##r_\text{eff annual, real} = 0.1## and the real effective weekly rate is therefore ##r_\text{eff weekly, real} = (1+0.1)^{1/52}-1 = 0.001834569##

All rates and cash flows are real, the inflation rate is 3% pa and there are 52 weeks per year. The boss will always pay wages one week late. The business will operate forever with constant real wages and the same number of employees.

What is the net present value (NPV) of the boss's decision to pay later?

A business project is expected to cost $100 now (t=0), then pay $10 at the end of the third (t=3), fourth, fifth and sixth years, and then grow by 5% pa every year forever. So the cash flow will be $10.5 at the end of the seventh year (t=7), then $11.025 at the end of the eighth year (t=8) and so on perpetually. The total required return is 10℅ pa.

Which of the following formulas will NOT give the correct net present value of the project?

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.

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

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

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

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

You have $100,000 in the bank. The bank pays interest at 10% pa, given as an effective annual rate.

You wish to consume an equal amount now (t=0), in one year (t=1) and in two years (t=2), and still have $50,000 in the bank after that (t=2).

How much can you consume at each time?

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.

A project to build a toll road will take 3 years to complete, costing three payments of $50 million, paid at the start of each year (at times 0, 1, and 2).

After completion, the toll road will yield a constant $10 million at the end of each year forever with no costs. So the first payment will be at t=4.

The required return of the project is 10% pa given as an effective nominal rate. All cash flows are nominal.

What is the payback period?

A project has the following cash flows:

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 has the following cash flows:

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?

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

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

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

Which of the following investable assets are NOT suitable for valuation using PE multiples techniques?

Which of the following investable assets are NOT suitable for valuation using PE multiples techniques?

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

Which of the following statements is NOT correct? Lenders:

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

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

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} ###

In Australia, nominal yields on semi-annual coupon paying Government Bonds with 2 years until maturity are currently 2.83% pa.

The inflation rate is currently 2.2% pa, given as an APR compounding per quarter. The inflation rate is not expected to change over the next 2 years.

What is the real yield on these bonds, given as an APR compounding every 6 months?

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 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.

To your surprise, you can actually afford to pay $2,000 per month and your mortgage allows early repayments without fees. If you maintain these higher monthly payments, how long will it take to pay off your mortgage?

You want to buy 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).

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?

A bank grants a borrower an interest-only residential mortgage loan with a very large 50% deposit and a nominal interest rate of 6% that is not expected to change. Assume that inflation is expected to be a constant 2% pa over the life of the loan. Ignore credit risk.

From the bank's point of view, what is the long term expected nominal capital return of the loan asset?

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

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

If a person can afford constant mortgage loan payments of $2,000 per month, how much more can they borrow when interest rates are 4.5% pa compared with 14.0% pa?

Give your answer as a proportional increase over the amount you could borrow when interest rates were high ##(V_\text{high rates})##, so:

###\text{Proportional increase} = \dfrac{V_\text{low rates}-V_\text{high rates}}{V_\text{high rates}} ###

Assume that:

• Interest rates are expected to be constant over the life of the loan.
• Loans are interest-only and have a life of 30 years.
• Mortgage loan payments are made every month in arrears and all interest rates are given as annualised percentage rates (APR's) compounding per month.

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 A and B are issued by the same company. They have the same face value, maturity, seniority and coupon payment frequency. The only difference is that bond A has a 5% coupon rate, while bond B has a 10% coupon rate. The yield curve is flat, which means that yields are expected to stay the same.

Which bond would have the higher current price?

Bonds A and B are issued by the same Australian company. Both bonds yield 7% pa, and they have the same face value ($100), maturity, seniority, and payment frequency.

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

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?

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

Bonds X and Y are issued by the same company. Both bonds yield 10% pa, and they have the same face value ($100), maturity, seniority, and payment frequency.

The only difference is that bond X pays coupons of 6% pa and bond Y pays coupons of 8% pa. Which of the following statements is true?

A 10 year Australian government bond was just issued at par with a yield of 3.9% pa. The fixed coupon payments are semi-annual. The bond has a face value of $1,000.

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

You're trying to save enough money to buy your first car which costs $2,500. You can save $100 at the end of each month starting from now. You currently have no money at all. You just opened a bank account with an interest rate of 6% pa payable monthly.

How many months will it take to save enough money to buy the car? Assume that the price of the car will stay the same over time.

You really want to go on a back packing trip to Europe when you finish university. Currently you have $1,500 in the bank. Bank interest rates are 8% pa, given as an APR compounding per month. If the holiday will cost $2,000, how long will it take for your bank account to reach that amount?

When using the dividend discount model, care must be taken to avoid using a nominal dividend growth rate that exceeds the country's nominal GDP growth rate. Otherwise the firm is forecast to take over the country since it grows faster than the average business forever.

Suppose a firm's nominal dividend grows at 10% pa forever, and nominal GDP growth is 5% pa forever. The firm's total dividends are currently $1 billion (t=0). The country's GDP is currently $1,000 billion (t=0).

In approximately how many years will the company's total dividends be as large as the country's GDP?

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.

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##

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

Which of the following statements is NOT correct? Borrowers:

Which of the following statements is NOT equivalent to the yield on debt?

Assume that the debt being referred to is fairly priced, but do not assume that it's priced at par.

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

When someone says that they're "buying American dollars" (USD), what type of asset are they probably buying? They're probably buying:

An American wishes to convert USD 1 million to Australian dollars (AUD). The exchange rate is 0.8 USD per AUD. How much is the USD 1 million worth in AUD?

If the current AUD exchange rate is USD 0.9686 = AUD 1, what is the European terms quote of the AUD against the USD?

Investors expect the Reserve Bank of Australia (RBA) to keep the policy rate steady at their next meeting.

Then unexpectedly, the RBA announce that they will increase the policy rate by 25 basis points due to fears that the economy is growing too fast and that inflation will be above their target rate of 2 to 3 per cent.

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

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

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

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

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

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

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

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

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

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

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?

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

(I) Weak form market efficiency is broken.

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

(III) Strong form market efficiency is broken.

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

Select the most correct response:

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

(i) Weak form market efficiency is broken.

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

(iii) Strong form market efficiency is broken.

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

Select the most correct response:

Select the most correct statement from the following.

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

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

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

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

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

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

A person is thinking about borrowing $100 from the bank at 7% pa and investing it in shares with an expected return of 10% pa. One year later the person intends to sell the shares and pay back the loan in full. Both the loan and the shares are fairly priced.

What is the Net Present Value (NPV) of this one year investment? Note that you are asked to find the present value (##V_0##), not the value in one year (##V_1##).

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

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

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

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

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

A man inherits $500,000 worth of shares.

He believes that by learning the secrets of trading, keeping up with the financial news and doing complex trend analysis with charts that he can quit his job and become a self-employed day trader in the equities markets.

What is the expected gain from doing this over the first year? Measure the net gain in wealth received at the end of this first year due to the decision to become a day trader. Assume the following:

• He earns $60,000 pa in his current job, paid in a lump sum at the end of each year.
• He enjoys examining share price graphs and day trading just as much as he enjoys his current job.
• Stock markets are weak form and semi-strong form efficient.
• He has no inside information.
• He makes 1 trade every day and there are 250 trading days in the year. Trading costs are $20 per trade. His broker invoices him for the trading costs at the end of the year.
• The shares that he currently owns and the shares that he intends to trade have the same level of systematic risk as the market portfolio.
• The market portfolio's expected return is 10% pa.

Measure the net gain over the first year as an expected wealth increase at the end of the year.

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

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

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

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

A company advertises an investment costing $1,000 which they say is underpriced. They say that it has an expected total return of 15% pa, but a required return of only 10% pa. Assume that there are no dividend payments so the entire 15% total return is all capital return.

Assuming that the company's statements are correct, what is the NPV of buying the investment if the 15% return lasts for the next 100 years (t=0 to 100), then reverts to 10% pa after that time? Also, what is the NPV of the investment if the 15% return lasts forever?

In both cases, assume that the required return of 10% remains constant. All returns are given as effective annual rates.

The answer choices below are given in the same order (15% for 100 years, and 15% forever):

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

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

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

You are thinking of investing $100,000 in the fund and keeping it there for 40 years when you plan to retire.

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

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

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

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

Which of the following statements is NOT correct?

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

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

Which of the following statements is NOT correct?

A European company just issued two bonds, a

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

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

A European company just issued two bonds, a

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

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

A European company just issued two bonds, a

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

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

An Australian company just issued two bonds:

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

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

An Australian company just issued two bonds 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.

An Australian company just issued two bonds:

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

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

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.

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

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

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

A three year bond has a face value of $100, a yield of 10% and a fixed coupon rate of 5%, paid semi-annually. What is its price?

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?

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?

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

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

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

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

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?

Bonds X and Y are issued by different companies, but they both pay a semi-annual coupon of 10% pa and they have the same face value ($100) and maturity (3 years).

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

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?

Bonds X and Y are issued by different companies, but they both pay a semi-annual coupon of 10% pa and they have the same face value ($100), maturity (3 years) and yield (10%) as each other.

Which of the following statements is true?

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

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

A five year bond has a face value of $100, a yield of 12% and a fixed coupon rate of 6%, paid semi-annually.

What is the bond's price?

Which one of the following bonds is trading at par?

A firm wishes to raise $8 million now. They will issue 7% pa semi-annual coupon bonds that will mature in 10 years and have a face value of $100 each. Bond yields are 10% pa, given as an APR compounding every 6 months, and the yield curve is flat.

How many bonds should the firm issue?

For a bond that pays fixed semi-annual coupons, how is the annual coupon rate defined, and how is the bond's annual income yield from time 0 to 1 defined mathematically?

Let: ##P_0## be the bond price now,

##F_T## be the bond's face value,

##T## be the bond's maturity in years,

##r_\text{total}## be the bond's total yield,

##r_\text{income}## be the bond's income yield,

##r_\text{capital}## be the bond's capital yield, and

##C_t## be the bond's coupon at time t in years. So ##C_{0.5}## is the coupon in 6 months, ##C_1## is the coupon in 1 year, and so on.

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

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

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

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

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

Select the most correct statement.

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

An investor bought two fixed-coupon bonds issued by the same company, a zero-coupon bond and a 7% pa semi-annual coupon bond. Both bonds have a face value of $1,000, mature in 10 years, and had a yield at the time of purchase of 8% pa.

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

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

How many bonds should the firm issue? All numbers are rounded up.

A four year bond has a face value of $100, a yield of 9% and a fixed coupon rate of 6%, paid semi-annually. What is its price?

In these tough economic times, central banks around the world have cut interest rates so low that they are practically zero. In some countries, government bond yields are also very close to zero.

A three year government bond with a face value of $100 and a coupon rate of 2% pa paid semi-annually was just issued at a yield of 0%. What is the price of the bond?

A 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?

A 30 year Japanese government bond was just issued at par with a yield of 1.7% pa. The fixed coupon payments are semi-annual. The bond has a face value of $100.

Six months later, just after the first coupon is paid, the yield of the bond increases to 2% pa. What is the bond's new price?

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

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

Where:

Bonds X and Y are issued by the same US company. Both bonds yield 6% pa, and they have the same face value ($100), maturity, seniority, and payment frequency.

The only difference is that bond X pays coupons of 8% pa and bond Y pays coupons of 12% pa. Which of the following statements is true?

Below are some statements about loans and bonds. The first descriptive sentence is correct. But one of the second sentences about the loans' or bonds' prices is not correct. Which statement is NOT correct? Assume that interest rates are positive.

Note that coupons or interest payments are the periodic payments made throughout a bond or loan's life. The face or par value of a bond or loan is the amount paid at the end when the debt matures.

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

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

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

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

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

How many bonds should the firm issue?

An investor bought a 10 year 2.5% pa fixed coupon government bond priced at par. The face value is $100. Coupons are paid semi-annually and the next one is in 6 months.

Six months later, just after the coupon at that time was paid, yields suddenly and unexpectedly fell to 2% pa. Note that all yields above are given as APR's compounding semi-annually.

What was the bond investors' historical total return over that first 6 month period, given as an effective semi-annual rate?

An investor bought a 20 year 5% pa fixed coupon government bond priced at par. The face value is $100. Coupons are paid semi-annually and the next one is in 6 months.

Six months later, just after the coupon at that time was paid, yields suddenly and unexpectedly rose to 5.5% pa. Note that all yields above are given as APR's compounding semi-annually.

What was the bond investors' historical total return over that first 6 month period, given as an effective semi-annual rate?

Your friend is trying to find the net present value of an investment which:

• Costs $1 million initially (t=0); and
• Pays a single positive cash flow of $1.1 million in one year (t=1).

The investment has a total required return of 10% pa due to its moderate level of undiversifiable risk.

Your friend is aware of the importance of opportunity costs and the time value of money, but he is unsure of how to find the NPV of the project.

He knows that the opportunity cost of investing the $1m in the project is the expected gain from investing the money in shares instead. Like the project, shares also have an expected return of 10% since they have moderate undiversifiable risk. This opportunity cost is $0.1m ##(=1m \times 10\%)## which occurs in one year (t=1).

He knows that the time value of money should be accounted for, and this can be done by finding the present value of the cash flows in one year.

Your friend has listed a few different ways to find the NPV which are written down below.

Method 1: ##-1m + \dfrac{1.1m}{(1+0.1)^1} ##

Method 2: ##-1m + 1.1m - 1m \times 0.1 ##

Method 3: ##-1m + \dfrac{1.1m}{(1+0.1)^1} - 1m \times 0.1 ##

Which of the above calculations give the correct NPV? Select the most correct answer.

A young lady is trying to decide if she should attend university or not.

The young lady's parents say that she must attend university because otherwise all of her hard work studying and attending school during her childhood was a waste.

What's the correct way to classify this item from a capital budgeting perspective when trying to decide whether to attend university?

The hard work studying at school in her childhood should be classified as:

A young lady is trying to decide if she should attend university. Her friends say that she should go to university because she is more likely to meet a clever young man than if she begins full time work straight away.

What's the correct way to classify this item from a capital budgeting perspective when trying to find the Net Present Value of going to university rather than working?

The opportunity to meet a desirable future spouse should be classified as:

A man is thinking about taking a day off from his casual painting job to relax.

He just woke up early in the morning and he's about to call his boss to say that he won't be coming in to work.

But he's thinking about the hours that he could work today (in the future) which are:

A man has taken a day off from his casual painting job to relax.

It's the end of the day and he's thinking about the hours that he could have spent working (in the past) which are now:

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.

Note: all figures are given in millions of dollars ($m).

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

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

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

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

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

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

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

Remember:

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:

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.

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.

Note: all figures are given in millions of dollars ($m).

The firm's free cash flow over the 2014 financial year was:

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

Note 1: Due to the project, the firm also anticipates finding some rare diamonds which will give before-tax revenues of $1m at the end of the year.

Note 2: The land that will be mined actually has thermal springs and a family of koalas that could be sold to an eco-tourist resort for an after-tax amount of $3m right now. However, if the mine goes ahead then this natural beauty will be destroyed.

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

Find the project's CFFA at time zero and one. Answers are given in millions of dollars ($m), with the first cash flow at time zero, and the second at time one.

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

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).

Value the following business project to manufacture a new product.

Notes

1. The firm's current assets and current liabilities are $3m and $2m respectively right now. This net working capital will not be used in this project, it will be used in other unrelated projects.
   Due to the project, current assets (mostly inventory) will grow by $2m initially (at t = 0), and then by $0.2m at the end of the first year (t=1).
   Current liabilities (mostly trade creditors) will increase by $0.1m at the end of the first year (t=1).
   At the end of the project, the net working capital accumulated due to the project can be sold for the same price that it was bought.
2. The project cost $0.5m to research which was incurred one year ago.

Assumptions

• All cash flows occur at the start or end of the year as appropriate, not in the middle or throughout the year.
• All rates and cash flows are real. The inflation rate is 3% pa.
• All rates are given as effective annual rates.
• The business considering the project is run as a 'sole tradership' (run by an individual without a company) and is therefore eligible for a 50% capital gains tax discount when the equipment is sold, as permitted by the Australian Tax Office.

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

Your friend just bought a house for $400,000. He financed it using a $320,000 mortgage loan and a deposit of $80,000.

In the context of residential housing and mortgages, the 'equity' tied up in the value of a person's house is the value of the house less the value of the mortgage. So the initial equity your friend has in his house is $80,000. Let this amount be E, let the value of the mortgage be D and the value of the house be V. So ##V=D+E##.

If house prices suddenly fall by 10%, what would be your friend's percentage change in equity (E)? Assume that the value of the mortgage is unchanged and that no income (rent) was received from the house during the short time over which house prices fell.

Remember:

### r_{0\rightarrow1}=\frac{p_1-p_0+c_1}{p_0} ###

where ##r_{0-1}## is the return (percentage change) of an asset with price ##p_0## initially, ##p_1## one period later, and paying a cash flow of ##c_1## at time ##t=1##.

Your friend just bought a house for $1,000,000. He financed it using a $900,000 mortgage loan and a deposit of $100,000.

In the context of residential housing and mortgages, the 'equity' or 'net wealth' tied up in a house is the value of the house less the value of the mortgage loan. Assuming that your friend's only asset is his house, his net wealth is $100,000.

If house prices suddenly fall by 15%, what would be your friend's percentage change in net wealth?

Assume that:

• No income (rent) was received from the house during the short time over which house prices fell.
• Your friend will not declare bankruptcy, he will always pay off his debts.

One year ago you bought $100,000 of shares partly funded using a margin loan. The margin loan size was $70,000 and the other $30,000 was your own wealth or 'equity' in the share assets.

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

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

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

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

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

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

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

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

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

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

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

Annual interest expense is equal to:

Which one of the following will 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:

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

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

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

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

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

The US firm Google operates in the online advertising business. In 2011 Google bought Motorola Mobility which manufactures mobile phones.

Assume the following:

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

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

The mobile phone manufacturing project's:

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

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

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

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

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

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:

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

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

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

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

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

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

###EBITDA=Rev - COGS - FC###

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

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

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

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

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

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

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

Assume that:

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

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

Fill in the missing words in the following sentence:

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

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

It's nominal unlevered cash flow from assets (##CFFA_U##) at the end of this year (t=1) is expected to be $1 million. After that it is expected to grow at a rate of:

• 12% pa for the next two years (from t=1 to 3),
• 5% over the fourth year (from t=3 to 4), and
• -1% forever after that (from t=4 onwards). Note that this is a negative one percent growth rate.

Assume that:

• The nominal WACC after tax is 9.5% pa and is not expected to change.
• The nominal WACC before tax is 10% pa and is not expected to change.
• The firm has a target debt-to-equity ratio that it plans to maintain.
• The inflation rate is 3% pa.
• All rates are given as nominal effective annual rates.

What is the levered value of this fast growing firm's assets?

A firm plans to issue equity and use the cash raised to pay off its debt. No assets will be bought or sold. Ignore the costs of financial distress.

Which of the following statements is NOT correct, all things remaining equal?

Diversification is achieved by investing in a large amount of stocks. What type of risk is reduced by diversification?

According to the theory of the Capital Asset Pricing Model (CAPM), total variance can be broken into two components, systematic variance and idiosyncratic variance. Which of the following events would be considered the most diversifiable according to the theory of the CAPM?

According to the theory of the Capital Asset Pricing Model (CAPM), total risk can be broken into two components, systematic risk and idiosyncratic risk. Which of the following events would be considered a systematic, undiversifiable event according to the theory of the CAPM?

Treasury bonds currently have a return of 5% pa. A stock has a beta of 0.5 and the market return is 10% pa. What is the expected return of the stock?

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

A stock has a beta of 0.5. Its next dividend is expected to be $3, paid one year from now. Dividends are expected to be paid annually and grow by 2% pa forever. Treasury bonds yield 5% pa and the market portfolio's expected return is 10% pa. All returns are effective annual rates.

What is the price of the stock now?

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?

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

Investment projects that plot on the SML would have:

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

Buying investment projects that plot above the SML would lead to:

What is the beta of the above portfolio?

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

Which statement is the most correct?

Which statement(s) are correct?

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

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

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

Select the most correct response:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Which of the equations are correct?

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

###r_i=r_f+β_i (r_m-r_f)###

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

You just bought a house worth $1,000,000. You financed it with an $800,000 mortgage loan and a deposit of $200,000.

You estimate that:

• The house has a beta of 1;
• The mortgage loan has a beta of 0.2.

What is the beta of the equity (the $200,000 deposit) that you have in your house?

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

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

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

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

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

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

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

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:

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

All things remaining equal, the variance of a portfolio of two positively-weighted stocks rises as:

What is the expected return of the above portfolio?

What is the standard deviation (not variance) of returns of the above portfolio?

What is the standard deviation (not variance) of the above portfolio? Note that the stocks' covariance is given, not correlation.

You're the boss of an investment bank's equities research team. Your five analysts are each trying to find the expected total return over the next year of shares in a mining company. The mining firm:

• Is regarded as a mature company since it's quite stable in size and was floated around 30 years ago. It is not a high-growth company;
• Share price is very sensitive to changes in the price of the market portfolio, economic growth, the exchange rate and commodities prices. Due to this, its standard deviation of total returns is much higher than that of the market index;
• Experienced tough times in the last 10 years due to unexpected falls in commodity prices.
• Shares are traded in an active liquid market.

• The analysts' source data is correct and true, but their inferences might be wrong;
• All returns and yields are given as effective annual nominal rates.

Two risky stocks A and B comprise an equal-weighted portfolio. The correlation between the stocks' returns is 70%.

If the variance of stock A's returns increases but the:

• Prices and expected returns of each stock stays the same,
• Variance of stock B's returns stays the same,
• Correlation of returns between the stocks stays the same.

Which of the following statements is NOT correct?

All things remaining equal, the higher the correlation of returns between two stocks:

Which of the following statements about short-selling is NOT true?

An investor wants to make a portfolio of two stocks A and B with a target expected portfolio return of 6% pa.

• Stock A has an expected return of 5% pa.
• Stock B has an expected return of 10% pa.

What portfolio weights should the investor have in stocks A and B respectively?

An investor wants to make a portfolio of two stocks A and B with a target expected portfolio return of 16% pa.

• Stock A has an expected return of 8% pa.
• Stock B has an expected return of 12% pa.

What portfolio weights should the investor have in stocks A and B respectively?

An investor wants to make a portfolio of two stocks A and B with a target expected portfolio return of 12% pa.

• Stock A has an expected return of 10% pa and a standard deviation of 20% pa.
• Stock B has an expected return of 15% pa and a standard deviation of 30% pa.

The correlation coefficient between stock A and B's expected returns is 70%.

What will be the annual standard deviation of the portfolio with this 12% pa target return?