Question 278 inflation, real and nominal returns and cash flows
Imagine that the interest rate on your savings account was 1% per year and inflation was 2% per year.
Jan asks you for a loan. He wants $100 now and offers to pay you back $120 in 1 year. You can borrow and lend from the bank at an interest rate of 10% pa, given as an effective annual rate.
Ignore credit risk. Remember:
### V_0 = \frac{V_t}{(1+r_\text{eff})^t} ###
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.
For a price of $6, Carlos will sell you a share which will pay a dividend of $1 in one year and every year after that forever. The required return of the stock is 10% pa.
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.
The saying "buy low, sell high" suggests that investors should make a:
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_1p_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} ##.
Question 295 inflation, real and nominal returns and cash flows, NPV
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?
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.
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?
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.
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}{rg}###
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?
The following is the Dividend Discount Model (DDM) used to price stocks:
###P_0=\dfrac{C_1}{rg}###
If the assumptions of the DDM hold, which one of the following statements is NOT correct? The long term expected:
In the dividend discount model:
###P_0 = \dfrac{C_1}{rg}###
The return ##r## is supposed to be the:
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 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.
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.
Question 488 income and capital returns, payout policy, payout ratio, DDM
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 zeroNPV.
All things remaining equal, which of the following statements is NOT correct?
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.
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 4year 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 4year old ones only last for another 11 years). Then he sells the old car for $2,000 and buys another 4year 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 taxexempt for individuals.
An industrial chicken farmer grows chickens for their meat. Chickens:
 Cost $0.50 each to buy as chicks. They are bought on the day they’re born, at t=0.
 Grow at a rate of $0.70 worth of meat per chicken per week for the first 6 weeks (t=0 to t=6).
 Grow at a rate of $0.40 worth of meat per chicken per week for the next 4 weeks (t=6 to t=10) since they’re older and grow more slowly.
 Feed costs are $0.30 per chicken per week for their whole life. Chicken feed is bought and fed to the chickens once per week at the beginning of the week. So the first amount of feed bought for a chicken at t=0 costs $0.30, and so on.
 Can be slaughtered (killed for their meat) and sold at no cost at the end of the week. The price received for the chicken is their total value of meat (note that the chicken grows fast then slow, see above).
The required return of the chicken farm is 0.5% given as an effective weekly rate.
Ignore taxes and the fixed costs of the factory. Ignore the chicken’s welfare and other environmental and ethical concerns.
Find the equivalent weekly cash flow of slaughtering a chicken at 6 weeks and at 10 weeks so the farmer can figure out the best time to slaughter his chickens. The choices below are given in the same order, 6 and 10 weeks.
There are many ways to write the ordinary annuity formula.
Which of the following is NOT equal to the ordinary annuity formula?
The following cash flows are expected:
 10 yearly payments of $60, with the first payment in 3 years from now (first payment at t=3).
 1 payment of $400 in 5 years and 6 months (t=5.5) from now.
What is the NPV of the cash flows if the discount rate is 10% given as an effective annual rate?
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:
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?
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 semiannual 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 semiannual 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?
Question 498 NPV, Annuity, perpetuity with growth, multi stage growth model
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?
Estimate the Chinese bank ICBC's share price using a backwardlooking 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 backwardlooking PE ratio is 4.59;
 BOC 's backwardlooking PE ratio is 4.78;
 ABC's backwardlooking PE ratio is also 4.78;
Note: Figures sourced from Google Finance on 25 March 2014. Share prices are from the Shanghai stock exchange.
Which firms tend to have low forwardlooking priceearnings (PE) ratios?
Only consider firms with positive earnings, disregard firms with negative earnings and therefore negative PE ratios.
Which of the following investable assets are NOT suitable for valuation using PE multiples techniques?
Which firms tend to have low forwardlooking priceearnings (PE) ratios? Only consider firms with positive PE ratios.
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 semiannually.
 An annual dividendpaying 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}##
You're advising your superstar client 40cent who is weighing up buying a private jet or a luxury yacht. 40cent is just as happy with either, but he wants to go with the more costeffective 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 40cent 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 40cent 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 40cent to buy the or the ?
Note that the effective monthly rate is ##r_\text{eff monthly}=(1+0.1)^{1/12}1=0.00797414##
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?
Question 543 price gains and returns over time, IRR, NPV, income and capital returns, effective return
For an asset price to triple every 5 years, what must be the expected future capital return, given as an effective annual rate?
Question 363 income and capital returns, inflation, real and nominal returns and cash flows, real estate
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.
Question 526 real and nominal returns and cash flows, inflation, no explanation
How can a nominal cash flow be precisely converted into a real cash flow?
Question 577 inflation, real and nominal returns and cash flows
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.
Question 554 inflation, real and nominal returns and cash flows
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.
Question 604 inflation, real and nominal returns and cash flows
Apples and oranges currently cost $1 each. Inflation is 5% pa, and apples and oranges are equally affected by this inflation rate. Note that when payments are not specified as real, as in this question, they're conventionally assumed to be nominal.
Which of the following statements is NOT correct?
Question 574 inflation, real and nominal returns and cash flows, NPV
What is the present value of a nominal payment of $100 in 5 years? The real discount rate is 10% pa and the inflation rate is 3% pa.
Question 576 inflation, real and nominal returns and cash flows
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.
Question 578 inflation, real and nominal returns and cash flows
Which of the following statements about inflation is NOT correct?
Which business structure or structures have the advantage of limited liability for equity investors?
Question 531 bankruptcy or insolvency, capital structure, risk, limited liability
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.
Question 452 limited liability, expected and historical returns
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_1p_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.
Question 445 financing decision, corporate financial decision theory
The financing decision primarily affects which part of a business?
Question 447 payout policy, corporate financial decision theory
Payout policy is most closely related to which part of a business?
Question 443 corporate financial decision theory, investment decision, financing decision, working capital decision, payout policy
Business people make lots of important decisions. Which of the following is the most important long term decision?
The expression 'you have to spend money to make money' relates to which business decision?
Which of the following decisions relates to the current assets and current liabilities of the firm?
Which of the following statements about book and market equity is NOT correct?
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 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 
If a project's net present value (NPV) is zero, then its internal rate of return (IRR) will be:
A project's NPV is positive. Select the most correct statement:
The required return of a project is 10%, given as an effective annual rate. Assume that the cash flows shown in the table are paid all at once at the given point in time.
What is the Net Present Value (NPV) of the project?
Project Cash Flows  
Time (yrs)  Cash flow ($) 
0  100 
1  11 
2  121 
The below graph shows a project's net present value (NPV) against its annual discount rate.
For what discount rate or range of discount rates would you accept and commence the project?
All answer choices are given as approximations from reading off the graph.
The below graph shows a project's net present value (NPV) against its annual discount rate.
Which of the following statements is NOT correct?
A firm is considering a business project which costs $11m now and is expected to pay a constant $1m at the end of every year forever.
Assume that the initial $11m cost is funded using the firm's existing cash so no new equity or debt will be raised. The cost of capital is 10% pa.
Which of the following statements about net present value (NPV), internal rate of return (IRR) and payback period is NOT correct?
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.
You want to buy an apartment worth $500,000. You have saved a deposit of $50,000. The bank has agreed to lend you the $450,000 as a fully amortising mortgage loan with a term of 25 years. The interest rate is 6% pa and is not expected to change.
What will be your monthly payments?
You want to buy an apartment worth $400,000. You have saved a deposit of $80,000. The bank has agreed to lend you the $320,000 as a fully amortising mortgage loan with a term of 30 years. The interest rate is 6% pa and is not expected to change. What will be your monthly payments?
You want to buy an apartment priced at $500,000. You have saved a deposit of $50,000. The bank has agreed to lend you the $450,000 as a fully amortising loan with a term of 30 years. The interest rate is 6% pa and is not expected to change. What will be your monthly payments?
You just signed up for a 30 year fully amortising mortgage with monthly payments of $1,000 per month. The interest rate is 6% pa which is not expected to change.
How much did you borrow? After 20 years, how much will be owing on the mortgage? The interest rate is still 6% and is not expected to change.
You just signed up for a 30 year fully amortising mortgage loan with monthly payments of $1,500 per month. The interest rate is 9% pa which is not expected to change.
How much did you borrow? After 10 years, how much will be owing on the mortgage? The interest rate is still 9% and is not expected to change.
You just agreed to a 30 year fully amortising mortgage loan with monthly payments of $2,500. The interest rate is 9% pa which is not expected to change.
How much did you borrow? After 10 years, how much will be owing on the mortgage? The interest rate is still 9% and is not expected to change. The below choices are given in the same order.
You want to buy a house priced at $400,000. You have saved a deposit of $40,000. The bank has agreed to lend you $360,000 as a fully amortising loan with a term of 30 years. The interest rate is 8% pa payable monthly and is not expected to change.
What will be your monthly payments?
You want to buy an apartment priced at $300,000. You have saved a deposit of $30,000. The bank has agreed to lend you the $270,000 as an interest only loan with a term of 25 years. The interest rate is 12% pa and is not expected to change.
What will be your monthly payments? Remember that mortgage payments are paid in arrears (at the end of the month).
You just signed up for a 30 year interestonly 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 interestonly 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?
You want to buy an apartment priced at $500,000. You have saved a deposit of $50,000. The bank has agreed to lend you the $450,000 as an interest only loan with a term of 30 years. The interest rate is 6% pa and is not expected to change. What will be your monthly payments?
A prospective home buyer can afford to pay $2,000 per month in mortgage loan repayments. The central bank recently lowered its policy rate by 0.25%, and residential home lenders cut their mortgage loan rates from 4.74% to 4.49%.
How much more can the prospective home buyer borrow now that interest rates are 4.49% rather than 4.74%? Give your answer as a proportional increase over the original amount he could borrow (##V_\text{before}##), so:
###\text{Proportional increase} = \frac{V_\text{after}V_\text{before}}{V_\text{before}} ###Assume that:
 Interest rates are expected to be constant over the life of the loan.
 Loans are interestonly and have a life of 30 years.
 Mortgage loan payments are made every month in arrears and all interest rates are given as annualised percentage rates compounding per month.
A firm wishes to raise $20 million now. They will issue 8% pa semiannual coupon bonds that will mature in 5 years and have a face value of $100 each. Bond yields are 6% pa, given as an APR compounding every 6 months, and the yield curve is flat.
How many bonds should the firm issue?
A five year bond has a face value of $100, a yield of 12% and a fixed coupon rate of 6%, paid semiannually.
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 semiannual 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?
Which one of the following bonds is trading at a premium?
An investor bought two fixedcoupon bonds issued by the same company, a zerocoupon bond and a 7% pa semiannual 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 semiannual coupon bonds that will mature in 8 years and have a face value of $1,000 each. Bond yields are 10% pa, given as an APR compounding every 6 months, and the yield curve is flat.
How many bonds should the firm issue?
A 10 year bond has a face value of $100, a yield of 6% pa and a fixed coupon rate of 8% pa, paid semiannually. What is its price?
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.
Question 143 bond pricing, zero coupon bond, term structure of interest rates, forward interest rate
An Australian company just issued two bonds:
 A 6month 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.
Question 35 bond pricing, zero coupon bond, term structure of interest rates, forward interest rate
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.
Let the 'income return' of a bond be the coupon at the end of the period divided by the market price now at the start of the period ##(C_1/P_0)##. The expected income return of a premium fixed coupon bond is:
Your main expense is fuel for your car which costs $100 per month. You just refueled, so you won't need any more fuel for another month (first payment at t=1 month).
You have $2,500 in a bank account which pays interest at a rate of 6% pa, payable monthly. Interest rates are not expected to change.
Assuming that you have no income, in how many months time will you not have enough money to fully refuel your car?
Question 548 equivalent annual cash flow, time calculation, no explanation
An Apple iPhone 6 smart phone can be bought now for $999. An Android Kogan Agora 4G+ smart phone can be bought now for $240.
If the Kogan phone lasts for one year, approximately how long must the Apple phone last for to have the same equivalent annual cost?
Assume that both phones have equivalent features besides their lifetimes, that both are worthless once they've outlasted their life, the discount rate is 10% pa given as an effective annual rate, and there are no extra costs or benefits from either phone.
A 180day Bank Accepted Bill has a face value of $1,000,000. The interest rate is 8% pa and there are 365 days in the year. What is its price now?
Question 327 bill pricing, simple interest rate, no explanation
On 27/09/13, three month Swiss government bills traded at a yield of 0.2%, given as a simple annual yield. That is, interest rates were negative.
If the face value of one of these 90 day bills is CHF1,000,000 (CHF represents Swiss Francs, the Swiss currency), what is the price of one of these bills?
A credit card company advertises an interest rate of 18% pa, payable monthly. Which of the following statements about the interest rate is NOT correct? All rates are given to four decimal places.
Question 64 inflation, real and nominal returns and cash flows, APR, effective rate
In Germany, nominal yields on semiannual coupon paying Government Bonds with 2 years until maturity are currently 0.04% pa.
The inflation rate is currently 1.4% 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?
Question 25 bond pricing, zero coupon bond, term structure of interest rates, forward interest rate
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.
Question 108 bond pricing, zero coupon bond, term structure of interest rates, forward interest rate
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.
Question 572 bond pricing, zero coupon bond, term structure of interest rates, expectations hypothesis, forward interest rate, yield curve
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_{03})^3 = (1+r_{01})(1+r_{12})(1+r_{23}) ###
Which of the following statements is NOT correct?
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 semiannually. So there are two coupons per year, paid in arrears every six months.
For a price of $100, Vera will sell you a 2 year bond paying semiannual 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 $95, Nicole will sell you a 10 year bond paying semiannual 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.
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?
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?
Question 48 IRR, NPV, bond pricing, premium par and discount bonds, market efficiency
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 underpriced. Buying or selling a fairly priced asset has an NPV of zero.
Considering this, which of the following statements is NOT correct?
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 semiannually. What is its price?
Question 56 income and capital returns, bond pricing, premium par and discount bonds
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_1p_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.
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 underpriced. 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 semiannually. The bond's yield is currently 6% pa. The face value of the bond is $100. What is its 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?
Bonds X and Y are issued by different companies, but they both pay a semiannual coupon of 10% pa and they have the same face value ($100) and maturity (3 years).
The only difference is that bond X and Y's yields are 8 and 12% pa respectively. Which of the following statements is true?
Bonds X and Y are issued by different companies, but they both pay a semiannual 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 semiannually. What is its price?
Which of the following investable assets is the LEAST suitable for valuation using PE multiples techniques?
A mature firm has constant expected future earnings and dividends. Both amounts are equal. So earnings and dividends are expected to be equal and unchanging.
Which of the following statements is NOT correct?
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 backwardslooking priceearnings ratio?
A firm has 1 million shares which trade at a price of $30 each. The firm is expected to announce earnings of $3 million at the end of the year and pay an annual dividend of $1.50 per share.
What is the firm's (forward looking) price/earnings (PE) ratio?
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 backwardslooking priceearnings ratio?
A firm has 2m shares and a market capitalisation of equity of $30m. The firm just announced earnings of $5m and paid an annual dividend of $0.75 per share.
What is the firm's (backward looking) price/earnings (PE) ratio?
Estimate the French bank Societe Generale's share price using a backwardlooking price earnings (PE) multiples approach with the following assumptions and figures only. Note that EUR is the euro, the European monetary union's currency.
 The 4 major European banks Credit Agricole (ACA), Deutsche Bank AG (DBK), UniCredit (UCG) and Banco Santander (SAN) are comparable companies to Societe Generale (GLE);
 Societe Generale's (GLE's) historical earnings per share (EPS) is EUR 2.92;
 ACA's backwardlooking PE ratio is 16.29 and historical EPS is EUR 0.84;
 DBK's backwardlooking PE ratio is 25.01 and historical EPS is EUR 1.26;
 SAN's backwardlooking PE ratio is 14.71 and historical EPS is EUR 0.47;
 UCG's backwardlooking PE ratio is 15.78 and historical EPS is EUR 0.40;
Note: Figures sourced from Google Finance on 27 March 2015.
For certain shares, the forwardlooking PriceEarnings Ratio (##P_0/EPS_1##) is equal to the inverse of the share's total expected return (##1/r_\text{total}##).
For what shares is this true?
Assume:
 The general accounting definition of 'payout ratio' which is dividends per share (DPS) divided by earnings per share (EPS).
 All cash flows, earnings and rates are real.
Question 121 capital structure, leverage, costs of financial distress, interest tax shield
Fill in the missing words in the following sentence:
All things remaining equal, as a firm's amount of debt funding falls, benefits of interest tax shields __________ and the costs of financial distress __________.
A 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:
Question 536 idiom, bond pricing, capital structure, leverage
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?
A firm has a debttoassets ratio of 20%. What is its debttoequity ratio?
A firm has a debttoequity ratio of 60%. What is its debttoassets ratio?
A firm has a debttoequity ratio of 25%. What is its debttoassets ratio?
Question 241 Miller and Modigliani, leverage, payout policy, diversification, NPV
One of Miller and Modigliani's (M&M's) important insights is that a firm's managers should not try to achieve a particular level of leverage or interest tax shields under certain assumptions. So the firm's capital structure is irrelevant. This is because investors can make their own personal leverage and interest tax shields, so there's no need for managers to try to make corporate leverage and interest tax shields. This is true under the assumptions of equal tax rates, interest rates and debt availability for the person and the corporation, no transaction costs and symmetric information.
This principal of 'homemade' or 'doityourself' leverage can also be applied to other topics. Read the following statements to decide which are true:
(I) Payout policy: a firm's managers should not try to achieve a particular pattern of equity payout.
(II) Agency costs: a firm's managers should not try to minimise agency costs.
(III) Diversification: a firm's managers should not try to diversify across industries.
(IV) Shareholder wealth: a firm's managers should not try to maximise shareholders' wealth.
Which of the above statement(s) are true?
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.
Question 337 capital structure, interest tax shield, leverage, real and nominal returns and cash flows, multi stage growth model
A fastgrowing firm is suitable for valuation using a multistage 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 debttoequity 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?
What type of present value equation is best suited to value a residential house investment property that is expected to pay constant rental payments forever? Note that 'constant' has the same meaning as 'level' in this context.
Question 397 financial distress, leverage, capital structure, NPV
A levered firm has a market value of assets of $10m. Its debt is all comprised of zerocoupon bonds which mature in one year and have a combined face value of $9.9m.
Investors are riskneutral and therefore all debt and equity holders demand the same required return of 10% pa.
Therefore the current market capitalisation of debt ##(D_0)## is $9m and equity ##(E_0)## is $1m.
A new project presents itself which requires an investment of $2m and will provide a:
 $6.6m cash flow with probability 0.5 in the good state of the world, and a
 $4.4m (notice the negative sign) cash flow with probability 0.5 in the bad state of the world.
The project can be funded using the company's excess cash, no debt or equity raisings are required.
What would be the new market capitalisation of equity ##(E_\text{0, with project})## if shareholders vote to proceed with the project, and therefore should shareholders proceed with the project?
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).
Question 408 leverage, portfolio beta, portfolio risk, real estate, CAPM
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 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 debttoassets ratio that it sticks to.
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% aftertax weighted average cost of capital (WACC) before it bought Motorola.
 Motorola had a 20% aftertax 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:
Here are the Net Income (NI) and Cash Flow From Assets (CFFA) equations:
###NI=(RevCOGSFCDeprIntExp).(1t_c)###
###CFFA=NI+DeprCapEx  \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.
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=(RevCOGSFCDeprIntExp).(1t_c)###
###CFFA=NI+DeprCapEx  \varDelta NWC+IntExp###
For a firm with debt, what is the formula for the present value of interest tax shields if the tax shields occur in perpetuity?
You may assume:
 the value of debt (D) is constant through time,
 The cost of debt and the yield on debt are equal and given by ##r_D##.
 the appropriate rate to discount interest tax shields is ##r_D##.
 ##\text{IntExp}=D.r_D##
Which one of the following will increase the Cash Flow From Assets in this year for a taxpaying 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 taxpaying firm, all else remaining constant?
Remember:
###NI=(RevCOGSFCDeprIntExp).(1t_c )### ###CFFA=NI+DeprCapEx  ΔNWC+IntExp###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 allequity financed.
In fact the firm has a target debttoequity 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 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:
There are many ways to calculate a firm's free cash flow (FFCF), also called cash flow from assets (CFFA). Some include the annual interest tax shield in the cash flow and some do not.
Which of the below FFCF formulas include the interest tax shield in the cash flow?
###(1) \quad FFCF=NI + Depr  CapEx ΔNWC + IntExp### ###(2) \quad FFCF=NI + Depr  CapEx ΔNWC + IntExp.(1t_c)### ###(3) \quad FFCF=EBIT.(1t_c )+ Depr CapEx ΔNWC+IntExp.t_c### ###(4) \quad FFCF=EBIT.(1t_c) + Depr CapEx ΔNWC### ###(5) \quad FFCF=EBITDA.(1t_c )+Depr.t_c CapEx ΔNWC+IntExp.t_c### ###(6) \quad FFCF=EBITDA.(1t_c )+Depr.t_c CapEx ΔNWC### ###(7) \quad FFCF=EBITTax + Depr  CapEx ΔNWC### ###(8) \quad FFCF=EBITTax + Depr  CapEx ΔNWCIntExp.t_c### ###(9) \quad FFCF=EBITDATax  CapEx ΔNWC### ###(10) \quad FFCF=EBITDATax  CapEx ΔNWCIntExp.t_c###The formulas for net income (NI also called earnings), EBIT and EBITDA are given below. Assume that depreciation and amortisation are both represented by 'Depr' and that 'FC' represents fixed costs such as rent.
###NI=(Rev  COGS  Depr  FC  IntExp).(1t_c )### ###EBIT=Rev  COGS  FCDepr### ###EBITDA=Rev  COGS  FC### ###Tax =(Rev  COGS  Depr  FC  IntExp).t_c= \dfrac{NI.t_c}{1t_c}###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)(1t_c) + Depr  CapEx \Delta NWC + IntExp.t_c \\ &= (Rev  COGS  Depr  FC)(1t_c) + Depr  CapEx \Delta NWC + IntExp.t_c \\ \end{aligned} \\###
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)(1t_c) + Depr  CapEx \Delta NWC + IntExp \\ &= (Rev  COGS  Depr  FC  0)(1t_c) + Depr  CapEx \Delta NWC  0\\ \end{aligned}###
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)(1t_c) + Depr  CapEx \Delta NWC \\ \end{aligned} \\###
Question 413 CFFA, interest tax shield, depreciation 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).(1t_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 company has:
 10 million common shares outstanding, each trading at a price of $90.
 1 million preferred shares which have a face (or par) value of $100 and pay a constant dividend of 9% of par. They currently trade at a price of $120 each.
 Debentures that have a total face value of $60,000,000 and a yield to maturity of 6% per annum. They are publicly traded and their market price is equal to 90% of their face value.
 The riskfree rate is 5% and the market return is 10%.
 Market analysts estimate that the company's common stock has a beta of 1.2. The corporate tax rate is 30%.
What is the company's aftertax Weighted Average Cost of Capital (WACC)? Assume a classical tax system.
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 has a debttoassets ratio of 50%. The firm then issues a large amount of equity to raise money for new projects of similar systematic risk to the company's existing projects. Assume a classical tax system. Which statement is correct?
Question 99 capital structure, interest tax shield, Miller and Modigliani, trade off theory of capital structure
A firm changes its capital structure by issuing a large amount of debt and using the funds to repurchase shares. Its assets are unchanged.
Assume that:
 The firm and individual investors can borrow at the same rate and have the same tax rates.
 The firm's debt and shares are fairly priced and the shares are repurchased at the market price, not at a premium.
 There are no market frictions relating to debt such as asymmetric information or transaction costs.
 Shareholders wealth is measured in terms of utiliity. Shareholders are wealthmaximising and riskaverse. 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?
Question 370 capital budgeting, NPV, interest tax shield, WACC, CFFA
Project Data  
Project life  2 yrs  
Initial investment in equipment  $600k  
Depreciation of equipment per year  $250k  
Expected sale price of equipment at end of project  $200k  
Revenue per job  $12k  
Variable cost per job  $4k  
Quantity of jobs per year  120  
Fixed costs per year, paid at the end of each year  $100k  
Interest expense in first year (at t=1)  $16.091k  
Interest expense in second year (at t=2)  $9.711k  
Tax rate  30%  
Government treasury bond yield  5%  
Bank loan debt yield  6%  
Levered cost of equity  12.5%  
Market portfolio return  10%  
Beta of assets  1.24  
Beta of levered equity  1.5  
Firm's and project's debttoequity ratio  25%  
Notes
 The project will require an immediate purchase of $50k of inventory, which will all be sold at cost when the project ends. Current liabilities are negligible so they can be ignored.
Assumptions
 The debttoequity ratio will be kept constant throughout the life of the project. The amount of interest expense at the end of each period has been correctly calculated to maintain this constant debttoequity ratio. Note that interest expense is different in each year.
 Thousands are represented by 'k' (kilo).
 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 nominal. The inflation rate is 2% pa.
 All rates are given as effective annual rates.
 The 50% capital gains tax discount is not available since the project is undertaken by a firm, not an individual.
What is the net present value (NPV) of the project?
Value the following business project to manufacture a new product.
Project Data  
Project life  2 yrs  
Initial investment in equipment  $6m  
Depreciation of equipment per year  $3m  
Expected sale price of equipment at end of project  $0.6m  
Unit sales per year  4m  
Sale price per unit  $8  
Variable cost per unit  $5  
Fixed costs per year, paid at the end of each year  $1m  
Interest expense per year  0  
Tax rate  30%  
Weighted average cost of capital after tax per annum  10%  
Notes
 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.  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?
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=(RevCOGSFCDeprIntExp).(1t_c)###
###CFFA=NI+DeprCapEx  \varDelta NWC+IntExp###
For a firm with debt, what is the amount of the interest tax shield per year?
A new company's Firm Free Cash Flow (FFCF, same as CFFA) is forecast in the graph below.
To value the firm's assets, the terminal value needs to be calculated using the perpetuity with growth formula:
###V_{\text{terminal, }t1} = \dfrac{FFCF_{\text{terminal, }t}}{rg}###
Which point corresponds to the best time to calculate the terminal value?
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  $m  
Assets  
Current assets  220  180 
PPE  
Cost  300  340 
Accumul. depr.  60  40 
Carrying amount  240  300 
Total assets  460  480 
Liabilities  
Current liabilities  175  190 
Noncurrent liabilities  135  130 
Owners' equity  
Retained earnings  50  60 
Contributed equity  100  100 
Total L and OE  460  480 
Note: all figures are given in millions of dollars ($m).
Why is Capital Expenditure (CapEx) subtracted in the Cash Flow From Assets (CFFA) formula?
###CFFA=NI+DeprCapEx  \Delta NWC+IntExp###
Find Trademark Corporation's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.
Trademark Corp  
Income Statement for  
year ending 30th June 2013  
$m  
Sales  100  
COGS  25  
Operating expense  5  
Depreciation  20  
Interest expense  20  
Income before tax  30  
Tax at 30%  9  
Net income  21  
Trademark Corp  
Balance Sheet  
as at 30th June  2013  2012 
$m  $m  
Assets  
Current assets  120  80 
PPE  
Cost  150  140 
Accumul. depr.  60  40 
Carrying amount  90  100 
Total assets  210  180 
Liabilities  
Current liabilities  75  65 
Noncurrent liabilities  75  55 
Owners' equity  
Retained earnings  10  10 
Contributed equity  50  50 
Total L and OE  210  180 
Note: all figures are given in millions of dollars ($m).
Find UniBar Corp's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.
UniBar Corp  
Income Statement for  
year ending 30th June 2013  
$m  
Sales  80  
COGS  40  
Operating expense  15  
Depreciation  10  
Interest expense  5  
Income before tax  10  
Tax at 30%  3  
Net income  7  
UniBar Corp  
Balance Sheet  
as at 30th June  2013  2012 
$m  $m  
Assets  
Current assets  120  90 
PPE  
Cost  360  320 
Accumul. depr.  40  30 
Carrying amount  320  290 
Total assets  440  380 
Liabilities  
Current liabilities  110  60 
Noncurrent liabilities  190  180 
Owners' equity  
Retained earnings  95  95 
Contributed equity  45  45 
Total L and OE  440  380 
Note: all figures are given in millions of dollars ($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  $m  
Assets  
Current assets  240  230 
PPE  
Cost  420  400 
Accumul. depr.  50  35 
Carrying amount  370  365 
Total assets  610  595 
Liabilities  
Current liabilities  180  190 
Noncurrent liabilities  290  265 
Owners' equity  
Retained earnings  90  90 
Contributed equity  50  50 
Total L and OE  610  595 
Note: all figures are given in millions of dollars ($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  $m  
Assets  
Current assets  200  230 
PPE  
Cost  400  400 
Accumul. depr.  75  35 
Carrying amount  325  365 
Total assets  525  595 
Liabilities  
Current liabilities  150  205 
Noncurrent liabilities  235  250 
Owners' equity  
Retained earnings  100  100 
Contributed equity  40  40 
Total L and OE  525  595 
Note: all figures above and below are given in millions of dollars ($m).
A 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.
Find Scubar Corporation's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.
Scubar Corp  
Income Statement for  
year ending 30th June 2013  
$m  
Sales  200  
COGS  60  
Depreciation  20  
Rent expense  11  
Interest expense  19  
Taxable Income  90  
Taxes at 30%  27  
Net income  63  
Scubar Corp  
Balance Sheet  
as at 30th June  2013  2012 
$m  $m  
Inventory  60  50 
Trade debtors  19  6 
Rent paid in advance  3  2 
PPE  420  400 
Total assets  502  458 
Trade creditors  10  8 
Bond liabilities  200  190 
Contributed equity  130  130 
Retained profits  162  130 
Total L and OE  502  458 
Note: All figures are given in millions of dollars ($m).
The cash flow from assets was:
Which one of the following will decrease net income (NI) but increase cash flow from assets (CFFA) in this year for a taxpaying firm, all else remaining constant?
Remember:
###NI = (RevCOGSFCDeprIntExp).(1t_c )### ###CFFA=NI+DeprCapEx  \Delta NWC+IntExp###Find Sidebar Corporation's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.
Sidebar Corp  
Income Statement for  
year ending 30th June 2013  
$m  
Sales  405  
COGS  100  
Depreciation  34  
Rent expense  22  
Interest expense  39  
Taxable Income  210  
Taxes at 30%  63  
Net income  147  
Sidebar Corp  
Balance Sheet  
as at 30th June  2013  2012 
$m  $m  
Inventory  70  50 
Trade debtors  11  16 
Rent paid in advance  4  3 
PPE  700  680 
Total assets  785  749 
Trade creditors  11  19 
Bond liabilities  400  390 
Contributed equity  220  220 
Retained profits  154  120 
Total L and OE  785  749 
Note: All figures are given in millions of dollars ($m).
The cash flow from assets was:
Over the next year, the management of an unlevered company plans to:
 Achieve firm free cash flow (FFCF or CFFA) of $1m.
 Pay dividends of $1.8m
 Complete a $1.3m share buyback.
 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 taxpaying firm, all else remaining constant?
Remember:
###NI=(RevCOGSFCDeprIntExp).(1t_c )### ###CFFA=NI+DeprCapEx  ΔNWC+IntExp###Find ChingALings Corporation's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.
ChingALings 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  
ChingALings 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 buyback.
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  $m  
Assets  
Cash  30  29 
Accounts receivable  5  7 
Prepaid rent expense  1  0 
Inventory  50  46 
PPE  290  300 
Total assets  376  382 
Liabilities  
Trade payables  20  18 
Accrued gas expense  3  2 
Noncurrent liabilities  0  0 
Contributed equity  212  212 
Retained profits  136  150 
Asset revaluation reserve  5  0 
Total L and OE  376  382 
Note: all figures are given in millions of dollars ($m).
The firm's free cash flow over the 2014 financial year was:
Your friend is trying to find the net present value of a project. The project is expected to last for just one year with:
 a negative cash flow of $1 million initially (t=0), and
 a positive cash flow of $1.1 million in one year (t=1).
The project has a total required return of 10% pa due to its moderate level of undiversifiable risk.
Your friend is aware of the importance of opportunity costs and the time value of money, but he is unsure of how to find the NPV of the project.
He knows that the opportunity cost of investing the $1m in the project is the expected gain from investing the money in shares instead. Like the project, shares also have an expected return of 10% since they have moderate undiversifiable risk. This opportunity cost is $0.1m ##(=1m \times 10\%)## which occurs in one year (t=1).
He knows that the time value of money should be accounted for, and this can be done by finding the present value of the cash flows in one year.
Your friend has listed a few different ways to find the NPV which are written down below.
(I) ##1m + \dfrac{1.1m}{(1+0.1)^1} ##
(II) ##1m + \dfrac{1.1m}{(1+0.1)^1}  \dfrac{1m}{(1+0.1)^1} \times 0.1 ##
(III) ##1m + \dfrac{1.1m}{(1+0.1)^1}  \dfrac{1.1m}{(1+0.1)^1} \times 0.1 ##
(IV) ##1m + 1.1m  \dfrac{1.1m}{(1+0.1)^1} \times 0.1 ##
(V) ##1m + 1.1m  1.1m \times 0.1 ##
Which of the above calculations give the correct NPV? Select the most correct answer.
What is the net present value (NPV) of undertaking a fulltime Australian undergraduate business degree as an Australian citizen? Only include the cash flows over the duration of the degree, ignore any benefits or costs of the degree after it's completed.
Assume the following:
 The degree takes 3 years to complete and all students pass all subjects.
 There are 2 semesters per year and 4 subjects per semester.
 University fees per subject per semester are $1,277, paid at the start of each semester. Fees are expected to stay constant for the next 3 years.
 There are 52 weeks per year.
 The first semester is just about to start (t=0). The first semester lasts for 19 weeks (t=0 to 19).
 The second semester starts immediately afterwards (t=19) and lasts for another 19 weeks (t=19 to 38).
 The summer holidays begin after the second semester ends and last for 14 weeks (t=38 to 52). Then the first semester begins the next year, and so on.
 Working full time at the grocery store instead of studying fulltime pays $20/hr and you can work 35 hours per week. Wages are paid at the end of each week.
 Fulltime students can work fulltime during the summer holiday at the grocery store for the same rate of $20/hr for 35 hours per week. Wages are paid at the end of each week.
 The discount rate is 9.8% pa. All rates and cash flows are real. Inflation is expected to be 3% pa. All rates are effective annual.
The NPV of costs from undertaking the university degree is:
Find the cash flow from assets (CFFA) of the following project.
One Year Mining Project Data  
Project life  1 year  
Initial investment in building mine and equipment  $9m  
Depreciation of mine and equipment over the year  $8m  
Kilograms of gold mined at end of year  1,000  
Sale price per kilogram  $0.05m  
Variable cost per kilogram  $0.03m  
Beforetax cost of closing mine at end of year  $4m  
Tax rate  30%  
Note 1: Due to the project, the firm also anticipates finding some rare diamonds which will give beforetax 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 ecotourist resort for an aftertax 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.
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).
The hardest and most important aspect of business project valuation is the estimation of the:
A pharmaceutical firm has just discovered a valuable new drug. So far the news has been kept a secret.
The net present value of making and commercialising the drug is $200 million, but $600 million of bonds will need to be issued to fund the project and buy the necessary plant and equipment.
The firm will release the news of the discovery and bond raising to shareholders simultaneously in the same announcement. The bonds will be issued shortly after.
Once the announcement is made and the bonds are issued, what is the expected increase in the value of the firm's assets (ΔV), market capitalisation of debt (ΔD) and market cap of equity (ΔE)?
The triangle symbol is the Greek letter capital delta which means change or increase in mathematics.
Ignore the benefit of interest tax shields from having more debt.
Remember: ##ΔV = ΔD+ΔE##
The CAPM can be used to find a business's expected opportunity cost of capital:
###r_i=r_f+β_i (r_mr_f)###
What should be used as the risk free rate ##r_f##?
Which of the following is NOT a valid method to estimate future revenues or costs in a proforma income statement when trying to value a company?
A young lady is trying to decide if she should attend university or begin working straight away in her home town.
The young lady's grandma says that she should not go to university because she is less likely to marry the local village boy whom she likes because she will spend less time with him if she attends university.
What's the correct way to classify this item from a capital budgeting perspective when trying to decide whether to attend university?
The cost of not marrying the local village boy should be classified as:
The 'time value of money' is most closely related to which of the following concepts?
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 taxdeductible 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).
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 balance sheet needed? Note that the balance sheet is sometimes also called the statement of financial position.
Question 658 CFFA, income statement, balance sheet, no explanation
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.
Question 104 CAPM, payout policy, capital structure, Miller and Modigliani, risk
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, semistrong form efficient markets, the CAPM holds, investors are rational and riskaverse and there are no other market frictions.
For a firm operating in this perfect world, which statement(s) are correct?
(i) When a firm changes its capital structure and/or payout policy, share holders' wealth is unaffected.
(ii) When the idiosyncratic risk of a firm's assets increases, share holders do not expect higher returns.
(iii) When the systematic risk of a firm's assets increases, share holders do not expect higher returns.
Select the most correct response:
A 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?
Question 418 capital budgeting, NPV, interest tax shield, WACC, CFFA, CAPM
Project Data  
Project life  1 year  
Initial investment in equipment  $8m  
Depreciation of equipment per year  $8m  
Expected sale price of equipment at end of project  0  
Unit sales per year  4m  
Sale price per unit  $10  
Variable cost per unit  $5  
Fixed costs per year, paid at the end of each year  $2m  
Interest expense in first year (at t=1)  $0.562m  
Corporate tax rate  30%  
Government treasury bond yield  5%  
Bank loan debt yield  9%  
Market portfolio return  10%  
Covariance of levered equity returns with market  0.32  
Variance of market portfolio returns  0.16  
Firm's and project's debttoequity ratio  50%  
Notes
 Due to the project, current assets will increase by $6m now (t=0) and fall by $6m at the end (t=1). Current liabilities will not be affected.
Assumptions
 The debttoequity ratio will be kept constant throughout the life of the project. The amount of interest expense at the end of each period has been correctly calculated to maintain this constant debttoequity ratio.
 Millions are represented by 'm'.
 All cash flows occur at the start or end of the year as appropriate, not in the middle or throughout the year.
 All rates and cash flows are real. The inflation rate is 2% pa. All rates are given as effective annual rates.
 The project is undertaken by a firm, not an individual.
What is the net present value (NPV) of the project?
Question 419 capital budgeting, NPV, interest tax shield, WACC, CFFA, CAPM, no explanation
Project Data  
Project life  1 year  
Initial investment in equipment  $6m  
Depreciation of equipment per year  $6m  
Expected sale price of equipment at end of project  0  
Unit sales per year  9m  
Sale price per unit  $8  
Variable cost per unit  $6  
Fixed costs per year, paid at the end of each year  $1m  
Interest expense in first year (at t=1)  $0.53m  
Tax rate  30%  
Government treasury bond yield  5%  
Bank loan debt yield  6%  
Market portfolio return  10%  
Covariance of levered equity returns with market  0.08  
Variance of market portfolio returns  0.16  
Firm's and project's debttoassets ratio  50%  
Notes
 Due to the project, current assets will increase by $5m now (t=0) and fall by $5m at the end (t=1). Current liabilities will not be affected.
Assumptions
 The debttoassets ratio will be kept constant throughout the life of the project. The amount of interest expense at the end of each period has been correctly calculated to maintain this constant debttoequity ratio.
 Millions are represented by 'm'.
 All cash flows occur at the start or end of the year as appropriate, not in the middle or throughout the year.
 All rates and cash flows are real. The inflation rate is 2% pa.
 All rates are given as effective annual rates.
 The 50% capital gains tax discount is not available since the project is undertaken by a firm, not an individual.
What is the net present value (NPV) of the project?
There are a number of ways that assets can be depreciated. Generally the government's tax office stipulates a certain method.
But if it didn't, what would be the ideal way to depreciate an asset from the perspective of a businesses owner?
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 reinvestment of the firm's cash back into the business. All of the firm's excess cash flow is paid out as dividends so real growth is zero.
 The firm operates in a mature industry with zero real growth.
 All cash flows and rates in the below equations are real (not nominal) and are expected to be stable forever. Therefore the perpetuity equation with no growth is suitable for valuation.
Where:
###r_\text{WACC before tax} = r_D.\frac{D}{V_L} + r_{EL}.\frac{E_L}{V_L} = \text{Weighted average cost of capital before tax}### ###r_\text{WACC after tax} = r_D.(1t_c).\frac{D}{V_L} + r_{EL}.\frac{E_L}{V_L} = \text{Weighted average cost of capital after tax}### ###NI_L=(RevCOGSFCDepr\mathbf{IntExp}).(1t_c) = \text{Net Income Levered}### ###CFFA_L=NI_L+DeprCapEx  \varDelta NWC+\mathbf{IntExp} = \text{Cash Flow From Assets Levered}### ###NI_U=(RevCOGSFCDepr).(1t_c) = \text{Net Income Unlevered}### ###CFFA_U=NI_U+DeprCapEx  \varDelta NWC= \text{Cash Flow From Assets Unlevered}###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 taxpayer's pretax 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 pretax 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:
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 semistrong 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's weighted average cost of capital before tax (##r_\text{WACC before tax}##) would increase due to:
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?
Question 524 risk, expected and historical returns, bankruptcy or insolvency, capital structure, corporate financial decision theory, limited liability
Which of the following statements is NOT correct?
Question 566 capital structure, capital raising, rights issue, on market repurchase, dividend, stock split, bonus issue
A company's share price fell by 20% and its number of shares rose by 25%. Assume that there are no taxes, no signalling effects and no transaction costs.
Which one of the following corporate events may have happened?
A company conducts a 4 for 3 stock split. What is the percentage change in the stock price and the number of shares outstanding? The answers are given in the same order.
Question 568 rights issue, capital raising, capital structure
A company conducts a 1 for 5 rights issue at a subscription price of $7 when the preannouncement 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 has:
 50 million shares outstanding.
 The market price of one share is currently $6.
 The riskfree rate is 5% and the market return is 10%.
 Market analysts believe that the company's ordinary shares have a beta of 2.
 The company has 1 million preferred stock which have a face (or par) value of $100 and pay a constant dividend of 10% of par. They currently trade for $80 each.
 The company's debentures are publicly traded and their market price is equal to 90% of their face value.
 The debentures have a total face value of $60,000,000 and the current yield to maturity of corporate debentures is 10% per annum. The corporate tax rate is 30%.
What is the company's aftertax weighted average cost of capital (WACC)? Assume a classical tax system.
A company has:
 140 million shares outstanding.
 The market price of one share is currently $2.
 The company's debentures are publicly traded and their market price is equal to 93% of the face value.
 The debentures have a total face value of $50,000,000 and the current yield to maturity of corporate debentures is 12% per annum.
 The riskfree 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 aftertax weighted average cost of capital (WACC) in a classical tax system?
A firm can issue 3 year annual coupon bonds at a yield of 10% pa and a coupon rate of 8% pa.
The beta of its levered equity is 2. The market's expected return is 10% pa and 3 year government bonds yield 6% pa with a coupon rate of 4% pa.
The market value of equity is $1 million and the market value of debt is $1 million. The corporate tax rate is 30%.
What is the firm's aftertax WACC? Assume a classical tax system.
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 debttoequity ratio is 2:1. The corporate tax rate is 30%.
What is the firm's aftertax WACC? Assume a classical tax system.
A company has:
 100 million ordinary shares outstanding which are trading at a price of $5 each. Market analysts estimated that the company's ordinary stock has a beta of 1.5. The riskfree rate is 5% and the market return is 10%.
 1 million preferred shares which have a face (or par) value of $100 and pay a constant annual dividend of 9% of par. The next dividend will be paid in one year. Assume that all preference dividends will be paid when promised. They currently trade at a price of $90 each.
 Debentures that have a total face value of $200 million and a yield to maturity of 6% per annum. They are publicly traded and their market price is equal to 110% of their face value.
The corporate tax rate is 30%. All returns and yields are given as effective annual rates.
What is the company's aftertax Weighted Average Cost of Capital (WACC)? Assume a classical tax system.
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:
Diversification is achieved by investing in a large amount of stocks. What type of risk is reduced by diversification?
Stock A and B's returns have a correlation of 0.3. Which statement is NOT correct?
Diversification in a portfolio of two assets works best when the correlation between their returns is:
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?
Portfolio Details  
Stock  Expected return 
Standard deviation 
Correlation  Beta  Dollars invested 

A  0.2  0.4  0.12  0.5  40  
B  0.3  0.8  1.5  80  
What is the beta of the above portfolio?
Stock A has a beta of 0.5 and stock B has a beta of 1. Which statement is NOT correct?
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 fairly priced stock has an expected return of 15% pa. Treasury bonds yield 5% pa and the market portfolio's expected return is 10% pa. What is the beta of the stock?
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?
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?
The security market line (SML) shows the relationship between beta and expected return.
Investment projects that plot above the SML would have:
A fairly priced stock has a beta that is the same as the market portfolio's beta. Treasury bonds yield 5% pa and the market portfolio's expected return is 10% pa. What is the expected return of the stock?
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?
A stock's required total return will increase when its:
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?
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?
Question 235 SML, NPV, CAPM, risk
The security market line (SML) shows the relationship between beta and expected return.
Investment projects that plot on the SML would have:
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?
Government bonds currently have a return of 5%. A stock has a beta of 2 and the market return is 7%. What is the expected return of the stock?
Question 244 CAPM, SML, NPV, risk
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?
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?
Question 556 portfolio risk, portfolio return, standard deviation
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?
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?
Question 558 portfolio weights, portfolio return, short selling
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?
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.
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?
All things remaining equal, the variance of a portfolio of two positivelyweighted stocks rises as:
Two risky stocks A and B comprise an equalweighted 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?
Which of the following statements about shortselling is NOT true?
You believe that the price of a share will fall significantly very soon, but the rest of the market does not. The market thinks that the share price will remain the same. Assuming that your prediction will soon be true, which of the following trades is a bad idea? In other words, which trade will NOT make money or prevent losses?
After doing extensive fundamental analysis of a company, you believe that their shares are overpriced and will soon fall significantly. The market believes that there will be no such fall.
Which of the following strategies is NOT a good idea, assuming that your prediction is true?
Question 589 future, contango, market efficiency
In general, stock prices tend to rise. What does this mean?
Let the variance of returns for a share per month be ##\sigma_\text{monthly}^2##.
What is the formula for the variance of the share's returns per year ##(\sigma_\text{yearly}^2)##?
Assume that returns are independently and identically distributed (iid) so they have zero auto correlation, meaning that if the return was higher than average today, it does not indicate that the return tomorrow will be higher or lower than average.
Question 308 risk, standard deviation, variance, no explanation
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 autocorrelation.
Question 559 variance, standard deviation, covariance, correlation
Which of the following statements about standard statistical mathematics notation is NOT correct?
The standard deviation and variance of a stock's annual returns are calculated over a number of years. The units of the returns are percent per annum ##(\% pa)##.
What are the units of the standard deviation ##(\sigma)## and variance ##(\sigma^2)## of returns respectively?
Hint: Visit Wikipedia to understand the difference between percentage points ##(\text{pp})## and percent ##(\%)##.
Which of the following is NOT a valid method for estimating the beta of a company's stock? Assume that markets are efficient, a long history of past data is available, the stock possesses idiosyncratic and market risk. The variances and standard deviations below denote total risks.
What is the correlation of a variable X with itself?
The corr(X, X) or ##\rho_{X,X}## equals:
The following is the Dividend Discount Model used to price stocks:
### p_0=\frac{d_1}{rg} ###
Which of the following statements about the Dividend Discount Model is NOT correct?
All things remaining equal, the higher the correlation of returns between two stocks:
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.
High risk firms in danger of bankruptcy tend to have:
An economy has only two investable assets: stocks and cash.
Stocks had a historical nominal average total return of negative two percent per annum (2% pa) over the last 20 years. Stocks are liquid and actively traded. Stock returns are variable, they have risk.
Cash is riskless and has a nominal constant return of zero percent per annum (0% pa), which it had in the past and will have in the future. Cash can be kept safely at zero cost. Cash can be converted into shares and vice versa at zero cost.
The nominal total return of the shares over the next year is expected to be:
Three important classes of investable risky assets are:
 Corporate debt which has low total risk,
 Real estate which has medium total risk,
 Equity which has high total risk.
Assume that the correlation between total returns on:
 Corporate debt and real estate is 0.1,
 Corporate debt and equity is 0.1,
 Real estate and equity is 0.5.
You are considering investing all of your wealth in one or more of these asset classes. Which portfolio will give the lowest total risk? You are restricted from shorting any of these assets. Disregard returns and the riskreturn tradeoff, pretend that you are only concerned with minimising risk.
The covariance and correlation of two stocks X and Y's annual returns are calculated over a number of years. The units of the returns are in percent per annum ##(\% pa)##.
What are the units of the covariance ##(\sigma_{X,Y})## and correlation ##(\rho_{X,Y})## of returns respectively?
Hint: Visit Wikipedia to understand the difference between percentage points ##(\text{pp})## and percent ##(\%)##.
The following table shows a sample of historical total returns of shares in two different companies A and B.
Stock Returns  
Total effective annual returns  
Year  ##r_A##  ##r_B## 
2007  0.2  0.4 
2008  0.04  0.2 
2009  0.1  0.3 
2010  0.18  0.5 
What is the historical sample covariance (##\hat{\sigma}_{A,B}##) and correlation (##\rho_{A,B}##) of stock A and B's total effective annual returns?
A person is thinking about borrowing $100 from the bank at 7% pa and investing it in shares with an expected return of 10% pa. One year later the person will sell the shares and pay back the loan in full. Both the loan and the shares are fairly priced.
What is the Net Present Value (NPV) of this one year investment? Note that you are asked to find the present value (##V_0##), not the value in one year (##V_1##).
The 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?
Mr Blue, Miss Red and Mrs Green are people with different utility functions. Which of the statements about the 3 utility functions is NOT correct?
Mr Blue, Miss Red and Mrs Green are people with different utility functions.
Which of the following statements is NOT correct?
Mr Blue, Miss Red and Mrs Green are people with different utility functions. Which of the statements about the 3 utility functions is NOT correct?
Mr Blue, Miss Red and Mrs Green are people with different utility functions. Which of the statements about the 3 utility functions is NOT correct?
A company conducts a 10 for 3 stock split. What is the percentage increase in the stock price and the number of shares outstanding? The answers are given in the same order.
Question 469 franking credit, personal tax on dividends, imputation tax system, no explanation
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?
Question 448 franking credit, personal tax on dividends, imputation 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 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 625 dividend reinvestment plan, capital raising
Which of the following statements about dividend reinvestment plans (DRP's) is NOT correct?
Due to floods overseas, there is a cut in the supply of the mineral iron ore and its price increases dramatically. An Australian iron ore mining company therefore expects a large but temporary increase in its profit and cash flows. The mining company does not have any positive NPV projects to begin, so what should it do? Select the most correct answer.
Question 550 fully amortising loan, interest only loan, APR, no explanation
Many Australian home loans that are interestonly actually require payments to be made on a fully amortising basis after a number of years.
You decide to borrow $600,000 from the bank at an interest rate of 4.25% pa for 25 years. The payments will be interestonly for the first 10 years (t=0 to 10 years), then they will have to be paid on a fully amortising basis for the last 15 years (t=10 to 25 years).
Assuming that interest rates will remain constant, what will be your monthly payments for the next 10 years from now, and then the next 15 years after that? The answer options are given in the same order.
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 interestonly 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.
Select the most correct statement from the following.
'Chartists', also known as 'technical traders', believe that:
Question 668 buy and hold, market efficiency, idiom
A quote from the famous investor Warren Buffet: "Much success can be attributed to inactivity. Most investors cannot resist the temptation to constantly buy and sell."
Buffet is referring to the buyandhold strategy which is to buy and never sell shares. Which of the following is a disadvantage of a buyandhold strategy? Assume that share markets are semistrong form efficient. Which of the following is NOT an advantage of the strict buyandhold strategy? A disadvantage of the buyandhold strategy is that it reduces:
The efficient markets hypothesis (EMH) and noarbitrage pricing theory is most closely related to which of the following concepts?
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. Of the 15% pa total expected return, the dividend yield is expected to always be 7% pa and rest is the capital yield.
Assuming 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 reinvested 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):
Question 339 bond pricing, inflation, market efficiency, income and capital returns
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 fixedcoupon 2year riskfree 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 (aftertax) value of the coupon the night before the excoupon date, as in real life.
Question 119 market efficiency, fundamental analysis, joint hypothesis problem
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) Semistrong 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 (misspecification 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:
A firm wishes to raise $10 million now. They will issue 6% pa semiannual 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?
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?
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 20142015 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 beforetax?
In 2014 the median starting salaries of male and female Australian bachelor degree accounting graduates aged less than 25 years in their first fulltime 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 20142015 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 beforetax?
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:
Currently, a mining company has a share price of $6 and pays constant annual dividends of $0.50. The next dividend will be paid in 1 year. Suddenly and unexpectedly the mining company announces that due to higher than expected profits, all of these windfall profits will be paid as a special dividend of $0.30 in 1 year.
If investors believe that the windfall profits and dividend is a oneoff event, what will be the new share price? If investors believe that the additional dividend is actually permanent and will continue to be paid, what will be the new share price? Assume that the required return on equity is unchanged. Choose from the following, where the first share price includes the oneoff increase in earnings and dividends for the first year only ##(P_\text{0 oneoff})## , and the second assumes that the increase is permanent ##(P_\text{0 permanent})##:
Note: When a firm makes excess profits they sometimes pay them out as special dividends. Special dividends are just like ordinary dividends but they are oneoff and investors do not expect them to continue, unlike ordinary dividends which are expected to persist.
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 approximate payout ratio over the 2014 financial year?
Note that the firm's interim and final dividends were $1.83 and $2.18 respectively over the 2014 financial year.
In late 2003 the listed bank ANZ announced a 2for11 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. 2for11 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 cumrights. Share price opens at $18.00 and closes at $18.14.
 29/10/2003. Shares trade exrights.
All things remaining equal, what would you expect ANZ's stock price to open at on the first day that it trades exrights (29/10/2003)? Ignore the time value of money since time is negligibly short. Also ignore taxes.
Question 345 capital budgeting, break even, NPV
Project Data  
Project life  10 yrs  
Initial investment in factory  $10m  
Depreciation of factory per year  $1m  
Expected scrap value of factory at end of project  $0  
Sale price per unit  $10  
Variable cost per unit  $6  
Fixed costs per year, paid at the end of each year  $2m  
Interest expense per year  0  
Tax rate  30%  
Cost of capital per annum  10%  
Notes
 The firm's current liabilities are forecast to stay at $0.5m. The firm's current assets (mostly inventory) is currently $1m, but is forecast to grow by $0.1m at the end of each year due to the project.
At the end of the project, the current assets accumulated due to the project can be sold for the same price that they were bought.  A marketing survey was used to forecast sales. It cost $1.4m which was just paid. The cost has been capitalised by the accountants and is taxdeductible over the life of the project, regardless of whether the project goes ahead or not. This amortisation expense is not included in the depreciation expense listed in the table above.
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.
Find the break even unit production (Q) per year to achieve a zero Net Income (NI) and Net Present Value (NPV), respectively. The answers below are listed in the same order.
The current gold price is $700, gold storage costs are 2% pa and the risk free rate is 10% pa, both with continuous compounding.
What should be the 3 year gold futures price?
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 one year?
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?
Question 691 continuously compounding rate, effective rate, continuously compounding rate conversion, no explanation
A bank quotes an interest rate of 6% pa with quarterly compounding. Note that another way of stating this rate is that it is an annual percentage rate (APR) compounding discretely every 3 months.
Which of the following statements about this rate is NOT correct? All percentages are given to 6 decimal places. The equivalent:
In the dividend discount model:
### P_0= \frac{d_1}{rg} ###
The pronumeral ##g## is supposed to be the:
Question 579 price gains and returns over time, time calculation, effective rate
How many years will it take for an asset's price to double if the price grows by 10% pa?
Question 282 expected and historical returns, income and capital returns
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 highgrowth 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.
Assume that:
 The analysts' source data is correct and true, but their inferences might be wrong;
 All returns and yields are given as effective annual nominal rates.
Question 659 APR, effective rate, effective rate conversion, no explanation
A home loan company advertises an interest rate of 9% pa, payable monthly. Which of the following statements about the interest rate is NOT correct? All rates are given with an accuracy of 4 decimal places.
You just entered into a fully amortising home loan with a principal of $600,000, a variable interest rate of 4.25% pa and a term of 25 years.
Immediately after settling the loan, the variable interest rate suddenly falls to 4% pa! You can't believe your luck. Despite this, you plan to continue paying the same home loan payments as you did before. How long will it now take to pay off your home loan?
Assume that the lower interest rate was granted immediately and that rates were and are now again expected to remain constant. Round your answer up to the nearest whole month.
Which one of the below statements about effective rates and annualised percentage rates (APR's) is NOT correct?
A 2 year corporate bond yields 3% pa with a coupon rate of 5% pa, paid semiannually.
Find the effective monthly rate, effective six month rate, and effective annual rate.
##r_\text{eff monthly}##, ##r_\text{eff 6 month}##, ##r_\text{eff annual}##.
You just started work at your new job which pays $48,000 per year.
The human resources department have given you the option of being paid at the end of every week or every month.
Assume that there are 4 weeks per month, 12 months per year and 48 weeks per year.
Bank interest rates are 12% pa given as an APR compounding per month.
What is the dollar gain over one year, as a net present value, of being paid every week rather than every month?
Harvey Norman the large retailer often runs sales advertising 2 years interest free when you purchase its products. This offer can be seen as a free personal loan from Harvey Norman to its customers.
Assume that banks charge an interest rate on personal loans of 12% pa given as an APR compounding per month. This is the interest rate that Harvey Norman deserves on the 2 year loan it extends to its customers. Therefore Harvey Norman must implicitly include the cost of this loan in the advertised sale price of its goods.
If you were a customer buying from Harvey Norman, and you were paying immediately, not in 2 years, what is the minimum percentage discount to the advertised sale price that you would insist on? (Hint: if it makes it easier, assume that you’re buying a product with an advertised price of $100).
A three year corporate bond yields 12% pa with a coupon rate of 10% pa, paid semiannually.
Find the effective six month yield, effective annual yield and the effective daily yield. Assume that each month has 30 days and that there are 360 days in a year.
All answers are given in the same order:
##r_\text{eff semiannual}##, ##r_\text{eff yearly}##, ##r_\text{eff daily}##.
A student just won the lottery. She won $1 million in cash after tax. She is trying to calculate how much she can spend per month for the rest of her life. She assumes that she will live for another 60 years. She wants to withdraw equal amounts at the beginning of every month, starting right now.
All of the cash is currently sitting in a bank account which pays interest at a rate of 6% pa, given as an APR compounding per month. On her last withdrawal, she intends to have nothing left in her bank account. How much can she withdraw at the beginning of each month?
Your credit card shows a $600 debt liability. The interest rate is 24% pa, payable monthly. You can't pay any of the debt off, except in 6 months when it's your birthday and you'll receive $50 which you'll use to pay off the credit card. If that is your only repayment, how much will the credit card debt liability be one year from now?
Your friend wants to borrow $1,000 and offers to pay you back $100 in 6 months, with more $100 payments at the end of every month for another 11 months. So there will be twelve $100 payments in total. She says that 12 payments of $100 equals $1,200 so she's being generous.
If interest rates are 12% pa, given as an APR compounding monthly, what is the Net Present Value (NPV) of your friend's deal?
Question 700 utility, risk aversion, utility function, gamble
Mr Blue, Miss Red and Mrs Green are people with different utility functions.
Each person has $50 of initial wealth. A coin toss game is offered to each person at a casino where the player can win or lose $50. Each player can flip a coin and if they flip heads, they receive $50. If they flip tails then they will lose $50. Which of the following statements is NOT correct?
Question 701 utility, risk aversion, utility function, gamble
Mr Blue, Miss Red and Mrs Green are people with different utility functions.
Each person has $50 of initial wealth. A coin toss game is offered to each person at a casino where the player can win or lose $50. Each player can flip a coin and if they flip heads, they receive $50. If they flip tails then they will lose $50. Which of the following statements is NOT correct?
Question 702 utility, risk aversion, utility function, gamble
Mr Blue, Miss Red and Mrs Green are people with different utility functions.
Each person has $50 of initial wealth. A coin toss game is offered to each person at a casino where the player can win or lose $50. Each player can flip a coin and if they flip heads, they receive $50. If they flip tails then they will lose $50. Which of the following statements is NOT correct?
Question 703 utility, risk aversion, utility function, gamble
Mr Blue, Miss Red and Mrs Green are people with different utility functions.
Each person has $500 of initial wealth. A coin toss game is offered to each person at a casino where the player can win or lose $500. Each player can flip a coin and if they flip heads, they receive $500. If they flip tails then they will lose $500. Which of the following statements is NOT correct?
Question 704 utility, risk aversion, utility function, gamble
Mr Blue, Miss Red and Mrs Green are people with different utility functions.
Each person has $256 of initial wealth. A coin toss game is offered to each person at a casino where the player can win or lose $256. Each player can flip a coin and if they flip heads, they receive $256. If they flip tails then they will lose $256. Which of the following statements is NOT correct?
A stock is expected to pay the following dividends:
Cash Flows of a Stock  
Time (yrs)  0  1  2  3  4  ... 
Dividend ($)  0.00  1.15  1.10  1.05  1.00  ... 
After year 4, the annual dividend will grow in perpetuity at 5% pa. Note that this is a negative growth rate, so the dividend will actually shrink. So,
 the dividend at t=5 will be ##$1(10.05) = $0.95##,
 the dividend at t=6 will be ##$1(10.05)^2 = $0.9025##, and so on.
The required return on the stock is 10% pa. Both the growth rate and required return are given as effective annual rates.
What is the current price of the stock?
A stock is expected to pay the following dividends:
Cash Flows of a Stock  
Time (yrs)  0  1  2  3  4  ... 
Dividend ($)  0.00  1.15  1.10  1.05  1.00  ... 
After year 4, the annual dividend will grow in perpetuity at 5% pa. Note that this is a negative growth rate, so the dividend will actually shrink. So,
 the dividend at t=5 will be ##$1(10.05) = $0.95##,
 the dividend at t=6 will be ##$1(10.05)^2 = $0.9025##, and so on.
The required return on the stock is 10% pa. Both the growth rate and required return are given as effective annual rates.
What will be the price of the stock in four and a half years (t = 4.5)?
A stock pays annual dividends. It just paid a dividend of $3. The growth rate in the dividend is 4% pa. You estimate that the stock's required return is 10% pa. Both the discount rate and growth rate are given as effective annual rates. Using the dividend discount model, what will be the share price?
A stock pays annual dividends. It just paid a dividend of $5. The growth rate in the dividend is 1% pa. You estimate that the stock's required return is 8% pa. Both the discount rate and growth rate are given as effective annual rates.
Using the dividend discount model, what will be the share price?
A share pays annual dividends. It just paid a dividend of $2. The growth rate in the dividend is 3% pa. You estimate that the stock's required return is 8% pa. Both the discount rate and growth rate are given as effective annual rates.
Using the dividend discount model, what is the share price?
A share just paid its semiannual dividend of $5. The dividend is expected to grow at 1% every 6 months forever. This 1% growth rate is an effective 6 month rate.
Therefore the next dividend will be $5.05 in six months. The required return of the stock 8% pa, given as an effective annual rate.
What is the price of the share now?
Stocks in the United States usually pay quarterly dividends. For example, the retailer WalMart Stores paid a $0.47 dividend every quarter over the 2013 calendar year and plans to pay a $0.48 dividend every quarter over the 2014 calendar year.
Using the dividend discount model and net present value techniques, calculate the stock price of WalMart Stores assuming that:
 The time now is the beginning of January 2014. The next dividend of $0.48 will be received in 3 months (end of March 2014), with another 3 quarterly payments of $0.48 after this (end of June, September and December 2014).
 The quarterly dividend will increase by 2% every year, but each quarterly dividend over the year will be equal. So each quarterly dividend paid in 2015 will be $0.4896 (##=0.48×(1+0.02)^1##), with the first at the end of March 2015 and the last at the end of December 2015. In 2016 each quarterly dividend will be $0.499392 (##=0.48×(1+0.02)^2##), with the first at the end of March 2016 and the last at the end of December 2016, and so on forever.
 The total required return on equity is 6% pa.
 The required return and growth rate are given as effective annual rates.
 All cash flows and rates are nominal. Inflation is 3% pa.
 Dividend payment dates and exdividend dates are at the same time.
 Remember that there are 4 quarters in a year and 3 months in a quarter.
What is the current stock price?
Stocks in the United States usually pay quarterly dividends. For example, the software giant Microsoft paid a $0.23 dividend every quarter over the 2013 financial year and plans to pay a $0.28 dividend every quarter over the 2014 financial year.
Using the dividend discount model and net present value techniques, calculate the stock price of Microsoft assuming that:
 The time now is the beginning of July 2014. The next dividend of $0.28 will be received in 3 months (end of September 2014), with another 3 quarterly payments of $0.28 after this (end of December 2014, March 2015 and June 2015).
 The quarterly dividend will increase by 2.5% every year, but each quarterly dividend over the year will be equal. So each quarterly dividend paid in the financial year beginning in September 2015 will be $ 0.287 ##(=0.28×(1+0.025)^1)##, with the last at the end of June 2016. In the next financial year beginning in September 2016 each quarterly dividend will be $0.294175 ##(=0.28×(1+0.025)^2)##, with the last at the end of June 2017, and so on forever.
 The total required return on equity is 6% pa.
 The required return and growth rate are given as effective annual rates.
 Dividend payment dates and exdividend dates are at the same time.
 Remember that there are 4 quarters in a year and 3 months in a quarter.
What is the current stock price?
A share currently worth $100 is expected to pay a constant dividend of $4 for the next 5 years with the first dividend in one year (t=1) and the last in 5 years (t=5).
The total required return is 10% pa.
What do you expected the share price to be in 5 years, just after the dividend at that time has been paid?
The following cash flows are expected:
 Constant perpetual yearly payments of $70, with the first payment in 2.5 years from now (first payment at t=2.5).
 A single payment of $600 in 3 years and 9 months (t=3.75) from now.
What is the NPV of the cash flows if the discount rate is 10% given as an effective annual rate?
Question 529 DDM, real and nominal returns and cash flows, inflation, real estate, no explanation
If housing rents are constrained from growing more than the maximum target inflation rate, and houses can be priced as a perpetuity of growing net rental cash flows, then what is the implication for house prices, all things remaining equal? Select the most correct answer.
Background: Since 1990, many central banks across the world have become 'inflation targeters'. They have adopted a policy of trying to keep inflation in a predictable narrow range, with the hope of encouraging longterm lending to fund more investment and maintain higher GDP growth.
Australia's central bank, the Reserve Bank of Australia (RBA), has specifically stated their inflation target range is between 2 and 3% pa.
Some Australian residential property market commentators suggest that because rental costs comprise a large part of the Australian consumer price index (CPI), rent costs across the nation cannot significantly exceed the maximum inflation target range of 3% pa without the prices of other goods growing by less than the target range for long periods, which is unlikely.
For a price of $129, Joanne will sell you a share which is expected to pay a $30 dividend in one year, and a $10 dividend every year after that forever. So the stock's dividends will be $30 at t=1, $10 at t=2, $10 at t=3, and $10 forever onwards.
The required return of the stock is 10% pa.
The phone company Telstra have 2 mobile service plans on offer which both have the same amount of phone call, text message and internet data credit. Both plans have a contract length of 24 months and the monthly cost is payable in advance. The only difference between the two plans is that one is a:
 'Bring Your Own' (BYO) mobile service plan, costing $50 per month. There is no phone included in this plan. The other plan is a:
 'Bundled' mobile service plan that comes with the latest smart phone, costing $71 per month. This plan includes the latest smart phone.
Neither plan has any additional payments at the start or end.
The only difference between the plans is the phone, so what is the implied cost of the phone as a present value?
Assume that the discount rate is 2% per month given as an effective monthly rate, the same high interest rate on credit cards.
In Australia, domestic university students are allowed to buy concession tickets for the bus, train and ferry which sell at a discount of 50% to fullprice tickets.
The Australian Government do not allow international university students to buy concession tickets, they have to pay the full price.
Some international students see this as unfair and they are willing to pay for fake university identification cards which have the concession sticker.
What is the most that an international student would be willing to pay for a fake identification card?
Assume that international students:
 consider buying their fake card on the morning of the first day of university from their neighbour, just before they leave to take the train into university.
 buy their weekly train tickets on the morning of the first day of each week.
 ride the train to university and back home again every day seven days per week until summer holidays 40 weeks from now. The concession card only lasts for those 40 weeks. Assume that there are 52 weeks in the year for the purpose of interest rate conversion.
 a single fullpriced oneway train ride costs $5.
 have a discount rate of 11% pa, given as an effective annual rate.
Approach this question from a purely financial view point, ignoring the illegality, embarrassment and the morality of committing fraud.
A project has an internal rate of return (IRR) which is greater than its required return. Select the most correct statement.
A text book publisher is thinking of asking some teachers to write a new textbook at a cost of $100,000, payable now. The book would be written, printed and ready to sell to students in 2 years. It will be ready just before semester begins.
A cash flow of $100 would be made from each book sold, after all costs such as printing and delivery. There are 600 students per semester. Assume that every student buys a new text book. Remember that there are 2 semesters per year and students buy text books at the beginning of the semester.
Assume that text book publishers will sell the books at the same price forever and that the number of students is constant.
If the discount rate is 8% pa, given as an effective annual rate, what is the NPV of the project?
The following cash flows are expected:
 10 yearly payments of $80, with the first payment in 3 years from now (first payment at t=3).
 1 payment of $600 in 5 years and 6 months (t=5.5) from now.
What is the NPV of the cash flows if the discount rate is 10% given as an effective annual rate?
A project's net present value (NPV) is negative. Select the most correct statement.
A stock is expected to pay the following dividends:
Cash Flows of a Stock  
Time (yrs)  0  1  2  3  4  ... 
Dividend ($)  8  8  8  20  8  ... 
After year 4, the dividend will grow in perpetuity at 4% pa. The required return on the stock is 10% pa. Both the growth rate and required return are given as effective annual rates.
What is the current price of the stock?
A stock is expected to pay the following dividends:
Cash Flows of a Stock  
Time (yrs)  0  1  2  3  4  ... 
Dividend ($)  8  8  8  20  8  ... 
After year 4, the dividend will grow in perpetuity at 4% pa. The required return on the stock is 10% pa. Both the growth rate and required return are given as effective annual rates.
What will be the price of the stock in 5 years (t = 5), just after the dividend at that time has been paid?
A stock is expected to pay the following dividends:
Cash Flows of a Stock  
Time (yrs)  0  1  2  3  4  ... 
Dividend ($)  2  2  2  10  3  ... 
After year 4, the dividend will grow in perpetuity at 4% pa. The required return on the stock is 10% pa. Both the growth rate and required return are given as effective annual rates.
What is the current price of the stock?
A stock is expected to pay the following dividends:
Cash Flows of a Stock  
Time (yrs)  0  1  2  3  4  ... 
Dividend ($)  2  2  2  10  3  ... 
After year 4, the dividend will grow in perpetuity at 4% pa. The required return on the stock is 10% pa. Both the growth rate and required return are given as effective annual rates.
What will be the price of the stock in 5 years (t = 5), just after the dividend at that time has been paid?
A project's Profitability Index (PI) is less than 1. Select the most correct statement:
A stock is expected to pay the following dividends:
Cash Flows of a Stock  
Time (yrs)  0  1  2  3  4  ... 
Dividend ($)  0  6  12  18  20  ... 
After year 4, the dividend will grow in perpetuity at 5% pa. The required return of the stock is 10% pa. Both the growth rate and required return are given as effective annual rates.
What is the current price of the stock?
A stock is expected to pay the following dividends:
Cash Flows of a Stock  
Time (yrs)  0  1  2  3  4  ... 
Dividend ($)  0  6  12  18  20  ... 
After year 4, the dividend will grow in perpetuity at 5% pa. The required return of the stock is 10% pa. Both the growth rate and required return are given as effective annual rates.
What will be the price of the stock in 7 years (t = 7), just after the dividend at that time has been paid?
A stock is expected to pay the following dividends:
Cash Flows of a Stock  
Time (yrs)  0  1  2  3  4  ... 
Dividend ($)  0  6  12  18  20  ... 
After year 4, the dividend will grow in perpetuity at 5% pa. The required return of the stock is 10% pa. Both the growth rate and required return are given as effective annual rates.
If all of the dividends since time period zero were deposited into a bank account yielding 8% pa as an effective annual rate, how much money will be in the bank account in 2.5 years (in other words, at t=2.5)?
Question 218 NPV, IRR, profitability index, average accounting return
Which of the following statements is NOT correct?
Your neighbour asks you for a loan of $100 and offers to pay you back $120 in one year.
You don't actually have any money right now, but you can borrow and lend from the bank at a rate of 10% pa. Rates are given as effective annual rates.
Assume that your neighbour will definitely pay you back. Ignore interest tax shields and transaction costs.
The Net Present Value (NPV) of lending to your neighbour is $9.09. Describe what you would do to actually receive a $9.09 cash flow right now with zero net cash flows in the future.
You have $100,000 in the bank. The bank pays interest at 10% pa, given as an effective annual rate.
You wish to consume an equal amount now (t=0), 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?
Your poor friend asks to borrow some money from you. He would like $1,000 now (t=0) and every year for the next 5 years, so there will be 6 payments of $1,000 from t=0 to t=5 inclusive. In return he will pay you $10,000 in seven years from now (t=7).
What is the net present value (NPV) of lending to your friend?
Assume that your friend will definitely pay you back so the loan is riskfree, and that the yield on riskfree government debt is 10% pa, given as an effective annual rate.
A firm is considering a business project which costs $10m now and is expected to pay a single cash flow of $12.1m in two years.
Assume that the initial $10m cost is funded using the firm's existing cash so no new equity or debt will be raised. The cost of capital is 10% pa.
Which of the following statements about net present value (NPV), internal rate of return (IRR) and payback period is NOT correct?
An investor owns an empty block of land that has local government approval to be developed into a petrol station, car wash or car park. The council will only allow a single development so the projects are mutually exclusive.
All of the development projects have the same risk and the required return of each is 10% pa. Each project has an immediate cost and once construction is finished in one year the land and development will be sold. The table below shows the estimated costs payable now, expected sale prices in one year and the internal rates of returns (IRR's).
Mutually Exclusive Projects  
Project  Cost now ($) 
Sale price in one year ($) 
IRR (% pa) 
Petrol station  9,000,000  11,000,000  22.22 
Car wash  800,000  1,100,000  37.50 
Car park  70,000  110,000  57.14 
Which project should the investor accept?
An investor owns a whole level of an old office building which is currently worth $1 million. There are three mutually exclusive projects that can be started by the investor. The office building level can be:
 Rented out to a tenant for one year at $0.1m paid immediately, and then sold for $0.99m in one year.
 Refurbished into more modern commercial office rooms at a cost of $1m now, and then sold for $2.3m when the refurbishment is finished in one year.
 Converted into residential apartments at a cost of $2m now, and then sold for $3.4m when the conversion is finished in one year.
All of the development projects have the same risk so the required return of each is 10% pa. The table below shows the estimated cash flows and internal rates of returns (IRR's).
Mutually Exclusive Projects  
Project  Cash flow now ($) 
Cash flow in one year ($) 
IRR (% pa) 
Rent then sell as is  900,000  990,000  10 
Refurbishment into modern offices  2,000,000  2,400,000  20 
Conversion into residential apartments  3,000,000  3,400,000  13.33 
Which project should the investor accept?
You have $100,000 in the bank. The bank pays interest at 10% pa, given as an effective annual rate.
You wish to consume twice as much now (t=0) as in one year (t=1) and have nothing left in the bank at the end.
How much can you consume at time zero and one? The answer choices are given in the same order.
You have $100,000 in the bank. The bank pays interest at 10% pa, given as an effective annual rate.
You wish to consume half as much now (t=0) as in one year (t=1) and have nothing left in the bank at the end.
How much can you consume at time zero and one? The answer choices are given in the same order.
Question 210 real estate, inflation, real and nominal returns and cash flows, income and capital returns
Assume that the Gordon Growth Model (same as the dividend discount model or perpetuity with growth formula) is an appropriate method to value real estate.
The rule of thumb in the real estate industry is that properties should yield a 5% pa rental return. Many investors also regard property to be as risky as the stock market, therefore property is thought to have a required total return of 9% pa which is the average total return on the stock market including dividends.
Assume that all returns are effective annual rates and they are nominal (not reduced by inflation). Inflation is expected to be 2% pa.
You're considering purchasing an investment property which has a rental yield of 5% pa and you expect it to have the same risk as the stock market. Select the most correct statement about this property.
Question 522 income and capital returns, real and nominal returns and cash flows, inflation, real estate
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.
Question 523 income and capital returns, real and nominal returns and cash flows, inflation
A lowgrowth 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.
Question 664 real and nominal returns and cash flows, inflation, no explanation
What is the present value of real payments of $100 every year forever, with the first payment in one year? The nominal discount rate is 7% pa and the inflation rate is 4% pa.
For a price of $100, Carol will sell you a 5 year bond paying semiannual 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 semiannual 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 semiannually. What is its price?
Question 538 bond pricing, income and capital returns, no explanation
Riskfree government bonds that have coupon rates greater than their yields:
Question 539 debt terminology, fully amortising loan, bond pricing
A 'fully amortising' loan can also be called a:
An investor bought a 10 year 2.5% pa fixed coupon government bond priced at par. The face value is $100. Coupons are paid semiannually 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 semiannually.
What was the bond investors' historical total return over that first 6 month period, given as an effective semiannual rate?
On 22Mar2013 the Australian Government issued series TB139 treasury bonds with a combined face value $23.4m, listed on the ASX with ticker code GSBG25.
The bonds mature on 21Apr2025, the fixed coupon rate is 3.25% pa and coupons are paid semiannually on the 21st of April and October of each year. Each bond's face value is $1,000.
At market close on Friday 11Sep2015 the bonds' yield was 2.736% pa.
At market close on Monday 14Sep2015 the bonds' yield was 2.701% pa. Both yields are given as annualised percentage rates (APR's) compounding every 6 months. For convenience, assume 183 days in 6 months and 366 days in a year.
What was the historical total return over those 3 calendar days between Friday 11Sep2015 and Monday 14Sep2015?
There are 183 calendar days from market close on the last coupon 21Apr2015 to the market close of the next coupon date on 21Oct2015.
Between the market close times from 21Apr2015 to 11Sep2015 there are 143 calendar days. From 21Apr2015 to 14Sep2015 there are 146 calendar days.
From 14Sep2015 there were 20 coupons remaining to be paid including the next one on 21Oct2015.
All of the below answers are given as effective 3 day rates.
Question 708 continuously compounding rate, continuously compounding rate conversion
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:
Question 710 continuously compounding rate, continuously compounding rate conversion
A continuously compounded monthly return of 1% ##(r_\text{cc monthly})## is equivalent to a continuously compounded annual return ##(r_\text{cc annual})## of:
Which of the following quantities is commonly assumed to be normally distributed?
The below three graphs show probability density functions (PDF) of three different random variables Red, Green and Blue.
Which of the below statements is NOT correct?
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.
Question 721 mean and median returns, return distribution, arithmetic and geometric averages, continuously compounding rate
Fred owns some Commonwealth Bank (CBA) shares. He has calculated CBA’s monthly returns for each month in the past 20 years using this formula:
###r_\text{t monthly}=\ln \left( \dfrac{P_t}{P_{t1}} \right)###He then took the arithmetic average and found it to be 1% per month using this formula:
###\bar{r}_\text{monthly}= \dfrac{ \displaystyle\sum\limits_{t=1}^T{\left( r_\text{t monthly} \right)} }{T} =0.01=1\% \text{ per month}###He also found the standard deviation of these monthly returns which was 5% per month:
###\sigma_\text{monthly} = \dfrac{ \displaystyle\sum\limits_{t=1}^T{\left( \left( r_\text{t monthly}  \bar{r}_\text{monthly} \right)^2 \right)} }{T} =0.05=5\%\text{ per month}###Which of the below statements about Fred’s CBA shares is NOT correct? Assume that the past historical average return is the true population average of future expected returns.
Question 722 mean and median returns, return distribution, arithmetic and geometric averages, continuously compounding rate
Here is a table of stock prices and returns. Which of the statements below the table is NOT correct?
Price and Return Population Statistics  
Time  Prices  LGDR  GDR  NDR 
0  100  
1  50  0.6931  0.5  0.5 
2  100  0.6931  2  1 
Arithmetic average  0  1.25  0.25  
Arithmetic standard deviation  0.6931  0.75  0.75  
The following equation is the Dividend Discount Model, also known as the 'Gordon Growth Model' or the 'Perpetuity with growth' equation.
### p_{0} = \frac{c_1}{r_{\text{eff}}  g_{\text{eff}}} ###
What is the discount rate '## r_\text{eff} ##' in this equation?
A share was bought for $20 (at t=0) and paid its annual dividend of $3 one year later (at t=1). Just after the dividend was paid, the share price was $16 (at t=1). What was the total return, capital return and income return? Calculate your answers as effective annual rates.
The choices are given in the same order: ## r_\text{total},r_\text{capital},r_\text{income} ##.
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 company conducts a 2 for 3 rights issue at a subscription price of $8 when the preannouncement 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.
Question 723 mean and median returns, return distribution, arithmetic and geometric averages, continuously compounding rate
Here is a table of stock prices and returns. Which of the statements below the table is NOT correct?
Price and Return Population Statistics  
Time  Prices  LGDR  GDR  NDR 
0  100  
1  99  0.010050  0.990000  0.010000 
2  180.40  0.600057  1.822222  0.822222 
3  112.73  0.470181  0.624889  0.375111 
Arithmetic average  0.0399  1.1457  0.1457  
Arithmetic standard deviation  0.4384  0.5011  0.5011  
Question 711 continuously compounding rate, continuously compounding rate conversion
A continuously compounded semiannual return of 5% ##(r_\text{cc 6mth})## is equivalent to a continuously compounded annual return ##(r_\text{cc annual})## of:
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 lognormally 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:
Question 719 mean and median returns, return distribution, arithmetic and geometric averages, continuously compounding rate
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 lognormally distributed.
In one year, what do you expect the mean and median prices to be? The answer options are given in the same order.
Question 720 mean and median returns, return distribution, arithmetic and geometric averages, continuously compounding rate
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 lognormally distributed.
In 5 years, what do you expect the mean and median prices to be? The answer options are given in the same order.
A share was bought for $4 and paid an dividend of $0.50 one year later (at t=1 year).
Just after the dividend was paid, the share price fell to $3.50 (at t=1 year). What were the total return, capital return and income returns given as effective annual rates? The answer choices are given in the same order:
##r_\text{total}##, ##r_\text{capital}##, ## r_\text{income}##
Three years ago Frederika bought a house for $400,000.
Now it's worth $600,000, based on recent similar sales in the area.
Frederika's residential property has an expected total return of 7% pa.
She rents her house out for $2,500 per month, paid in advance. Every 12 months she plans to increase the rental payments.
The present value of 12 months of rental payments is $29,089.48.
The future value of 12 months of rental payments one year ahead is $31,125.74.
What is the expected annual capital yield of the property?
Question 405 DDM, income and capital returns, no explanation
The perpetuity with growth formula is:
###P_0= \dfrac{C_1}{rg}###
Which of the following is NOT equal to the total required return (r)?
The perpetuity with growth equation is:
###P_0=\dfrac{C_1}{rg}###
Which of the following is NOT equal to the expected capital return as an effective annual rate?
A company runs a number of slaughterhouses which supply hamburger meat to McDonalds. The company is afraid that live cattle prices will increase over the next year, even though there is widespread belief in the market that they will be stable. What can the company do to hedge against the risk of increasing live cattle prices? Which statement(s) are correct?
(i) buy call options on live cattle.
(ii) buy put options on live cattle.
(iii) sell call options on live cattle.
Select the most correct response:
Below are 4 option graphs. Note that the yaxis is payoff at maturity (T). What options do they depict? List them in the order that they are numbered.
Below are 4 option graphs. Note that the yaxis is payoff at maturity (T). What options do they depict? List them in the order that they are numbered
Question 636 option, option payoff at maturity, no explanation
Which of the below formulas gives the payoff ##(f)## at maturity ##(T)## from being long a call option? Let the underlying asset price at maturity be ##S_T## and the exercise price be ##X_T##.
Question 637 option, option payoff at maturity, no explanation
Which of the below formulas gives the payoff ##(f)## at maturity ##(T)## from being short a call option? Let the underlying asset price at maturity be ##S_T## and the exercise price be ##X_T##.
Question 638 option, option payoff at maturity, no explanation
Which of the below formulas gives the payoff ##(f)## at maturity ##(T)## from being long a put option? Let the underlying asset price at maturity be ##S_T## and the exercise price be ##X_T##.
Question 639 option, option payoff at maturity, no explanation
Which of the below formulas gives the payoff ##(f)## at maturity ##(T)## from being short a put option? Let the underlying asset price at maturity be ##S_T## and the exercise price be ##X_T##.
Which one of the below option and futures contracts gives the possibility of potentially unlimited gains?
Which of the below formulas gives the payoff at maturity ##(f_T)## from being long a future? Let the underlying asset price at maturity be ##S_T## and the lockedin futures price be ##K_T##.
Which of the below formulas gives the payoff at maturity ##(f_T)## from being short a future? Let the underlying asset price at maturity be ##S_T## and the lockedin futures price be ##K_T##.
A trader buys one crude oil futures contract on the CME expiring in one year with a lockedin futures price of $38.94 per barrel. If the trader doesn’t close out her contract before expiry then in one year she will have the:
A trader sells one crude oil futures contract on the CME expiring in one year with a lockedin futures price of $38.94 per barrel. The crude oil spot price is $40.33. If the trader doesn’t close out her contract before expiry then in one year she will have the:
A trader buys one crude oil European style call option contract on the CME expiring in one year with an exercise price of $44 per barrel for a price of $6.64. The crude oil spot price is $40.33. If the trader doesn’t close out her contract before maturity, then at maturity she will have the:
Alice, Bob, Chris and Delta are traders in the futures market. The following trades occur over a single day in a newlyopened equity index future that matures in one year which the exchange just made available.
1. Alice buys a future from Bob.
2. Chris buys a future from Delta.
3. Delta buys a future from Alice.
These were the only trades made in this equity index future. What was the trading volume and what is the open interest?
A trader buys a one year futures contract on crude oil. The contract is for the delivery of 1,000 barrels. The current futures price is $38.94 per barrel. The initial margin is $3,410 per contract, and the maintenance margin is $3,100 per contract.
What is the smallest price change that would lead to a margin call for the buyer?
A trader sells a one year futures contract on crude oil. The contract is for the delivery of 1,000 barrels. The current futures price is $38.94 per barrel. The initial margin is $3,410 per contract, and the maintenance margin is $3,100 per contract.
What is the smallest price change that would lead to a margin call for the seller?
In February a company sold one December 40,000 pound (about 18 metric tons) lean hog futures contract. It closed out its position in May.
The spot price was $0.68 per pound in February. The December futures price was $0.70 per pound when the trader entered into the contract in February, $0.60 when he closed out his position in May, and $0.55 when the contract matured in December.
What was the total profit?
An equity index is currently at 5,200 points. The 6 month futures price is 5,300 points and the total required return is 6% pa with continuous compounding. Each index point is worth $25.
What is the implied dividend yield as a continuously compounded rate per annum?
An equity index is currently at 4,800 points. The 1.5 year futures price is 5,100 points and the total required return is 6% pa with continuous compounding. Each index point is worth $25.
What is the implied dividend yield as a continuously compounded rate per annum?
Which of the following statements about futures and forward contracts is NOT correct?
A trader buys one December futures contract on orange juice. Each contract is for the delivery of 10,000 pounds. The current futures price is $1.20 per pound. The initial margin is $5,000 per contract, and the maintenance margin is $4,000 per contract.
What is the smallest price change would that would lead to a margin call for the buyer?
The price of gold is currently $700 per ounce. The forward price for delivery in 1 year is $800. An arbitrageur can borrow money at 10% per annum given as an effective discrete annual rate. Assume that gold is fairly priced and the cost of storing gold is zero.
What is the best way to conduct an arbitrage in this situation? The best arbitrage strategy requires zero capital, has zero risk and makes money straight away. An arbitrageur should sell 1 forward on gold and:
A 2year futures contract on a stock paying a continuous dividend yield of 3% pa was bought when the underlying stock price was $10 and the risk free rate was 10% per annum with continuous compounding. Assume that investors are riskneutral, so the stock's total required return is the risk free rate.
Find the forward price ##(F_2)## and value of the contract ##(V_0)## initially. Also find the value of the contract in 6 months ##(V_{0.5})## if the stock price rose to $12.
Alice, Bob, Chris and Delta are traders in the futures market. The following trades occur over a single day in a newlyopened equity index future that matures in one year which the exchange just made available.
1. Alice buys a future from Bob.
2. Chris buys a future from Delta.
3. Bob buys a future from Chris.
These were the only trades made in this equity index future. What was the trading volume and what is the open interest?
Alice, Bob, Chris and Delta are traders in the futures market. The following trades occur over a single day in a newlyopened equity index future that matures in one year which the exchange just made available.
1. Alice buys a future from Bob.
2. Chris buys a future from Delta.
3. Alice buys a future from Chris.
These were the only trades made in this equity index future. What was the trading volume and what is the open interest?
When someone says that they're "buying American dollars" (USD), what type of asset are they probably buying? They're probably buying:
Question 312 foreign exchange rate, American and European terms
If the current AUD exchange rate is USD 0.9686 = AUD 1, what is the American terms quote of the AUD against the USD?
Question 315 foreign exchange rate, American and European terms
If the current AUD exchange rate is USD 0.9686 = AUD 1, what is the European terms quote of the AUD against the USD?
Question 319 foreign exchange rate, monetary policy, American and European terms
Investors expect the Reserve Bank of Australia (RBA) to keep the policy rate steady at their next meeting.
Then unexpectedly, the RBA announce that they will increase the policy rate by 25 basis points due to fears that the economy is growing too fast and that inflation will be above their target rate of 2 to 3 per cent.
What do you expect to happen to Australia's exchange rate in the short term? The Australian dollar is likely to:
Question 381 Merton model of corporate debt, option, real option
In the Merton model of corporate debt, buying a levered company's debt is equivalent to buying risk free government bonds and:
Question 382 Merton model of corporate debt, real option, option
In the Merton model of corporate debt, buying a levered company's shares is equivalent to:
Question 383 Merton model of corporate debt, real option, option
In the Merton model of corporate debt, buying a levered company's debt is equivalent to buying the company's assets and:
Which of the following is the least useful method or model to calculate the value of a real option in a project?
Question 245 foreign exchange rate, monetary policy, foreign exchange rate direct quote, no explanation
Investors expect Australia's central bank, the RBA, to leave the policy rate unchanged at their next meeting.
Then unexpectedly, the policy rate is reduced due to fears that Australia's GDP growth is slowing.
What do you expect to happen to Australia's exchange rate? Direct and indirect quotes are given from the perspective of an Australian.
The Australian dollar will:
Question 320 foreign exchange rate, monetary policy, American and European terms
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:
Question 321 foreign exchange rate, monetary policy, American and European terms
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:
Question 246 foreign exchange rate, forward foreign exchange rate, cross currency interest rate parity
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?
Question 322 foreign exchange rate, monetary policy, American and European 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:
Question 323 foreign exchange rate, monetary policy, American and European terms
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:
The Australian dollar's value was:
Did the Australian dollar or against the US dollar between these dates?
One of the reasons why firms may not begin projects with relatively small positive net present values (NPV's) is because they wish to maximise the value of their:
You're thinking of starting a new cafe business, but you're not sure if it will be profitable.
You have to decide what type of cups, mugs and glasses you wish to buy. You can have your cafe's name printed on them, or plain unmarked ones. For marketing reasons it's better to have the cafe name printed, but the plain unmarked cups, mugs and glasses maximise your: