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} ###
Katya offers to pay you $10 at the end of every year for the next 5 years (t=1,2,3,4,5) if you pay her $50 now (t=0). You can borrow and lend from the bank at an interest rate of 10% pa, given as an effective annual rate.
Ignore credit risk.
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.
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 22 NPV, perpetuity with growth, effective rate, effective rate conversion
What is the NPV of the following series of cash flows when the discount rate is 10% given as an effective annual rate?
The first payment of $90 is in 3 years, followed by payments every 6 months in perpetuity after that which shrink by 3% every 6 months. That is, the growth rate every 6 months is actually negative 3%, given as an effective 6 month rate. So the payment at ## t=3.5 ## years will be ## 90(10.03)^1=87.3 ##, and so on.
The required return of a project is 10%, given as an effective annual rate. Assume that the cash flows shown in the table are paid all at once at the given point in time.
What is the Net Present Value (NPV) of the project?
Project Cash Flows  
Time (yrs)  Cash flow ($) 
0  100 
1  0 
2  121 
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?
Question 58 NPV, inflation, real and nominal returns and cash flows, Annuity
A project to build a toll bridge will take two years to complete, costing three payments of $100 million at the start of each year for the next three years, that is at t=0, 1 and 2.
After completion, the toll bridge will yield a constant $50 million at the end of each year for the next 10 years. So the first payment will be at t=3 and the last at t=12. After the last payment at t=12, the bridge will be given to the government.
The required return of the project is 21% pa given as an effective annual nominal rate.
All cash flows are real and the expected inflation rate is 10% pa given as an effective annual rate. Ignore taxes.
The Net Present Value is:
The required return of a project is 10%, given as an effective annual rate. Assume that the cash flows shown in the table are paid all at once at the given point in time.
What is the Net Present Value (NPV) of the project?
Project Cash Flows  
Time (yrs)  Cash flow ($) 
0  100 
1  11 
2  121 
In Australia, domestic university students are allowed to buy concession tickets for the bus, train and ferry which sell at a discount of 50% to 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.
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 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 security market line (SML) shows the relationship between beta and expected return.
Investment projects that plot above the SML would have:
The following cash flows are expected:
 10 yearly payments of $60, with the first payment in 3 years from now (first payment at t=3).
 1 payment of $400 in 5 years and 6 months (t=5.5) from now.
What is the NPV of the cash flows if the discount rate is 10% given as an effective annual rate?
A 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?
A student just won the lottery. She won $1 million in cash after tax. She is trying to calculate how much she can spend per month for the rest of her life. She assumes that she will live for another 60 years. She wants to withdraw equal amounts at the beginning of every month, starting right now.
All of the cash is currently sitting in a bank account which pays interest at a rate of 6% pa, given as an APR compounding per month. On her last withdrawal, she intends to have nothing left in her bank account. How much can she withdraw at the beginning of each month?
The following cash flows are expected:
 10 yearly payments of $80, with the first payment in 3 years from now (first payment at t=3).
 1 payment of $600 in 5 years and 6 months (t=5.5) from now.
What is the NPV of the cash flows if the discount rate is 10% given as an effective annual rate?
A project's net present value (NPV) is negative. Select the most correct statement.
A project's NPV is positive. Select the most correct statement:
A project's Profitability Index (PI) is less than 1. Select the most correct statement:
Harvey Norman the large retailer often runs sales advertising 2 years interest free when you purchase its products. This offer can be seen as a free personal loan from Harvey Norman to its customers.
Assume that banks charge an interest rate on personal loans of 12% pa given as an APR compounding per month. This is the interest rate that Harvey Norman deserves on the 2 year loan it extends to its customers. Therefore Harvey Norman must implicitly include the cost of this loan in the advertised sale price of its goods.
If you were a customer buying from Harvey Norman, and you were paying immediately, not in 2 years, what is the minimum percentage discount to the advertised sale price that you would insist on? (Hint: if it makes it easier, assume that you’re buying a product with an advertised price of $100).
A stock is expected to pay the following dividends:
Cash Flows of a Stock  
Time (yrs)  0  1  2  3  4  ... 
Dividend ($)  0  6  12  18  20  ... 
After year 4, the dividend will grow in perpetuity at 5% pa. The required return of the stock is 10% pa. Both the growth rate and required return are given as effective annual rates.
If all of the dividends since time period zero were deposited into a bank account yielding 8% pa as an effective annual rate, how much money will be in the bank account in 2.5 years (in other words, at t=2.5)?
A stock is expected to pay a dividend of $15 in one year (t=1), then $25 for 9 years after that (payments at t=2 ,3,...10), and on the 11th year (t=11) the dividend will be 2% less than at t=10, and will continue to shrink at the same rate every year after that forever. The required return of the stock is 10%. All rates are effective annual rates.
What is the price of the stock now?
Question 218 NPV, IRR, profitability index, average accounting return
Which of the following statements is NOT correct?
A very lowrisk stock just paid its semiannual dividend of $0.14, as it has for the last 5 years. You conservatively estimate that from now on the dividend will fall at a rate of 1% every 6 months.
If the stock currently sells for $3 per share, what must be its required total return as an effective annual rate?
If risk free government bonds are trading at a yield of 4% pa, given as an effective annual rate, would you consider buying or selling the stock?
The stock's required total return is:
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?
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?
You have $100,000 in the bank. The bank pays interest at 10% pa, given as an effective annual rate.
You wish to consume an equal amount now (t=0), in one year (t=1) and in two years (t=2), and still have $50,000 in the bank after that (t=2).
How much can you consume at each time?
You just started work at your new job which pays $48,000 per year.
The human resources department have given you the option of being paid at the end of every week or every month.
Assume that there are 4 weeks per month, 12 months per year and 48 weeks per year.
Bank interest rates are 12% pa given as an APR compounding per month.
What is the dollar gain over one year, as a net present value, of being paid every week rather than every month?
Suppose you had $100 in a savings account and the interest rate was 2% per year.
After 5 years, how much do you think you would have in the account if you left the money to grow?
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:
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.
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.
Your friend overheard that you need some cash and asks if you would like to borrow some money. She can lend you $5,000 now (t=0), and in return she wants you to pay her back $1,000 in two years (t=2) and every year after that for the next 5 years, so there will be 6 payments of $1,000 from t=2 to t=7 inclusive.
What is the net present value (NPV) of borrowing from your friend?
Assume that banks loan funds at interest rates of 10% pa, given as an effective annual rate.
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.
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?
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?
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:
Estimate Microsoft's (MSFT) share price using a price earnings (PE) multiples approach with the following assumptions and figures only:
 Apple, Google and Microsoft are comparable companies,
 Apple's (AAPL) share price is $526.24 and historical EPS is $40.32.
 Google's (GOOG) share price is $1,215.65 and historical EPS is $36.23.
 Micrsoft's (MSFT) historical earnings per share (EPS) is $2.71.
Source: Google Finance 28 Feb 2014.
Which of the following investable assets are NOT suitable for valuation using PE multiples techniques?
Estimate the US bank JP Morgan's share price using a price earnings (PE) multiples approach with the following assumptions and figures only:
 The major US banks JP Morgan Chase (JPM), Citi Group (C) and Wells Fargo (WFC) are comparable companies;
 JP Morgan Chase's historical earnings per share (EPS) is $4.37;
 Citi Group's share price is $50.05 and historical EPS is $4.26;
 Wells Fargo's share price is $48.98 and historical EPS is $3.89.
Note: Figures sourced from Google Finance on 24 March 2014.
Which firms tend to have low forwardlooking priceearnings (PE) ratios?
Only consider firms with positive earnings, disregard firms with negative earnings and therefore negative PE ratios.
Estimate the Chinese bank ICBC's share price using a 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.
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 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:
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:
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:
Question 385 Merton model of corporate debt, real option, option
A risky firm will last for one period only (t=0 to 1), then it will be liquidated. So it's assets will be sold and the debt holders and equity holders will be paid out in that order. The firm has the following quantities:
##V## = Market value of assets.
##E## = Market value of (levered) equity.
##D## = Market value of zero coupon bonds.
##F_1## = Total face value of zero coupon bonds which is promised to be paid in one year.
The levered equity graph above contains bold labels a to e. Which of the following statements about those labels is NOT correct?
Question 386 Merton model of corporate debt, real option, option
A risky firm will last for one period only (t=0 to 1), then it will be liquidated. So it's assets will be sold and the debt holders and equity holders will be paid out in that order. The firm has the following quantities:
##V## = Market value of assets.
##E## = Market value of (levered) equity.
##D## = Market value of zero coupon bonds.
##F_1## = Total face value of zero coupon bonds which is promised to be paid in one year.
The risky corporate debt graph above contains bold labels a to e. Which of the following statements about those labels is NOT correct?
Question 433 Merton model of corporate debt, real option, option, no explanation
A risky firm will last for one period only (t=0 to 1), then it will be liquidated. So it's assets will be sold and the debt holders and equity holders will be paid out in that order. The firm has the following quantities:
##V## = Market value of assets.
##E## = Market value of (levered) equity.
##D## = Market value of zero coupon bonds.
##F_1## = Total face value of zero coupon bonds which is promised to be paid in one year.
What is the payoff to equity holders at maturity, assuming that they keep their shares until maturity?
Suppose that the US government recently announced that subsidies for fresh milk producers will be gradually phased out over the next year. Newspapers say that there are expectations of a 40% increase in the spot price of fresh milk over the next year.
Option prices on fresh milk trading on the Chicago Mercantile Exchange (CME) reflect expectations of this 40% increase in spot prices over the next year. Similarly to the rest of the market, you believe that prices will rise by 40% over the next year.
What option trades are likely to be profitable, or to be more specific, result in a positive Net Present Value (NPV)?
Assume that:
 Only the spot price is expected to increase and there is no change in expected volatility or other variables that affect option prices.
 No taxes, transaction costs, information asymmetry, bidask spreads or other market frictions.
Select the most correct statement from the following.
'Chartists', also known as 'technical traders', believe that:
Question 338 market efficiency, CAPM, opportunity cost, technical analysis
A man inherits $500,000 worth of shares.
He believes that by learning the secrets of trading, keeping up with the financial news and doing complex trend analysis with charts that he can quit his job and become a selfemployed day trader in the equities markets.
What is the expected gain from doing this over the first year? Measure the net gain in wealth received at the end of this first year due to the decision to become a day trader. Assume the following:
 He earns $60,000 pa in his current job, paid in a lump sum at the end of each year.
 He enjoys examining share price graphs and day trading just as much as he enjoys his current job.
 Stock markets are weak form and semistrong form efficient.
 He has no inside information.
 He makes 1 trade every day and there are 250 trading days in the year. Trading costs are $20 per trade. His broker invoices him for the trading costs at the end of the year.
 The shares that he currently owns and the shares that he intends to trade have the same level of systematic risk as the market portfolio.
 The market portfolio's expected return is 10% pa.
Measure the net gain over the first year as an expected wealth increase at the end of the year.
A managed fund charges fees based on the amount of money that you keep with them. The fee is 2% of the startofyear amount, but it is paid at the end of every year.
This fee is charged regardless of whether the fund makes gains or losses on your money.
The fund offers to invest your money in shares which have an expected return of 10% pa before fees.
You are thinking of investing $100,000 in the fund and keeping it there for 40 years when you plan to retire.
What is the Net Present Value (NPV) of investing your money in the fund? Note that the question is not asking how much money you will have in 40 years, it is asking: what is the NPV of investing in the fund? Assume that:
 The fund has no private information.
 Markets are weak and semistrong form efficient.
 The fund's transaction costs are negligible.
 The cost and trouble of investing your money in shares by yourself, without the managed fund, is negligible.
Question 155 inflation, real and nominal returns and cash flows, Loan, effective rate conversion
You are a banker about to grant a 2 year loan to a customer. The loan's principal and interest will be repaid in a single payment at maturity, sometimes called a zerocoupon loan, discount loan or bullet loan.
You require a real return of 6% pa over the two years, given as an effective annual rate. Inflation is expected to be 2% this year and 4% next year, both given as effective annual rates.
You judge that the customer can afford to pay back $1,000,000 in 2 years, given as a nominal cash flow. How much should you lend to her right now?
Question 69 interest tax shield, capital structure, leverage, WACC
Which statement about risk, required return and capital structure is the most correct?
Your friend just bought a house for $400,000. He financed it using a $320,000 mortgage loan and a deposit of $80,000.
In the context of residential housing and mortgages, the 'equity' tied up in the value of a person's house is the value of the house less the value of the mortgage. So the initial equity your friend has in his house is $80,000. Let this amount be E, let the value of the mortgage be D and the value of the house be V. So ##V=D+E##.
If house prices suddenly fall by 10%, what would be your friend's percentage change in equity (E)? Assume that the value of the mortgage is unchanged and that no income (rent) was received from the house during the short time over which house prices fell.
Remember:
### r_{0\rightarrow1}=\frac{p_1p_0+c_1}{p_0} ###
where ##r_{01}## is the return (percentage change) of an asset with price ##p_0## initially, ##p_1## one period later, and paying a cash flow of ##c_1## at time ##t=1##.
A firm has a debttoassets ratio of 50%. The firm then issues a large amount of debt to raise money for new projects of similar risk to the company's existing projects. Assume a classical tax system. Which statement is correct?
Question 121 capital structure, leverage, 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 __________.
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 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 $200,000 deposit) that you have in your house?
Also, if the risk free rate is 5% pa and the market portfolio's return is 10% pa, what is the expected return on equity in your house? Ignore taxes, assume that all cash flows (interest payments and rent) were paid and received at the end of the year, and all rates are effective annual rates.
If a project's net present value (NPV) is zero, then its internal rate of return (IRR) will be:
A three year project's NPV is negative. The cash flows of the project include a negative cash flow at the very start and positive cash flows over its short life. The required return of the project is 10% pa. Select the most correct statement.
A project has the following cash flows:
Project Cash Flows  
Time (yrs)  Cash flow ($) 
0  400 
1  0 
2  500 
The required return on the project is 10%, given as an effective annual rate.
What is the Internal Rate of Return (IRR) of this project? The following choices are effective annual rates. Assume that the cash flows shown in the table are paid all at once at the given point in time.
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.
A retail furniture company buys furniture wholesale and distributes it through its retail stores. The owner believes that she has some good ideas for making stylish new furniture. She is considering a project to buy a factory and employ workers to manufacture the new furniture she's designed. Furniture manufacturing has more systematic risk than furniture retailing.
Her furniture retailing firm's aftertax WACC is 20%. Furniture manufacturing firms have an aftertax WACC of 30%. Both firms are optimally geared. Assume a classical tax system.
Which method(s) will give the correct valuation of the new furnituremaking project? Select the most correct answer.
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###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?
Question 50 DDM, stock pricing, inflation, real and nominal returns and cash flows
Most listed Australian companies pay dividends twice per year, the 'interim' and 'final' dividends, which are roughly 6 months apart.
You are an equities analyst trying to value the company BHP. You decide to use the Dividend Discount Model (DDM) as a starting point, so you study BHP's dividend history and you find that BHP tends to pay the same interim and final dividend each year, and that both grow by the same rate.
You expect BHP will pay a $0.55 interim dividend in six months and a $0.55 final dividend in one year. You expect each to grow by 4% next year and forever, so the interim and final dividends next year will be $0.572 each, and so on in perpetuity.
Assume BHP's cost of equity is 8% pa. All rates are quoted as nominal effective rates. The dividends are nominal cash flows and the inflation rate is 2.5% pa.
What is the current price of a BHP share?
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 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 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.
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?
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.
The following equation is called the Dividend Discount Model (DDM), Gordon Growth Model or the perpetuity with growth formula: ### P_0 = \frac{ C_1 }{ r  g } ###
What is ##g##? The value ##g## is the long term expected:
The 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?
The following is the Dividend Discount Model (DDM) used to price stocks:
### P_0 = \frac{d_1}{rg} ###Assume that the assumptions of the DDM hold and that the time period is measured in years.
Which of the following is equal to the expected dividend in 3 years, ## d_3 ##?
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}##.
When using the dividend discount model to price a stock:
### p_{0} = \frac{d_1}{r  g} ###
The growth rate of dividends (g):
The following equation is the Dividend Discount Model, also known as the 'Gordon Growth Model' or the 'Perpetuity with growth' equation.
### p_0 = \frac{d_1}{r  g} ###
Which expression is NOT equal to the expected dividend yield?
A share was bought for $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}##.
The following equation is the Dividend Discount Model, also known as the 'Gordon Growth Model' or the 'Perpetuity with growth' equation.
###p_0=\frac{d_1}{r_\text{eff}g_\text{eff}}###
Which expression is NOT equal to the expected capital return?
A share was bought for $10 (at t=0) and paid its annual dividend of $0.50 one year later (at t=1). Just after the dividend was paid, the share price was $11 (at t=1).
What was the total return, capital return and income return? Calculate your answers as effective annual rates. The choices are given in the same order:
##r_\text{total}##, ##r_\text{capital}##, ##r_\text{dividend}##.
The following is the Dividend Discount Model used to price stocks:
### p_0=\frac{d_1}{rg} ###
Which of the following statements about the Dividend Discount Model is NOT correct?
The following is the Dividend Discount Model used to price stocks:
### p_0=\frac{d_1}{rg} ###
All rates are effective annual rates and the cash flows (##d_1##) are received every year. Note that the r and g terms in the above DDM could also be labelled as below: ###r = r_{\text{total, 0}\rightarrow\text{1yr, eff 1yr}}### ###g = r_{\text{capital, 0}\rightarrow\text{1yr, eff 1yr}}### Which of the following statements is NOT correct?
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}##
A 90day $1 million Bank Accepted Bill (BAB) was bought for $990,000 and sold 30 days later for $996,000 (at t=30 days).
What was the total return, capital return and income return over the 30 days it was held?
Despite the fact that money market instruments such as bills are normally quoted with simple interest rates, please calculate your answers as compound interest rates, specifically, as effective 30day rates, which is how the below answer choices are listed.
##r_\text{total}##, ##r_\text{capital}##, ## r_\text{income}##
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.
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}{rg} ###
Which expression is equal to the expected dividend return?
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%?
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?
One and a half years ago Frank bought a house for $600,000. Now it's worth only $500,000, based on recent similar sales in the area.
The expected total return on Frank's residential property is 7% pa.
He rents his house out for $1,600 per month, paid in advance. Every 12 months he plans to increase the rental payments.
The present value of 12 months of rental payments is $18,617.27.
The future value of 12 months of rental payments one year in the future is $19,920.48.
What is the expected annual rental yield of the property? Ignore the costs of renting such as maintenance, real estate agent fees and so on.
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)?
Question 415 income and capital returns, real estate, no explanation
You just bought a residential apartment as an investment property for $500,000.
You intend to rent it out to tenants. They are ready to move in, they would just like to know how much the monthly rental payments will be, then they will sign a twelvemonth lease.
You require a total return of 8% pa and a rental yield of 5% pa.
What would the monthly paidinadvance rental payments have to be this year to receive that 5% annual rental yield?
Also, if monthly rental payments can be increased each year when a new lease agreement is signed, by how much must you increase rents per year to realise the 8% pa total return on the property?
Ignore all taxes and the costs of renting such as maintenance costs, real estate agent fees, utilities and so on. Assume that there will be no periods of vacancy and that tenants will promptly pay the rental prices you charge.
Note that the first rental payment will be received at t=0. The first lease agreement specifies the first 12 equal payments from t=0 to 11. The next lease agreement can have a rental increase, so the next twelve equal payments from t=12 to 23 can be higher than previously, and so on forever.
You want to buy an apartment worth $500,000. You have saved a deposit of $50,000. The bank has agreed to lend you the $450,000 as a fully amortising mortgage loan with a term of 25 years. The interest rate is 6% pa and is not expected to change.
What will be your monthly payments?
You want to buy an apartment worth $400,000. You have saved a deposit of $80,000. The bank has agreed to lend you the $320,000 as a fully amortising mortgage loan with a term of 30 years. The interest rate is 6% pa and is not expected to change. What will be your monthly payments?
You want to buy an apartment priced at $500,000. You have saved a deposit of $50,000. The bank has agreed to lend you the $450,000 as a fully amortising loan with a term of 30 years. The interest rate is 6% pa and is not expected to change. What will be your monthly payments?
You just signed up for a 30 year fully amortising mortgage loan with monthly payments of $2,000 per month. The interest rate is 9% pa which is not expected to change.
How much did you borrow? After 5 years, how much will be owing on the mortgage? The interest rate is still 9% and is not expected to change.
You just signed up for a 30 year fully amortising mortgage with monthly payments of $1,000 per month. The interest rate is 6% pa which is not expected to change.
How much did you borrow? After 20 years, how much will be owing on the mortgage? The interest rate is still 6% and is not expected to change.
You just signed up for a 30 year fully amortising mortgage loan with monthly payments of $1,500 per month. The interest rate is 9% pa which is not expected to change.
To your surprise, you can actually afford to pay $2,000 per month and your mortgage allows early repayments without fees. If you maintain these higher monthly payments, how long will it take to pay off your mortgage?
You 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?
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.
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.
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 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 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?
The Australian cash rate is expected to be 6% pa while the US federal funds rate is expected to be 4% pa over the next 3 years, both given as effective annual rates. The current exchange rate is 0.80 AUD per USD.
What is the implied 3 year forward foreign exchange rate?
In the dividend discount model:
###P_0 = \dfrac{C_1}{rg}###
The return ##r## is supposed to be the:
In the dividend discount model:
### P_0= \frac{d_1}{rg} ###
The pronumeral ##g## is supposed to be the:
A credit card offers an interest rate of 18% pa, compounding monthly.
Find the effective monthly rate, effective annual rate and the effective daily rate. Assume that there are 365 days in a year.
All answers are given in the same order:
### r_\text{eff monthly} , r_\text{eff yearly} , r_\text{eff daily} ###
A European bond paying annual coupons of 6% offers a yield of 10% pa.
Convert the yield into an effective monthly rate, an effective annual rate and an effective daily rate. Assume that there are 365 days in a year.
All answers are given in the same order:
### r_\text{eff, monthly} , r_\text{eff, yearly} , r_\text{eff, daily} ###
Calculate the effective annual rates of the following three APR's:
 A credit card offering an interest rate of 18% pa, compounding monthly.
 A bond offering a yield of 6% pa, compounding 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}##
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 is 10% pa, given as an effective annual rate.
What is the price of the share now?
A 2 year government bond yields 5% pa with a coupon rate of 6% pa, paid semiannually.
Find the effective six month rate, effective annual rate and the effective daily rate. Assume that each month has 30 days and that there are 360 days in a year.
All answers are given in the same order:
##r_\text{eff semiannual}##, ##r_\text{eff yrly}##, ##r_\text{eff daily}##.
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}##.
Which of the following statements about effective rates and annualised percentage rates (APR's) is NOT correct?
Diversification is achieved by investing in a large amount of stocks. What type of risk is reduced by diversification?
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###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 $10.20 each, Renee will sell you 100 shares. Each share is expected to pay dividends in perpetuity, growing at a rate of 5% pa. The next dividend is one year away (t=1) and is expected to be $1 per share.
The required return of the stock is 15% pa.
For a price of $95, Sherylanne will sell you a share which is expected to pay its first dividend of $10 in 7 years (t=7), and will continue to pay the same $10 dividend every year after that forever.
The required return of the stock is 10% pa.
Question 31 DDM, perpetuity with growth, effective rate conversion
What is the NPV of the following series of cash flows when the discount rate is 5% given as an effective annual rate?
The first payment of $10 is in 4 years, followed by payments every 6 months forever after that which shrink by 2% every 6 months. That is, the growth rate every 6 months is actually negative 2%, given as an effective 6 month rate. So the payment at ## t=4.5 ## years will be ## 10(10.02)^1=9.80 ##, and so on.
A stock pays annual dividends which are expected to continue forever. It just paid a dividend of $10. The growth rate in the dividend is 2% pa. You estimate that the stock's required return is 10% pa. Both the discount rate and growth rate are given as effective annual rates. Using the dividend discount model, what will be the share price?
A stock is expected to pay the following dividends:
Cash Flows of a Stock  
Time (yrs)  0  1  2  3  4  ... 
Dividend ($)  0.00  1.00  1.05  1.10  1.15  ... 
After year 4, the annual dividend will grow in perpetuity at 5% pa, so;
 the dividend at t=5 will be $1.15(1+0.05),
 the dividend at t=6 will be $1.15(1+0.05)^2, and so on.
The required return on the stock is 10% pa. Both the growth rate and required return are given as effective annual rates. What is the current price of the stock?
A stock is expected to pay the following dividends:
Cash Flows of a Stock  
Time (yrs)  0  1  2  3  4  ... 
Dividend ($)  0.00  1.00  1.05  1.10  1.15  ... 
After year 4, the annual dividend will grow in perpetuity at 5% pa, so;
 the dividend at t=5 will be $1.15(1+0.05),
 the dividend at t=6 will be $1.15(1+0.05)^2, and so on.
The required return on the stock is 10% pa. Both the growth rate and required return are given as effective annual rates.
What will be the price of the stock in three and a half years (t = 3.5)?
A stock pays semiannual dividends. It just paid a dividend of $10. The growth rate in the dividend is 1% every 6 months, given as an effective 6 month rate. You estimate that the stock's required return is 21% pa, as an effective annual rate.
Using the dividend discount model, what will be the share price?
A stock is expected to pay the following dividends:
Cash Flows of a Stock  
Time (yrs)  0  1  2  3  4  ... 
Dividend ($)  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 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 annual dividends. It just paid a dividend of $3. The growth rate in the dividend is 4% pa. You estimate that the stock's required return is 10% pa. Both the discount rate and growth rate are given as effective annual rates. Using the dividend discount model, what will be the share price?
A stock is expected to pay the following dividends:
Cash Flows of a Stock  
Time (yrs)  0  1  2  3  4  ... 
Dividend ($)  8  8  8  20  8  ... 
After year 4, the dividend will grow in perpetuity at 4% pa. The required return on the stock is 10% pa. Both the growth rate and required return are given as effective annual rates.
What is the current price of the stock?
A stock is expected to pay the following dividends:
Cash Flows of a Stock  
Time (yrs)  0  1  2  3  4  ... 
Dividend ($)  8  8  8  20  8  ... 
After year 4, the dividend will grow in perpetuity at 4% pa. The required return on the stock is 10% pa. Both the growth rate and required return are given as effective annual rates.
What will be the price of the stock in 5 years (t = 5), just after the dividend at that time has been paid?
A stock pays annual dividends. It just paid a dividend of $5. The growth rate in the dividend is 1% pa. You estimate that the stock's required return is 8% pa. Both the discount rate and growth rate are given as effective annual rates.
Using the dividend discount model, what will be the share price?
A stock is expected to pay the following dividends:
Cash Flows of a Stock  
Time (yrs)  0  1  2  3  4  ... 
Dividend ($)  2  2  2  10  3  ... 
After year 4, the dividend will grow in perpetuity at 4% pa. The required return on the stock is 10% pa. Both the growth rate and required return are given as effective annual rates.
What is the current price of the stock?
A stock is expected to pay the following dividends:
Cash Flows of a Stock  
Time (yrs)  0  1  2  3  4  ... 
Dividend ($)  2  2  2  10  3  ... 
After year 4, the dividend will grow in perpetuity at 4% pa. The required return on the stock is 10% pa. Both the growth rate and required return are given as effective annual rates.
What will be the price of the stock in 5 years (t = 5), just after the dividend at that time has been paid?
A share pays annual dividends. It just paid a dividend of $2. The growth rate in the dividend is 3% pa. You estimate that the stock's required return is 8% pa. Both the discount rate and growth rate are given as effective annual rates.
Using the dividend discount model, what is the share price?
A stock is expected to pay the following dividends:
Cash Flows of a Stock  
Time (yrs)  0  1  2  3  4  ... 
Dividend ($)  0  6  12  18  20  ... 
After year 4, the dividend will grow in perpetuity at 5% pa. The required return of the stock is 10% pa. Both the growth rate and required return are given as effective annual rates.
What is the current price of the stock?
A stock is expected to pay the following dividends:
Cash Flows of a Stock  
Time (yrs)  0  1  2  3  4  ... 
Dividend ($)  0  6  12  18  20  ... 
After year 4, the dividend will grow in perpetuity at 5% pa. The required return of the stock is 10% pa. Both the growth rate and required return are given as effective annual rates.
What will be the price of the stock in 7 years (t = 7), just after the dividend at that time has been paid?
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.
A stock just paid its annual dividend of $9. The share price is $60. The required return of the stock is 10% pa as an effective annual rate.
What is the implied growth rate of the dividend per year?
A stock 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 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?
The following equation is the Dividend Discount Model, also known as the 'Gordon Growth Model' or the 'Perpetuity with growth' equation.
###P_0=\frac{d_1}{rg}###
A stock pays dividends annually. It just paid a dividend, but the next dividend (##d_1##) will be paid in one year.
According to the DDM, what is the correct formula for the expected price of the stock in 2.5 years?
When using the dividend discount model, care must be taken to avoid using a nominal dividend growth rate that exceeds the country's nominal GDP growth rate. Otherwise the firm is forecast to take over the country since it grows faster than the average business forever.
Suppose a firm's nominal dividend grows at 10% pa forever, and nominal GDP growth is 5% pa forever. The firm's total dividends are currently $1 billion (t=0). The country's GDP is currently $1,000 billion (t=0).
In approximately how many years will the company's total dividends be as large as the country's GDP?
Stocks in the United States usually pay quarterly dividends. For example, the retailer 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?
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?
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?
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.
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:
There are many ways to write the ordinary annuity formula.
Which of the following is NOT equal to the ordinary annuity formula?
You really want to go on a back packing trip to Europe when you finish university. Currently you have $1,500 in the bank. Bank interest rates are 8% pa, given as an APR compounding per month. If the holiday will cost $2,000, how long will it take for your bank account to reach that amount?
You're trying to save enough money for a deposit to buy a house. You want to buy a house worth $400,000 and the bank requires a 20% deposit ($80,000) before it will give you a loan for the other $320,000 that you need.
You currently have no savings, but you just started working and can save $2,000 per month, with the first payment in one month from now. Bank interest rates on savings accounts are 4.8% pa with interest paid monthly and interest rates are not expected to change.
How long will it take to save the $80,000 deposit? Round your answer up to the nearest month.
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}###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?
A 90day Bank Accepted Bill (BAB) has a face value of $1,000,000. The simple interest rate is 10% pa and there are 365 days in the year. What is its price now?
Question 147 bill pricing, simple interest rate, no explanation
A 30day 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 157 bill pricing, simple interest rate, no explanation
A 90day Bank Accepted Bill has a face value of $1,000,000. The interest rate is 6% pa and there are 365 days in the year. What is its price?
A 60day 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?
A 30day Bank Accepted Bill has a face value of $1,000,000. The interest rate is 2.5% pa and there are 365 days in the year. What 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 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.
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:
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?
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?
An old 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?
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?
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##?
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?
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 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?
A firm plans to issue equity and use the cash raised to pay off its debt. No assets will be bought or sold. Ignore the costs of financial distress.
Which of the following statements is NOT correct, all things remaining equal?
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 $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 $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.
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?
Bonds X and Y are issued by the same US company. Both bonds yield 10% pa, and they have the same face value ($100), maturity, seniority, and payment frequency.
The only difference is that bond X and Y's coupon rates are 8 and 12% pa respectively. Which of the following statements is true?
A two year Government bond has a face value of $100, a yield of 0.5% and a fixed coupon rate of 0.5%, paid semiannually. What is its price?
A two year Government bond has a face value of $100, a yield of 2.5% pa and a fixed coupon rate of 0.5% pa, paid semiannually. What is its price?
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?
A three year bond has a fixed coupon rate of 12% pa, paid semiannually. The bond's yield is currently 6% pa. The face value is $100. What is its price?
Bonds X and Y are issued by different companies, but they both pay a 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 one of the following bonds is trading at a discount?
A five year bond has a face value of $100, a yield of 12% and a fixed coupon rate of 6%, paid semiannually.
What is the bond's price?
Which one of the following bonds is trading at par?
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 four year bond has a face value of $100, a yield of 9% and a fixed coupon rate of 6%, paid semiannually. What is its price?
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 company. Both bonds yield 10% pa, and they have the same face value ($100), maturity, seniority, and payment frequency.
The only difference is that bond X pays coupons of 6% pa and bond Y pays coupons of 8% pa. Which of the following statements is true?
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?
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?
Stock A has a beta of 0.5 and stock B has a beta of 1. Which statement is NOT correct?
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?
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?
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 risk can be broken into two components, systematic risk and idiosyncratic risk. Which of the following events would be considered a systematic, undiversifiable event according to the theory of the CAPM?
A fairly priced stock has 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 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?
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 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 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:
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 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 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.
Which of the following statements about the weighted average cost of capital (WACC) is NOT correct?
Acquirer firm plans to launch a takeover of Target firm. The deal is expected to create a present value of synergies totaling $105 million. A cash offer will be made that pays the fair price for the target's shares plus 75% of the total synergy value. The cash will be paid out of the firm's cash holdings, no new debt or equity will be raised.
Firms Involved in the Takeover  
Acquirer  Target  
Assets ($m)  6,000  700 
Debt ($m)  4,800  400 
Share price ($)  40  20 
Number of shares (m)  30  15 
Ignore transaction costs and fees. Assume that the firms' debt and equity are fairly priced, and that each firms' debts' risk, yield and values remain constant. The acquisition is planned to occur immediately, so ignore the time value of money.
Calculate the merged firm's share price and total number of shares after the takeover has been completed.
Acquirer firm plans to launch a takeover of Target firm. The deal is expected to create a present value of synergies totaling $105 million. A scrip offer will be made that pays the fair price for the target's shares plus 75% of the total synergy value.
Firms Involved in the Takeover  
Acquirer  Target  
Assets ($m)  6,000  700 
Debt ($m)  4,800  400 
Share price ($)  40  20 
Number of shares (m)  30  15 
Ignore transaction costs and fees. Assume that the firms' debt and equity are fairly priced, and that each firms' debts' risk, yield and values remain constant. The acquisition is planned to occur immediately, so ignore the time value of money.
Calculate the merged firm's share price and total number of shares after the takeover has been completed.
Acquirer firm plans to launch a takeover of Target firm. The firms operate in different industries and the CEO's rationale for the merger is to increase diversification and thereby decrease risk. The deal is not expected to create any synergies. An 80% scrip and 20% cash offer will be made that pays the fair price for the target's shares. The cash will be paid out of the firms' cash holdings, no new debt or equity will be raised.
Firms Involved in the Takeover  
Acquirer  Target  
Assets ($m)  6,000  700 
Debt ($m)  4,800  400 
Share price ($)  40  20 
Number of shares (m)  30  15 
Ignore transaction costs and fees. Assume that the firms' debt and equity are fairly priced, and that each firms' debts' risk, yield and values remain constant. The acquisition is planned to occur immediately, so ignore the time value of money.
Calculate the merged firm's share price and total number of shares after the takeover has been completed.
Acquirer firm plans to launch a takeover of Target firm. The deal is expected to create a present value of synergies totaling $105 million. A 40% scrip and 60% cash offer will be made that pays the fair price for the target's shares plus 75% of the total synergy value. The cash will be paid out of the firm's cash holdings, no new debt or equity will be raised.
Firms Involved in the Takeover  
Acquirer  Target  
Assets ($m)  6,000  700 
Debt ($m)  4,800  400 
Share price ($)  40  20 
Number of shares (m)  30  15 
Ignore transaction costs and fees. Assume that the firms' debt and equity are fairly priced, and that each firms' debts' risk, yield and values remain constant. The acquisition is planned to occur immediately, so ignore the time value of money.
Calculate the merged firm's share price and total number of shares after the takeover has been completed.
Acquirer firm plans to launch a takeover of Target firm. The deal is expected to create a present value of synergies totaling $2 million. A cash offer will be made that pays the fair price for the target's shares plus 70% of the total synergy value. The cash will be paid out of the firm's cash holdings, no new debt or equity will be raised.
Firms Involved in the Takeover  
Acquirer  Target  
Assets ($m)  60  10 
Debt ($m)  20  2 
Share price ($)  10  8 
Number of shares (m)  4  1 
Ignore transaction costs and fees. Assume that the firms' debt and equity are fairly priced, and that each firms' debts' risk, yield and values remain constant. The acquisition is planned to occur immediately, so ignore the time value of money.
Calculate the merged firm's share price and total number of shares after the takeover has been completed.
Acquirer firm plans to launch a takeover of Target firm. The deal is expected to create a present value of synergies totaling $2 million. A scrip offer will be made that pays the fair price for the target's shares plus 70% of the total synergy value.
Firms Involved in the Takeover  
Acquirer  Target  
Assets ($m)  60  10 
Debt ($m)  20  2 
Share price ($)  10  8 
Number of shares (m)  4  1 
Ignore transaction costs and fees. Assume that the firms' debt and equity are fairly priced, and that each firms' debts' risk, yield and values remain constant. The acquisition is planned to occur immediately, so ignore the time value of money.
Calculate the merged firm's share price and total number of shares after the takeover has been completed.
Acquirer firm plans to launch a takeover of Target firm. The deal is expected to create a present value of synergies totaling $0.5 million, but investment bank fees and integration costs with a present value of $1.5 million is expected. A 10% cash and 90% scrip offer will be made that pays the fair price for the target's shares only. Assume that the Target and Acquirer agree to the deal. The cash will be paid out of the firms' cash holdings, no new debt or equity will be raised.
Firms Involved in the Takeover  
Acquirer  Target  
Assets ($m)  60  10 
Debt ($m)  20  2 
Share price ($)  10  8 
Number of shares (m)  4  1 
Assume that the firms' debt and equity are fairly priced, and that each firms' debts' risk, yield and values remain constant. The acquisition is planned to occur immediately, so ignore the time value of money.
Calculate the merged firm's share price and total number of shares after the takeover has been completed.
Which of the following is the least useful method or model to calculate the value of a real option in a project?
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:
A moped is a bicycle with pedals and a little motor that can be switched on to assist the rider. Mopeds offer the rider:
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 pay to have your cafe's name printed on them, or just buy the 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:
Some financially minded people insist on a prenuptial agreement before committing to marry their partner. This agreement states how the couple's assets should be divided in case they divorce. Prenuptial agreements are designed to give the richer partner more of the couples' assets if they divorce, thus maximising the richer partner's:
The cheapest mobile phones available tend to be those that are 'locked' into a cell phone operator's network. Locked phones can not be used with other cell phone operators' networks.
Locked mobile phones are cheaper than unlocked phones because the lockedin network operator helps create a monopoly by:
Your firm's research scientists can begin an exciting new project at a cost of $10m now, after which there’s a:
 70% chance that cash flows will be $1m per year forever, starting in 5 years (t=5). This is the A state of the world.
 20% chance that cash flows will be $3m per year forever, starting in 5 years (t=5). This is the B state of the world.
 10% chance of a major break through in which case the cash flows will be $20m per year forever starting in 5 years (t=5), or the project can be expanded by investing another $10m (at t=5) which is expected to give cash flows of $60m per year forever, starting at year 9 (t=9). This is the C state of the world.
The firm's cost of capital is 10% pa.
What's the present value (at t=0) of the option to expand in year 5?
Which of the following companies is most suitable for valuation using PE multiples techniques?
Which of the following investable assets is the LEAST suitable for valuation using PE multiples techniques?
A mature firm has constant expected future earnings and dividends. Both amounts are equal. So earnings and dividends are expected to be equal and unchanging.
Which of the following statements is NOT correct?
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.
You have just sold an 'in the money' 6 month European put option on the mining company BHP at an exercise price of $40 for a premium of $3.
Which of the following statements best describes your situation?
Below are 4 option graphs. Note that the yaxis is payoff at maturity (T). What options do they depict? List them in the order that they are numbered
You operate a cattle farm that supplies hamburger meat to the big fast food chains. You buy a lot of grain to feed your cattle, and you sell the fully grown cattle on the livestock market.
You're afraid of adverse movements in grain and livestock prices. What options should you buy to hedge your exposures in the grain and cattle livestock markets?
Select the most correct response:
Which one of the following is NOT usually considered an 'investable' asset for longterm wealth creation?
A European call option will mature in ##T## years with a strike price of ##K## dollars. The underlying asset has a price of ##S## dollars.
What is an expression for the payoff at maturity ##(f_T)## in dollars from owning (being long) the call option?
A European put option will mature in ##T## years with a strike price of ##K## dollars. The underlying asset has a price of ##S## dollars.
What is an expression for the payoff at maturity ##(f_T)## in dollars from owning (being long) the put option?
A European call option will mature in ##T## years with a strike price of ##K## dollars. The underlying asset has a price of ##S## dollars.
What is an expression for the payoff at maturity ##(f_T)## in dollars from having written (being short) the call option?
A European put option will mature in ##T## years with a strike price of ##K## dollars. The underlying asset has a price of ##S## dollars.
What is an expression for the payoff at maturity ##(f_T)## in dollars from having written (being short) the put option?
Question 432 option, option intrinsic value, no explanation
An American call option with a strike price of ##K## dollars will mature in ##T## years. The underlying asset has a price of ##S## dollars.
What is an expression for the current intrinsic value in dollars from owning (being long) the American call option? Note that the intrinsic value of an option does not subtract the premium paid to buy the option.
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.
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##
Question 215 equivalent annual cash flow, effective rate conversion
You're about to buy a car. These are the cash flows of the two different cars that you can buy:
 You can buy an old car for $5,000 now, for which you will have to buy $90 of fuel at the end of each week from the date of purchase. The old car will last for 3 years, at which point you will sell the old car for $500.
 Or you can buy a new car for $14,000 now for which you will have to buy $50 of fuel at the end of each week from the date of purchase. The new car will last for 4 years, at which point you will sell the new car for $1,000.
Bank interest rates are 10% pa, given as an effective annual rate. Assume that there are exactly 52 weeks in a year. Ignore taxes and environmental and pollution factors.
Should you buy the or the ?
Question 249 equivalent annual cash flow, effective rate conversion
Details of two different types of desserts or edible treats are given below:
 Highsugar treats like candy, chocolate and ice cream make a person very happy. High sugar treats are cheap at only $2 per day.
 Lowsugar treats like nuts, cheese and fruit make a person equally happy if these foods are of high quality. Low sugar treats are more expensive at $4 per day.
The advantage of lowsugar treats is that a person only needs to pay the dentist $2,000 for fillings and root canal therapy once every 15 years. Whereas with highsugar treats, that treatment needs to be done every 5 years.
The real discount rate is 10%, given as an effective annual rate. Assume that there are 365 days in every year and that all cash flows are real. The inflation rate is 3% given as an effective annual rate.
Find the equivalent annual cash flow (EAC) of the highsugar treats and lowsugar treats, including dental costs. The below choices are listed in that order.
Ignore the pain of dental therapy, personal preferences and other factors.
You just bought a nice dress which you plan to wear once per month on nights out. You bought it a moment ago for $600 (at t=0). In your experience, dresses used once per month last for 6 years.
Your younger sister is a student with no money and wants to borrow your dress once a month when she hits the town. With the increased use, your dress will only last for another 3 years rather than 6.
What is the present value of the cost of letting your sister use your current dress for the next 3 years?
Assume: that bank interest rates are 10% pa, given as an effective annual rate; you will buy a new dress when your current one wears out; your sister will only use the current dress, not the next one that you will buy; and the price of a new dress never changes.
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).