Fight Finance

Question 1  NPV

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

Ignore credit risk. Remember:

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

Will you or Jan's deal?

Question 2  NPV, Annuity

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

Will you or politely Katya's deal?

Question 3  DDM, income and capital returns

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:

(a) Income return of the stock.

(b) Capital return of the stock.

(c) Total return of the stock.

(d) Dividend yield of the stock.

(e) Price-earnings ratio of the stock.

Question 4  DDM

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

Would you like to Carla's share or politely ?

Question 5  DDM

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

Would you like to his share or politely ?

Question 6  DDM

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

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

The required return of the stock is 15% pa.

Would you like to the share or politely ?

Question 10  DDM

For a price of $95, Sherylanne will sell you a share which is expected to pay its first dividend of $10 in 7 years (t=7), and will continue to pay the same $10 dividend every year after that forever.

The required return of the stock is 10% pa.

Would you like to the share or politely ?

Question 16  credit card, APR, effective rate

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) 0.0072, 0.09, 0.0002.

(b) 0.0139, 0.18, 0.0005.

(c) 0.0139, 6.2876, 0.0055.

(d) 0.015, 0.1956, 0.0005.

(e) 0.015, 0.1956, 0.006.

Question 18  DDM, income and capital returns

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

### p_{0} = \frac{c_1}{r_{\text{eff}} - g_{\text{eff}}} ###

What is the discount rate '## r_\text{eff} ##' in this equation?

(a) The expected total return of the stock.

(b) The expected capital return of the stock.

(c) The expected dividend return of the stock.

(d) The expected income return of the stock.

(e) The expected growth rate of the stock price.

Question 23  bond pricing, premium par and discount bonds

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) Bonds X and Y are premium bonds.

(b) Bonds X and Y are discount bonds.

(c) Bond X is a discount bond but bond Y is a premium bond.

(d) Bond X is a premium bond but bond Y is a discount bond.

(e) Bonds X and Y are par bonds.

Question 28  DDM, income and capital returns

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

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

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

(a) The expected total return of the stock.

(b) The expected income return of the stock.

(c) The expected capital return of the stock.

(d) The expected growth rate of the dividend.

(e) The expected growth rate of the stock price.

Question 29  interest only loan

You want to buy an apartment priced at $300,000. You have saved a deposit of $30,000. The bank has agreed to lend you the $270,000 as an interest only loan with a term of 25 years. The interest rate is 12% pa and is not expected to change.

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

(a) 900

(b) 2,700

(c) 2,722.1

(d) 2,843.71

(e) 34,424.99

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(1-0.02)^1=9.80 ##, and so on.

(a) $188.62

(b) $184.07

(c) $120.43

(d) $117.53

(e) $8.07

Question 33  bond pricing, premium par and discount bonds

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

Which bond would have the higher current price?

(a) Bond A will have a higher price.

(b) Bond B will have a higher price.

(c) Bonds A and B will have the same price.

(d) The higher priced bond can't be determined without knowing their yields.

(e) The higher priced bond can't be determined without knowing the inflation rate.

Question 37  IRR

If a project's net present value (NPV) is zero, then its internal rate of return (IRR) will be:

(a) Positive infinity (##+\infty##)

(b) Zero (0).

(c) Less than the project's required return.

(d) More than the project's required return.

(e) Equal to the project's required return.

Question 41  DDM, income and capital returns

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

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

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

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

(a) ## d_1(1+g)^3 ##

(b) ## P_3(r-g) ##

(c) ## d_2(1+g)^2 ##

(d) ## P_0(1+g)^3(r-g) ##

(e) ## P_0(1+g)^2(r-g) ##

Question 42  interest only loan

You just signed up for a 30 year interest-only mortgage with monthly payments of $3,000 per month. The interest rate is 6% pa which is not expected to change.

How much did you borrow? After 15 years, just after the 180th payment at that time, how much will be owing on the mortgage? The interest rate is still 6% and is not expected to change. Remember that the mortgage is interest-only and that mortgage payments are paid in arrears (at the end of the month).

(a) $495,533.92, $349,640.96

(b) $500,374.84, $355,510.54

(c) $500,374.84, $250,187.42

(d) $600,000.00, $600,000.00

(e) $600,000.00, $300,000.00

Question 45  profitability index

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

What is the Profitability Index (PI) of the project?

Project Cash Flows
Time (yrs)	Cash flow ($)
0	-100
1	0
2	121

(a) 1.21

(b) 1.1

(c) 1

(d) 0.82845

(e) 0

Question 46  NPV, annuity due

The phone company Telstra have 2 mobile service plans on offer which both have the same amount of phone call, text message and internet data credit. Both plans have a contract length of 24 months and the monthly cost is payable in advance. The only difference between the two plans is that one is a:

• 'Bring Your Own' (BYO) mobile service plan, costing $50 per month. There is no phone included in this plan. The other plan is a:
• 'Bundled' mobile service plan that comes with the latest smart phone, costing $71 per month. This plan includes the latest smart phone.

Neither plan has any additional payments at the start or end.

The only difference between the plans is the phone, so what is the implied cost of the phone as a present value?

Assume that the discount rate is 2% per month given as an effective monthly rate, the same high interest rate on credit cards.

(a) $389.4044

(b) $397.1924

(c) $405.1363

(d) $504.0000

(e) $964.6102

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 under-priced. Buying or selling a fairly priced asset has an NPV of zero.

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

(a) The internal rate of return (IRR) of buying a fairly priced bond is equal to the bond's yield.

(b) The Present Value of a fairly priced bond's coupons and face value is equal to its price.

(c) If a fairly priced bond's required return rises, its price will fall.

(d) Fairly priced premium bonds' yields are less than their coupon rates, prices are more than their face values, and the NPV of buying them is therefore positive.

(e) The NPV of buying a fairly priced bond is zero.

Question 52  IRR, pay back period

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) The payback period is negative.

(b) The project's IRR is negative.

(c) The project's IRR is less than its required return.

(d) The project's IRR is more than its required return.

(e) The project's IRR is equal to its required return.

Question 56  income and capital returns, bond pricing, premium par and discount bonds

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

(a) Premium bonds have a positive expected capital return.

(b) Discount bonds have a positive expected capital return.

(c) Par bonds have a zero expected capital return.

(d) Par bonds have a total expected yield equal to their coupon yield.

(e) Zero coupon bonds selling at par would have zero expected total, income and capital yields.

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

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

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

Question 63  bond pricing, NPV, 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 under-priced. Buying or selling a fairly priced asset has an NPV of zero.

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

(a) The internal rate of return (IRR) of buying a bond is equal to the bond's yield.

(b) The present value of a fairly priced bond's coupons and face value is equal to its price.

(c) If the required return of a bond falls, its price will fall.

(d) Fairly priced discount bonds' yield is more than the coupon rate, price is less than face value, and the NPV of buying them is zero.

(e) The NPV of buying a fairly priced bond is zero.

Question 64  inflation, real and nominal returns and cash flows, APR, effective rate

In Germany, nominal yields on semi-annual 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?

(a) -1.3529627%

(b) -0.4977348%

(c) 0.4977348%

(d) 1.3529627%

(e) 1.3621776%

Question 65  annuity with growth, needs refinement

Which of the below formulas gives the present value of an annuity with growth?

(a) ##\dfrac{C_1}{r-g}\left(1-\dfrac{1}{(1+r)^T}\right)##

(b) ##\dfrac{C_1(1+g)^T}{r-g}\left(1-\dfrac{1}{(1+r)^T}\right)##

(c) ##\dfrac{C_1}{r-g}\left(1-\dfrac{1+g}{(1+r)^T}\right)##

(d) ##\dfrac{C_1}{r-g}\left(1-\left(\dfrac{1+g}{1+r}\right)^T \right)##

(e) ##\dfrac{C_1(1+g)}{r-g}\left(1-\dfrac{1}{(1+r)^T}\right)##

Hint: The equation of a perpetuity without growth is: ###V_\text{0, perp without growth} = \frac{C_\text{1}}{r}###

The formula for the present value of an annuity without growth is derived from the formula for a perpetuity without growth.

The idea is than an annuity with T payments from t=1 to T inclusive is equivalent to a perpetuity starting at t=1 with fixed positive cash flows, plus a perpetuity starting T periods later (t=T+1) with fixed negative cash flows. The positive and negative cash flows after time period T cancel each other out, leaving the positive cash flows between t=1 to T, which is the annuity.

###\begin{aligned} V_\text{0, annuity} &= V_\text{0, perp without growth from t=1} - V_\text{0, perp without growth from t=T+1} \\ &= \dfrac{C_\text{1}}{r} - \dfrac{ \left( \dfrac{C_\text{T+1}}{r} \right) }{(1+r)^T} \\ &= \dfrac{C_\text{1}}{r} - \dfrac{ \left( \dfrac{C_\text{1}}{r} \right) }{(1+r)^T} \\ &= \dfrac{C_\text{1}}{r}\left(1 - \dfrac{1}{(1+r)^T}\right) \\ \end{aligned}###

The equation of a perpetuity with growth is:

###V_\text{0, perp with growth} = \dfrac{C_\text{1}}{r-g}###

Question 67  CFFA, interest tax shield

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

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

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

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

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

(a) ##D(1+r_D)##

(b) ##D/(1+r_D) ##

(c) ##D.r_D ##

(d) ##D / r_D##

(e) ##NI.r_D##

Question 68  WACC, CFFA, capital budgeting

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

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

(a) The manufacturing firm's before-tax WACC.

(b) The manufacturing firm's after-tax WACC.

(c) A services firm's before-tax WACC, assuming that the services firm has the same debt-to-assets ratio as the manufacturing firm.

(d) A services firm's after-tax WACC, assuming that the services firm has the same debt-to-assets ratio as the manufacturing firm.

(e) The services firm's levered cost of equity.

Question 70  payout policy

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

(a) Pay out the excess cash by increasing the regular dividend, and cutting it later.

(b) Pay out a special dividend.

(c) Conduct an on or off-market share repurchase.

(d) Conduct a share dividend (also called a 'bonus issue').

(e) Either b or c.

Question 74  WACC, capital structure, CAPM

A firm's weighted average cost of capital before tax (##r_\text{WACC before tax}##) would increase due to:

(a) The firm issuing more debt and using the proceeds to repurchase stock.

(b) The firm issuing more equity and using the proceeds to pay off debt holders.

(c) The firm's industry becoming more systematically risky, for example if it was a mining company whose performance became more sensitive to countries' GDP growth, so the correlation of the firm's returns with the market was higher.

(d) The firm's industry becoming less systematically risky, for example if it was a child care centre and the government announced higher subsidies for parents using child care centres, so the correlation of the firm's returns with the market was lower.

(e) None of the above.

Question 77  interest tax shield

The equations for Net Income (NI, also known as Earnings or Net Profit After Tax) and Cash Flow From Assets (CFFA, also known as Free Cash Flow to the Firm) per year are:

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

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

For a firm with debt, what is the amount of the interest tax shield per year?

(a) ##IntExp.t_c##

(b) ##IntExp/t_c##

(c) ##IntExp.(1-t_c)##

(d) ##IntExp/(1-t_c)##

(e) ##IntExp.(t_c-1)##

Question 78  WACC, capital structure

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) The debt-to-assets (D/V) ratio will increase.

(b) The debt-to-equity ratio (D/E) will increase.

(c) Firm value is likely to have increased due to the higher amount of interest tax shields, assuming that there will not be any costs of financial distress.

(d) The company's after-tax WACC is likely to have decreased.

(e) The company's before-tax WACC is likely to have decreased.

Question 84  WACC, capital structure, capital budgeting

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

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

(a) The required return on equity, ##r_E##

(b) The required return on debt, ##r_D##

(c) The after-tax required return on debt, ##r_D.(1-t_c)##

(d) The after-tax WACC, ##\text{WACC after tax}=\frac{D}{V_L}.r_D.(1-t_c )+\frac{E_L}{V_L}.r_E##

(e) The pre-tax WACC, ##\text{WACC before tax}=\frac{D}{V_L}.r_D+\frac{E_L}{V_L}.r_E##

Question 95  interest tax shield

The equations for Net Income (NI, also known as Earnings or Net Profit After Tax) and Cash Flow From Assets (CFFA, also known as Free Cash Flow to the Firm) per year are:

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

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

For a firm with debt, what is the formula for the present value of interest tax shields if the tax shields occur in perpetuity?

You may assume:

• the value of debt (D) is constant through time,
• The cost of debt and the yield on debt are equal and given by ##r_D##.
• the appropriate rate to discount interest tax shields is ##r_D##.
• ##\text{IntExp}=D.r_D##

(a) ##D.t_c##

(b) ##D.r_D/t_c ##

(c) ##D.r_D.(1-t_c)##

(d) ##D.r_D/(1-t_c)##

(e) ##D.r_D.(t_c-1)##

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

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

Assume that:

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

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

(a) The firm's share price and shareholder wealth will both decrease. This is because the firm will have more debt and therefore more risk so the discount rate applied to its cash flows will be higher, decreasing the value of the firm and therefore the value of the firm's equity and share price.

(b) The firm's share price and shareholder wealth will both increase. This is because the firm will have more debt which will amplify the returns of equity investors. This will mean that returns on equity can be much higher and investors will pay a premium for this, leading to an increase in the stock price.

(c) The firm's share price and shareholder wealth will both increase since it has more debt and therefore more tax shields.

(d) The firm's share price will increase due to the higher value of tax shields. But shareholder wealth will remain unchanged because capital structure is irrelevant when investors can use home-made leverage to create tax-shields themselves.

(e) The firm's share price and shareholder wealth will both increase. This is because the cost of debt is cheaper than equity, leading to a lower (before and after tax) WACC. This lower WACC will lead to a higher value of the firm and a higher share price.

Question 107  interest only loan

You want to buy an apartment worth $300,000. You have saved a deposit of $60,000.

The bank has agreed to lend you $240,000 as an interest only mortgage loan with a term of 30 years. The interest rate is 6% pa and is not expected to change. What will be your monthly payments?

(a) 17,435.74

(b) 1,438.92

(c) 1,414.49

(d) 1,200.00

(e) 666.67

Question 113  WACC, CFFA, capital budgeting

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

Assume the following:

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

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

The mobile phone manufacturing project's:

(a) Unlevered CFFA should be discounted by Google's 10% WACC after tax.

(b) Unlevered CFFA should be discounted by Motorola's 20% WACC after tax.

(c) Levered CFFA should be discounted by Google's 10% WACC after tax.

(d) Levered CFFA should be discounted by Motorola's 20% WACC after tax.

(e) Unlevered CFFA by 15%, the average of Google and Motorola's WACC after tax.

Question 114  WACC, capital structure, risk

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

(a) the firm's industry becoming more systematically risky, for example if it was a mining company and commodities prices varied more strongly and were more positively correlated with the market portfolio.

(b) the firm's industry becoming less systematically risky, for example if it was a child care centre and the government announced permanently higher subsidies for parents' child care expenses.

(c) the firm issuing more debt and using the proceeds to repurchase stock.

(d) the firm issuing more equity and using the proceeds to pay off debt holders.

(e) none of the above.

Question 115  capital structure, leverage, WACC

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

(a) The debt-to-assets (D/V) ratio will decrease.

(b) The debt-to-equity ratio (D/E) will decrease.

(c) The firm's cost of equity will decrease.

(d) The company's after-tax WACC will decrease.

(e) The company's before-tax WACC will decrease.

Question 127  interest expense

A zero coupon bond that matures in 6 months has a face value of $1,000.

The firm that issued this bond is trying to forecast its income statement for the year. It needs to calculate the interest expense of the bond this year.

The bond is highly illiquid and hasn't traded on the market. But the finance department have assessed the bond's fair value to be $950 and this is its book value right now at the start of the year.

Assume that:

• the firm uses the 'effective interest method' to calculate interest expense.
• the market value of the bond is the same as the book value.
• the firm is only interested in this bond's interest expense. Do not include the interest expense for a new bond issued to refinance the current one, as would normally happen.

What will be the interest expense of the bond this year for the purpose of forecasting the income statement?

(a) $0

(b) $50.0000

(c) $51.3158

(d) $102.6316

(e) $1,000.0000

Question 130  debt terminology

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

Question 140  IRR, NPV, profitability index

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

(a) The NPV will be negative and the profitability index will be less than 1.

(b) The NPV will be positive and the profitability index will be more than 1.

(c) The payback period will be positive and the Accounting Rate of Return will be more than the target return.

(d) The NPV will be positive and the profitability index will be negative.

(e) The NPV will be negative and the profitability index will be positive.

Question 142  DDM, income and capital returns

When using the dividend discount model to price a stock:

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

The growth rate of dividends (g):

(a) Is the stock's required return.

(b) Is the stock's expected total return.

(c) Is the stock's expected dividend return.

(d) Is the stock's expected real yield.

(e) Should be less than the expected GDP growth rate of the country where the company does business.

Question 145  NPV, APR, annuity due

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?

(a) $1,388.89

(b) $5,116.18

(c) $5,141.76

(d) $18,966.13

(e) $19,332.80

Question 148  DDM, income and capital returns

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) ## r-g ##

(b) ## \dfrac{d_1}{p_0} ##

(c) ## \dfrac{d_5}{p_4} ##

(d) ## \dfrac{d_5(1+g)^2}{p_6} ##

(e) ## \dfrac{d_3}{p_0(1+r)^2} ##

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 zero-coupon loan, discount loan or bullet loan.

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

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

(a) $838,907.00

(b) $838,986.09

(c) $841,754.97

(d) $889,996.44

(e) $944,108.22

Question 158  DDM, income and capital returns

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) ## g_\text{eff} ##

(b) ## \dfrac{p_1}{p_0} -1 ##

(c) ## \dfrac{d_5}{d_4} -1 ##

(d) ## \dfrac{d_1}{p_0} - 1 ##

(e) ## \dfrac{p_1-p_0}{p_0} ##

Question 163  bond pricing, premium par and discount bonds

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

Which of the following statements is true?

(a) Bonds X and Y are premium bonds.

(b) Bonds X and Y are discount bonds.

(c) Bond X is a discount bond but bond Y is a premium bond.

(d) Bond X is a premium bond but bond Y is a discount bond.

(e) Bonds X and Y are par bonds.

Question 165  DDM, PE ratio, payout ratio

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

Use the general accounting definition of 'payout ratio' which is dividends per share (DPS) divided by earnings per share (EPS) and assume that all cash flows, earnings and rates are real rather than nominal.

A company's forward-looking PE ratio will be the inverse of its total expected return on equity when it has a:

(a) 100% payout ratio and high expected growth in earnings and dividends.

(b) 100% payout ratio and negative expected growth in earnings and dividends.

(c) 100% payout ratio and no expected growth in earnings or dividends.

(d) 0% payout ratio and no expected growth in earnings or dividends.

(e) 0% payout ratio and negative expected growth in earnings and dividends.

Question 167  NPV, IRR

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

(a) The project should be accepted.

(b) The project's IRR is less than its required return.

(c) The project's IRR is more than its required return.

(d) The project's IRR is equal to its required return.

(e) The project is under-priced.

Question 171  DDM, income and capital returns

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

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

Which of the following statements about the Dividend Discount Model is NOT correct?

(a) The dividend yield is equal to ##(r-g)##.

(b) The dividend yield is equal to ##\left( \dfrac{d_1}{p_0} \right)##.

(c) The total return of the stock is equal to ##(r)##.

(d) The total return of the stock is equal to ##\left( \dfrac{d_1+p_0.g}{p_0} \right)##.

(e) The total return of the stock is equal to ##(r+g)##.

Question 175  pay back period, no explanation

A project has the following cash flows. Normally cash flows are assumed to happen at the given time. But here, assume that the cash flows are received smoothly over the year. So the $250 at time 2 is actually earned smoothly from t=1 to t=2:

Project Cash Flows
Time (yrs)	Cash flow ($)
0	-400
1	200
2	250

What is the payback period of the project in years?

(a) 0.20

(b) 1.20

(c) 1.80

(d) 2.25

(e) 2.80

Question 176  CFFA

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

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

(a) CapEx is added in the Net Income (NI) equation so it needs subtracting in the CFFA equation.

(b) CapEx is a financing cash flow that needs to be ignored. Therefore it should be subtracted.

(c) CapEx is not a cash flow, it's a non-cash expense made up by accountants that needs to be subtracted.

(d) CapEx is subtracted to account for the net cash spent on capital assets.

(e) CapEx is subtracted because it's too hard to predict, therefore we exclude it.

Question 178  bond pricing, premium par and discount bonds

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

(a) a ten-year bond with a $4000 face value whose yield to maturity is 6.0% and coupon rate is 6.5% paid semi-annually.

(b) a 6-year bond with a principal of $40,000 and a price of $45,000.

(c) a 15-year bond with a $10,000 face value whose yield to maturity is 8.0% and coupon rate is 10.0% paid semi-annually.

(d) a two-year bond with a $50,000 face value whose yield to maturity is 5.2% and coupon rate is 5.2% paid semi-annually.

(e) None of the above bonds are discount bonds.

Question 182  NPV, IRR, pay back period

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

(a) The project should be rejected.

(b) The project's IRR is more than its required return.

(c) The project's IRR is less than its required return.

(d) The project's IRR is equal to its required return.

(e) The project will never pay itself off, assuming that the discount rate is positive.

Question 186  DDM, income and capital returns

Here's the Dividend Discount Model, used to price stocks:

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

All rates are effective annual rates and the cash flows (##d_1##) are received every year. Note that the r and g terms in the above DDM could also be labelled: ###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) The expected dividend in 3 years will be: ##d_3 = d_1 (1+g)^2##.

(b) The expected price in 3 years will be: ##p_3 = p_0 (1+g)^3##.

(c) The expected effective 3 year total return measured over 3 years is equal to: ##r_{\text{total, 0}\rightarrow\text{3yr, eff 3yr}} = (1+r)^3-1##.

(d) The expected effective 3 year total return measured over 3 years will be: ##r_{\text{total, 0}\rightarrow\text{3yr, eff 3yr}} = \dfrac{p_3-p_0+d_3}{p_0}##.

(e) The expected effective annual dividend yield will be: ##r_{\text{dividend, 0}\rightarrow\text{3yr, eff annual}} = \dfrac{d_1}{p_0}##.

Question 191  NPV, IRR, profitability index, pay back period

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

(a) The project should be rejected.

(b) The project's IRR is more than its required return.

(c) The project's payback period will be less than 3 years.

(d) The project's IRR is equal to its required return.

(e) The project's NPV is greater than 1.

Question 192  NPV, APR

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) 79.72%

(b) 24.00%

(c) 21.24%

(d) 20.28%

(e) 12.00%

Question 200  NPV, no explanation

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) 14.85

(b) 15.84

(c) 16.89

(d) 19.20

(e) 21.82

Question 201  DDM, income and capital returns

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

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

If the assumptions of the DDM hold and the stock is fairly priced, which one of the following statements is NOT correct? The long term expected:

(a) Dividend growth rate is equal to the long term expected growth rate of the stock price.

(b) Dividend growth rate is equal to the long term expected capital return of the stock.

(c) Dividend growth rate is equal to the long term expected dividend yield.

(d) Total return of the stock is equal to its long term required return.

(e) Total return of the stock is equal to the company's long term cost of equity.

Question 204  time calculation, fully amortising loan, APR

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?

(a) 38.87 months, which is 3.24 yrs.

(b) 47.91 months, which is 3.99 yrs.

(c) 160.72 months, which is 13.39 yrs.

(d) 164.65 months, which is 13.72 yrs.

(e) None of the above.

Question 205  depreciation tax shield, CFFA

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

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

(a) 'Straight line' or 'prime cost' depreciation, which allocates equal depreciation expenses over each year of the asset's life.

(b) 'Diminishing value' or 'reducing balance' depreciation, which allocates more depreciation expense at the start of the asset's life and less towards the end.

(c) No depreciation at all, so the asset is always kept on the books as being the same value that it was bought for. The asset will cause no depreciation expense in any year.

(d) Allocating all of the depreciation expense to the final year of the asset's life.

(e) Allocating all of the depreciation expense to the first year of the asset's life. Accountants would call this 'expensing' the asset, rather than 'capitalising' it and depreciating it slowly.

Question 206  CFFA, interest expense, interest tax shield

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

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

Annual interest expense is equal to:

(a) the bond's face value multiplied by its annual yield to maturity.

(b) the bond's face value multiplied by its annual coupon rate.

(c) the bond's market price at the start of the year multiplied by its annual yield to maturity.

(d) the bond's market price at the start of the year multiplied by its annual coupon rate.

(e) the future value of the actual cash payments of the bond over the year, grown to the end of the year, and grown by the bond's yield to maturity.

Question 207  income and capital returns, bond pricing, coupon rate, no explanation

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

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

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

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

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

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

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

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

(a) coupon rate = ##\dfrac{C_{0.5}+C_{1}}{F_T}##, ##r_\text{income, 0 to 1}=\dfrac{C_{0.5}(1+r_\text{total})^{0.5}+C_{1}}{P_0}##

(b) coupon rate = ##\dfrac{2 \times C_{0.5}}{F_T}##, ##r_\text{income, 0 to 1}=\dfrac{C_{0.5}(1+r_\text{capital})^{0.5}+C_{1}}{P_0}##

(c) coupon rate = ##\dfrac{2 \times C_{1}}{P_0}##, ##r_\text{income, 0 to 1}=\dfrac{C_{0.5}+C_{1}}{P_0}##

(d) coupon rate = ##\dfrac{2 \times C_{1}}{P_0}##, ##r_\text{income, 0 to 1}=\dfrac{2 \times C_{1}}{P_0}##

(e) coupon rate = ##\dfrac{2 \times C_{1}}{F_T}##, ##r_\text{income, 0 to 1}=\dfrac{C_{0.5}(1+r_\text{total})^{0.5}+C_{1}}{F_T}##

Question 208  CFFA

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

UniBar Corp
Income Statement for
year ending 30th June 2013
	$m
Sales	80
COGS	40
Operating expense	15
Depreciation	10
Interest expense	5
Income before tax	10
Tax at 30%	3
Net income	7

UniBar Corp
Balance Sheet
as at 30th June	2013	2012
	$m	$m
Assets
Current assets	120	90
PPE
Cost	360	320
Accumul. depr.	40	30
Carrying amount	320	290
Total assets	440	380
Liabilities
Current liabilities	110	60
Non-current liabilities	190	180
Owners' equity
Retained earnings	95	95
Contributed equity	45	45
Total L and OE	440	380

 

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

(a) 12

(b) 2

(c) -8

(d) -18

(e) 48

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.

An old rule of thumb in the real estate industry is that properties should yield a 5% pa rental return. Some 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.

(a) The nominal property price is expected to grow by approximately 9% pa.

(b) The nominal property price is expected to grow by approximately 5% pa.

(c) The nominal property price is expected to grow by approximately 4% pa.

(d) The real property price is expected to grow by approximately 7% pa.

(e) The real property price is expected to grow by approximately 6% pa.

Question 213  income and capital returns, bond pricing, premium par and discount bonds

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

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

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

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

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

Select the most correct statement.

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

(a) Premium bond will increase.

(b) Premium bond will decrease.

(c) Premium bond will remain constant.

(d) Par bond will increase.

(e) Par bond will decrease.

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 227  bond pricing, premium par and discount bonds

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

(a) a ten-year bond with a $4,000 face value whose yield to maturity is 6.0% and coupon rate is 5.9% paid semi-annually.

(b) a fifteen-year bond with a $10,000 face value whose yield to maturity is 8.0% and coupon rate is 7.8% paid semi-annually.

(c) a five-year bond with a $2,000 face value whose yield to maturity is 7.0% and coupon rate is 7.2% paid semi-annually.

(d) a two-year bond with a $50,000 face value whose yield to maturity is 5.2% and coupon rate is 5.2% paid semi-annually.

(e) None of the above bonds are premium bonds.

Question 229  bond pricing

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

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

(a) The zero-coupon bond and the 7% semi-annual coupon bond were both discount bonds but now they are both premium bonds.

(b) The zero-coupon bond and the 7% semi-annual coupon bond were both premium bonds but now they are both discount bonds.

(c) When yields fell, the investor made a capital loss on both bonds.

(d) When yields fell, the investor made a capital gain on both bonds.

(e) When yields fell, the investor made a capital gain on the zero coupon bond but a loss on the 7% semi-annual coupon bond.

Question 234  debt terminology

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

(a) Discount loan

(b) Par loan

(c) Premium loan

(d) Deferred repayment loan

(e) Fully amortising loan.

Question 237  WACC, Miller and Modigliani, interest tax shield

Which of the following discount rates should be the highest for a levered company? Ignore the costs of financial distress.

(a) Cost of debt (##r_\text{D}##).

(b) Unlevered cost of equity (##r_\text{E, U}##).

(c) Levered cost of equity (##r_\text{E, L}##).

(d) Levered before-tax WACC (##r_\text{V, LxITS}##).

(e) Levered after-tax WACC (##r_\text{V, LwITS}##).

Question 238  CFFA, leverage, interest tax shield

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

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

(a) The company is increasing its debt-to-assets and debt-to-equity ratios. These are types of 'leverage' or 'gearing' ratios.

(b) The company will pay less tax to the government due to the benefit of interest tax shields.

(c) The company's net income, also known as earnings or net profit after tax, will fall.

(d) The company's expected levered firm free cash flow (FFCF or CFFA) will be higher due to tax shields.

(e) The company's expected levered equity free cash flow (EFCF) will not change.

Question 239  income and capital returns, inflation, real and nominal returns and cash flows, interest only loan

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

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

(a) Approximately 6%.

(b) Approximately 4%.

(c) Approximately 2%.

(d) Approximately 0%.

(e) Approximately -2%.

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 in a world with zero taxes and perfect information since investors can make their own leverage. Therefore corporate capital structure policy is irrelevant since investors can achieve their own desired leverage at the personal level by borrowing or lending on their own.

This principal of 'home-made' or 'do-it-yourself' leverage can also be applied to other topics. Read the following statements to decide which are true:

(I) Payout policy: a firm's managers should not try to achieve a particular pattern of equity payout.

(II) Agency costs: a firm's managers should not try to minimise agency costs.

(III) Diversification: a firm's managers should not try to diversify across industries.

(IV) Shareholder wealth: a firm's managers should not try to maximise shareholders' wealth.

Which of the above statement(s) are true?

(a) I only.

(b) I and II only.

(c) I and III only.

(d) III only.

(e) All are true.

Question 252  NPV

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?

(a) $36,555.8912

(b) $23,666.6667

(c) $21,450.1511

(d) $18,277.9456

(e) $16,666.6667

Question 255  bond pricing

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

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

(a) 94.20452353

(b) 100

(c) 106

(d) 112

(e) The bond is priceless.

Question 263  DDM, income and capital returns

A company's shares just paid their annual dividend of $2 each.

The stock price is now $40 (just after the dividend payment). The annual dividend is expected to grow by 3% every year forever. The assumptions of the dividend discount model are valid for this company.

What do you expect the effective annual dividend yield to be in 3 years (dividend yield from t=3 to t=4)?

(a) 0.03

(b) 0.0409

(c) 0.044

(d) 0.05

(e) 0.0515

Question 264  DDM

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

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

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

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

(a) ##P_{2.5}=P_0 (1+g)^{2.5} ##

(b) ##P_{2.5}=P_0 (1+r)^{2.5} ##

(c) ##P_{2.5}=P_0 (1+g)^2 (1+r)^{0.5} ##

(d) ##P_{2.5}=P_0 (1+r)^2 (1+g)^{0.5} ##

(e) ##P_{2.5}=P_0 (1+r)^3 (1+g)^{-0.5} ##

Question 268  time calculation, APR

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.

(a) 27 months (t=27 months).

(b) 38 months (t=38 months).

(c) 40 months (t=40 months).

(d) 43 months (t=43 months).

(e) 79 months (t=79 months).

Question 270  real estate, DDM, effective rate conversion

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

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

Assume that:

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

(a) $415,149.4048

(b) $438,252.6707

(c) $441,067.7356

(d) $444,155.5276

(e) $455,263.0844

Question 289  DDM, expected and historical returns, ROE

In the dividend discount model:

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

The return ##r## is supposed to be the:

(a) Expected future total return of the market price of equity.

(b) Expected future total return of the book price of equity.

(c) Actual historical total return on the market price of equity.

(d) Actual historical total return on the book price of equity.

(e) Actual historical return on equity (ROE) defined as (Net Income / Owners Equity).

Question 290  APR, effective rate, debt terminology

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

(a) An effective annual rate could be called: "a yearly rate compounding per year".

(b) An APR compounding monthly could be called: "a yearly rate compounding per month".

(c) An effective monthly rate could be called: "a yearly rate compounding per month".

(d) An APR compounding daily could be called: "a yearly rate compounding per day".

(e) An effective 2-year rate could be called: "a 2-year rate compounding every 2 years".

Question 303  WACC, CAPM, CFFA

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

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

(a) ##V_L = n_\text{shares}.P_\text{share} + n_\text{bonds}.P_\text{bond}##

(b) ##V_L = n_\text{shares}.\dfrac{\text{Dividend per share}}{r_f + \beta_{EL}(r_m - r_f)} + n_\text{bonds}.\dfrac{\text{Coupon per bond}}{r_f + \beta_D(r_m - r_f)}##

(c) ##V_L = \dfrac{\text{CFFA}_{L}}{r_\text{WACC before tax}}##

(d) ##V_L = \dfrac{\text{CFFA}_{U}}{r_\text{WACC after tax}}##

(e) ##V_L = \dfrac{\text{CFFA}_{L}}{r_\text{WACC after tax}}##

Where:

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

Question 309  stock pricing, ex dividend date

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

The share price is expected to fall during the:

(a) Day of the payment date, between the payment date's morning opening price and afternoon closing price.

(b) Night before the payment date, between the previous day's afternoon closing price and the payment date's morning opening price.

(c) Day of the ex-dividend date, between the ex-dividend date's morning opening price and afternoon closing price.

(d) Night before the ex-dividend date, between the last with-dividend date's afternoon closing price and the ex-dividend date's morning opening price.

(e) Day of the last with-dividend date, between the with-dividend date's morning opening price and afternoon closing price.

Question 328  bond pricing, APR

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

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

(a) $1,000

(b) $1,019.9181

(c) $1,033.8330

(d) $1,052.7005

(e) $1,060.5226

Question 329  DDM, expected and historical returns

In the dividend discount model:

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

The pronumeral ##g## is supposed to be the:

(a) Expected future growth rate of the dividend.

(b) Actual historical growth rate of the dividend.

(c) Expected future growth rate of the total required return on equity r.

(d) Actual historical growth rate of the market share price.

(e) Actual historical growth rate of the return on equity (ROE) defined as (Net Income / Owners Equity).

Question 331  DDM, income and capital returns

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

### p_0= \frac{c_1}{r-g} ###

Which expression is equal to the expected dividend return?

(a) ##(c_1/p_0 ) -1##

(b) ##(p_1/p_0) -1##

(c) ##(c_5/c_4) -1##

(d) ##c_3/p_2##

(e) ##(p_1-p_0)/p_0##

Question 332  bond pricing, premium par and discount bonds

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?

(a) Bonds X and Y are premium bonds.

(b) Bonds X and Y are discount bonds.

(c) Bond X is a discount bond but bond Y is a premium bond.

(d) Bond X is a premium bond but bond Y is a discount bond.

(e) Bonds X and Y are par bonds.

Question 342  CFFA, capital budgeting

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, }t-1} = \dfrac{FFCF_{\text{terminal, }t}}{r-g}###

Which point corresponds to the best time to calculate the terminal value?

(a) Point A.

(b) Point B.

(c) Point C.

(d) Any of the points.

(e) None of the points.

Question 343  CFFA, capital budgeting

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, }t-1} = \dfrac{FFCF_{\text{terminal, }t}}{r-g}###

Which point corresponds to the best time to calculate the terminal value?

(a) Point A.

(b) Point B.

(c) Point C.

(d) Any of the points.

(e) None of the points.

Question 344  CFFA, capital budgeting

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, }t-1} = \dfrac{FFCF_{\text{terminal, }t}}{r-g}###

Which point corresponds to the best time to calculate the terminal value?

(a) Point A.

(b) Point B.

(c) Point C.

(d) Any of the points.

(e) None of the points.

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

1. 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.
2. 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 tax-deductible 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.

(a) 750,000 and 750,000.

(b) 750,000 and 951,682.

(c) 750,000 and 987,396.

(d) 750,000 and 1,009,805.

(e) 750,000 and 1,024,807.

Question 347  PE ratio, Multiples valuation

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

(a) Common equity in small private companies.

(b) Common equity in large private companies.

(c) Common equity in listed public companies.

(d) Fixed term bonds of listed public companies.

(e) Real estate.

Question 350  CFFA

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

Sidebar Corp
Income Statement for
year ending 30th June 2013
	$m
Sales	405
COGS	100
Depreciation	34
Rent expense	22
Interest expense	39
Taxable Income	210
Taxes at 30%	63
Net income	147

Sidebar Corp
Balance Sheet
as at 30th June	2013	2012
	$m	$m
Cash	0	0
Inventory	70	50
Trade debtors	11	16
Rent paid in advance	4	3
PPE	700	680
Total assets	785	749
Trade creditors	11	19
Bond liabilities	400	390
Contributed equity	220	220
Retained profits	154	120
Total L and OE	785	749

 

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

The cash flow from assets was:

(a) $138m

(b) $142m

(c) $143m

(d) $172m

(e) $176m

Question 353  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 6% pa and nominal capital return of 3% pa.

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

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

(a) 3.9216%, 2.9412%, 0.9804%.

(b) 3.9216%, 0.9804%, 2.9412%.

(c) 3.9216%, 0.9804%, 0.9804%.

(d) 1.9804%, 1.0000%, 0.9804%.

(e) 1.9608%, 0.9804%, 0.9804%.

Question 354  PE ratio, Multiples valuation

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

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

(a) Illiquid small private companies.

(b) High growth technology firms.

(c) Firms expected to have temporarily low earnings over the next year, but with higher earnings later.

(d) Firms with a very low level of systematic risk.

(e) Firms whose assets include a very large proportion of cash.

Question 361  CFFA

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

• Make $5m in sales, $1.9m in net income and $2m in equity free cash flow (EFCF).
• Pay dividends of $1m.
• Complete a $1.3m share buy-back.

Assume that:

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

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

(a) $2m

(b) $1m

(c) $0.4m

(d) $0.3m

(e) No new shares need to be issued, the firm will be sufficiently financed.

Question 366  opportunity cost, NPV, CFFA

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

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

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

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

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

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

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

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

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

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

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

(a) Method 1 only.

(b) Method 2 only.

(c) Method 3 only.

(d) Methods 1 and 2 only.

(e) Methods 1 and 3 only.

Question 372  debt terminology

Which of the following statements is NOT correct? Borrowers:

(a) Receive cash at the start and promise to pay cash in the future, as set out in the debt contract.

(b) Are debtors.

(c) Owe money.

(d) Are funded by debt.

(e) Buy debt.

Question 373  debt terminology

Which of the following statements is NOT correct? Lenders:

(a) Are long debt.

(b) Invest in debt.

(c) Are owed money.

(d) Provide debt funding.

(e) Have debt liabilities.

Question 380  leverage, capital structure

The "interest expense" on a company's annual income statement is equal to the cash interest payments (but not principal payments) made to debt holders during the year. or ?

Question 401  capital budgeting, CFFA

The hardest and most important aspect of business project valuation is the estimation of the:

(a) Diversifiable standard deviation of asset returns.

(b) Systematic standard deviation of asset returns.

(c) Proportion of debt and equity used to fund the assets.

(d) Cash flows from assets.

(e) Risk free rate.

Question 411  WACC, capital structure

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?

(a) The firm's WACC before tax will rise.

(b) The firm's WACC after tax will rise.

(c) The firm's required return on equity will be lower.

(d) The firm's net income will be higher.

(e) The firm's free cash flow will be lower.

Question 414  PE ratio, pay back period, no explanation

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) This firm's expected capital return equals zero.

(b) This firm's expected total return and income return are equal.

(c) This firm's forward looking PE ratio will equal the inverse of the firm's expected income return.

(d) This firm's forward looking PE ratio will equal the inverse of the firm's expected capital return.

(e) This firm's forward looking PE ratio is equal to the expected payback period, which is the time it will take for the sum of the cash flows to equal the share price.

Question 442  economic depreciation, no explanation

A fairly valued share's current price is $4 and it has a total required return of 30%. Dividends are paid annually and next year's dividend is expected to be $1. After that, dividends are expected to grow by 5% pa. All rates are effective annual returns.

What is the expected dividend cash flow, economic depreciation, and economic income and economic value added (EVA) that will be earned over the second year (from t=1 to t=2) and paid at the end of that year (t=2)?

(a) $1.3, -$0.26, $1.56, $0

(b) $1.25, -$0.25, $1.5, $0

(c) $1.1025, -$0.2205, $1.323, $0

(d) $1.05, -$0.21, $1.26, $0

(e) $1, -$0.2, $1.2, $0

Question 443  corporate financial decision theory, investment decision, financing decision, working capital decision, payout policy

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

(a) Investment decision.

(b) Financing decision.

(c) Working capital decision.

(d) Payout policy decision.

(e) Capital or labour decision.

Question 444  investment decision, corporate financial decision theory

The investment decision primarily affects which part of a business?

(a) Assets.

(b) Liabilities and owner's equity.

(c) Current assets and current liabilities.

(d) Dividends and buy backs.

(e) Net income, also known as earnings or net profit after tax.

Question 445  financing decision, corporate financial decision theory

The financing decision primarily affects which part of a business?

(a) Assets.

(b) Liabilities and owner's equity.

(c) Current assets and current liabilities.

(d) Dividends and buy backs.

(e) Net income, also known as earnings or net profit after tax.

Question 446  working capital decision, corporate financial decision theory

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

(a) Assets.

(b) Liabilities and owner's equity.

(c) Current assets and current liabilities.

(d) Dividends and buy backs.

(e) Net income, also known as earnings or net profit after tax.

Question 447  payout policy, corporate financial decision theory

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

(a) Assets.

(b) Liabilities and owner's equity.

(c) Current assets and current liabilities.

(d) Dividends and buy backs.

(e) Net income, also known as earnings or net profit after tax.

Question 452  limited liability, expected and historical returns

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

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

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

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

(a) ##0≤p<∞## and ##0≤r< 1##

(b) ##0≤p<∞## and ##-1≤r< ∞##

(c) ##0≤p<∞## and ##0≤r< ∞##

(d) ##0≤p<∞## and ##-∞≤r< ∞##

(e) ##-∞<p<∞## and ##-∞<r< ∞##

Question 453  DDM, income and capital returns

The perpetuity with growth equation is:

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

Which of the following is NOT equal to the expected capital return as an effective annual rate?

(a) ##g##

(b) ##r+\dfrac{C_1}{P_0}##

(c) ##\dfrac{C_2}{C_1} -1##

(d) ##\dfrac{C_3-C_2}{C_2} ##

(e) ##\left( \dfrac{P_5}{P_3} \right)^{1/2}-1##

Question 457  PE ratio, Multiples valuation

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

(a) Highly liquid publically listed firms.

(b) Firms in a declining industry with very low or negative earnings growth.

(c) Firms expected to have temporarily low earnings over the next year, but with higher earnings later.

(d) Firms whose returns have a very low level of systematic risk.

(e) Firms whose assets include a very large proportion of cash.

Question 460  bond pricing, premium par and discount bonds

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

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

(a) A bullet loan has no interest payments but it does have a face value. Therefore it's a discount loan.

(b) A fully amortising loan has interest payments but does not have a face value. Therefore it's a premium loan.

(c) An interest only loan has interest payments and its price and face value are equal. Therefore it's a par loan.

(d) A zero coupon bond has no coupon payments but it does have a face value. Therefore it's a premium bond.

(e) A balloon loan has interest payments and its face value is more than its price. Therefore it's a discount loan.

Question 467  book and market values

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

(a) The market value of equity of a listed company's common stock is equal to the number of common shares multiplied by the share price.

(b) The book value of equity is the sum of contributed equity, retained profits and reserves.

(c) A company's book value of equity is recorded in its income statement, also known as the 'profit and loss' or the 'statement of financial performance'.

(d) A new company's market value of equity equals its book value of equity the moment that its shares are first sold. From then on, the market value changes continuously but the book value is recorded at historical cost which typically only changes due to retained profits.

(e) To buy all of the firm's shares, generally a price close to the market value of equity will have to be paid.

Question 468  PE ratio

A firm has 1 million shares which trade at a price of $30 each. The firm is expected to announce earnings of $3 million at the end of the year and pay an annual dividend of $1.50 per share.

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

(a) 20

(b) 10

(c) 3

(d) 2

(e) 0.5

Question 471  risk, accounting ratio

High risk firms in danger of bankruptcy tend to have:

(a) Low debt to assets ratios.

(b) High quick ratios.

(c) Low interest coverage ratios.

(d) Positive amounts of net working capital.

(e) High net profit margins.

Question 474  PE ratio

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

What was CBA's backwards-looking price-earnings ratio?

(a)17.06

(b) 0.063

(c) 15.88

(d) 3.21

(e) 8.44

Question 477  income and capital returns

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

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

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

Which of the following is the expected capital return?

(a) ##c_1##

(b) ##p_1-p_0##

(c) ##\dfrac{c_1}{p_0} ##

(d) ##\dfrac{p_1}{p_0} -1##

(e) ##\dfrac{p_1}{p_0} ##

Question 480  NPV, real estate, DDM

What type of present value equation is best suited to value a residential house investment property that is expected to pay constant rental payments forever? Note that 'constant' has the same meaning as 'level' in this context.

(a) The single cash flow equation.

(b) The level annuity equation.

(c) The annuity with growth equation.

(d) The level perpetuity equation.

(e) The perpetuity with growth equation.

Question 483  PE ratio

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

What was MSFT's backwards-looking price-earnings ratio?

(a) $21.01

(b) 21.01

(c) $18.75

(d) 18.75

(e) 18.75%

Question 485  capital budgeting, opportunity cost, sunk cost

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

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

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

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

(a) A sunk cost.

(b) An opportunity cost.

(c) A negative side effect.

(d) A positive side effect.

(e) A depreciation expense.

Question 487  capital budgeting, opportunity cost, sunk cost

A young lady is trying to decide if she should attend university or begin working straight away in her home town.

The young lady's grandma says that she should not go to university because she is less likely to marry the local village boy whom she likes because she will spend less time with him if she attends university.

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

The cost of not marrying the local village boy should be classified as:

(a) A sunk cost.

(b) An opportunity cost.

(c) A non-pecuniary cost that should be disregarded.

(d) A positive side effect.

(e) A depreciation expense.

Question 488  income and capital returns, payout policy, payout ratio, DDM

Two companies BigDiv and ZeroDiv are exactly the same except for their dividend payouts.

BigDiv pays large dividends and ZeroDiv doesn't pay any dividends.

Currently the two firms have the same earnings, assets, number of shares, share price, expected total return and risk.

Assume a perfect world with no taxes, no transaction costs, no asymmetric information and that all assets including business projects are fairly priced and therefore zero-NPV.

All things remaining equal, which of the following statements is NOT correct?

(a) BigDiv is expected to have a lower capital return than ZeroDiv in the future.

(b) BigDiv is expected to have a lower total return than ZeroDiv in the future.

(c) ZeroDiv's assets are likely to grow faster than BigDiv's.

(d) ZeroDiv's share price will increase faster than BigDiv's.

(e) BigDiv currently has a higher payout ratio than ZeroDiv.

Question 490  expected and historical returns, accounting ratio

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

(a) total required yield

(b) cost of capital

(c) discount rate

(d) opportunity cost of capital

(e) accounting rate of return

Question 491  capital budgeting, opportunity cost, sunk cost

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

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

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

(a) A sunk cost.

(b) An opportunity cost.

(c) A negative side effect.

(d) A capital expense.

(e) A depreciation expense.

Question 492  capital budgeting, opportunity cost, sunk cost

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

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

(a) A sunk cost.

(b) An opportunity cost.

(c) A negative side effect.

(d) A capital expense.

(e) A depreciation expense.

Question 493  PE ratio

A firm has 2m shares and a market capitalisation of equity of $30m. The firm just announced earnings of $5m and paid an annual dividend of $0.75 per share.

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

(a) 2.5

(b) 3

(c) 6

(d) 15

(e) 20

Question 496  NPV, IRR, pay back period

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

Assume that the initial $10m cost is funded using the firm's existing cash so no new equity or debt will be raised. The cost of capital is 10% pa.

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

(a) The NPV is zero.

(b) The IRR is 10% pa, equal to the 10% cost of capital.

(c) The payback period is two years assuming that the whole $12.1m cash flow occurs at t=2, or 1.826 years if the $12.1m cash flow is paid smoothly over the second year.

(d) The project could be accepted or rejected, the owners would be indifferent.

(e) If the project is accepted then the market value of the firm's assets will increase by $2.1m more than it would otherwise if the project was rejected.

Question 497  income and capital returns, DDM, ex dividend date

A stock will pay you a dividend of $10 tonight if you buy it today. Thereafter the annual dividend is expected to grow by 5% pa, so the next dividend after the $10 one tonight will be $10.50 in one year, then in two years it will be $11.025 and so on. The stock's required return is 10% pa.

What is the stock price today and what do you expect the stock price to be tomorrow, approximately?

(a) $200 today and $210 tomorrow.

(b) $210 today and $220 tomorrow.

(c) $220 today and $230 tomorrow.

(d) $210 today and $200 tomorrow.

(e) $220 today and $210 tomorrow.

Question 504  CFFA

Read the following financial statements and calculate the firm's free cash flow over the 2014 financial year.

UBar Corp
Income Statement for
year ending 30th June 2014
	$m
Sales	293
COGS	200
Rent expense	15
Gas expense	8
Depreciation	10
EBIT	60
Interest expense	0
Taxable income	60
Taxes	18
Net income	42

UBar Corp
Balance Sheet
as at 30th June	2014	2013
	$m	$m
Assets
Cash	30	29
Accounts receivable	5	7
Pre-paid rent expense	1	0
Inventory	50	46
PPE	290	300
Total assets	376	382
Liabilities
Trade payables	20	18
Accrued gas expense	3	2
Non-current liabilities	0	0
Contributed equity	212	212
Retained profits	136	150
Asset revaluation reserve	5	0
Total L and OE	376	382

 

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

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

(a) $51

(b) $52

(c) $58

(d) $61

(e) $62

Question 508  income and capital returns

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

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

(a) ##r_\text{total} = \dfrac{c_1+p_1-p_0}{p_0} ##

(b) ##r_\text{total} = \dfrac{c_1+p_1}{p_0} - 1##

(c) ##r_\text{total} = \dfrac{c_1}{p_0} + \dfrac{p_1-p_0}{p_0}##

(d) ##r_\text{total} = \dfrac{c_1}{p_0} + \dfrac{p_1}{p_0} ##

(e) ##r_\text{total} = \dfrac{c_1}{p_0} + \dfrac{p_1}{p_0} - 1##

Question 512  capital budgeting, CFFA

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

Project Data
Project life	2 years
Initial investment in equipment	$6m
Depreciation of equipment per year for tax purposes	$1m
Unit sales per year	4m
Sale price per unit	$8
Variable cost per unit	$3
Fixed costs per year, paid at the end of each year	$1.5m
Tax rate	30%

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

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

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

(a) -6,   12.25,   16.68

(b) -6.8,   13.25,   14.05

(c) -6.8,   13.25,   15.88

(d) -6.8,   13.25,   18.51

(e) -6.8,   13.25,   17.71

Question 514  corporate financial decision theory, idiom

The expression 'cash is king' emphasizes the importance of having enough cash to pay your short term debts to avoid bankruptcy. Which business decision is this expression most closely related to?

(a) Investment decision.

(b) Financing decision.

(c) Working capital decision.

(d) Payout policy decision.

(e) Capital or labour decision.

Question 515  corporate financial decision theory, idiom

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

(a) Investment decision.

(b) Financing decision.

(c) Working capital decision.

(d) Payout policy decision.

(e) Diversification decision.

Question 516  corporate financial decision theory

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

(a) Investment decision.

(b) Financing decision.

(c) Working capital decision.

(d) Payout policy decision.

(e) Capital or labour decision.

Question 519  DDM

A stock is just about to pay a dividend of $1 tonight. Future annual dividends are expected to grow by 2% pa. The next dividend of $1 will be paid tonight, and the year after that the dividend will be $1.02 (=1*(1+0.02)^1), and a year later 1.0404 (=1*(1+0.04)^2) and so on forever.

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

Calculate the current stock price.

(a) $10

(b) $12.254902

(c) $12.5

(d) $12.75

(e) $13.75

Question 520  NPV, DDM

The following cash flows are expected:

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

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

(a) $875.549502

(b) $921.135446

(c) $971.279985

(d) $1,026.438978

(e) $1,119.690058

Question 521  NPV, Annuity

The following cash flows are expected:

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

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

(a) $573.977303

(b) $598.028469

(c) $624.484752

(d) $700.028893

(e) $736.685218

Question 525  income and capital returns, real and nominal returns and cash flows, inflation

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

Notes and coins:

(a) Pay no income cash flow.

(b) Have a nominal total return of zero.

(c) Have a nominal capital return of zero.

(d) Have a nominal income return of zero.

(e) Have a real total return of zero.

Question 526  real and nominal returns and cash flows, inflation, no explanation

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

(a) ##C_\text{real, t}=C_\text{nominal,t}.(1+r_\text{inflation})^t##

(b) ##C_\text{real,t}=\dfrac{C_\text{nominal,t}}{(1+r_\text{inflation})^t} ##

(c) ##C_\text{real,t}=\dfrac{C_\text{nominal,t}}{r_\text{inflation}} ##

(d) ##C_\text{real,t}=C_\text{nominal,t}.r_\text{inflation} ##

(e) ##C_\text{real,t}=C_\text{nominal,t}.r_\text{inflation}.t##

Question 538  bond pricing, income and capital returns, no explanation

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

(a) Are discount bonds.

(b) Have positive expected capital returns.

(c) Have higher expected income returns than total returns.

(d) Have prices less than their face values.

(e) Have significant credit risk.

Question 539  debt terminology, fully amortising loan, bond pricing

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

(a) Discount loan

(b) Par loan

(c) Premium loan

(d) Deferred repayment loan

(e) Interest only loan

Question 540  APR, effective rate, no explanation

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

(a) An effective semi-annual rate could be called: "a six month rate compounding per six months".

(b) An APR compounding semi-annually could be called: "a yearly rate compounding per six months".

(c) An effective monthly rate could be called: "a monthly rate compounding every month".

(d) An APR compounding monthly could be called: "a monthly rate compounding per year".

(e) An effective daily rate could be called: "a daily rate compounding every day".

Question 541  debt terminology

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

(a) Buy debt.

(b) Are debtors.

(c) Have debt assets.

(d) Provide debt funding.

(e) Are lenders.

Question 545  income and capital returns, fully amortising loan, no explanation

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

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

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

(a) Income and capital returns both rise.

(b) Income and capital returns both fall.

(c) Income return rises and its capital return falls.

(d) Income return falls and its capital return rises.

(e) Income and capital returns are constant.

Question 546  income and capital returns, interest only loan, no explanation

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

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

An interest-only loan's expected:

(a) Income and capital returns both rise over time.

(b) Income and capital returns both fall over time.

(c) Income return rises and its capital return falls over time.

(d) Income return falls and its capital return rises over time.

(e) Income and capital returns are constant through time.

Question 547  PE ratio, Multiples valuation, DDM, income and capital returns, no explanation

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

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

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

(a) Equal the inverse of the firm's nominal income return.

(b) Equal the inverse of the firm's real total return.

(c) Equal the inverse of the firm's real capital return.

(d) Equal the expected payback period of an investor who intends to buy the firm's equity at the current price.

(e) Be lower than that of faster growing firms that pay lower dividends and re-invest in themselves.

Note: The inverse of x is 1/x.

Question 554  inflation, real and nominal returns and cash flows

On his 20th birthday, a man makes a resolution. He will put $30 cash under his bed at the end of every month starting from today. His birthday today is the first day of the month. So the first addition to his cash stash will be in one month. He will write in his will that when he dies the cash under the bed should be given to charity.

If the man lives for another 60 years, how much money will be under his bed if he dies just after making his last (720th) addition?

Also, what will be the real value of that cash in today's prices if inflation is expected to 2.5% pa? Assume that the inflation rate is an effective annual rate and is not expected to change.

The answers are given in the same order, the amount of money under his bed in 60 years, and the real value of that money in today's prices.

(a) $21,600,     $95,035.46

(b) $21,600,     $49,515.44

(c) $21,600,     $4,909.33

(d) $21,600,     $2,557.86

(e) $11,254.05,     $2,557.86

Question 572  bond pricing, zero coupon bond, term structure of interest rates, expectations hypothesis, forward interest rate, yield curve

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

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

Which of the following statements is NOT correct?

(a) ##r_{0-3}## is the three year spot rate, given as an effective annual rate.

(b) ##r_{0-1}## is the one year forward rate, given as an effective annual rate.

(c) ##r_{1-2}## is the one year forward rate one year ahead, given as an effective annual rate.

(d) ##r_{2-3}## is the one year forward rate two years ahead, given as an effective annual rate.

(e) ##r_{1-3} = \left((1+r_{1-2})(1+r_{2-3})\right)^{1/2}-1## is the two year forward rate, one year ahead, given as an effective annual rate.

Question 573  bond pricing, zero coupon bond, term structure of interest rates, expectations hypothesis, liquidity premium theory, forward interest rate, yield curve

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

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

Which of the following statements is NOT correct?

(a) If the expectations hypothesis is true, then the forward rates are the expected future spot rates.

(b) If the liquidity premium theory is true, then the forward rates are lower than the expected future spot rates due to the liquidity premium.

(c) The yield curve is normal when: ##r_{0-1} < r_{1-2} < r_{2-3}##.

(d) The yield curve is flat when: ##r_{0-1} = r_{1-2} = r_{2-3}##.

(e) The yield curve is inverse when: ##r_{0-1} > r_{1-2} > r_{2-3}##.

Question 578  inflation, real and nominal returns and cash flows

Which of the following statements about inflation is NOT correct?

(a) Real returns approximately equal nominal returns less the inflation rate.

(b) Constant prices are the same as real prices.

(c) Current prices are the same as nominal prices.

(d) If your nominal wage grows by inflation, then your real wage won't change because you will be able to buy the same amount of goods and services as before.

(e) Interest rates advertised at the bank are usually quoted in real terms.

Question 607  debt terminology

You deposit cash into your bank account. Have you or your money?

Question 608  debt terminology

You deposit cash into your bank account. Have you or debt?

Question 609  debt terminology

You deposit cash into your bank account. Have you or debt?

Question 610  debt terminology

You deposit cash into your bank account. Does the deposit account represent a debt or to you?

Question 611  debt terminology

You owe money. Are you a or a ?

Question 612  debt terminology

You are owed money. Are you a or a ?

Question 613  debt terminology

You own a debt asset. Are you a or a ?

Question 614  debt terminology

You buy a house funded using a home loan. Have you or debt?

Question 615  debt terminology

You buy a house funded using a home loan. Have you or debt?

Question 620  bond pricing, income and capital returns

Let the 'income return' of a bond be the coupon at the end of the period divided by the market price now at the start of the period ##(C_1/P_0)##. The expected income return of a premium fixed coupon bond is:

(a) Less than its expected total return.

(b) Equal to its expected total return.

(c) More than its expected total return.

(d) More than its coupon rate.

(e) Equal to its coupon rate.

Question 619  CFFA

To value a business's assets, the free cash flow of the firm (FCFF, also called CFFA) needs to be calculated. This requires figures from the firm's income statement and balance sheet. For what figures is the balance sheet needed? Note that the balance sheet is sometimes also called the statement of financial position.

(a) Net income, depreciation and interest expense.

(b) Depreciation and capital expenditure.

(c) Current assets, current liabilities and cost of goods sold (COGS).

(d) Current assets, current liabilities and capital expenditure.

(e) Current assets, current liabilities and depreciation expense.

Question 622  expected and historical returns, risk

An economy has only two investable assets: stocks and cash.

Stocks had a historical nominal average total return of negative two percent per annum (-2% pa) over the last 20 years. Stocks are liquid and actively traded. Stock returns are variable, they have risk.

Cash is riskless and has a nominal constant return of zero percent per annum (0% pa), which it had in the past and will have in the future. Cash can be kept safely at zero cost. Cash can be converted into shares and vice versa at zero cost.

The nominal total return of the shares over the next year is expected to be:

(a) Less than or equal to negative two percent per annum ##(r_\text{shares} \leq -0.02)##.

(b) Exactly negative two percent per annum ##(r_\text{shares} = -0.02)##.

(c) More than or equal to negative two percent per annum ##(r_\text{shares} \geq -0.02)##.

(d) Less than or equal to zero percent per annum ##(r_\text{shares} \leq 0)##.

(e) More than or equal to zero percent per annum ##(r_\text{shares} \geq 0)##.

Question 629  yield curve, forward interest rate

Which of the following statements about yield curves is NOT correct?

(a) A yield curve graph shows bonds' spot yields at different maturities. The y-axis shows spot yields and the x-axis shows the bonds' times to maturity.

(b) A yield curve is a graph of forward rates.

(c) Normal yield curves slope upwards, they have a positive gradient.

(d) A yield curve is 'as at' a certain date, it's a snapshot in time.

(e) Every point on the yield curve corresponds to a different bond with a different maturity.

Question 655  capital budgeting, opportunity cost, sunk cost

The 'time value of money' is most closely related to which of the following concepts?

(a) Competition: Firms in competitive markets earn zero economic profit.

(b) Opportunity cost: The cost of the next best alternative foregone should be subtracted.

(c) Separation of the investment and financing decisions.

(d) Diversification: Risks can often be reduced by pooling them together.

(e) Sunk costs: Costs that cannot be recouped should be ignored.

Question 656  debt terminology

Which of the following statements is NOT correct? Lenders:

(a) Buy debt.

(b) Own debt.

(c) Are owed money.

(d) Write debt.

(e) Have debt assets.

Question 659  APR, effective rate, effective rate conversion, no explanation

A home loan company advertises an interest rate of 9% pa, payable monthly. Which of the following statements about the interest rate is NOT correct? All rates are given with an accuracy of 4 decimal places.

(a) The APR compounding monthly is 9.000% pa.

(b) The effective monthly rate is 0.7500% pa.

(c) The effective annual rate is 9.3807% pa.

(d) The effective 6 month rate is 4.5000% pa.

(e) The APR compounding semi-annually is 9.1704% pa.

Question 662  APR, effective rate, effective rate conversion, no explanation

Which of the following interest rate labels does NOT make sense?

(a) Annualised percentage rate compounding per month.

(b) Effective monthly rate compounding per year.

(c) Annualised percentage rate compounding per year.

(d) Effective annual rate compounding per year.

(e) Annualised percentage rate compounding semi-annually.

Question 668  buy and hold, market efficiency, idiom

A quote from the famous investor Warren Buffet: "Much success can be attributed to inactivity. Most investors cannot resist the temptation to constantly buy and sell."

Buffet is referring to the buy-and-hold strategy which is to buy and never sell shares. Which of the following is a disadvantage of a buy-and-hold strategy? Assume that share markets are semi-strong form efficient. Which of the following is NOT an advantage of the strict buy-and-hold strategy? A disadvantage of the buy-and-hold strategy is that it reduces:

(a) Capital gains tax.

(b) Explicit transaction costs such as brokerage fees.

(c) Implicit transaction costs such as bid-ask spreads.

(d) Portfolio rebalancing.

(e) Time wasted on researching whether it's better to buy or sell.

Question 713  effective rate conversion

An effective semi-annual return of 5% ##(r_\text{eff 6mth})## is equivalent to an effective annual return ##(r_\text{eff annual})## of:

(a) 30% pa

(b) 26.236426% pa

(c) 10.254219% pa

(d) 10.25% pa

(e) 10% pa

Question 712  effective rate conversion

An effective monthly return of 1% ##(r_\text{eff monthly})## is equivalent to an effective annual return ##(r_\text{eff annual})## of:

(a) 12.682503% pa

(b) 12.060201% pa

(c) 12% pa

(d) 11.940397% pa

(e) 3.464102% pa

Question 728  inflation, real and nominal returns and cash flows, income and capital returns, no explanation

Which of the following statements about gold is NOT correct? Assume that the gold price increases by inflation. Gold has a:

(a) Nil income cash flow.

(b) Real total return of zero.

(c) Real capital return equal to the inflation rate.

(d) Real income return of zero.

(e) Nominal income return of zero.

Question 729  book and market values, balance sheet, no explanation

If a firm makes a profit and pays no dividends, which of the firm’s accounts will increase?

(a) Asset revaluation reserve.

(b) Foreign currency translation reserve.

(c) Retained earnings, also known as retained profits.

(d) Contributed equity, also known as paid up capital.

(e) General reserve.

Question 731  DDM, income and capital returns

In the dividend discount model (DDM), share prices fall when dividends are paid. Let the high price before the fall be called the peak, and the low price after the fall be called the trough.

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

Which of the following statements about the DDM is NOT correct?

(a) In between dividends, the stock price is expected to grow by the total return ‘r’.

(b) From trough to trough, the stock price is expected to grow by the capital return ‘g’.

(c) From peak to peak, the stock price is expected to grow by the capital return ‘g’.

(d) Dividends are expected to grow by the total return ‘r’.

(e) If the stock’s dividends are re-invested by using the cash to buy more stocks, then the growth rate of the shareholder’s wealth will be the total return ‘r’.

Question 735  debt terminology

You deposit money into a bank. Which of the following statements is NOT correct? You:

(a) Are a lender.

(b) Issued debt.

(c) Bought debt.

(d) Are a debt holder.

(e) Own a debt asset.

Question 736  debt terminology

You bought a house, primarily funded using a home loan from a bank. Which of the following statements is NOT correct?

(a) The home loan is a debt liability to the bank.

(b) The bank invested in your debt.

(c) You are indebted to the bank.

(d) You owe the bank principal and interest payments.

(e) You sold your promise to the bank to pay the principal and interest.

Question 739  real and nominal returns and cash flows, inflation

There are a number of different formulas involving real and nominal returns and cash flows. Which one of the following formulas is NOT correct? All returns are effective annual rates. Note that the symbol ##\approx## means 'approximately equal to'.

(a) ##r_\text{real} \approx r_\text{nominal} - r_\text{inflation}##

(b) ##(1+r_\text{real})^t = \left( \dfrac{1+r_\text{nominal}}{1+r_\text{inflation}} \right)^t ##

(c) ##V_\text{t,real} = V_\text{t,nominal}.(1+r_\text{inflation})^t##

(d) ##V_\text{0} = \dfrac{V_\text{t,nominal}}{(1+r_\text{nominal})^t}##

(e) ##V_\text{0} = \dfrac{V_\text{t,real}}{(1+r_\text{real})^t}##

Question 740  real and nominal returns and cash flows, DDM, inflation

Taking inflation into account when using the DDM can be hard. Which of the following formulas will NOT give a company's current stock price ##(P_0)##? Assume that the annual dividend was just paid ##(C_0)##, and the next dividend will be paid in one year ##(C_1)##.

(a) ##P_0=\dfrac{C_\text{1,nominal}}{r_\text{nominal} - g_\text{nominal}}##

(b) ##P_0 =\dfrac{C_0 (1+g_\text{nominal} )^1}{r_\text{nominal} - g_\text{nominal}}##

(c) ##P_0=\dfrac{C_\text{1,real}}{r_\text{real} - g_\text{real}}##

(d) ##P_0=\dfrac{C_0 (1+r_\text{real})^1}{r_\text{real} - g_\text{real}}##

(e) ##P_0=\dfrac{C_0(1+r_\text{nominal} )^1}{r_\text{nominal} - g_\text{nominal}} - C_0##

Question 741  APR, effective rate

A home loan company advertises an interest rate of 4.5% pa, payable monthly. Which of the following statements about the interest rate is NOT correct?

(a) The APR compounding monthly is 4.5% pa.

(b) The effective monthly rate is 0.3675% pa.

(c) The effective annual rate is 4.594% pa.

(d) The effective 6 month rate is 2.2712% pa.

(e) The APR compounding semi-annually is 4.5424% pa.

Question 743  price gains and returns over time, no explanation

How many years will it take for an asset's price to triple (increase from say $1 to $3) if it grows by 5% pa?

(a) 17.7643 years

(b) 22.5171 years

(c) 29.2722 years

(d) 40 years

(e) 60 years

Question 745  real and nominal returns and cash flows, inflation, income and capital returns

If the nominal gold price is expected to increase at the same rate as inflation which is 3% pa, which of the following statements is NOT correct?

(a) The nominal income return of gold is 0% pa.

(b) The nominal capital return of gold is 3% pa.

(c) The nominal total return of gold is 3% pa.

(d) The real income return of gold is -3% pa.

(e) The real capital return of gold is 0% pa.

Question 748  income and capital returns, DDM, ex dividend date

A stock will pay you a dividend of $2 tonight if you buy it today.

Thereafter the annual dividend is expected to grow by 3% pa, so the next dividend after the $2 one tonight will be $2.06 in one year, then in two years it will be $2.1218 and so on. The stock's required return is 8% pa.

What is the stock price today and what do you expect the stock price to be tomorrow, approximately?

(a) $40 tonight and $38 tomorrow.

(b) $41.2 tonight and $39.2 tomorrow.

(c) $41.2 tonight and $43.2 tomorrow.

(d) $43.2 tonight and $41.2 tomorrow.

(e) $45.2 tonight and $43.2 tomorrow.

Question 749  Multiples valuation, PE ratio, price to revenue ratio, price to book ratio, NPV

A real estate agent says that the price of a house in Sydney Australia is approximately equal to the gross weekly rent times 1000.

What type of valuation method is the real estate agent using?

(a) Price to EBITDA multiple.

(b) Price to book multiple.

(c) Price to earnings multiple.

(d) Price to revenue multiple.

(e) Discounted cash flow (DCF).

Question 750  PE ratio, Multiples valuation

Itau Unibanco is a major listed bank in Brazil with a market capitalisation of equity equal to BRL 85.744 billion, EPS of BRL 3.96 and 2.97 billion shares on issue.

Banco Bradesco is another major bank with total earnings of BRL 8.77 billion and 2.52 billion shares on issue.

Estimate Banco Bradesco's current share price using a price-earnings multiples approach assuming that Itau Unibanco is a comparable firm.

Note that BRL is the Brazilian Real, their currency. Figures sourced from Google Finance on the market close of the BVMF on 24 July 2015.

(a) BRL 28.87

(b) BRL 25.372

(c) BRL 22.1

(d) BRL 21.653

(e) BRL 21.528

Question 756  bond pricing, capital raising, no explanation

A firm wishes to raise $50 million now. They will issue 5% pa semi-annual coupon bonds that will mature in 3 years and have a face value of $100 each. Bond yields are 6% pa, given as an APR compounding every 6 months, and the yield curve is flat.

How many bonds should the firm issue?

(a) 418,743

(b) 420,478

(c) 513,921

(d) 552,365

(e) 594,562

Question 761  NPV, annuity due, no explanation

The phone company Optus have 2 mobile service plans on offer which both have the same amount of phone call, text message and internet data credit. Both plans have a contract length of 24 months and the monthly cost is payable in advance. The only difference between the two plans is that one is a:

• 'Bring Your Own' (BYO) mobile service plan, costing $80 per month. There is no phone included in this plan. The other plan is a:
• 'Bundled' mobile service plan that comes with the latest smart phone, costing $100 per month. This plan includes the latest smart phone.

Neither plan has any additional payments at the start or end. Assume that the discount rate is 1% per month given as an effective monthly rate.

The only difference between the plans is the phone, so what is the implied cost of the phone as a present value? Given that the latest smart phone actually costs $600 to purchase outright from another retailer, should you commit to the BYO plan or the bundled plan?

(a) $480, so the bundled plan is best.

(b) $462.94, so the BYO plan is best.

(c) $429.12, so the bundled plan is best.

(d) $424.87, so the BYO plan is best.

(e) $420.66, so the bundled plan is best.

Question 762  equivalent annual cash flow, no explanation

Radio-Rentals.com offers the Apple iphone 5S smart phone for rent at $12.95 per week paid in advance on a 2 year contract. After renting the phone, you must return it to Radio-Rentals.

Kogan.com offers the Apple iphone 5S smart phone for sale at $699. You estimate that the phone will last for 3 years before it will break and be worthless.

Currently, the effective annual interest rate is 11.351%, the effective monthly interest rate 0.9% and the effective weekly interest rate is 0.207%. Assume that there are exactly 52 weeks per year and 12 months per year.

Find the equivalent annual cost of renting the phone and also buying the phone. The answers below are listed in the same order.

(a) $362.33,   $287.79

(b) $362.33,   $506.29

(c) $516.29,   $506.29

(d) $673.40,   $233.00

(e) $711.67,   $287.79

Question 763  multi stage growth model, DDM

A stock is expected to pay its first dividend of $20 in 3 years (t=3), which it will continue to pay for the next nine years, so there will be ten $20 payments altogether with the last payment in year 12 (t=12).

From the thirteenth year onward, the dividend is expected to be 4% more than the previous year, forever. So the dividend in the thirteenth year (t=13) will be $20.80, then $21.632 in year 14, and so on forever. The required return of the stock is 10% pa. All rates are effective annual rates. Calculate the current (t=0) stock price.

(a) $202.7888

(b) $212.0218

(c) $233.35

(d) $448.2298

(e) $469.558

Question 764  bond pricing, no explanation

A 4.5% fixed coupon Australian Government bond was issued at par in mid-April 2009. Coupons are paid semi-annually in arrears in mid-April and mid-October each year. The face value is $1,000. The bond will mature in mid-April 2020, so the bond had an original tenor of 11 years.

Today is mid-September 2015 and similar bonds now yield 1.9% pa.

What is the bond's new price? Note: there are 10 semi-annual coupon payments remaining from now (mid-September 2015) until maturity (mid-April 2020); both yields are given as APR's compounding semi-annually; assume that the yield curve was flat before the change in yields, and remained flat afterwards as well.

(a) $1,108.390216

(b) $1,114.640575

(c) $1,123.457853

(d) $1,127.892613

(e) $1,132.344879

Question 765  bond pricing, no explanation

An investor bought a 5 year government bond with a 2% pa coupon rate at par. Coupons are paid semi-annually. The face value is $100.

Calculate the bond's new price 8 months later after yields have increased to 3% pa. Note that both yields are given as APR's compounding semi-annually. Assume that the yield curve was flat before the change in yields, and remained flat afterwards as well.

(a) $95.345378

(b) $95.819741

(c) $96.138082

(d) $96.296464

(e) $96.775559

Question 617  systematic and idiosyncratic risk, risk, CAPM

A stock's required total return will increase when its:

(a) Systematic risk increases.

(b) Idiosyncratic risk increases.

(c) Total risk increases.

(d) Systematic risk decreases.

(e) Idiosyncratic risk decreases.

Question 621  market efficiency, technical analysis

Technical traders:

(a) Believe that asset prices follow a random walk.

(b) Believe that markets are weak form efficient

(c) Are pessimists, they believe that they cannot beat the market

(d) Base their investment decisions on past publicly available news

(e) Believe that the theory of weak form market efficiency is broken.

Question 623  market efficiency

The efficient markets hypothesis (EMH) and no-arbitrage pricing theory are most closely related to which of the following concepts?

(a) Competition.

(b) Opportunity costs.

(c) Separation of the investment and financing decisions.

(d) Diversification.

(e) The stand-alone principle, incremental cash flows and sunk costs.

Question 624  franking credit, personal tax on dividends, imputation tax system, no explanation

Which of the following statements about Australian franking credits is NOT correct? Franking credits:

(a) Refund the corporate tax paid by companies to their individual shareholders. Therefore they prevent the double-taxation of dividends at the corporate and personal level.

(b) Are distributed to shareholders together with cash dividends.

(c) Are also called imputation credits.

(d) Are worthless to individuals who earn less than the tax-free threshold because they have a zero marginal personal tax rate.

(e) Are worthless to individual shareholders who are foreigners for tax purposes.

Question 625  dividend re-investment plan, capital raising

Which of the following statements about dividend re-investment plans (DRP's) is NOT correct?

(a) DRP's are voluntary, shareholders only participate if they choose.

(b) DRP's increase the number of shares.

(c) The number of shares issued to a shareholder participating in a DRP is usually calculated as their total dividends owed, divided by the allocation share price which is usually close to the current market share price.

(d) DRP's do not incur brokerage costs for the shareholder. This is unlike the case where the shareholder uses the cash dividend to buy more shares herself.

(e) If all shareholders participated in a company's DRP, the company would not pay any dividends and the firm's share price would not fall due to the cash dividend or the DRP.

Question 627  CAPM, SML, NPV, Jensens alpha

Assets A, B, M and ##r_f## are shown on the graphs above. Asset M is the market portfolio and ##r_f## is the risk free yield on government bonds. Which of the below statements is NOT correct?

(a) Asset A has a Jensen's alpha of 4.5% pa.

(b) Asset A is under-priced.

(c) The NPV of buying asset A is zero.

(d) Asset B has a Jensen's alpha of zero.

(e) Asset B is fairly priced.

Question 628  CAPM, SML, risk

Assets A, B, M and ##r_f## are shown on the graphs above. Asset M is the market portfolio and ##r_f## is the risk free yield on government bonds. Assume that investors can borrow and lend at the risk free rate. Which of the below statements is NOT correct?

(a) Asset A has the same systematic risk as asset B.

(b) Asset A has more total variance than asset B.

(c) Asset B has zero idiosyncratic risk. Asset B must be a portfolio of half the market portfolio and half government bonds.

(d) If risk-averse investors were forced to invest all of their wealth in a single risky asset, so they could not diversify, every investor would logically choose asset A over the other three assets.

(e) Assets M and B have the highest Sharpe ratios, which is defined as the gradient of the capital allocation line (CAL) from the government bonds through the asset on the graph of expected return versus total standard deviation.

Question 657  systematic and idiosyncratic risk, CAPM, no explanation

A stock's required total return will decrease when its:

(a) Systematic risk increases.

(b) Idiosyncratic risk increases.

(c) Total risk increases.

(d) Systematic risk decreases.

(e) Idiosyncratic risk decreases.

Question 665  stock split

A company conducts a 10 for 3 stock split. What is the percentage increase in the stock price and the number of shares outstanding? The answers are given in the same order.

(a) -76.92%,   333.33%

(b) -70%,   333.33%

(c) -70%, 233.33%

(d) -57.14%,   233.33%

(e) 233.33%,   -70%

Question 769  short selling, idiom, no explanation

"Buy low, sell high" is a well-known saying. It suggests that investors should buy low then sell high, in that order.

How would you re-phrase that saying to describe short selling?

(a) Buy high, then sell low.

(b) Buy low, then sell high.

(c) Sell high, then buy low.

(d) Sell low, then buy high.

(e) Sell high, then buy high.

Question 770  expected and historical returns, income and capital returns, coupon rate, bond pricing

Which of the following statements is NOT correct? Assume that all events are a surprise and that all other things remain equal. So for example, don't assume that just because a company's dividends and profit rise that its required return will also rise, assume the required return stays the same.

(a) If a company's dividend (and profit and free cash flow to equity) rises, its share price will rise.

(b) If a fixed coupon bond's yield to maturity rises, its price will rise.

(c) If a residential property's rent revenue rises, its price will rise.

(d) If a patent's royalty revenue rises, its price will also rise.

(e) If a software asset's licensing revenue rises, its price will also rise.

Question 771  debt terminology, interest expense, interest tax shield, credit risk, no explanation

You deposit money into a bank account. Which of the following statements about this deposit is NOT correct?

(a) You have a debt asset.

(b) The bank sold you its promise to pay back interest and principal payments.

(c) The bank is exposed to your credit risk, it’s afraid that you’ll default on your debt.

(d) The interest income you’re paid is taxable income for you.

(e) The interest expense that the bank pays is tax-deductible for the bank.

Question 772  interest tax shield, capital structure, leverage

A firm issues debt and uses the funds to buy back equity. Assume that there are no costs of financial distress or transactions costs. Which of the following statements about interest tax shields is NOT correct?

(a) Higher debt leads to higher interest expense.

(b) Higher interest expense leads to lower profit before tax, following on from above.

(c) Lower profit before tax leads to lower tax payments, following on from above.

(d) Lower tax payments lead to higher cash flow from assets, following on from above.

(e) Lower profit after tax leads to a lower share price, following on from above.

Question 775  utility, utility function

Below is a graph of 3 peoples’ utility functions, Mr Blue (U=W^(1/2) ), Miss Red (U=W/10) and Mrs Green (U=W^2/1000). Assume that each of them currently have $50 of wealth.

Which of the following statements about them is NOT correct?

(a) Mr Blue would prefer to invest his wealth in a well diversified portfolio of stocks rather than a single stock, assuming that all stocks had the same total risk and return.

(b) Mrs Green would prefer to invest her wealth in a single stock rather than a well diversified portfolio of stocks, assuming that all stocks had the same total risk and return.

(c) The popularity of insurance only makes sense if people are similar to Mr Blue.

(d) CAPM theory only makes sense if people are similar to Miss Red.

(e) The popularity of casino gambling and lottery tickets only make sense if people are similar to Mrs Green.

Question 778  CML, systematic and idiosyncratic risk, portfolio risk, CAPM

The capital market line (CML) is shown in the graph below. The total standard deviation is denoted by σ and the expected return is μ. Assume that markets are efficient so all assets are fairly priced.

Which of the below statements is NOT correct?

(a) The risk free security has zero systematic variance and zero idiosyncratic variance.

(b) The market portfolio has zero idiosyncratic variance.

(c) Any portfolio comprised of the market portfolio and risk free security has zero idiosyncratic variance.

(d) Portfolios that plot on the CML must only be comprised of the risk free security and the market portfolio.

(e) Portfolios that plot on the CML have some idiosyncratic variance and some systematic variance.

Question 779  mean and median returns, return distribution, arithmetic and geometric averages, continuously compounding rate

Fred owns some BHP shares. He has calculated BHP’s monthly returns for each month in the past 30 years using this formula:

###r_\text{t monthly}=\ln⁡ \left( \dfrac{P_t}{P_{t-1}} \right)###

He then took the arithmetic average and found it to be 0.8% per month using this formula:

###\bar{r}_\text{monthly}= \dfrac{ \displaystyle\sum\limits_{t=1}^T{\left( r_\text{t monthly} \right)} }{T} =0.008=0.8\% \text{ per month}###

He also found the standard deviation of these monthly returns which was 15% per month:

###\sigma_\text{monthly} = \dfrac{ \displaystyle\sum\limits_{t=1}^T{\left( \left( r_\text{t monthly} - \bar{r}_\text{monthly} \right)^2 \right)} }{T} =0.15=15\%\text{ per month}###

Assume that the past historical average return is the true population average of future expected returns and the stock's returns calculated above ##(r_\text{t monthly})## are normally distributed. Which of the below statements about Fred’s BHP shares is NOT correct?

(a) The returns ##r_\text{t monthly}## are continuously compounded monthly returns.

(b) The mean, median and mode of the continuously compounded annual return is expected to equal 0.8% per month.

(c) The annualised average continuously compounded return is ##\bar{r}_\text{cc annual}=12×0.008=0.096=9.6\%\text{ pa}##. The annualised standard deviation is ##\sigma_\text{annual} = \sqrt{12}×0.15=0.519615242 = 52\%\text{ pa}##.

(d) If the current price of the BHP shares is $20, they're expected to have a median value of $52.2339 ##(= 20×e^{0.008×12×10})## in 10 years.

(e) If the current price of the BHP shares is $20, they're expected to have a mean value of $13.5411 ##(= 20×e^{(0.008 - 0.15^2/2)×12×10})## in 10 years.

Question 707  continuously compounding rate, continuously compounding rate conversion

Convert a 10% effective annual rate ##(r_\text{eff annual})## into a continuously compounded annual rate ##(r_\text{cc annual})##. The equivalent continuously compounded annual rate is:

(a) 230.258509% pa

(b) 10.536052% pa

(c) 10.517092% pa

(d) 10.468982% pa

(e) 9.531018% pa

Question 711  continuously compounding rate, continuously compounding rate conversion

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

(a) 30% pa

(b) 26.236426% pa

(c) 10.254219% pa

(d) 10.25% pa

(e) 10% pa

Question 691  continuously compounding rate, effective rate, continuously compounding rate conversion, no explanation

A bank quotes an interest rate of 6% pa with quarterly compounding. Note that another way of stating this rate is that it is an annual percentage rate (APR) compounding discretely every 3 months.

Which of the following statements about this rate is NOT correct? All percentages are given to 6 decimal places. The equivalent:

(a) Continuously compounded rate is 5.955445% per annum. Note that this rate is the annual rate with continuous compounding.

(b) Continuously compounded rate is 1.500000% per quarter. Note that this rate is the quarterly rate with continuous compounding.

(c) Effective quarterly rate is 1.500000% per quarter. Note that this rate is the quarterly rate with discrete quarterly compounding.

(d) Effective annual rate is 6.136355% per annum. Note that this rate is the annual rate with discrete annual compounding.

(e) $1,000,000 invested in this bank account for one year will give $1,061,363.551 at the end of the year.

Question 717  return distribution

The below three graphs show probability density functions (PDF) of three different random variables Red, Green and Blue. Let ##P_1## be the unknown price of a stock in one year. ##P_1## is a random variable. Let ##P_0 = 1##, so the share price now is $1. This one dollar is a constant, it is not a variable.

Which of the below statements is NOT correct? Financial practitioners commonly assume that the shape of the PDF represented in the colour:

(a) Green is a stock's continuously compounded rate of return, also called the log gross discrete return. ##r_\text{cc} = \ln(P_1/P_0)##

(b) Blue is a stock's future price, ##P_1##

(c) Blue is a stock's gross discrete return. ##\text{GDR} = P_1/P_0##

(d) Blue is a stock's effective rate of return. ##r_\text{eff} = (P_1-P_0)/P_0##

(e) Red is a stock's net discrete return. ##\text{NDR} = \text{GDR}-1##