Fight Finance

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 40  DDM, perpetuity with growth

A stock is expected to pay the following dividends:

Cash Flows of a Stock
Time (yrs)	0	1	2	3	4	...
Dividend ($)	0.00	1.00	1.05	1.10	1.15	...

After year 4, the annual dividend will grow in perpetuity at 5% pa, so;

• the dividend at t=5 will be $1.15(1+0.05),
• the dividend at t=6 will be $1.15(1+0.05)^2, and so on.

The required return on the stock is 10% pa. Both the growth rate and required return are given as effective annual rates.

What will be the price of the stock in three and a half years (t = 3.5)?

(a) $27.7567

(b) $24.1226

(c) $23.5680

(d) $22.4457

(e) $3.6341

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 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 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 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 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 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 202  DDM, payout policy

Currently, a mining company has a share price of $6 and pays constant annual dividends of $0.50. The next dividend will be paid in 1 year. Suddenly and unexpectedly the mining company announces that due to higher than expected profits, all of these windfall profits will be paid as a special dividend of $0.30 in 1 year.

If investors believe that the windfall profits and dividend is a one-off event, what will be the new share price? If investors believe that the additional dividend is actually permanent and will continue to be paid, what will be the new share price? Assume that the required return on equity is unchanged. Choose from the following, where the first share price includes the one-off increase in earnings and dividends for the first year only ##(P_\text{0 one-off})## , and the second assumes that the increase is permanent ##(P_\text{0 permanent})##:

(a) ##P_\text{0 one-off} = 9.6000, \space \space P_\text{0 permanent} = 6.2766##

(b) ##P_\text{0 one-off} = 6.3000, \space \space P_\text{0 permanent} = 6.2769##

(c) ##P_\text{0 one-off} = 9.6000, \space \space P_\text{0 permanent} = 6.3000##

(d) ##P_\text{0 one-off} = 6.2769, \space \space P_\text{0 permanent} = 9.6000##

(e) ##P_\text{0 one-off} = 6.3000, \space \space P_\text{0 permanent} = 9.6000##

Note: When a firm makes excess profits they sometimes pay them out as special dividends. Special dividends are just like ordinary dividends but they are one-off and investors do not expect them to continue, unlike ordinary dividends which are expected to persist.

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 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 341  Multiples valuation, PE ratio

Estimate Microsoft's (MSFT) share price using a price earnings (PE) multiples approach with the following assumptions and figures only:

• Apple, Google and Microsoft are comparable companies,
• Apple's (AAPL) share price is $526.24 and historical EPS is $40.32.
• Google's (GOOG) share price is $1,215.65 and historical EPS is $36.23.
• Micrsoft's (MSFT) historical earnings per share (EPS) is $2.71.

Source: Google Finance 28 Feb 2014.

(a) $63.15

(b) $61.67

(c) $30.83

(d) $28.25

(e) $8.60

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 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 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 58  NPV, inflation, real and nominal returns and cash flows, Annuity

A project to build a toll bridge will take two years to complete, costing three payments of $100 million at the start of each year for the next three years, that is at t=0, 1 and 2.

After completion, the toll bridge will yield a constant $50 million at the end of each year for the next 10 years. So the first payment will be at t=3 and the last at t=12. After the last payment at t=12, the bridge will be given to the government.

The required return of the project is 21% pa given as an effective annual nominal rate.

All cash flows are real and the expected inflation rate is 10% pa given as an effective annual rate. Ignore taxes.

The Net Present Value is:

(a) -$112,496,484

(b) -$32,260,693

(c) -$19,645,987

(d) $5,222,533

(e) $200,000,000

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 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 173  CFFA

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

Candys Corp
Income Statement for
year ending 30th June 2013
	$m
Sales	200
COGS	50
Operating expense	10
Depreciation	20
Interest expense	10
Income before tax	110
Tax at 30%	33
Net income	77

Candys Corp
Balance Sheet
as at 30th June	2013	2012
	$m	$m
Assets
Current assets	220	180
PPE
Cost	300	340
Accumul. depr.	60	40
Carrying amount	240	300
Total assets	460	480
Liabilities
Current liabilities	175	190
Non-current liabilities	135	130
Owners' equity
Retained earnings	50	60
Contributed equity	100	100
Total L and OE	460	480

 

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

(a) 242

(b) 182

(c) 112

(d) 92

(e) 52

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 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 223  CFFA, interest tax shield

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

(a) An increase in net capital spending.

(b) A decrease in the cash flow to creditors.

(c) An increase in interest expense.

(d) An increase in net working capital.

(e) A decrease in dividends paid.

Question 224  CFFA

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

(a) Cash available to distribute to creditors and stockholders.

(b) Cash flow to creditors minus cash flow to stockholders.

(c) Net income (or earnings) plus depreciation plus interest expense.

(d) Net income minus the increase in net working capital.

(e) Net income minus net capital spending minus the increase in net working capital.

Question 225  CFFA

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

(a) Buy less land, buildings and trucks than what was planned. Assume that this has no impact on revenue.

(b) Pay off more debt than was planned, to reduce the firm’s interest expense.

(c) Change the depreciation method used for tax purposes from diminishing value to straight line, so less depreciation occurs this year and more occurs in later years. Assume that the government’s tax department allow this.

(d) Buying more inventory than was planned, so there is an increase in net working capital. Assume that there is no increase in sales.

(e) Raising new equity through a rights issue. Assume that all of the money raised is spent on new capital assets such as land and trucks, but they will be fitted out and delivered in one year so no new cash will be earned from them.

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 296  CFFA, interest tax shield

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

Remember:

###NI=(Rev-COGS-FC-Depr-IntExp).(1-t_c )### ###CFFA=NI+Depr-CapEx - ΔNWC+IntExp###

(a) An increase in revenue (##Rev##).

(b) An decrease in revenue (##Rev##).

(c) An increase in rent expense (part of fixed costs, ##FC##).

(d) An increase in interest expense (##IntExp##).

(e) An increase in dividends.

Question 105  NPV, risk, market efficiency

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

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

(a) $10

(b) $3

(c) $2.8037

(d) $2.7273

(e) $0

Question 119  market efficiency, fundamental analysis, joint hypothesis problem

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

(i) Weak form market efficiency is broken.

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

(iii) Strong form market efficiency is broken.

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

Select the most correct response:

(a) Only (iii) is true.

(b) Only (ii) and (iii) are true.

(c) Only (i), (ii) and (iii) are true.

(d) Either (ii) and (iii) are true, or (iv) is true, or (ii), (iii) and (iv) are true.

(e) Either (i), (ii) and (iii) are true, or (iv) is true, or all are true.

Question 242  technical analysis, market efficiency

Select the most correct statement from the following.

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

(a) Markets are weak-form efficient.

(b) Markets are semi-strong-form efficient.

(c) Past prices cannot be used to predict future prices.

(d) Past returns can be used to predict future returns.

(e) Stock prices reflect all publically available information.

Question 243  fundamental analysis, market efficiency

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

(a) Markets are weak and semi-strong form efficient but strong-form inefficient.

(b) Markets are weak form efficient but semi-strong and strong-form inefficient.

(c) Chartists make negative excess returns.

(d) Insiders make positive excess returns.

(e) Insiders make negative excess returns.

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 232  CAPM, DDM

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

What is the price of the stock now?

(a) $55.6364

(b) $54.5455

(c) $40.8

(d) $40

(e) $37.5

Question 248  CAPM, DDM, income and capital returns

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Which of the equations are correct?

(a) I, IV and V only.

(b) II, III and V only.

(c) V only.

(d) All are true.

(e) None are true.

Question 76  CAPM, SML

Government bonds currently have a return of 5%. A stock has a beta of 2 and the market return is 7%. What is the expected return of the stock?

(a) 5%

(b) 7%

(c) 9%

(d) 12%

(e) 19%

Question 80  CAPM, risk, diversification

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

(a) Idiosyncratic risk.

(b) Systematic risk.

(c) Both idiosyncratic and systematic risk.

(d) Market risk.

(e) Beta risk.

Question 92  CAPM, SML, CML

Which statement(s) are correct?

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

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

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

Select the most correct response:

(a) Only (i) is true.

(b) Only (ii) is true.

(c) Only (iii) is true.

(d) All statements (i), (ii) and (iii) are true.

(e) Only statements (i) and (iii) are true.

Question 244  CAPM, SML, NPV, risk

Examine the following graph which shows stocks' betas ##(\beta)## and expected returns ##(\mu)##:

Assume that the CAPM holds and that future expectations of stocks' returns and betas are correctly measured. Which statement is NOT correct?

(a) Asset A is underpriced.

(b) Asset B has a negative alpha (a negative excess return or abnormal return).

(c) Buying asset C would be a positive NPV investment.

(d) Asset D has less systematic variance than the market portfolio (M).

(e) Asset E is fairly priced.

Question 282  expected and historical returns, income and capital returns

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

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

Your team of analysts present their findings, and everyone has different views. While there's no definitive true answer, whose calculation of the expected total return is the most plausible? Assume that:

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

(a) Alice says 5% pa since she calculated that this was the average total yield on government bonds over the last 10 years. She says that this is also the expected total yield implied by current prices on one year government bonds.

(b) Bob says 4% pa since he calculated that this was the average total return on the mining stock over the last 10 years.

(c) Cate says 3% pa since she calculated that this was the average growth rate of the share price over the last 10 years.

(d) Dave says 6% pa since he calculated that this was the average growth rate of the share market price index (not the accumulation index) over the last 10 years.

(e) Eve says 15% pa since she calculated that this was the discount rate implied by the dividend discount model using the current share price, forecast dividend in one year and a 3% growth rate in dividends thereafter, which is the expected long term inflation rate.

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 121  capital structure, leverage, financial distress, interest tax shield

Fill in the missing words in the following sentence:

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

(a) Fall, fall.

(b) Fall, rises.

(c) Rise, fall.

(d) Rise, rise.

(e) Remain unchanged, remain unchanged.

Question 302  WACC, CAPM

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

(a) WACC before tax ##= r_D.\dfrac{D}{V_L} + r_{EL}.\dfrac{E_L}{V_L}##

(b) WACC before tax ##= r_f + \beta_{VL}.(r_m - r_f)##

(c) WACC after tax ##= r_D.(1-t_c).\dfrac{D}{V_L} + r_{EL}.\dfrac{E_L}{V_L}##

(d) WACC after tax ##= r_f + \beta_{VL}.(r_m - r_f) - \dfrac{r_D.D.t_c}{V_L}##

(e) WACC after tax ##= r_f + \beta_{VL}.(r_m - r_f)##

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 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 69  interest tax shield, capital structure, leverage, WACC

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

(a) The before-tax cost of debt is less than the before-tax cost of equity. Therefore debt is a cheaper form of financing than equity so companies should try to finance their projects with debt only.

(b) Debt makes a firm's equity more risky. Therefore the higher the amount of debt, the higher the cost of equity.

(c) The more debt a firm has, the higher its tax shields. Therefore firms should seek to have as much debt and as little equity as possible.

(d) The more debt, the lower the firm's after tax WACC. The after tax WACC is the discount rate that discounts the firm's cash flows, so the lower it is the more the firm is worth. Therefore firms should try to make their after tax WACC as low as possible by using as much debt as possible.

(e) The less debt, the lower the chance of bankruptcy. Therefore firms should try to pay off all of their debt so that they are financed by equity only.

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 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 91  WACC, capital structure

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

(a) 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 stay the same.

(e) The company's before-tax WACC is likely to stay the same.

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 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 104  CAPM, payout policy, capital structure, Miller and Modigliani, risk

Assume that there exists a perfect world with no transaction costs, no asymmetric information, no taxes, no agency costs, equal borrowing rates for corporations and individual investors, the ability to short the risk free asset, semi-strong form efficient markets, the CAPM holds, investors are rational and risk-averse and there are no other market frictions.

For a firm operating in this perfect world, which statement(s) are correct?

(i) When a firm changes its capital structure and/or payout policy, share holders' wealth is unaffected.

(ii) When the idiosyncratic risk of a firm's assets increases, share holders do not expect higher returns.

(iii) When the systematic risk of a firm's assets increases, share holders do not expect higher returns.

Select the most correct response:

(a) Only (i) is true.

(b) Only (ii) is true.

(c) Only (iii) is true.

(d) Only (i) and (ii) are true.

(e) All statements (i), (ii) and (iii) are true.

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 337  capital structure, interest tax shield, leverage, real and nominal returns and cash flows, multi stage growth model

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

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

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

Assume that:

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

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

(a) $13.19m

(b) $12.36m

(c) $11.77m

(d) $11.53m

(e) $11.20m

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 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 89  WACC, CFFA, interest tax shield

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

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

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

(a) Discount the project's unlevered CFFA by the furniture manufacturing firms' 30% WACC after tax.

(b) Discount the project's unlevered CFFA by the company's 20% WACC after tax.

(c) Discount the project's levered CFFA by the company's 20% WACC after tax.

(d) Discount the project's levered CFFA by the furniture manufacturing firms' 30% WACC after tax.

(e) The methods outlined in answers (a) and (c) will give the same valuations, both are correct.

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 7  DDM

For a price of $1040, Camille will sell you a share which just paid a dividend of $100, and is expected to pay dividends every year forever, growing at a rate of 5% pa.

So the next dividend will be ##100(1+0.05)^1=$105.00##, and the year after it will be ##100(1+0.05)^2=110.25## and so on.

The required return of the stock is 15% pa.

Would you like to the share or politely ?

Question 8  DDM

For a price of $10.20 each, Renee will sell you 100 shares. Each share is expected to pay dividends in perpetuity, growing at a rate of 5% pa. The next dividend is one year away (t=1) and is expected to be $1 per share.

The required return of the stock is 15% pa.

Would you like to the shares or politely ?

Question 9  DDM, NPV

For a price of $129, Joanne will sell you a share which is expected to pay a $30 dividend in one year, and a $10 dividend every year after that forever. So the stock's dividends will be $30 at t=1, $10 at t=2, $10 at t=3, and $10 forever onwards.

The required return of the stock is 10% pa.

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 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 36  DDM, perpetuity with growth

A stock pays annual dividends which are expected to continue forever. It just paid a dividend of $10. The growth rate in the dividend is 2% pa. You estimate that the stock's required return is 10% pa. Both the discount rate and growth rate are given as effective annual rates. Using the dividend discount model, what will be the share price?

(a) $127.5

(b) $125

(c) $102

(d) $101.98

(e) $100

Question 39  DDM, perpetuity with growth

A stock is expected to pay the following dividends:

Cash Flows of a Stock
Time (yrs)	0	1	2	3	4	...
Dividend ($)	0.00	1.00	1.05	1.10	1.15	...

After year 4, the annual dividend will grow in perpetuity at 5% pa, so;

• the dividend at t=5 will be $1.15(1+0.05),
• the dividend at t=6 will be $1.15(1+0.05)^2, and so on.

The required return on the stock is 10% pa. Both the growth rate and required return are given as effective annual rates. What is the current price of the stock?

(a) $25.6033

(b) $20.7476

(c) $20.0000

(d) $19.8835

(e) $18.3126

Question 51  DDM

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

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

(a) $50.00

(b) $50.50

(c) $100.00

(d) $111.11

(e) $112.22

Question 54  NPV, DDM

A stock is expected to pay the following dividends:

Cash Flows of a Stock
Time (yrs)	0	1	2	3	4	...
Dividend ($)	0.00	1.15	1.10	1.05	1.00	...

After year 4, the annual dividend will grow in perpetuity at -5% pa. Note that this is a negative growth rate, so the dividend will actually shrink. So,

• the dividend at t=5 will be ##$1(1-0.05) = $0.95##,
• the dividend at t=6 will be ##$1(1-0.05)^2 = $0.9025##, and so on.

The required return on the stock is 10% pa. Both the growth rate and required return are given as effective annual rates.

What is the current price of the stock?

(a) $7.2968

(b) $7.5018

(c) $7.6667

(d) $7.7522

(e) $9.4101

Question 150  DDM, effective rate

A share just paid its semi-annual dividend of $10. The dividend is expected to grow at 2% every 6 months forever. This 2% growth rate is an effective 6 month rate. Therefore the next dividend will be $10.20 in six months. The required return of the stock is 10% pa, given as an effective annual rate.

What is the price of the share now?

(a) $127.50

(b) $171.14

(c) $173.33

(d) $174.56

(e) $354.06

Question 161  DDM

A share just paid its semi-annual dividend of $10. The dividend is expected to grow at 2% every 6 months forever. This 2% growth rate is an effective 6 month rate. Therefore the next dividend will be $10.20 in six months. The required return of the stock 10% pa, given as an effective annual rate.

What is the price of the share now?

(a) $127.50

(b) $171.14

(c) $173.33

(d) $174.56

(e) $354.06

Question 166  DDM, no explanation

A stock pays annual dividends. It just paid a dividend of $3. The growth rate in the dividend is 4% pa. You estimate that the stock's required return is 10% pa. Both the discount rate and growth rate are given as effective annual rates. Using the dividend discount model, what will be the share price?

(a) 30

(b) 31.16

(c) 31.2

(d) 50

(e) 52

Question 169  NPV, DDM

A stock is expected to pay the following dividends:

Cash Flows of a Stock
Time (yrs)	0	1	2	3	4	...
Dividend ($)	8	8	8	20	8	...

After year 4, the dividend will grow in perpetuity at 4% pa. The required return on the stock is 10% pa. Both the growth rate and required return are given as effective annual rates. Note that the $8 dividend at time zero is about to be paid tonight.

What is the current price of the stock?

(a) 170.24

(b) 141.09

(c) 137.09

(d) 131.62

(e) 127.98

Question 181  DDM

A stock pays annual dividends. It just paid a dividend of $5. The growth rate in the dividend is 1% pa. You estimate that the stock's required return is 8% pa. Both the discount rate and growth rate are given as effective annual rates.

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

(a) 72.1429

(b) 71.4286

(c) 63.1250

(d) 63.1150

(e) 62.5000

Question 184  NPV, DDM

A stock is expected to pay the following dividends:

Cash Flows of a Stock
Time (yrs)	0	1	2	3	4	...
Dividend ($)	2	2	2	10	3	...

After year 4, the dividend will grow in perpetuity at 4% pa. The required return on the stock is 10% pa. Both the growth rate and required return are given as effective annual rates.

What is the current price of the stock?

(a) 62.9842

(b) 52.0526

(c) 50.5500

(d) 48.5009

(e) 47.1349

Question 196  DDM, no explanation

A share pays annual dividends. It just paid a dividend of $2. The growth rate in the dividend is 3% pa. You estimate that the stock's required return is 8% pa. Both the discount rate and growth rate are given as effective annual rates.

Using the dividend discount model, what is the share price?

(a) 25

(b) 25.72

(c) 25.75

(d) 40

(e) 41.2

Question 198  NPV, DDM, 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.

What is the current price of the stock?

(a) 302.10

(b) 315.76

(c) 329.42

(d) 344.45

(e) 428.90

Question 199  NPV, DDM, 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.

What will be the price of the stock in 7 years (t = 7), just after the dividend at that time has been paid?

(a) 420.00

(b) 463.05

(c) 463.53

(d) 486.20

(e) 510.51

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 260  DDM

A share just paid its semi-annual dividend of $5. The dividend is expected to grow at 1% every 6 months forever. This 1% growth rate is an effective 6 month rate.

Therefore the next dividend will be $5.05 in six months. The required return of the stock 8% pa, given as an effective annual rate.

What is the price of the share now?

(a) $71.4286

(b) $72.1429

(c) $84.3072

(d) $85.1503

(e) $172.7648

Question 66  CAPM, SML

Government bonds currently have a return of 5% pa. A stock has an expected return of 6% pa and the market return is 7% pa. What is the beta of the stock?

(a) -0.5

(b) 0

(c) 0.5

(d) 1

(e) 7

Question 72  CAPM, portfolio beta, portfolio risk

Portfolio Details
Stock	Expected return	Standard deviation	Correlation	Beta	Dollars invested
A	0.2	0.4	0.12	0.5	40
B	0.3	0.8		1.5	80

What is the beta of the above portfolio?

(a) 0.75

(b) 0.833333333

(c) 1

(d) 1.166666667

(e) 1.4

Question 86  CAPM

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

(a) 5% pa

(b) 7.5% pa

(c) 10% pa

(d) 12.5% pa

(e) 20% pa

Question 90  CAPM, risk

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

(a) Global economic recession.

(b) A major terrorist attack, grounding all commercial aircraft in the US and Europe.

(c) An increase in corporate tax rates.

(d) The outbreak of world war.

(e) A company's poor earnings announcement.

Question 98  capital structure, CAPM

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

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

(a) The beta of the firm's assets will increase.

(b) The beta of the firm's assets will decrease.

(c) The beta of the firm's equity will increase.

(d) The beta of the firm's equity will decrease.

(e) The beta of the firm's equity will be unchanged.

Question 106  CAPM

A fairly priced stock has an expected return of 15% pa. Treasury bonds yield 5% pa and the market portfolio's expected return is 10% pa. What is the beta of the stock?

(a) 0

(b) 0.5

(c) 1

(d) 1.5

(e) 2

Question 111  portfolio risk, correlation

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

(a) The correlation between the stocks' returns rise.

(b) The correlation between the stocks' returns decline.

(c) The portfolio standard deviation declines.

(d) Both stocks' individual variances decline.

(e) Both stocks' individual standard deviations decline.

Question 112  CAPM, risk

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

(a) A decrease in house prices in one city.

(b) An increase in mining industry tax rates.

(c) An increase in corporate tax rates.

(d) A case of fraud at a major retailer.

(e) A poor earnings announcement from a major firm.

Question 231  CAPM

A fairly priced stock has a beta that is the same as the market portfolio's beta. Treasury bonds yield 5% pa and the market portfolio's expected return is 10% pa. What is the expected return of the stock?

(a) 5%

(b) 7.5%

(c) 10%

(d) 15%

(e) 20%

Question 235  SML, NPV, CAPM, risk

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

Investment projects that plot on the SML would have:

(a) A positive NPV and should be accepted.

(b) A zero NPV.

(c) A negative NPV and should be rejected.

(d) A large amount of diversifiable risk.

(e) Zero diversifiable risk.

Question 326  CAPM

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

(a) 0

(b) 0.5

(c) 1

(d) 1.5

(e) 2

Question 349  CFFA, depreciation tax shield

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

Remember:

###NI = (Rev-COGS-FC-Depr-IntExp).(1-t_c )### ###CFFA=NI+Depr-CapEx - \Delta NWC+IntExp###

(a) An increase in revenue (Rev).

(b) An increase in rent expense (part of fixed costs, FC).

(c) An increase in depreciation expense (Depr).

(d) An decrease in net working capital (ΔNWC).

(e) An increase in dividends.

Question 351  CFFA

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

• Achieve firm free cash flow (FFCF or CFFA) of $1m.
• Pay dividends of $1.8m
• Complete a $1.3m share buy-back.
• Spend $0.8m on new buildings without buying or selling any other fixed assets. This capital expenditure is included in the CFFA figure quoted above.

Assume that:

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

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

(a) $2.1m

(b) $1.3m

(c) $0.8m

(d) $0.3m

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

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 369  interest tax shield, CFFA

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

###\begin{aligned} FFCF &= (EBIT)(1-t_c) + Depr - CapEx -\Delta NWC + IntExp.t_c \\ &= (Rev - COGS - Depr - FC)(1-t_c) + Depr - CapEx -\Delta NWC + IntExp.t_c \\ \end{aligned} \\###

Does this annual FFCF or the annual interest tax shield?

Question 370  capital budgeting, NPV, interest tax shield, WACC, CFFA

Project Data
Project life	2 yrs
Initial investment in equipment	$600k
Depreciation of equipment per year	$250k
Expected sale price of equipment at end of project	$200k
Revenue per job	$12k
Variable cost per job	$4k
Quantity of jobs per year	120
Fixed costs per year, paid at the end of each year	$100k
Interest expense in first year (at t=1)	$16.091k
Interest expense in second year (at t=2)	$9.711k
Tax rate	30%
Government treasury bond yield	5%
Bank loan debt yield	6%
Levered cost of equity	12.5%
Market portfolio return	10%
Beta of assets	1.24
Beta of levered equity	1.5
Firm's and project's debt-to-equity ratio	25%

Notes

1. The project will require an immediate purchase of $50k of inventory, which will all be sold at cost when the project ends. Current liabilities are negligible so they can be ignored.

Assumptions

• The debt-to-equity ratio will be kept constant throughout the life of the project. The amount of interest expense at the end of each period has been correctly calculated to maintain this constant debt-to-equity ratio. Note that interest expense is different in each year.
• Thousands are represented by 'k' (kilo).
• All cash flows occur at the start or end of the year as appropriate, not in the middle or throughout the year.
• All rates and cash flows are nominal. The inflation rate is 2% pa.
• All rates are given as effective annual rates.
• The 50% capital gains tax discount is not available since the project is undertaken by a firm, not an individual.

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

(a) $684.222k

(b) $690.919k

(c) $697.616k

(d) $698.713k

(e) $710.601k

Question 371  interest tax shield, CFFA

One method for calculating a firm's free cash flow (FFCF, or CFFA) is to ignore interest expense. That is, pretend that interest expense ##(IntExp)## is zero:

###\begin{aligned} FFCF &= (Rev - COGS - Depr - FC - IntExp)(1-t_c) + Depr - CapEx -\Delta NWC + IntExp \\ &= (Rev - COGS - Depr - FC - 0)(1-t_c) + Depr - CapEx -\Delta NWC - 0\\ \end{aligned}###

Does this annual FFCF with zero interest expense or the annual interest tax shield?

Question 85  WACC, CAPM

A company has:

• 140 million shares outstanding.
• The market price of one share is currently $2.
• The company's debentures are publicly traded and their market price is equal to 93% of the face value.
• The debentures have a total face value of $50,000,000 and the current yield to maturity of corporate debentures is 12% per annum.
• The risk-free rate is 8.50% and the market return is 13.7%.
• Market analysts estimated that the company's stock has a beta of 0.90.
• The corporate tax rate is 30%.

What is the company's after-tax weighted average cost of capital (WACC) in a classical tax system?

(a) 13.18%

(b) 11.10%

(c) 12.50%

(d) 14.24%

(e) 15.00%

Question 88  WACC, CAPM

A firm can issue 3 year annual coupon bonds at a yield of 10% pa and a coupon rate of 8% pa.

The beta of its levered equity is 2. The market's expected return is 10% pa and 3 year government bonds yield 6% pa with a coupon rate of 4% pa.

The market value of equity is $1 million and the market value of debt is $1 million. The corporate tax rate is 30%.

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

(a) 8.40%

(b) 10.50%

(c) 10.80%

(d) 12.00%

(e) 21.00%

Question 97  WACC, no explanation

A company has:

• 10 million common shares outstanding, each trading at a price of $90.
• 1 million preferred shares which have a face (or par) value of $100 and pay a constant dividend of 9% of par. They currently trade at a price of $120 each.
• Debentures that have a total face value of $60,000,000 and a yield to maturity of 6% per annum. They are publicly traded and their market price is equal to 90% of their face value.
• The risk-free rate is 5% and the market return is 10%.
• Market analysts estimate that the company's common stock has a beta of 1.2. The corporate tax rate is 30%.

What is the company's after-tax Weighted Average Cost of Capital (WACC)? Assume a classical tax system.

(a) 10.27%

(b) 10.39%

(c) 10.43%

(d) 11.47%

(e) 17.22%

Question 118  WACC

A company has:

• 100 million ordinary shares outstanding which are trading at a price of $5 each. Market analysts estimated that the company's ordinary stock has a beta of 1.5. The risk-free rate is 5% and the market return is 10%.
• 1 million preferred shares which have a face (or par) value of $100 and pay a constant annual dividend of 9% of par. The next dividend will be paid in one year. Assume that all preference dividends will be paid when promised. They currently trade at a price of $90 each.
• Debentures that have a total face value of $200 million and a yield to maturity of 6% per annum. They are publicly traded and their market price is equal to 110% of their face value.

The corporate tax rate is 30%. All returns and yields are given as effective annual rates.

What is the company's after-tax Weighted Average Cost of Capital (WACC)? Assume a classical tax system.

(a) 17.22%

(b) 11.47%

(c) 10.46%

(d) 10.11%

(e) 9.97%

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 374  debt terminology

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

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

(a) Debt coupon rate.

(b) Required return on debt.

(c) Total return on debt.

(d) Opportunity cost of debt.

(e) Cost of debt capital.

Question 109  credit rating, credit risk

Bonds with lower (worse) credit ratings tend to have:

(a) Lower yields to maturity.

(b) Higher probabilities of default.

(c) Lower coupon rates when priced at par.

(d) Lower total risk.

(e) Lower credit risk.

Question 221  credit risk

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

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

(a) Junior debt is the safest. Preference shares have the highest expected returns.

(b) Preference shares are the safest. Ordinary shares have the highest expected returns.

(c) Senior debt is the safest. Ordinary shares have the highest expected returns.

(d) Junior debt is the safest. Ordinary shares have the highest expected returns.

(e) Senior debt is the safest. Junior debt have the highest expected returns.

Question 128  debt terminology, needs refinement

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

Question 129  debt terminology

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

Question 130  debt terminology

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

Question 146  APR, effective rate

A three year corporate bond yields 12% pa with a coupon rate of 10% pa, paid semi-annually.

Find the effective six month yield, effective annual yield and the effective daily yield. Assume that each month has 30 days and that there are 360 days in a year.

All answers are given in the same order:

##r_\text{eff semi-annual}##, ##r_\text{eff yearly}##, ##r_\text{eff daily}##.

(a) 0.06, 0.1236, 0.000324.

(b) 0.058301, 0.12, 0.000315.

(c) 0.05, 0.1025, 0.000271.

(d) 0.05, 0.1, 0.000278.

(e) 0.048809, 0.1, 0.000265.

Question 133  bond pricing

A bond maturing in 10 years has a coupon rate of 4% pa, paid semi-annually. The bond's yield is currently 6% pa. The face value of the bond is $100. What is its price?

(a) $33.93

(b) $55.37

(c) $57.61

(d) $68.28

(e) $85.12

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 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 25  bond pricing, zero coupon bond, term structure of interest rates, forward interest rate

A European company just issued two bonds, a

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

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

(a) 0.0374

(b) 0.0604

(c) 0.1204

(d) 0.1250

(e) 0.1411

Question 179  bond pricing, capital raising

A firm wishes to raise $20 million now. They will issue 8% pa semi-annual coupon bonds that will mature in 5 years and have a face value of $100 each. Bond yields are 6% pa, given as an APR compounding every 6 months, and the yield curve is flat.

How many bonds should the firm issue?

(a) 140,202

(b) 184,280

(c) 184,460

(d) 186,881

(e) 200,000

Question 339  bond pricing, inflation, market efficiency, income and capital returns

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

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

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

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

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

(a) Today the price would have increased significantly.
Over the next 2 years, the bond price is expected to increase, measured on each ex-coupon date.

(b) Today the price would have increased significantly.
Over the next 2 years, the bond price is expected to be unchanged, measured on each ex-coupon date.

(c) Today the price would have been unchanged.
Over the next 2 years, the bond price is expected to increase, measured on each ex-coupon date.

(d) Today the price would have decreased significantly.
Over the next 2 years, the bond price is expected to increase, measured on each ex-coupon date.

(e) Today the price would have decreased significantly.
Over the next 2 years, the bond price is expected to be unchanged, measured on each ex-coupon date.

Question 297  implicit interest rate in wholesale credit

You just bought $100,000 worth of inventory from a wholesale supplier. You are given the option of paying within 5 days and receiving a 2% discount, or paying the full price within 60 days.

You actually don't have the cash to pay within 5 days, but you could borrow it from the bank (as an overdraft) at 10% pa, given as an effective annual rate.

In 60 days you will have enough money to pay the full cost without having to borrow from the bank.

What is the implicit interest rate charged by the wholesale supplier, given as an effective annual rate? Also, should you borrow from the bank in 5 days to pay the supplier and receive the discount? Or just pay the full price on the last possible date?

Assume that there are 365 days per year.

(a) 0.143476 is the implicit rate. The buying firm should borrow from the bank and pay at day 5.

(b) 0.130771 is the implicit rate. The buying firm should NOT borrow from the bank and just pay at day 60.

(c) 0.125473 is the implicit rate. The buying firm should borrow from the bank and pay at day 5.

(d) 0.120131 is the implicit rate. The buying firm should NOT borrow from the bank and just pay at day 60.

(e) 0.020408 is the implicit rate. The buying firm should borrow from the bank and pay at day 5.

Question 103  option

Below are 4 option graphs. Note that the y-axis is payoff at maturity (T). What options do they depict? List them in the order that they are numbered.

(a) 1: short call, 2: long call, 3: short put, 4: long put.

(b) 1: long call, 2: long put, 3: short call, 4: short put.

(c) 1: short put, 2: long put, 3: short call, 4: long call.

(d) 1: long put, 2: short put, 3: long call, 4: short call.

(e) 1: long put, 2: short call, 3: short put, 4: long call.

Question 274  derivative terminology, option

The 'option price' in an option contract is paid at the start when the option contract is agreed to. or ?

Question 276  derivative terminology, option

The 'option strike price' in an option contract, also known as the exercise price, is paid at the start when the option contract is agreed to. or ?

Question 304  option

Which one of the following is NOT usually considered an 'investable' asset for long-term wealth creation?

(a) Shares (ordinary and preference stocks).

(b) Real estate (land and buildings).

(c) Options (calls and puts).

(d) Human capital (education)

(e) Debt (bond and loan assets)

Question 334  option

Which option position has the possibility of unlimited potential losses?

(a) Long call options.

(b) Short call options.

(c) Long put options.

(d) Short put options.

(e) No option positions have the possibility of unlimited potential losses.

Question 402  PE ratio, no explanation

Which of the following companies is most suitable for valuation using PE multiples techniques?

(a) A company with positive earnings that does not have any comparable firms.

(b) A company with positive earnings that has comparable firms with positive earnings.

(c) A company with positive earnings that has comparable firms with negative earnings.

(d) A company with negative earnings that has comparable firms with negative earnings.

(e) A company with negative earnings that has comparable firms with positive earnings.

Question 403  PE ratio, no explanation

Which of the following investable assets is the LEAST suitable for valuation using PE multiples techniques?

(a) Common equity in a small private company.

(b) Common equity in a listed public company.

(c) Commercial real estate.

(d) Ten year commercial real estate lease.

(e) Residential real estate.

Question 404  income and capital returns, real estate

One and a half years ago Frank bought a house for $600,000. Now it's worth only $500,000, based on recent similar sales in the area.

The expected total return on Frank's residential property is 7% pa.

He rents his house out for $1,600 per month, paid in advance. Every 12 months he plans to increase the rental payments.

The present value of 12 months of rental payments is $18,617.27.

The future value of 12 months of rental payments one year in the future is $19,920.48.

What is the expected annual rental yield of the property? Ignore the costs of renting such as maintenance, real estate agent fees and so on.

(a) 3.1029%

(b) 3.3201%

(c) 3.7235%

(d) 3.9841%

(e) 7%

Question 405  DDM, income and capital returns, no explanation

The perpetuity with growth formula is:

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

Which of the following is NOT equal to the total required return (r)?

(a) ## \dfrac{C_1}{P_0} +g ##

(b) ## \dfrac{C_1}{P_0} + \dfrac{P_1}{P_0} -1 ##

(c) ## \dfrac{C_1+P_1 - 1}{P_0} ##

(d) ## \dfrac{C_1}{P_0} + \dfrac{P_1-P_0}{P_0} ##

(e) ## \dfrac{C_1+P_0.g}{P_0} ##

Question 407  income and capital returns, inflation, real and nominal returns and cash flows

A stock has a real expected total return of 7% pa and a real expected capital return of 2% pa.

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

What is the nominal expected total return, capital return and dividend yield? The answers below are given in the same order.

(a) 11.100%, 4.000%, 7.100%.

(b) 11.140%, 4.040%, 7.100%.

(c) 4.902%, 0.000%, 4.902%.

(d) 9.140%, 4.040%, 5.100%.

(e) 9.140%, 4.040%, 7.100%.

Question 408  leverage, portfolio beta, portfolio risk, real estate, CAPM

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

You estimate that:

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

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

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

(a) The beta of equity is 5 and the expected return on equity is 30% pa.

(b) The beta of equity is 4.2 and the expected return on equity is 26% pa.

(c) The beta of equity is 0.86 and the expected return on equity is 9.3% pa.

(d) The beta of equity is 1 and the expected return on equity is 10% pa.

(e) The beta of equity is 0.6 and the expected return on equity is 8% pa.

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 413  CFFA, interest tax shield, depreciation tax shield

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

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

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

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

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

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

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

(a) ##FFCF=EBITDA+ Depr - CapEx -ΔNWC + IntExp##

(b) ##FFCF=EBITDA.(1-t_c )+Depr- CapEx -ΔNWC##

(c) ##FFCF=EBITDA.(1-t_c )+ Depr.t_c - CapEx -ΔNWC + IntExp.t_c##

(d) ##FFCF=EBITDA.(1-t_c )+Depr.(1-t_c )- CapEx -ΔNWC+IntExp.(1-t_c)##

(e) ##FFCF=EBITDA.(1-t_c )- CapEx -ΔNWC##

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 418  capital budgeting, NPV, interest tax shield, WACC, CFFA, CAPM

Project Data
Project life	1 year
Initial investment in equipment	$8m
Depreciation of equipment per year	$8m
Expected sale price of equipment at end of project	0
Unit sales per year	4m
Sale price per unit	$10
Variable cost per unit	$5
Fixed costs per year, paid at the end of each year	$2m
Interest expense in first year (at t=1)	$0.562m
Corporate tax rate	30%
Government treasury bond yield	5%
Bank loan debt yield	9%
Market portfolio return	10%
Covariance of levered equity returns with market	0.32
Variance of market portfolio returns	0.16
Firm's and project's debt-to-equity ratio	50%

Notes

1. Due to the project, current assets will increase by $6m now (t=0) and fall by $6m at the end (t=1). Current liabilities will not be affected.

Assumptions

• The debt-to-equity ratio will be kept constant throughout the life of the project. The amount of interest expense at the end of each period has been correctly calculated to maintain this constant debt-to-equity ratio.
• Millions are represented by 'm'.
• All cash flows occur at the start or end of the year as appropriate, not in the middle or throughout the year.
• All rates and cash flows are real. The inflation rate is 2% pa. All rates are given as effective annual rates.
• The project is undertaken by a firm, not an individual.

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

(a) $5.772m

(b) $4.979m

(c) $4.959m

(d) $4.733m

(e) $4.584m

Question 416  real estate, market efficiency, income and capital returns, DDM, CAPM

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

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

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

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

(a) The rental yield will fall and approach zero.

(b) The total return will fall and approach the capital return (5% pa).

(c) One or all of the following must fall: the systematic risk of real estate, the risk free rate or the market risk premium.

(d) If the country's nominal wealth growth rate is 4% pa and the nominal real estate growth rate is 5% pa then real estate will approach 100% of the country's wealth over time.

(e) If the country's nominal gross domestic production (GDP) growth rate is 4% pa and the nominal real estate rent growth rate is 2% pa then real estate rent will approach 100% of the country's GDP over time.

Question 215  equivalent annual cash flow, effective rate conversion

You're about to buy a car. These are the cash flows of the two different cars that you can buy:

• You can buy an old car for $5,000 now, for which you will have to buy $90 of fuel at the end of each week from the date of purchase. The old car will last for 3 years, at which point you will sell the old car for $500.
• Or you can buy a new car for $14,000 now for which you will have to buy $50 of fuel at the end of each week from the date of purchase. The new car will last for 4 years, at which point you will sell the new car for $1,000.

Bank interest rates are 10% pa, given as an effective annual rate. Assume that there are exactly 52 weeks in a year. Ignore taxes and environmental and pollution factors.

Should you buy the or the ?

Question 249  equivalent annual cash flow, effective rate conversion

Details of two different types of desserts or edible treats are given below:

• High-sugar treats like candy, chocolate and ice cream make a person very happy. High sugar treats are cheap at only $2 per day.
• Low-sugar treats like nuts, cheese and fruit make a person equally happy if these foods are of high quality. Low sugar treats are more expensive at $4 per day.

The advantage of low-sugar treats is that a person only needs to pay the dentist $2,000 for fillings and root canal therapy once every 15 years. Whereas with high-sugar treats, that treatment needs to be done every 5 years.

The real discount rate is 10%, given as an effective annual rate. Assume that there are 365 days in every year and that all cash flows are real. The inflation rate is 3% given as an effective annual rate.

Find the equivalent annual cash flow (EAC) of the high-sugar treats and low-sugar treats, including dental costs. The below choices are listed in that order.

Ignore the pain of dental therapy, personal preferences and other factors.

(a) -$332.8709, -$68.2065

(b) -$327.595, -$62.9476

(c) -$828.9808, -$808.5709

(d) -$829.6304, -$810.2613

(e) -$1,093.4153, -$1,594.5881

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 20  NPV, APR, Annuity

Your friend wants to borrow $1,000 and offers to pay you back $100 in 6 months, with more $100 payments at the end of every month for another 11 months. So there will be twelve $100 payments in total. She says that 12 payments of $100 equals $1,200 so she's being generous.

If interest rates are 12% pa, given as an APR compounding monthly, what is the Net Present Value (NPV) of your friend's deal?

(a) -648.51

(b) 60.28

(c) 70.88

(d) 125.51

(e) 200

Question 87  fully amortising loan, APR

You want to buy an apartment worth $500,000. You have saved a deposit of $50,000. The bank has agreed to lend you the $450,000 as a fully amortising mortgage loan with a term of 25 years. The interest rate is 6% pa and is not expected to change.

What will be your monthly payments?

(a) 1,500.00

(b) 2,250.00

(c) 2,855.79

(d) 2,899.36

(e) 35,202.02

Question 131  APR, effective rate

Calculate the effective annual rates of the following three APR's:

• A credit card offering an interest rate of 18% pa, compounding monthly.
• A bond offering a yield of 6% pa, compounding semi-annually.
• An annual dividend-paying stock offering a return of 10% pa compounding annually.

All answers are given in the same order:

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

(a) 0.1956, 0.0609, 0.1.

(b) 0.015, 0.09, 0.1.

(c) 0.1881, 0.0609, 0.1025.

(d) 0.1956, 0.0617, 0.1047.

(e) 6.2876, 0.1236, 0.1.

Question 134  fully amortising loan, APR

You want to buy an apartment worth $400,000. You have saved a deposit of $80,000. The bank has agreed to lend you the $320,000 as a fully amortising mortgage loan with a term of 30 years. The interest rate is 6% pa and is not expected to change. What will be your monthly payments?

(a) $888.89

(b) $1,600.00

(c) $1,885.99

(d) $1,918.56

(e) $23,247.65

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 149  fully amortising loan, APR

You want to buy an apartment priced at $500,000. You have saved a deposit of $50,000. The bank has agreed to lend you the $450,000 as a fully amortising loan with a term of 30 years. The interest rate is 6% pa and is not expected to change. What will be your monthly payments?

(a) $32,692.01

(b) $2,697.98

(c) $2,652.17

(d) $2,250.00

(e) $1,250.00

Question 156  APR, effective rate

A 2 year government bond yields 5% pa with a coupon rate of 6% pa, paid semi-annually.

Find the effective six month rate, effective annual rate and the effective daily rate. Assume that each month has 30 days and that there are 360 days in a year.

All answers are given in the same order:

##r_\text{eff semi-annual}##, ##r_\text{eff yrly}##, ##r_\text{eff daily}##.

(a) 0.024695, 0.05, 0.000136.

(b) 0.025, 0.050625, 0.000137.

(c) 0.029563, 0.06, 0.000162.

(d) 0.03, 0.06, 0.000167.

(e) 0.03, 0.0609, 0.000164.

Question 172  fully amortising loan, APR

You just signed up for a 30 year fully amortising mortgage loan with monthly payments of $2,000 per month. The interest rate is 9% pa which is not expected to change.

How much did you borrow? After 5 years, how much will be owing on the mortgage? The interest rate is still 9% and is not expected to change.

(a) 246,567.70,   93,351.63

(b) 246,567.70,   235,741.91

(c) 248,563.73,   96,346.75

(d) 248,563.73,   238,323.24

(e) 256,580.38,   245,314.97

Question 187  fully amortising loan, APR

You just signed up for a 30 year fully amortising mortgage with monthly payments of $1,000 per month. The interest rate is 6% pa which is not expected to change.

How much did you borrow? After 20 years, how much will be owing on the mortgage? The interest rate is still 6% and is not expected to change.

(a) 169,672.58,     90,724.32

(b) 166,791.61,     90,073.45

(c) 166,791.61,     139,580.77

(d) 165,177.97,     88,321.04

(e) 165,177.97,     137,639.05

Question 222  fully amortising loan, APR

You just agreed to a 30 year fully amortising mortgage loan with monthly payments of $2,500. The interest rate is 9% pa which is not expected to change.

How much did you borrow? After 10 years, how much will be owing on the mortgage? The interest rate is still 9% and is not expected to change. The below choices are given in the same order.

(a) $320,725.47,     $284,977.19

(b) $310,704.66,     $277,862.39

(c) $310,704.66,     $197,354.23

(d) $308,209.62,     $273,856.37

(e) $308,209.62,     $192,529.73

Question 256  APR, effective rate

A 2 year corporate bond yields 3% pa with a coupon rate of 5% pa, paid semi-annually.

Find the effective monthly rate, effective six month rate, and effective annual rate.

##r_\text{eff monthly}##, ##r_\text{eff 6 month}##, ##r_\text{eff annual}##.

(a) 0.002466, 0.014889, 0.03.

(b) 0.002485, 0.015, 0.030225.

(c) 0.004074, 0.024695, 0.05.

(d) 0.004124, 0.025, 0.050625.

(e) 0.004167, 0.025, 0.05.

Question 259  fully amortising loan, APR

You want to buy a house priced at $400,000. You have saved a deposit of $40,000. The bank has agreed to lend you $360,000 as a fully amortising loan with a term of 30 years. The interest rate is 8% pa payable monthly and is not expected to change.

What will be your monthly payments?

(a) $1,000

(b) $1,106.6497

(c) $2,400

(d) $2,571.8327

(e) $2,641.5525

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 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 381  Merton model of corporate debt, option, real option

In the Merton model of corporate debt, buying a levered company's debt is equivalent to buying risk free government bonds and:

(a) Selling the company's assets.

(b) Buying a call option on the company's assets.

(c) Buying a put option on the company's assets.

(d) Selling a call option on the company's assets.

(e) Selling a put option on the company's assets.

Question 383  Merton model of corporate debt, real option, option

In the Merton model of corporate debt, buying a levered company's debt is equivalent to buying the company's assets and:

(a) Selling government bonds.

(b) Buying a call option on the company's assets.

(c) Buying a put option on the company's assets.

(d) Selling a call option on the company's assets.

(e) Selling a put option on the company's assets.

Question 384  option, real option

Which of the following is the least useful method or model to calculate the value of a real option in a project?

(a) Project value with the option less project value without the option.

(b) No-arbitrage binomial option pricing model.

(c) Risk-neutral binomial option pricing model.

(d) Gordon growth model.

(e) Black-Sholes option pricing model.

Question 385  Merton model of corporate debt, real option, option

A risky firm will last for one period only (t=0 to 1), then it will be liquidated. So it's assets will be sold and the debt holders and equity holders will be paid out in that order. The firm has the following quantities:

##V## = Market value of assets.

##E## = Market value of (levered) equity.

##D## = Market value of zero coupon bonds.

##F_1## = Total face value of zero coupon bonds which is promised to be paid in one year.

The levered equity graph above contains bold labels a to e. Which of the following statements about those labels is NOT correct?

(a) Label a represents the market value of equity ##(E)## at t=0 on the red curved line or t=1 on the blue crooked line.

(b) Label b represents the market value of equity now ##(E_0)##.

(c) Label c represents the market value of equity if the assets were liquidated right now.

(d) Label d represents the face value of debt at maturity ##(F_1)##.

(e) Label e represents the market value of debt ##(D)## at t=0 on the red curved line or t=1 on the blue crooked line.

Question 386  Merton model of corporate debt, real option, option

A risky firm will last for one period only (t=0 to 1), then it will be liquidated. So it's assets will be sold and the debt holders and equity holders will be paid out in that order. The firm has the following quantities:

##V## = Market value of assets.

##E## = Market value of (levered) equity.

##D## = Market value of zero coupon bonds.

##F_1## = Total face value of zero coupon bonds which is promised to be paid in one year.

The risky corporate debt graph above contains bold labels a to e. Which of the following statements about those labels is NOT correct?

(a) Label a represents the market value of equity ##(E)## at t=0 on the red curved line or t=1 on the blue crooked line.

(b) Label b represents the face value of debt at maturity ##(F_1)##.

(c) Label c represents the market value of debt now ##(D_0)##.

(d) Label d represents the face value of debt at maturity ##(F_1)##.

(e) Label e represents the market value of assets ##(V)## at t=0 on the red curved line or t=1 on the blue crooked line.

Question 388  real option, option

A moped is a bicycle with pedals and a little motor that can be switched on to assist the rider. Mopeds are useful for quick transport using the motor, and for physical exercise when using the pedals unassisted. This offers the rider:

(a) An expansion option.

(b) An abandonment option.

(c) A timing (or delaying) option.

(d) A production (or switching) option.

(e) Lots of options to exercise if they're out-of-money and have no fuel.

Question 392  real option, option

An abandonment option is best modeled as a or option?

Question 393  real option, option

A timing option is best modeled as a or option?

Question 394  real option, option

According to option theory, it's rational for students to submit their assignments as or as possible?

Question 395  real option, option

The cheapest mobile phones available tend to be those that are 'locked' into a cell phone operator's network. Locked phones can not be used with other cell phone operators' networks.

Locked mobile phones are cheaper than unlocked phones because the locked-in network operator helps create a monopoly by:

(a) Destroying customers' expansion option.

(b) Destroying customers' abandonment option.

(c) Destroying customers' timing (or delaying) option.

(d) Destroying customers' production (or switching) option.

(e) Growing customers' binomial tree.

Question 397  financial distress, leverage, capital structure, NPV

A levered firm has a market value of assets of $10m. Its debt is all comprised of zero-coupon bonds which mature in one year and have a combined face value of $9.9m.

Investors are risk-neutral and therefore all debt and equity holders demand the same required return of 10% pa.

Therefore the current market capitalisation of debt ##(D_0)## is $9m and equity ##(E_0)## is $1m.

A new project presents itself which requires an investment of $2m and will provide a:

• $6.6m cash flow with probability 0.5 in the good state of the world, and a
• -$4.4m (notice the negative sign) cash flow with probability 0.5 in the bad state of the world.

The project can be funded using the company's excess cash, no debt or equity raisings are required.

What would be the new market capitalisation of equity ##(E_\text{0, with project})## if shareholders vote to proceed with the project, and therefore should shareholders proceed with the project?

(a) $2.5m, so they should vote yes.

(b) $2.045455m, so they should vote yes.

(c) $0.9m, so they should vote no.

(d) $0, so they should vote no.

(e) -$0.9m, so they should vote no.

Question 427  takeover

In a takeover deal where the offer is 100% cash, the merged firm's number of shares will be equal to the acquirer firm's original number of shares. or ?

Question 428  takeover

In a takeover deal where the offer is 100% scrip (shares), the merged firm's number of shares will be equal to the acquirer firm's original number of shares. or ?

Question 429  takeover

In a takeover deal where the offer is 100% scrip (shares), the merged firm's number of shares will be equal to the sum of the acquirer and target firms' original number of shares. or ?

Question 421  takeover

Acquirer firm plans to launch a takeover of Target firm. The deal is expected to create a present value of synergies totaling $105 million. A scrip offer will be made that pays the fair price for the target's shares plus 75% of the total synergy value.

Firms Involved in the Takeover
	Acquirer	Target
Assets ($m)	6,000	700
Debt ($m)	4,800	400
Share price ($)	40	20
Number of shares (m)	30	15

Ignore transaction costs and fees. Assume that the firms' debt and equity are fairly priced, and that each firms' debts' risk, yield and values remain constant. The acquisition is planned to occur immediately, so ignore the time value of money.

Calculate the merged firm's share price and total number of shares after the takeover has been completed.

(a) $26.7778 share price and 45m shares on issue.

(b) $40.875 share price and 39.266055m shares on issue.

(c) $42.0639 share price and 38.15625m shares on issue.

(d) $42.8 share price and 37.5m shares on issue.

(e) $50.875 share price and 30m shares on issue.

Question 424  takeover

Acquirer firm plans to launch a takeover of Target firm. The deal is expected to create a present value of synergies totaling $2 million. A cash offer will be made that pays the fair price for the target's shares plus 70% of the total synergy value. The cash will be paid out of the firm's cash holdings, no new debt or equity will be raised.

Firms Involved in the Takeover
	Acquirer	Target
Assets ($m)	60	10
Debt ($m)	20	2
Share price ($)	10	8
Number of shares (m)	4	1

Ignore transaction costs and fees. Assume that the firms' debt and equity are fairly priced, and that each firms' debts' risk, yield and values remain constant. The acquisition is planned to occur immediately, so ignore the time value of money.

Calculate the merged firm's share price and total number of shares after the takeover has been completed.

(a) $10.15 share price and 4m shares on issue.

(b) $11.6279 share price and 4.3m shares on issue.

(c) $7.72 share price and 5m shares on issue.

(d) $9.3 share price and 4m shares on issue.

(e) $9.65 share price and 4m shares on issue.

Question 425  takeover

Acquirer firm plans to launch a takeover of Target firm. The deal is expected to create a present value of synergies totaling $2 million. A scrip offer will be made that pays the fair price for the target's shares plus 70% of the total synergy value.

Firms Involved in the Takeover
	Acquirer	Target
Assets ($m)	60	10
Debt ($m)	20	2
Share price ($)	10	8
Number of shares (m)	4	1

Ignore transaction costs and fees. Assume that the firms' debt and equity are fairly priced, and that each firms' debts' risk, yield and values remain constant. The acquisition is planned to occur immediately, so ignore the time value of money.

Calculate the merged firm's share price and total number of shares after the takeover has been completed.

(a) $10.15 share price and 4.926108m shares on issue.

(b) $10.2881 share price and 4.86m shares on issue.

(c) $10.4167 share price and 4.8m shares on issue.

(d) $11.6279 share price and 4.3m shares on issue.

(e) $9.6 share price and 5m shares on issue.