Fight Finance

Question 714  return distribution, no explanation

Which of the following quantities is commonly assumed to be normally distributed?

(a) Prices, ##P_1##.

(b) Gross discrete returns per annum, ##r_{\text{gdr 0 }\rightarrow \text{ 1}} = \dfrac{P_1}{P_0} ##.

(c) Effective annual returns per annum also known as net discrete returns, ##r_{\text{eff 0 }\rightarrow \text{ 1}} = \dfrac{P_1 - P_0}{P_0} = \dfrac{P_1}{P_0}-1##.

(d) Continuously compounded returns per annum, ##r_{\text{cc 0 }\rightarrow \text{ 1}} = \ln \left( \dfrac{P_1}{P_0} \right)##.

(e) Annualised percentage rates compounding per month, ##r_{\text{apr comp monthly 0 }\rightarrow \text{ 1 mth}} = \left( \dfrac{P_1 - P_0}{P_0} \right) \times 12##.

Question 716  return distribution

The below three graphs show probability density functions (PDF) of three different random variables Red, Green and Blue.

Which of the below statements is NOT correct?

(a)##-1 < \text{Red} < \infty## if Red is log-normally distributed.

(b) ##-2 < \text{Green} < 2## if Green is normally distributed.

(c) ##0 < \text{Blue} < \infty## if Blue is log-normally distributed.

(d) If the Green distribution is normal, then the mode = median = mean.

(e) If the Red and Blue distributions are log-normal, then the mode < median < mean.

Question 718  arithmetic and geometric averages

The symbol ##\text{GDR}_{0\rightarrow 1}## represents a stock's gross discrete return per annum over the first year. ##\text{GDR}_{0\rightarrow 1} = P_1/P_0##. The subscript indicates the time period that the return is mentioned over. So for example, ##\text{AAGDR}_{1 \rightarrow 3}## is the arithmetic average GDR measured over the two year period from years 1 to 3, but it is expressed as a per annum rate.

Which of the below statements about the arithmetic and geometric average GDR is NOT correct?

(a) Arithmetic average gross discrete return is ##\text{AAGDR}_{0\rightarrow T} = \dfrac{\text{GDR}_{0 \rightarrow 1}+\text{GDR}_{1\rightarrow 2}+...+\text{GDR}_{T-1 \rightarrow T}}{T}##

(b) Geometric average gross discrete return is ##\text{GAGDR}_{0\rightarrow T} = \dfrac{\text{GDR}_{0 \rightarrow 1} . \text{GDR}_{1\rightarrow 2} ... \text{GDR}_{T-1 \rightarrow T}}{T}##

(c) The geometric average gross discrete return can be quickly found using the first ##(P_0)## and last ##(P_T)## prices. ##\text{GAGDR}_{0\rightarrow T} = \left( \dfrac{P_T}{P_0} \right)^{1/T}##

(d) The arithmetic average is always bigger than or equal to the geometric average, ##\text{AAGDR} \ge \text{GAGDR}##.

(e) The arithmetic and geometric averages of returns will be equal if the variance of the stock's returns is zero.

Question 707  continuously compounding rate, continuously compounding rate conversion

Convert a 10% effective annual rate ##(r_\text{eff annual})## into a continuously compounded annual rate ##(r_\text{cc annual})##. The equivalent continuously compounded annual rate is:

(a) 230.258509% pa

(b) 10.536052% pa

(c) 10.517092% pa

(d) 10.468982% pa

(e) 9.531018% pa

Question 711  continuously compounding rate, continuously compounding rate conversion

A continuously compounded semi-annual return of 5% ##(r_\text{cc 6mth})## is equivalent to a continuously compounded annual return ##(r_\text{cc annual})## of:

(a) 30% pa

(b) 26.236426% pa

(c) 10.254219% pa

(d) 10.25% pa

(e) 10% pa

Question 713  effective rate conversion

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

(a) 30% pa

(b) 26.236426% pa

(c) 10.254219% pa

(d) 10.25% pa

(e) 10% pa

Question 691  continuously compounding rate, effective rate, continuously compounding rate conversion, no explanation

A bank quotes an interest rate of 6% pa with quarterly compounding. Note that another way of stating this rate is that it is an annual percentage rate (APR) compounding discretely every 3 months.

Which of the following statements about this rate is NOT correct? All percentages are given to 6 decimal places. The equivalent:

(a) Continuously compounded rate is 5.955445% per annum. Note that this rate is the annual rate with continuous compounding.

(b) Continuously compounded rate is 1.500000% per quarter. Note that this rate is the quarterly rate with continuous compounding.

(c) Effective quarterly rate is 1.500000% per quarter. Note that this rate is the quarterly rate with discrete quarterly compounding.

(d) Effective annual rate is 6.136355% per annum. Note that this rate is the annual rate with discrete annual compounding.

(e) $1,000,000 invested in this bank account for one year will give $1,061,363.551 at the end of the year.

Question 715  return distribution

If a variable, say X, is normally distributed with mean ##\mu## and variance ##\sigma^2## then mathematicians write ##X \sim \mathcal{N}(\mu, \sigma^2)##.

If a variable, say Y, is log-normally distributed and the underlying normal distribution has mean ##\mu## and variance ##\sigma^2## then mathematicians write ## Y \sim \mathbf{ln} \mathcal{N}(\mu, \sigma^2)##.

The below three graphs show probability density functions (PDF) of three different random variables Red, Green and Blue.

Select the most correct statement:

(a)##Red \sim \mathcal{N}(\mu, \sigma^2)##,   ##Green \sim \mathcal{N}(\mu, \sigma^2)##   and   ##Blue \sim \mathcal{N}(\mu, \sigma^2)##

(b) ##Red \sim \mathcal{N}(\mu, \sigma^2)##,   ##Green \sim \mathcal{N}(\mu, \sigma^2)##   and   ##Blue \sim \mathbf{ln} \mathcal{N}(\mu, \sigma^2)##

(c) ##Red \sim \mathcal{N}(\mu, \sigma^2)##,   ##Green \sim \mathbf{ln} \mathcal{N}(\mu, \sigma^2)##   and   ##Blue \sim \mathbf{ln} \mathcal{N}(\mu, \sigma^2)##

(d) ##Red \sim \mathbf{ln} \mathcal{N}(\mu, \sigma^2)##,   ##Green \sim \mathcal{N}(\mu, \sigma^2)##   and   ##Blue \sim \mathbf{ln} \mathcal{N}(\mu, \sigma^2)##

(e) ##Red \sim \mathbf{ln} \mathcal{N}(\mu, \sigma^2)##,   ##Green \sim \mathbf{ln} \mathcal{N}(\mu, \sigma^2)##   and   ##Blue \sim \mathbf{ln} \mathcal{N}(\mu, \sigma^2)##

Question 726  return distribution, mean and median returns

If a stock's expected future prices are log-normally distributed, what will be bigger, the stock's or future price? Or would you expect them to be ?

Question 724  return distribution, mean and median returns

If a stock's future expected continuously compounded annual returns are normally distributed, what will be bigger, the stock's or continuously compounded annual return? Or would you expect them to be ?

Question 719  mean and median returns, return distribution, arithmetic and geometric averages, continuously compounding rate

A stock has an arithmetic average continuously compounded return (AALGDR) of 10% pa, a standard deviation of continuously compounded returns (SDLGDR) of 80% pa and current stock price of $1. Assume that stock prices are log-normally distributed. The graph below summarises this information and provides some helpful formulas.

In one year, what do you expect the median and mean prices to be? The answer options are given in the same order.

(a) P1median = $1.105171,   P1mean = $1.521962

(b) P1median = $1.1,             P1mean = $1.42

(c) P1median = $1.521962,   P1mean = $1.105171

(d) P1median = $0.802519,   P1mean = $1.105171

(e) P1median = $1.42,           P1mean = $1.1

Question 720  mean and median returns, return distribution, arithmetic and geometric averages, continuously compounding rate

A stock has an arithmetic average continuously compounded return (AALGDR) of 10% pa, a standard deviation of continuously compounded returns (SDLGDR) of 80% pa and current stock price of $1. Assume that stock prices are log-normally distributed.

In 5 years, what do you expect the median and mean prices to be? The answer options are given in the same order.

(a) $0.332871, $1.648721

(b) $8.16617, $1.648721

(c) $1.61051, $1.648721

(d) $1.61051, $5.773534

(e) $1.648721, $8.16617

Question 723  mean and median returns, return distribution, arithmetic and geometric averages, continuously compounding rate

Here is a table of stock prices and returns. Which of the statements below the table is NOT correct?

Price and Return Population Statistics
Time	Prices	LGDR	GDR	NDR
0	100
1	99	-0.010050	0.990000	-0.010000
2	180.40	0.600057	1.822222	0.822222
3	112.73	0.470181	0.624889	0.375111
Arithmetic average		0.0399	1.1457	0.1457
Arithmetic standard deviation		0.4384	0.5011	0.5011

 

(a) The geometric average of the gross discrete returns (GAGDR) equals 1.04075 which is 104.075%.

(b) ##\exp \left( \text{GAGDR} \right) = \text{AALGDR}##. The natural exponent of the GAGDR equals the arithmetic average of the logarithms of the gross discrete returns (AALGDR).

(c) ##\text{GAGDR}^T = \left( P_T/P_0 \right)##. The GAGDR raised to the power of the number of time period that it's measured over equals the ratio of the first and last prices.

(d) ##\text{GAGDR} = \exp \left( \text{AALGDR} \right)##. This is always true, regardless of the distribution of the prices or returns. The logarithm of the geometric average of the gross discrete returns (LGAGDR) is always equal to the arithmetic average of the logarithm of the gross discrete returns (AALGDR).

(e) ##\text{AAGDR} \approx \exp \left( \text{AALGDR} + \text{SDLGDR}^2/2 \right)##. This is only approximately true and depends on the distribution of the prices and returns. It's asymptotically true as the time period that the returns are measured over reaches infinity.

Question 725  return distribution, mean and median returns

If a stock's future expected effective annual returns are log-normally distributed, what will be bigger, the stock's or effective annual return? Or would you expect them to be ?

Question 779  mean and median returns, return distribution, arithmetic and geometric averages, continuously compounding rate

Fred owns some BHP shares. He has calculated BHP’s monthly returns for each month in the past 30 years using this formula:

###r_\text{t monthly}=\ln⁡ \left( \dfrac{P_t}{P_{t-1}} \right)###

He then took the arithmetic average and found it to be 0.8% per month using this formula:

###\bar{r}_\text{monthly}= \dfrac{ \displaystyle\sum\limits_{t=1}^T{\left( r_\text{t monthly} \right)} }{T} =0.008=0.8\% \text{ per month}###

He also found the standard deviation of these monthly returns which was 15% per month:

###\sigma_\text{monthly} = \dfrac{ \displaystyle\sum\limits_{t=1}^T{\left( \left( r_\text{t monthly} - \bar{r}_\text{monthly} \right)^2 \right)} }{T} =0.15=15\%\text{ per month}###

Assume that the past historical average return is the true population average of future expected returns and the stock's returns calculated above ##(r_\text{t monthly})## are normally distributed. Which of the below statements about Fred’s BHP shares is NOT correct?

(a) The returns ##r_\text{t monthly}## are continuously compounded monthly returns.

(b) The mean, median and mode of the continuously compounded annual return is expected to equal 0.8% per month.

(c) The annualised average continuously compounded return is ##\bar{r}_\text{cc annual}=12×0.008=0.096=9.6\%\text{ pa}##. The annualised standard deviation is ##\sigma_\text{annual} = \sqrt{12}×0.15=0.519615242 = 52\%\text{ pa}##.

(d) If the current price of the BHP shares is $20, they're expected to have a median value of $52.2339 ##(= 20×e^{0.008×12×10})## in 10 years.

(e) If the current price of the BHP shares is $20, they're expected to have a mean value of $13.5411 ##(= 20×e^{(0.008 - 0.15^2/2)×12×10})## in 10 years.

Question 708  continuously compounding rate, continuously compounding rate conversion

Convert a 10% continuously compounded annual rate ##(r_\text{cc annual})## into an effective annual rate ##(r_\text{eff annual})##. The equivalent effective annual rate is:

(a) 230.258509% pa

(b) 10.536052% pa

(c) 10.517092% pa

(d) 10.468982% pa

(e) 9.531018% pa

Question 710  continuously compounding rate, continuously compounding rate conversion

A continuously compounded monthly return of 1% ##(r_\text{cc monthly})## is equivalent to a continuously compounded annual return ##(r_\text{cc annual})## of:

(a) 12.682503% pa

(b) 12.060201% pa

(c) 12% pa

(d) 11.940397% pa

(e) 3.464102% pa

Question 709  continuously compounding rate, APR

Which of the following interest rate quotes is NOT equivalent to a 10% effective annual rate of return? Assume that each year has 12 months, each month has 30 days, each day has 24 hours, each hour has 60 minutes and each minute has 60 seconds. APR stands for Annualised Percentage Rate.

(a) 9.7617696% is the APR compounding semi-annually ##(r_\text{apr comp 6mth})##

(b) 9.5689685% is the APR compounding monthly ##(r_\text{apr comp monthly})##

(c) 9.6454756% is the APR compounding daily ##(r_\text{apr comp daily})##

(d) 9.5310182% is the APR compounding per second ##(r_\text{apr comp per second})##

(e) 9.5310180% is the continuously compounded rate per annum ##(r_\text{cc annual})##

Question 653  future, continuously compounding rate

An equity index is currently at 4,800 points. The 1.5 year futures price is 5,100 points and the total required return is 6% pa with continuous compounding. Each index point is worth $25.

What is the implied dividend yield as a continuously compounded rate per annum?

(a) -0.0625% pa

(b) 1.9584% pa

(c) 3.0937% pa

(d) 4.0416% pa

(e) 6.0625% pa

Question 634  continuously compounding rate

A $100 stock has a continuously compounded expected total return of 10% pa. Its dividend yield is 2% pa with continuous compounding. What do you expect its price to be in one year?

(a) $112.749685

(b) $110.517092

(c) $110

(d) $108.328707

(e) $108

Question 596  future, continuously compounding rate

An equity index is currently at 5,000 points. The 2 year futures price is 5,400 points and the total required return is 8% pa with continuous compounding. Each index point is worth $25.

What is the implied continuous dividend yield as a continuously compounded rate per annum?

(a) 0.3039% pa

(b) 3.8481% pa

(c) 4.1519% pa

(d) 7.3922% pa

(e) 7.6961% pa

Question 594  future, continuously compounding rate

The current gold price is $700, gold storage costs are 2% pa and the risk free rate is 10% pa, both with continuous compounding.

What should be the 3 year gold futures price?

(a) $758.30

(b) $773.62

(c) $889.87

(d) $944.90

(e) $1,003.33

Question 666  rights issue, capital raising

A company conducts a 2 for 3 rights issue at a subscription price of $8 when the pre-announcement stock price was $9. Assume that all investors use their rights to buy those extra shares.

What is the percentage increase in the stock price and the number of shares outstanding? The answers are given in the same order.

(a) -60%,   150%

(b) -42.22%,   150%

(c) -40%,   66.67%

(d) -22.22%,   66.67%

(e) -4.44%,   66.67%

Question 665  stock split

A company conducts a 10 for 3 stock split. What is the percentage increase in the stock price and the number of shares outstanding? The answers are given in the same order.

(a) -76.92%,   333.33%

(b) -70%,   333.33%

(c) -70%, 233.33%

(d) -57.14%,   233.33%

(e) 233.33%,   -70%

Question 566  capital structure, capital raising, rights issue, on market repurchase, dividend, stock split, bonus issue

A company's share price fell by 20% and its number of shares rose by 25%. Assume that there are no taxes, no signalling effects and no transaction costs.

Which one of the following corporate events may have happened?

(a) $1 cash dividend when the pre-announcement stock price was $5.

(b) On-market buy-back of 20% of the company's outstanding stock.

(c) 5 for 4 stock split.

(d) 1 for 5 bonus issue.

(e) 1 for 4 rights issue at a subscription price of $3 when the pre-announcement stock price was $5.

Question 513  stock split, reverse stock split, stock dividend, bonus issue, rights issue

Which of the following statements is NOT correct?

(a) A 3 for 2 stock split means that for every 2 existing shares, all shareholders will receive 1 extra share.

(b) A 3 for 10 bonus issue means that for every 10 existing shares, all shareholders will receive 3 extra shares.

(c) A 20% stock dividend means that for every 10 existing shares, all shareholders will receive 2 extra shares.

(d) A 1 for 10 reverse stock split means that for every 10 existing shares, all shareholders will lose 9 shares, so they will only be left with 1 share.

(e) A 3 for 10 rights issue at a subscription price of $8 means that for every 10 existing shares, all shareholders can sell 3 of their shares back to the company at a price of $8 each, so shareholders receive money.

Question 555  capital budgeting, CFFA

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

Project Data
Project life	2 years
Initial investment in equipment	$8m
Depreciation of equipment per year for tax purposes	$3m
Unit sales per year	10m
Sale price per unit	$9
Variable cost per unit	$4
Fixed costs per year, paid at the end of each year	$2m
Tax rate	30%

Note 1: Due to the project, the firm will have to purchase $40m of inventory initially (at t=0). Half of this inventory will be sold at t=1 and the other half at t=2.

Note 2: The equipment will have a book value of $2m at the end of the project for tax purposes. However, the equipment is expected to fetch $1m when it is sold. Assume that the full capital loss is tax-deductible and taxed at the full corporate tax rate.

Note 3: The project will be fully funded by equity which investors will expect to pay dividends totaling $10m at the end of each year.

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

(a) -48,   54.5,   55.8

(b) -48,   54.5,   74.5

(c) -48,   74.5,   35.8

(d) -48,   74.5,   75.8

(e) -8,   74.5,   75.8

Question 655  capital budgeting, opportunity cost, sunk cost

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

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

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

(c) Separation of the investment and financing decisions.

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

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

Question 512  capital budgeting, CFFA

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

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

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

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

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

(a) -6,   12.25,   16.68

(b) -6.8,   13.25,   14.05

(c) -6.8,   13.25,   15.88

(d) -6.8,   13.25,   18.51

(e) -6.8,   13.25,   17.71

Question 492  capital budgeting, opportunity cost, sunk cost

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

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

(a) A sunk cost.

(b) An opportunity cost.

(c) A negative side effect.

(d) A capital expense.

(e) A depreciation expense.

Question 491  capital budgeting, opportunity cost, sunk cost

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

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

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

(a) A sunk cost.

(b) An opportunity cost.

(c) A negative side effect.

(d) A capital expense.

(e) A depreciation expense.

Question 486  capital budgeting, opportunity cost, sunk cost

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

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

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

(a) A sunk cost.

(b) An opportunity cost.

(c) A negative side effect.

(d) A positive side effect.

(e) A depreciation expense.

Question 485  capital budgeting, opportunity cost, sunk cost

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

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

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

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

(a) A sunk cost.

(b) An opportunity cost.

(c) A negative side effect.

(d) A positive side effect.

(e) A depreciation expense.

Question 419  capital budgeting, NPV, interest tax shield, WACC, CFFA, CAPM, no explanation

Project Data
Project life	1 year
Initial investment in equipment	$6m
Depreciation of equipment per year	$6m
Expected sale price of equipment at end of project	0
Unit sales per year	9m
Sale price per unit	$8
Variable cost per unit	$6
Fixed costs per year, paid at the end of each year	$1m
Interest expense in first year (at t=1)	$0.53m
Tax rate	30%
Government treasury bond yield	5%
Bank loan debt yield	6%
Market portfolio return	10%
Covariance of levered equity returns with market	0.08
Variance of market portfolio returns	0.16
Firm's and project's debt-to-assets ratio	50%

Notes

1. Due to the project, current assets will increase by $5m now (t=0) and fall by $5m at the end (t=1). Current liabilities will not be affected.

Assumptions

• The debt-to-assets 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 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) $7.33k

(b) $7.299k

(c) $6.946k

(d) $6.729k

(e) $6.667k

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 410  CAPM, capital budgeting

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

###r_i=r_f+β_i (r_m-r_f)###

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

(a) The current central bank policy rate (RBA overnight money market rate).

(b) The current 30 day federal government treasury bill rate.

(c) The average historical 30 day federal government treasury bill rate over the last 20 years.

(d) The current 30 year federal government treasury bond rate.

(e) The average historical 30 year federal government treasury bond rate over the last 20 years.

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 273  CFFA, capital budgeting

Value the following business project to manufacture a new product.

Project Data
Project life	2 yrs
Initial investment in equipment	$6m
Depreciation of equipment per year	$3m
Expected sale price of equipment at end of project	$0.6m
Unit sales per year	4m
Sale price per unit	$8
Variable cost per unit	$5
Fixed costs per year, paid at the end of each year	$1m
Interest expense per year	0
Tax rate	30%
Weighted average cost of capital after tax per annum	10%

Notes

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

Assumptions

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

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

(a) $5.2m

(b) $8.481735m

(c) $8.743802m

(d) $8.991736m

(e) $9.719008m

Question 559  variance, standard deviation, covariance, correlation

Which of the following statements about standard statistical mathematics notation is NOT correct?

(a) The arithmetic average of variable X is represented by ##\bar{X}##.

(b) The standard deviation of variable X is represented by ##\sigma_X##.

(c) The variance of variable X is represented by ##\sigma_X^2##.

(d) The covariance between variables X and Y is represented by ##\sigma_{X,Y}^2##.

(e) The correlation between variables X and Y is represented by ##\rho_{X,Y}##.

Question 284  covariance, correlation

The following table shows a sample of historical total returns of shares in two different companies A and B.

Stock Returns
Total effective annual returns
Year	##r_A##	##r_B##
2007	0.2	0.4
2008	0.04	-0.2
2009	-0.1	-0.3
2010	0.18	0.5

What is the historical sample covariance (##\hat{\sigma}_{A,B}##) and correlation (##\rho_{A,B}##) of stock A and B's total effective annual returns?

(a) 0.05696, 0.702247

(b) 0.05696, 0.238663

(c) 0.053333, 0.936329

(d) 0.040889, 0.930519

(e) 0.04, 0.930519

Question 82  portfolio return

Portfolio Details
Stock	Expected return	Standard deviation	Correlation	Dollars invested
A	0.1	0.4	0.5	60
B	0.2	0.6		140

What is the expected return of the above portfolio?

(a) 0.15

(b) 0.17

(c) 0.1908

(d) 0.2412

(e) 0.34

Question 73  portfolio risk, standard deviation

Portfolio Details
Stock	Expected return	Standard deviation	Covariance ##(\sigma_{A,B})##	Beta	Dollars invested
A	0.2	0.4	0.12	0.5	40
B	0.3	0.8		1.5	80

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

(a) 0.5497

(b) 0.5651

(c) 0.5963

(d) 0.6156

(e) 0.8165

Question 279  diversification

Do you think that the following statement is or ? “Buying a single company stock usually provides a safer return than a stock mutual fund.”

Question 558  portfolio weights, portfolio return, short selling

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

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

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

(a) 200%, -100%

(b) 200%, 100%

(c) -100%, 200%

(d) 100%, 200%

(e) -100%, 100%

Question 564  covariance

What is the covariance of a variable X with a constant C?

The cov(X, C) or ##\sigma_{X,C}## equals:

(a) var(X) or ##\sigma_X^2##

(b) sd(X) or ##\sigma_X##

(c) 1

(d) 0

(e) Mathematically undefined

Question 563  correlation

What is the correlation of a variable X with itself?

The corr(X, X) or ##\rho_{X,X}## equals:

(a) var(X) or ##\sigma_X^2##

(b) sd(X) or ##\sigma_X##

(c) 1

(d) 0

(e) Mathematically undefined

Question 556  portfolio risk, portfolio return, standard deviation

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

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

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

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

(a) 24.28168% pa

(b) 24% pa

(c) 22.126907% pa

(d) 19.697716% pa

(e) 16.970563% pa

Question 557  portfolio weights, portfolio return

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

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

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

(a) 80%, 20%

(b) 60%, 40%

(c) 40%, 60%

(d) 20%, 80%

(e) 20%, 20%

Question 83  portfolio risk, standard deviation

Portfolio Details
Stock	Expected return	Standard deviation	Correlation ##(\rho_{A,B})##	Dollars invested
A	0.1	0.4	0.5	60
B	0.2	0.6		140

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

(a) 0.4368

(b) 0.4911

(c) 0.6331

(d) 0.6564

(e) 0.7348

Question 293  covariance, correlation, portfolio risk

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

(a) The more diversification is possible when those stocks are combined in a portfolio.

(b) The lower the variance of returns of an equally-weighted portfolio of those stocks.

(c) The lower the volatility of returns of an equal-weighted portfolio of those stocks.

(d) The higher the covariance between those stocks' returns.

(e) The more likely that when one stock has a positive return, the other has a negative return.

Question 285  covariance, portfolio risk

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

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

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

Which of the following statements is NOT correct?

(a) The variance of the portfolio returns will increase.

(b) The standard deviation of the portfolio returns will increase.

(c) The covariance of returns between stocks A and B will stay the same.

(d) The portfolio expected return will stay the same.

(e) The portfolio value will stay the same.

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 778  CML, systematic and idiosyncratic risk, portfolio risk, CAPM

The capital market line (CML) is shown in the graph below. The total standard deviation is denoted by σ and the expected return is μ. Assume that markets are efficient so all assets are fairly priced.

Which of the below statements is NOT correct?

(a) The risk free security has zero systematic variance and zero idiosyncratic variance.

(b) The market portfolio has zero idiosyncratic variance.

(c) Any portfolio comprised of the market portfolio and risk free security has zero idiosyncratic variance.

(d) Portfolios that plot on the CML must only be comprised of the risk free security and the market portfolio.

(e) Portfolios that plot on the CML have some idiosyncratic variance and some systematic variance.

Question 450  CAPM, risk, portfolio risk, no explanation

The accounting identity states that the book value of a company's assets (A) equals its liabilities (L) plus owners equity (OE), so A = L + OE.

The finance version states that the market value of a company's assets (V) equals the market value of its debt (D) plus equity (E), so V = D + E.

Therefore a business's assets can be seen as a portfolio of the debt and equity that fund the assets.

Let ##\sigma_\text{V total}^2## be the total variance of returns on assets, ##\sigma_\text{V syst}^2## be the systematic variance of returns on assets, and ##\sigma_\text{V idio}^2## be the idiosyncratic variance of returns on assets, and ##\rho_\text{D idio, E idio}## be the correlation between the idiosyncratic returns on debt and equity.

Which of the following equations is NOT correct?

(a) ##r_V = \dfrac{D}{V}.r_D + \dfrac{E}{V}.r_E##

(b) ##\beta_V = \dfrac{D}{V}.\beta_D + \dfrac{E}{V}.\beta_E##

(c) ##\sigma_\text{V syst}^2 = \left(\dfrac{D}{V}\right)^2.\sigma_\text{D syst}^2 + \left(\dfrac{E}{V}\right)^2.\sigma_\text{E syst}^2##

(d) ##\sigma_\text{V idio}^2 = \left(\dfrac{D}{V}\right)^2.\sigma_\text{D idio}^2 + \left(\dfrac{E}{V}\right)^2.\sigma_\text{E idio}^2 + 2.\dfrac{D}{V}.\dfrac{E}{V}.\rho_\text{D idio, E idio}.\sigma_\text{D idio}.\sigma_\text{E idio}##

(e) ##\sigma_\text{V total}^2 = \left(\dfrac{D}{V}\right)^2.\sigma_\text{D total}^2 + \left(\dfrac{E}{V}\right)^2.\sigma_\text{E total}^2##

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 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 706  utility, risk aversion, utility function

Mr Blue, Miss Red and Mrs Green are people with different utility functions.

Note that a fair gamble is a bet that has an expected value of zero, such as paying $0.50 to win $1 in a coin flip with heads or nothing if it lands tails. Fairly priced insurance is when the expected present value of the insurance premiums is equal to the expected loss from the disaster that the insurance protects against, such as the cost of rebuilding a home after a catastrophic fire.

Which of the following statements is NOT correct?

(a) Mr Blue, Miss Red and Mrs Green all prefer more wealth to less. This is rational from an economist's point of view.

(b) Mr Blue is risk averse. He will not enjoy a fair gamble and would like to buy fairly priced insurance.

(c) Miss Red is risk-neutral. She will not enjoy a fair gamble but wouldn't oppose it either. Similarly with fairly priced insurance.

(d) Mrs Green is risk-loving. She would enjoy a fair gamble and would dislike fairly priced insurance.

(e) Mr Blue would like to buy insurance, but only if it is fairly or under priced.

Question 703  utility, risk aversion, utility function, gamble

Mr Blue, Miss Red and Mrs Green are people with different utility functions.

Each person has $500 of initial wealth. A coin toss game is offered to each person at a casino where the player can win or lose $500. Each player can flip a coin and if they flip heads, they receive $500. If they flip tails then they will lose $500. Which of the following statements is NOT correct?

(a) All people prefer more rather than less wealth which is rational.

(b) Mr Blue is risk averse, Miss Red is risk neutral and Mrs Green is risk loving.

(c) Mr Blue's certainty equivalent of the gamble is $225. This is less than his current $500 which is why he would dislike the gamble.

(d) Miss Red's certainty equivalent of the gamble is $500. This is the same as her current $500 which is why she would be indifferent to gambling.

(e) Mrs Green's certainty equivalent of the gamble is $793.70. This is more than her current $500 which is why she would like the gamble.

Question 704  utility, risk aversion, utility function, gamble

Mr Blue, Miss Red and Mrs Green are people with different utility functions.

Each person has $256 of initial wealth. A coin toss game is offered to each person at a casino where the player can win or lose $256. Each player can flip a coin and if they flip heads, they receive $256. If they flip tails then they will lose $256. Which of the following statements is NOT correct?

(a) All people would appear rational to an economist since they prefer more wealth to less.

(b) Mrs Green and Miss Red would appear unusual to an economist since they are not risk averse.

(c) Mr Blue's certainty equivalent of the gamble is $64. This is less than his current wealth of $256 which is why he would refuse the gamble.

(d) Miss Red's certainty equivalent of the gamble is $256. This is the same as her current wealth of $256 which is why she would be indifferent to playing or not.

(e) Mrs Green's certainty equivalent of the gamble is $512. This is more than her current wealth of $256 which is why she would love to play.

Question 694  utility

Which of the below statements about utility is NOT generally accepted by economists? Most people are thought to:

(a) Prefer more to less, meaning that they will always like to have more wealth.

(b) Be risk averse, meaning that they dislike risk as measured by the standard deviation of wealth.

(c) Have a positively sloped utility function, so the gradient or first derivative of the utility function is always positive.

(d) Have a utility function that increases at a diminishing rate. So the shape is concave down like a frown, or the second derivative is always negative.

(e) Have a utility function that rises until it reaches the satiation point, then it falls because too much wealth causes problems.

Question 695  utility, risk aversion, utility function

Mr Blue, Miss Red and Mrs Green are people with different utility functions. Which of the statements about the 3 utility functions is NOT correct?

(a) All rational people prefer more wealth to less.

(b) Mr Blue is risk averse.

(c) Miss Red is risk neutral.

(d) Mrs Green is risk averse.

(e) Mrs Green may enjoy gambling.

Question 696  utility, risk aversion, utility function

Mr Blue, Miss Red and Mrs Green are people with different utility functions. Which of the statements about the 3 utility functions is NOT correct?

(a) Mr Blue prefers more wealth to less. Mrs Green enjoys losing wealth.

(b) Miss Red has the same utility no matter how much wealth she has.

(c) Mr Blue is risk averse.

(d) Miss Red is risk averse.

(e) Mrs Green is risk loving.

Question 697  utility, risk aversion, utility function

Mr Blue, Miss Red and Mrs Green are people with different utility functions. Which of the statements about the 3 utility functions is NOT correct?

(a) Mr Blue and Miss Red prefer more wealth to less.

(b) Mrs Green enjoys losing wealth.

(c) Mr Blue is risk averse.

(d) Miss Red is risk neutral.

(e) Mrs Green is risk averse.

Question 698  utility, risk aversion, utility function

Mr Blue, Miss Red and Mrs Green are people with different utility functions. Which of the statements about the 3 utility functions is NOT correct?

(a) Neither Miss Red nor Mrs Green would appear rational to an economist.

(b) Mrs Green is satiated when she has $25 of wealth. That is her bliss point.

(c) Mrs Green is risk loving when she has between zero and $25 of wealth, same as Mr Blue.

(d) Mrs Green is risk averse when she has between $25 and $50 of wealth.

(e) Mrs Green is risk loving when she has between $50 and $100 of wealth, same as Mr Blue.

Question 699  utility, risk aversion, utility function, gamble

Mr Blue, Miss Red and Mrs Green are people with different utility functions.

Each person has $50 of initial wealth. A coin toss game is offered to each person at a casino where the player can win or lose $50. Each player can flip a coin and if they flip heads, they receive $50. If they flip tails then they will lose $50. Which of the following statements is NOT correct?

(a) Mr Blue's expected utility of wealth from gambling is 5 while refusing is 7.07. So the gamble makes him less happy.

(b) Mrs Green's expected utility of wealth from gambling is 7.07 while refusing is 5. So the gamble makes her more happy.

(c) Mr Blue's certainty equivalent of the risky gamble is $25. This is less than his current wealth of $50 which is why he would refuse.

(d) Miss Red's certainty equivalent of the risky gamble is $50. This is equal to her current wealth of $50 which is why she is indifferent to gambling or not.

(e) Mrs Green's certainty equivalent of the risky gamble is $70.71. This is more than her current wealth of $50 which is why she would accept.

Question 700  utility, risk aversion, utility function, gamble

Mr Blue, Miss Red and Mrs Green are people with different utility functions.

Each person has $50 of initial wealth. A coin toss game is offered to each person at a casino where the player can win or lose $50. Each player can flip a coin and if they flip heads, they receive $50. If they flip tails then they will lose $50. Which of the following statements is NOT correct?

(a) Mr Blue's expected utility of wealth from gambling is 7.5 while refusing is 8.54. So the gamble makes him less happy.

(b) Miss Red's expected utility of wealth from gambling is 5 and refusing is also 5. So the gamble doesn't affect her happiness at all.

(c) Mr Blue's certainty equivalent of the risky gamble is $25. This is less than his current wealth which is why he would refuse.

(d) Miss Red's certainty equivalent of the risky gamble is any wealth. She's indifferent since she always has the same level of happiness.

(e) Mrs Green's certainty equivalent of the risky gamble is $25. This is less than her current wealth which is why she would refuse.

Question 701  utility, risk aversion, utility function, gamble

Mr Blue, Miss Red and Mrs Green are people with different utility functions.

Each person has $50 of initial wealth. A coin toss game is offered to each person at a casino where the player can win or lose $50. Each player can flip a coin and if they flip heads, they receive $50. If they flip tails then they will lose $50. Which of the following statements is NOT correct?

(a) Mr Blue's expected utility of wealth from gambling is 7.5 while refusing is 6.25. So the gamble makes him more happy.

(b) Miss Red's expected utility of wealth from gambling is 7.5 and refusing is also 7.5. This is why she is indifferent.

(c) Mr Blue's certainty equivalent of the risky gamble is $70.71. So he would pay to take part in the gamble.

(d) Miss Red's certainty equivalent of the risky gamble is $50.

(e) Mrs Green's certainty equivalent of the risky gamble is $70.71. She would enjoy taking part in the gamble.

Question 702  utility, risk aversion, utility function, gamble

Mr Blue, Miss Red and Mrs Green are people with different utility functions.

Each person has $50 of initial wealth. A coin toss game is offered to each person at a casino where the player can win or lose $50. Each player can flip a coin and if they flip heads, they receive $50. If they flip tails then they will lose $50. Which of the following statements is NOT correct?

(a) Mr Blue would enjoy the gamble.

(b) Miss Red would be indifferent to gambling or not.

(c) Mrs Green would dislike the gamble.

(d) Mr Blue's certainty equivalent of the risky gamble is $70.71. This is more than his current wealth which is why he would like to gamble.

(e) Miss Red's certainty equivalent of the risky gamble is $50. This is the same as her current wealth which is why she is indifferent to gambling or not.

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 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 110  CAPM, SML, NPV

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

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

(a) A positive NPV.

(b) A zero NPV.

(c) A negative NPV.

(d) A large amount of diversifiable risk.

(e) Zero diversifiable risk.

Question 71  CAPM, risk

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

(a) Stock A has less systematic risk than stock B, so stock A's return should be less than stock B's.

(b) Stock B has the same systematic risk as the market, so its return should be the same as the market's.

(c) Stock B has the same beta as the market, so it also has the same total risk as the market.

(d) If stock A and B were combined in a portfolio with weights of 50% each, the beta of the portfolio would be 0.75.

(e) Stocks A and B have more systematic risk than the risk free security (government bonds) so their return should be greater than the risk free rate.

Question 79  CAPM, risk

Which statement is the most correct?

(a) The risk free rate has zero systematic risk and zero idiosyncratic risk.

(b) The market portfolio has zero idiosyncratic risk.

(c) The market portfolio has zero systematic risk.

(d) a and b are true.

(e) a and c are true.

Question 93  correlation, CAPM, systematic risk

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

(a) The stock will have a higher return and higher systematic risk.

(b) The stock will have a lower return and higher systematic risk.

(c) The stock will have a higher return and lower systematic risk.

(d) The stock will have a lower return and lower systematic risk.

(e) The stock's return and systematic risk will be unchanged.

Question 627  CAPM, SML, NPV, Jensens alpha

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

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

(b) Asset A is under-priced.

(c) The NPV of buying asset A is zero.

(d) Asset B has a Jensen's alpha of zero.

(e) Asset B is fairly priced.

Question 628  CAPM, SML, risk

Assets A, B, M and ##r_f## are shown on the graphs above. Asset M is the market portfolio and ##r_f## is the risk free yield on government bonds. Assume that investors can borrow and lend at the risk free rate. Which of the below statements is NOT correct?

(a) Asset A has the same systematic risk as asset B.

(b) Asset A has more total variance than asset B.

(c) Asset B has zero idiosyncratic risk. Asset B must be a portfolio of half the market portfolio and half government bonds.

(d) If risk-averse investors were forced to invest all of their wealth in a single risky asset, so they could not diversify, every investor would logically choose asset A over the other three assets.

(e) Assets M and B have the highest Sharpe ratios, which is defined as the gradient of the capital allocation line (CAL) from the government bonds through the asset on the graph of expected return versus total standard deviation.

Question 672  CAPM, beta

A stock has a beta of 1.5. The market's expected total return is 10% pa and the risk free rate is 5% pa, both given as effective annual rates.

What do you think will be the stock's expected return over the next year, given as an effective annual rate?

(a) 5% pa

(b) 7.5% pa

(c) 10% pa

(d) 12.5% pa

(e) 20% pa

Question 673  CAPM, beta, expected and historical returns

A stock has a beta of 1.5. The market's expected total return is 10% pa and the risk free rate is 5% pa, both given as effective annual rates.

In the last 5 minutes, bad economic news was released showing a higher chance of recession. Over this time the share market fell by 1%. The risk free rate was unchanged.

What do you think was the stock's historical return over the last 5 minutes, given as an effective 5 minute rate?

(a) -12.5%

(b) -4%

(c) -1.5%

(d) -1%

(e) 12.5%

Question 674  CAPM, beta, expected and historical returns

A stock has a beta of 1.5. The market's expected total return is 10% pa and the risk free rate is 5% pa, both given as effective annual rates.

Over the last year, bad economic news was released showing a higher chance of recession. Over this time the share market fell by 1%. So ##r_{m} = (P_{0} - P_{-1})/P_{-1} = -0.01##, where the current time is zero and one year ago is time -1. The risk free rate was unchanged.

What do you think was the stock's historical return over the last year, given as an effective annual rate?

(a) -12.5% pa

(b) -4% pa

(c) -1.5% pa

(d) -1% pa

(e) 12.5% pa

Question 116  capital structure, CAPM

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

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

(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 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 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 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 617  systematic and idiosyncratic risk, risk, CAPM

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

(a) Systematic risk increases.

(b) Idiosyncratic risk increases.

(c) Total risk increases.

(d) Systematic risk decreases.

(e) Idiosyncratic risk decreases.

Question 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 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 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 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 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 117  WACC

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

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

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

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

(a) 9.47%

(b) 8.93%

(c) 8.53%

(d) 7.80%

(e) 7.07%

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 777  CAPM, beta

The market's expected total return is 10% pa and the risk free rate is 5% pa, both given as effective annual rates.

A stock has a beta of 0.5.

In the last 5 minutes, the federal government unexpectedly raised taxes. Over this time the share market fell by 3%. The risk free rate was unchanged.

What do you think was the stock's historical return over the last 5 minutes, given as an effective 5 minute rate?

(a) -1%

(b) -1.5%

(c) -2.5%

(d) -3%

(e) -7.5%

Question 669  beta, CAPM, risk

Which of the following is NOT a valid method for estimating the beta of a company's stock? Assume that markets are efficient, a long history of past data is available, the stock possesses idiosyncratic and market risk. The variances and standard deviations below denote total risks.

(a) ##Β_E=\dfrac{cov(r_E,r_M )}{var(r_M)}##

(b) ##Β_E=\dfrac{correl(r_E,r_M ).sd(r_E)}{sd(r_M)} ##

(c) ##Β_E=\dfrac{sd(r_E)}{sd(r_M)}##,   since ##var(r_E)=β_E^2.var(r_M)##

(d) ##Β_E=\dfrac{r_E-r_f}{r_M-r_f }##,   since ##r_E=r_f+Β_E. (r_M-r_f )##

(e) ##Β_E= \left(B_V - \dfrac{D}{V}.Β_D \right).\dfrac{V}{E}##,   since ##B_V=\dfrac{E}{V}.Β_E+\dfrac{D}{V}.Β_D ##

Question 657  systematic and idiosyncratic risk, CAPM, no explanation

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

(a) Systematic risk increases.

(b) Idiosyncratic risk increases.

(c) Total risk increases.

(d) Systematic risk decreases.

(e) Idiosyncratic risk decreases.

Question 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 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 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 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 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 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 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 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 569  personal tax

The average weekly earnings of an Australian adult worker before tax was $1,542.40 per week in November 2014 according to the Australian Bureau of Statistics. Therefore average annual earnings before tax were $80,204.80 assuming 52 weeks per year. Personal income tax rates published by the Australian Tax Office are reproduced for the 2014-2015 financial year in the table below:

Taxable income	Tax on this income
0 – $18,200	Nil
$18,201 – $37,000	19c for each $1 over $18,200
$37,001 – $80,000	$3,572 plus 32.5c for each $1 over $37,000
$80,001 – $180,000	$17,547 plus 37c for each $1 over $80,000
$180,001 and over	$54,547 plus 45c for each $1 over $180,000

The above rates do not include the Medicare levy of 2%. Exclude the Medicare levy from your calculations

How much personal income tax would you have to pay per year if you earned $80,204.80 per annum before-tax?

(a) $36,092.16

(b) $29,675.78

(c) $21,185.56

(d) $17,622.78

(e) $3,638.56

Question 449  personal tax on dividends, classical tax system

A small private company has a single shareholder. This year the firm earned a $100 profit before tax. All of the firm's after tax profits will be paid out as dividends to the owner.

The corporate tax rate is 30% and the sole shareholder's personal marginal tax rate is 45%.

The United States' classical tax system applies because the company generates all of its income in the US and pays corporate tax to the Internal Revenue Service. The shareholder is also an American for tax purposes.

What will be the personal tax payable by the shareholder and the corporate tax payable by the company?

(a) Personal tax of $6.43 and corporate tax of $45.

(b) Personal tax of $15 and corporate tax of $30.

(c) Personal tax of $16.5 and corporate tax of $45.

(d) Personal tax of $31.5 and corporate tax of $30.

(e) Personal tax of $45 and corporate tax of $0.

Question 448  franking credit, personal tax on dividends, imputation tax system

A small private company has a single shareholder. This year the firm earned a $100 profit before tax. All of the firm's after tax profits will be paid out as dividends to the owner.

The corporate tax rate is 30% and the sole shareholder's personal marginal tax rate is 45%.

The Australian imputation tax system applies because the company generates all of its income in Australia and pays corporate tax to the Australian Tax Office. Therefore all of the company's dividends are fully franked. The sole shareholder is an Australian for tax purposes and can therefore use the franking credits to offset his personal income tax liability.

What will be the personal tax payable by the shareholder and the corporate tax payable by the company?

(a) Personal tax of $6.43 and corporate tax of $45.

(b) Personal tax of $15 and corporate tax of $30.

(c) Personal tax of $16.5 and corporate tax of $45.

(d) Personal tax of $31.5 and corporate tax of $30.

(e) Personal tax of $45 and corporate tax of $0.

Question 494  franking credit, personal tax on dividends, imputation tax system

A firm pays a fully franked cash dividend of $100 to one of its Australian shareholders who has a personal marginal tax rate of 15%. The corporate tax rate is 30%.

What will be the shareholder's personal tax payable due to the dividend payment?

(a) -$21.4286

(b) -$7.563

(c) $15

(d) $21.4286

(e) $78.5714

Question 454  NPV, capital structure, capital budgeting

A mining firm has just discovered a new mine. So far the news has been kept a secret.

The net present value of digging the mine and selling the minerals is $250 million, but $500 million of new equity and $300 million of new bonds will need to be issued to fund the project and buy the necessary plant and equipment.

The firm will release the news of the discovery and equity and bond raising to shareholders simultaneously in the same announcement. The shares and bonds will be issued shortly after.

Once the announcement is made and the new shares and bonds are issued, what is the expected increase in the value of the firm's assets ##(\Delta V)##, market capitalisation of debt ##(\Delta D)## and market cap of equity ##(\Delta E)##? Assume that markets are semi-strong form efficient.

The triangle symbol ##\Delta## is the Greek letter capital delta which means change or increase in mathematics.

Ignore the benefit of interest tax shields from having more debt.

Remember: ##\Delta V = \Delta D+ \Delta E##

(a) ##\Delta V = 250m##, ##ΔD = 300m##, ##ΔE= 250##

(b) ##\Delta V = 250m##, ##ΔD = 300m##, ##ΔE= 750##

(c) ##\Delta V = 400m##, ##ΔD = 300m##, ##ΔE= -250##

(d) ##\Delta V = 1,050m##, ##ΔD = 300m##, ##ΔE= 750##

(e) ##\Delta V = 1,050m##, ##ΔD = 300m##, ##ΔE= 250##

Question 568  rights issue, capital raising, capital structure

A company conducts a 1 for 5 rights issue at a subscription price of $7 when the pre-announcement stock price was $10. What is the percentage change in the stock price and the number of shares outstanding? The answers are given in the same order. Ignore all taxes, transaction costs and signalling effects.

(a) -16.67%, 20%

(b) -5%, 20%

(c) 0%, 20%

(d) 7.14%, 20%

(e) 11.67%, 0%

Question 625  dividend re-investment plan, capital raising

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

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

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

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

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

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

Question 214  rights issue

In late 2003 the listed bank ANZ announced a 2-for-11 rights issue to fund the takeover of New Zealand bank NBNZ. Below is the chronology of events:

• 23/10/2003. Share price closes at $18.30.

• 24/10/2003. 2-for-11 rights issue announced at a subscription price of $13. The proceeds of the rights issue will be used to acquire New Zealand bank NBNZ. Trading halt announced in morning before market opens.

• 28/10/2003. Trading halt lifted. Last (and only) day that shares trade cum-rights. Share price opens at $18.00 and closes at $18.14.

• 29/10/2003. Shares trade ex-rights.

All things remaining equal, what would you expect ANZ's stock price to open at on the first day that it trades ex-rights (29/10/2003)? Ignore the time value of money since time is negligibly short. Also ignore taxes.

(a) 17.3492

(b) 17.2308

(c) 14.8418

(d) 13.7908

(e) 13.7692

Question 633  personal tax

In 2014 the median starting salaries of male and female Australian bachelor degree accounting graduates aged less than 25 years in their first full-time industry job was $50,000 before tax, according to Graduate Careers Australia. See page 9 of this report. Personal income tax rates published by the Australian Tax Office are reproduced for the 2014-2015 financial year in the table below.

Taxable income	Tax on this income
0 – $18,200	Nil
$18,201 – $37,000	19c for each $1 over $18,200
$37,001 – $80,000	$3,572 plus 32.5c for each $1 over $37,000
$80,001 – $180,000	$17,547 plus 37c for each $1 over $80,000
$180,001 and over	$54,547 plus 45c for each $1 over $180,000

The above rates do not include the Medicare levy of 2%. Exclude the Medicare levy from your calculations

How much personal income tax would you have to pay per year if you earned $50,000 per annum before-tax?

(a) $6,042

(b) $7,797

(c) $9,614

(d) $18,500

(e) $22,500

Question 70  payout policy

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

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

(b) Pay out a special dividend.

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

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

(e) Either b or c.

Question 409  NPV, capital structure, capital budgeting

A pharmaceutical firm has just discovered a valuable new drug. So far the news has been kept a secret.

The net present value of making and commercialising the drug is $200 million, but $600 million of bonds will need to be issued to fund the project and buy the necessary plant and equipment.

The firm will release the news of the discovery and bond raising to shareholders simultaneously in the same announcement. The bonds will be issued shortly after.

Once the announcement is made and the bonds are issued, what is the expected increase in the value of the firm's assets (ΔV), market capitalisation of debt (ΔD) and market cap of equity (ΔE)?

The triangle symbol is the Greek letter capital delta which means change or increase in mathematics.

Ignore the benefit of interest tax shields from having more debt.

Remember: ##ΔV = ΔD+ΔE##

(a) ##ΔV=800m, ΔD = 600m, ΔE=200m##

(b) ##ΔV=200m, ΔD = 600m, ΔE= 0##

(c) ##ΔV=200m, ΔD =0m, \quad ΔE=200m##

(d) ##ΔV=400m, ΔD = 600m, ΔE=-200m##

(e) ##ΔV=800m, ΔD = 800m, ΔE= 0##

Question 212  rights issue

In mid 2009 the listed mining company Rio Tinto announced a 21-for-40 renounceable rights issue. Below is the chronology of events:

• 04/06/2009. Share price opens at $69.00 and closes at $66.90.

• 05/06/2009. 21-for-40 rights issue announced at a subscription price of $28.29.

• 16/06/2009. Last day that shares trade cum-rights. Share price opens at $76.40 and closes at $75.50.

• 17/06/2009. Shares trade ex-rights. Rights trading commences.

All things remaining equal, what would you expect Rio Tinto's stock price to open at on the first day that it trades ex-rights (17/6/2009)? Ignore the time value of money since time is negligibly short. Also ignore taxes.

(a) $28.29

(b) $35.8625

(c) $44.5426

(d) $47.2100

(e) $59.2473

Question 455  income and capital returns, payout policy, DDM, market efficiency

A fairly priced unlevered firm plans to pay a dividend of $1 next year (t=1) which is expected to grow by 3% pa every year after that. The firm's required return on equity is 8% pa.

The firm is thinking about reducing its future dividend payments by 10% so that it can use the extra cash to invest in more projects which are expected to return 8% pa, and have the same risk as the existing projects. Therefore, next year's dividend will be $0.90. No new equity or debt will be issued to fund the new projects, they'll all be funded by the cut in dividends.

What will be the stock's new annual capital return (proportional increase in price per year) if the change in payout policy goes ahead?

Assume that payout policy is irrelevant to firm value (so there's no signalling effects) and that all rates are effective annual rates.

(a) 2.7% pa.

(b) 3.0% pa.

(c) 3.5% pa.

(d) 3.3% pa.

(e) 3.8% pa.

Question 120  credit risk, payout policy

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

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

(a) Preferred stock only.

(b) The senior and junior bonds only.

(c) Common stock only.

(d) The senior and junior bonds and the preferred stock.

(e) No payments on any security is required since the firm made a loss.

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

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

(a) Investment decision.

(b) Financing decision.

(c) Working capital decision.

(d) Payout policy decision.

(e) Capital or labour decision.

Question 447  payout policy, corporate financial decision theory

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

(a) Assets.

(b) Liabilities and owner's equity.

(c) Current assets and current liabilities.

(d) Dividends and buy backs.

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

Question 712  effective rate conversion

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

(a) 12.682503% pa

(b) 12.060201% pa

(c) 12% pa

(d) 11.940397% pa

(e) 3.464102% pa

Question 377  leverage, capital structure

Issuing debt doesn't give away control of the firm because debt holders can't cast votes to determine the company's affairs, such as at the annual general meeting (AGM), and can't appoint directors to the board. or ?

Question 94  leverage, capital structure, real estate

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

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

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

Remember:

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

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

(a) -100%

(b) -50%

(c) -12.5%

(d) -10%

(e) -8%

Question 406  leverage, WACC, margin loan, portfolio return

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

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

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

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

(a) 1.0757%

(b) 2.7067%

(c) 5.1333%

(d) 9.0000%

(e) 11.7067%

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

Question 506  leverage, accounting ratio

A firm has a debt-to-equity ratio of 25%. What is its debt-to-assets ratio?

(a) 20%

(b) 36%

(c) 60%

(d) 75%

(e) 93.75%

Question 68  WACC, CFFA, capital budgeting

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

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

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

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

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

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

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

Question 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 367  CFFA, interest tax shield

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

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

###(1) \quad FFCF=NI + Depr - CapEx -ΔNWC + IntExp### ###(2) \quad FFCF=NI + Depr - CapEx -ΔNWC + IntExp.(1-t_c)### ###(3) \quad FFCF=EBIT.(1-t_c )+ Depr- CapEx -ΔNWC+IntExp.t_c### ###(4) \quad FFCF=EBIT.(1-t_c) + Depr- CapEx -ΔNWC### ###(5) \quad FFCF=EBITDA.(1-t_c )+Depr.t_c- CapEx -ΔNWC+IntExp.t_c### ###(6) \quad FFCF=EBITDA.(1-t_c )+Depr.t_c- CapEx -ΔNWC### ###(7) \quad FFCF=EBIT-Tax + Depr - CapEx -ΔNWC### ###(8) \quad FFCF=EBIT-Tax + Depr - CapEx -ΔNWC-IntExp.t_c### ###(9) \quad FFCF=EBITDA-Tax - CapEx -ΔNWC### ###(10) \quad FFCF=EBITDA-Tax - CapEx -ΔNWC-IntExp.t_c###

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

###NI=(Rev - COGS - Depr - FC - IntExp).(1-t_c )### ###EBIT=Rev - COGS - FC-Depr### ###EBITDA=Rev - COGS - FC### ###Tax =(Rev - COGS - Depr - FC - IntExp).t_c= \dfrac{NI.t_c}{1-t_c}###

(a) 1, 3, 5, 7, 9.

(b) 2, 4, 6, 8, 10.

(c) 1, 4, 6, 8, 10.

(d) 2, 3, 5, 7, 9.

(e) 1, 3, 5, 8, 10.

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 375  interest tax shield, CFFA

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

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

Does this annual FFCF or the annual interest tax shield?

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 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 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 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 301  leverage, capital structure, real estate

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

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

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

Assume that:

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

(a) -1,000%

(b) -150%

(c) -100%

(d) -15%

(e) -10%

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 378  leverage, capital structure, no explanation

A levered company's required return on debt is always less than its required return on equity. or ?

Question 379  leverage, capital structure, payout policy

Companies must pay interest and principal payments to debt-holders. They're compulsory. But companies are not forced to pay dividends to share holders. or ?

Question 380  leverage, capital structure

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

Question 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 524  risk, expected and historical returns, bankruptcy or insolvency, capital structure, corporate financial decision theory, limited liability

Which of the following statements is NOT correct?

(a) Stocks are higher risk investments than debt.

(b) Stocks have higher expected returns than debt.

(c) Firms' past realised stock returns are always higher than their past realised debt returns.

(d) In the event of bankruptcy, stock holders are paid after debt holders are fully paid.

(e) Stock holders have a residual claim on the firm's assets.

Question 536  idiom, bond pricing, capital structure, leverage

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

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

(a) Because bonds are higher risk investments than shares.

(b) Because issuers must pay bond holders or face bankruptcy, while payments to shareholders are discretionary.

(c) Because bond holders are paid last in the event of bankruptcy, while shareholders are paid first.

(d) Because bonds always pay higher returns than shares.

(e) Because bonds are generally more liquid than shares.

Question 618  capital structure, no explanation

Who owns a company's shares? The:

(a) Company.

(b) Debt holders.

(c) Equity holders.

(d) Chief Executive Officer (CEO).

(e) Board of directors.

Question 772  interest tax shield, capital structure, leverage

A firm issues debt and uses the funds to buy back equity. Assume that there are no costs of financial distress or transactions costs. Which of the following statements about interest tax shields is NOT correct?

(a) Higher debt leads to higher interest expense.

(b) Higher interest expense leads to lower profit before tax, following on from above.

(c) Lower profit before tax leads to lower tax payments, following on from above.

(d) Lower tax payments lead to higher cash flow from assets, following on from above.

(e) Lower profit after tax leads to a lower share price, following on from above.

Question 735  debt terminology

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

(a) Are a lender.

(b) Issued debt.

(c) Bought debt.

(d) Are a debt holder.

(e) Own a debt asset.

Question 736  debt terminology

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

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

(b) The bank invested in your debt.

(c) You are indebted to the bank.

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

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

Question 737  financial statement, balance sheet, income statement

Where can a publicly listed firm's book value of equity be found? It can be sourced from the company's:

(a) Income statement

(b) Balance sheet

(c) Cash flow statement

(d) Stock exchange data

(e) It's not published, it can only be estimated using multiples or discounted cash flow methods.

Question 738  financial statement, balance sheet, income statement

Where can a private firm's market value of equity be found? It can be sourced from the company's:

(a) Income statement

(b) Balance sheet

(c) Cash flow statement

(d) Stock exchange data.

(e) It's not published, it can only be estimated using multiples or discounted cash flow methods.

Question 739  real and nominal returns and cash flows, inflation

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

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

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

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

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

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

Question 741  APR, effective rate

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

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

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

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

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

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

Question 767  idiom, corporate financial decision theory, no explanation

The sayings "Don't cry over spilt milk", "Don't regret the things that you can't change" and "What's done is done" are most closely related to which financial concept?

(a) Competition.

(b) Opportunity costs.

(c) Separation of the investment and financing decisions.

(d) Diversification.

(e) Sunk costs.

Question 768  accounting terminology, book and market values, no explanation

Accountants and finance professionals have lots of names for the same things which can be quite confusing.

Which of the following groups of items are NOT synonyms?

(a) Revenue, sales, turn over.

(b) Paid up capital, contributed equity.

(c) Shares, stock, equity.

(d) Net income, earnings, net profit after tax, the bottom line.

(e) Market capitalisation of equity, book value of equity.

Question 769  short selling, idiom, no explanation

"Buy low, sell high" is a well-known saying. It suggests that investors should buy low then sell high, in that order.

How would you re-phrase that saying to describe short selling?

(a) Buy high, then sell low.

(b) Buy low, then sell high.

(c) Sell high, then buy low.

(d) Sell low, then buy high.

(e) Sell high, then buy high.

Question 770  expected and historical returns, income and capital returns, coupon rate, bond pricing

Which of the following statements is NOT correct? Assume that all events are a surprise and that all other things remain equal. So for example, don't assume that just because a company's dividends and profit rise that its required return will also rise, assume the required return stays the same.

(a) If a company's dividend (and profit and free cash flow to equity) rises, its share price will rise.

(b) If a fixed coupon bond's yield to maturity rises, its price will rise.

(c) If a residential property's rent revenue rises, its price will rise.

(d) If a patent's royalty revenue rises, its price will also rise.

(e) If a software asset's licensing revenue rises, its price will also rise.

Question 771  debt terminology, interest expense, interest tax shield, credit risk, no explanation

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

(a) You have a debt asset.

(b) The bank sold you its promise to pay back interest and principal payments.

(c) The bank is exposed to your credit risk, it’s afraid that you’ll default on your debt.

(d) The interest income you’re paid is taxable income for you.

(e) The interest expense that the bank pays is tax-deductible for the bank.

Question 773  CFFA, WACC, interest tax shield, DDM

Use the below information to value a levered company with constant annual perpetual cash flows from assets. The next cash flow will be generated in one year from now, so a perpetuity can be used to value this firm. Both the operating and firm free cash flows are constant (but not equal to each other).

Data on a Levered Firm with Perpetual Cash Flows
Item abbreviation	Value	Item full name
##\text{OFCF}##	$48.5m	Operating free cash flow
##\text{FFCF or CFFA}##	$50m	Firm free cash flow or cash flow from assets
##g##	0% pa	Growth rate of OFCF and FFCF
##\text{WACC}_\text{BeforeTax}##	10% pa	Weighted average cost of capital before tax
##\text{WACC}_\text{AfterTax}##	9.7% pa	Weighted average cost of capital after tax
##r_\text{D}##	5% pa	Cost of debt
##r_\text{EL}##	11.25% pa	Cost of levered equity
##D/V_L##	20% pa	Debt to assets ratio, where the asset value includes tax shields
##t_c##	30%	Corporate tax rate

 

What is the value of the levered firm including interest tax shields?

(a) $515.464m

(b) $500m

(c) $485m

(d) $444.444m

(e) $431.111m

Question 774  leverage, WACC, real estate

One year ago you bought a $1,000,000 house partly funded using a mortgage loan. The loan size was $800,000 and the other $200,000 was your wealth or 'equity' in the house asset.

The interest rate on the home loan was 4% pa.

Over the year, the house produced a net rental yield of 2% pa and a capital gain of 2.5% pa.

Assuming that all cash flows (interest payments and net rental payments) were paid and received at the end of the year, and all rates are given as effective annual rates, what was the total return on your wealth over the past year?

(a) 0.4808% pa

(b) 2% pa

(c) 4.5% pa

(d) 6.5% pa

(e) 8.5% pa

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

Question 776  market efficiency, systematic and idiosyncratic risk, beta, income and capital returns

Which of the following statements about returns is NOT correct? A stock's:

(a) Expected total return will equal its required total return if the stock is fairly priced.

(b) Expected total return will be less than its required total return if the stock is over-priced.

(c) Required total return should be higher than the risk free government bond yield if the stock has a positive beta.

(d) Required total return depends on its total variance, required capital return depends on systematic variance and the dividend yield depends on idiosyncratic variance.

(e) Expected capital return equals the expected total return less whatever the management decide that they will pay as an income return (which is the dividend yield).

Question 775  utility, utility function

Below is a graph of 3 peoples’ utility functions, Mr Blue (U=W^(1/2) ), Miss Red (U=W/10) and Mrs Green (U=W^2/1000). Assume that each of them currently have $50 of wealth.

Which of the following statements about them is NOT correct?

(a) Mr Blue would prefer to invest his wealth in a well diversified portfolio of stocks rather than a single stock, assuming that all stocks had the same total risk and return.

(b) Mrs Green would prefer to invest her wealth in a single stock rather than a well diversified portfolio of stocks, assuming that all stocks had the same total risk and return.

(c) The popularity of insurance only makes sense if people are similar to Mr Blue.

(d) CAPM theory only makes sense if people are similar to Miss Red.

(e) The popularity of casino gambling and lottery tickets only make sense if people are similar to Mrs Green.

Question 780  mispriced asset, NPV, DDM, market efficiency, no explanation

A company advertises an investment costing $1,000 which they say is under priced. They say that it has an expected total return of 15% pa, but a required return of only 10% pa. Of the 15% pa total expected return, the dividend yield is expected to be 4% pa and the capital yield 11% pa. Assume that the company's statements are correct.

What is the NPV of buying the investment if the 15% total return lasts for the next 100 years (t=0 to 100), then reverts to 10% after that time? Also, what is the NPV of the investment if the 15% return lasts forever?

In both cases, assume that the required return of 10% remains constant, the dividends can only be re-invested at 10% pa and all returns are given as effective annual rates. The answer choices below are given in the same order (15% for 100 years, and 15% forever):

(a) $7,359.46, Infinite

(b) $4,887.57, $10,000

(c) $1,786.35, -$5,000 (Note the negative sign)

(d) $1,471.89, $830.28

(e) $830.28, $3,000

Question 656  debt terminology

Which of the following statements is NOT correct? Lenders:

(a) Buy debt.

(b) Own debt.

(c) Are owed money.

(d) Write debt.

(e) Have debt assets.

Question 658  CFFA, income statement, balance sheet, no explanation

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

(a) Net income, depreciation and interest expense.

(b) Depreciation and capital expenditure.

(c) Current assets and current liabilities.

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

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

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

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

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

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

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

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

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

Question 660  fully amortising loan, interest only loan, APR

How much more can you borrow using an interest-only loan compared to a 25-year fully amortising loan if interest rates are 6% pa compounding per month and are not expected to change? If it makes it easier, assume that you can afford to pay $2,000 per month on either loan. Express your answer as a proportional increase using the following formula:

###\text{Proportional Increase} = \dfrac{V_\text{0,interest only}}{V_\text{0,fully amortising}} - 1###

(a) 77.6034%

(b) 30.3779%

(c) 28.8603%

(d) 22.3966%

(e) 7.5304%

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

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

(a) Annualised percentage rate compounding per month.

(b) Effective monthly rate compounding per year.

(c) Annualised percentage rate compounding per year.

(d) Effective annual rate compounding per year.

(e) Annualised percentage rate compounding semi-annually.

Question 664  real and nominal returns and cash flows, inflation, no explanation

What is the present value of real payments of $100 every year forever, with the first payment in one year? The nominal discount rate is 7% pa and the inflation rate is 4% pa.

(a) $3,466.6667

(b) $3,333.3333

(c) $3,205.1282

(d) $1,485.7143

(e) $1,428.5714

Question 616  idiom, debt terminology, bond pricing

"Buy low, sell high" is a phrase commonly heard in financial markets. It states that traders should try to buy assets at low prices and sell at high prices.

Traders in the fixed-coupon bond markets often quote promised bond yields rather than prices. Fixed-coupon bond traders should try to:

(a) Buy at low yields, sell at high yields.

(b) Buy at high yields, sell at low yields.

(c) Buy at high yields, sell at high yields.

(d) Buy at low yields, sell at low yields.

(e) There is no preferable yield to buy or sell fixed-coupon debt.

Question 619  CFFA

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

(a) Net income, depreciation and interest expense.

(b) Depreciation and capital expenditure.

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

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

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

Question 629  yield curve, forward interest rate

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

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

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

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

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

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

Question 630  mispriced asset, NPV, DDM, market efficiency

A company advertises an investment costing $1,000 which they say is underpriced. They say that it has an expected total return of 15% pa, but a required return of only 10% pa. Of the 15% pa total expected return, the dividend yield is expected to always be 7% pa and rest is the capital yield.

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

In both cases, assume that the required return of 10% remains constant, the dividends can only be re-invested at 10% pa and all returns are given as effective annual rates.

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

(a) 84,214.90,   Infinite

(b)  2,521.12,   3,000

(c)  2,100.93,   2,500

(d)  1,249.38,   1,333.33

(e)          0,               0