Fight Finance

Question 45  profitability index

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

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

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

(a) 1.21

(b) 1.1

(c) 1

(d) 0.82845

(e) 0

Question 174  profitability index

A project has the following cash flows:

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

What is the Profitability Index (PI) of the project? Assume that the cash flows shown in the table are paid all at once at the given point in time. The required return is 10% pa, given as an effective annual rate.

(a) 0.9711

(b) 1.1750

(c) 1.3063

(d) 1.5537

(e) 1.8800

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

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

(a) The project should be rejected.

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

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

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

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

Question 219  profitability index

A project has the following cash flows:

Project Cash Flows
Time (yrs)	Cash flow ($)
0	-90
1	30
2	105

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

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

(a) 1.0862

(b) 1.2672

(c) 1.3143

(d) 1.5333

(e) 1.7783

Question 44  NPV

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

What is the Net Present Value (NPV) of the project?

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

(a) -100

(b) 0

(c) 10

(d) 21

(e) 121

Question 126  IRR

What is the Internal Rate of Return (IRR) of the project detailed in the table below?

Assume that the cash flows shown in the table are paid all at once at the given point in time. All answers are given as effective annual rates.

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

(a) 0.21

(b) 0.105

(c) 0.1111

(d) 0.1

(e) 0

Question 37  IRR

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

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

(b) Zero (0).

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

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

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

Question 60  pay back period

The required return of a project is 10%, given as an effective annual rate.

What is the payback period of the project in years?

Assume that the cash flows shown in the table are received smoothly over the year. So the $121 at time 2 is actually earned smoothly from t=1 to t=2.

Project Cash Flows
Time (yrs)	Cash flow ($)
0	-100
1	11
2	121

(a) 2.7355

(b) 2.3596

(c) 1.7355

(d) 1.2645

(e) 0.2645

Question 190  pay back period

A project has the following cash flows:

Project Cash Flows
Time (yrs)	Cash flow ($)
0	-400
1	0
2	500

What is the payback period of the project in years?

Normally cash flows are assumed to happen at the given time. But here, assume that the cash flows are received smoothly over the year. So the $500 at time 2 is actually earned smoothly from t=1 to t=2.

(a) -0.80

(b) 0.80

(c) 1.20

(d) 1.80

(e) 2.20

Question 500  NPV, IRR

The below graph shows a project's net present value (NPV) against its annual discount rate.

For what discount rate or range of discount rates would you accept and commence the project?

All answer choices are given as approximations from reading off the graph.

(a) From 0 to 10% pa.

(b) From 0 to 5% pa.

(c) At 5.5% pa.

(d) From 6 to 20% pa.

(e) From 0 to 20% pa.

Question 501  NPV, IRR, pay back period

The below graph shows a project's net present value (NPV) against its annual discount rate.

Which of the following statements is NOT correct?

(a) When the project's discount rate is 18% pa, the NPV is approximately -$30m.

(b) The payback period is infinite, the project never pays itself off.

(c) The addition of the project's cash flows, ignoring the time value of money, is approximately $20m.

(d) The project's IRR is approximately 5.5% pa.

(e) As the discount rate rises, the NPV falls.

Question 251  NPV

You have $100,000 in the bank. The bank pays interest at 10% pa, given as an effective annual rate.

You wish to consume an equal amount now (t=0) and in one year (t=1) and have nothing left in the bank at the end (t=1).

How much can you consume at each time?

(a) $57,619.0476

(b) $55,000

(c) $53,809.5238

(d) $52,380.9524

(e) $50,000

Question 502  NPV, IRR, mutually exclusive projects

An investor owns an empty block of land that has local government approval to be developed into a petrol station, car wash or car park. The council will only allow a single development so the projects are mutually exclusive.

All of the development projects have the same risk and the required return of each is 10% pa. Each project has an immediate cost and once construction is finished in one year the land and development will be sold. The table below shows the estimated costs payable now, expected sale prices in one year and the internal rates of returns (IRR's).

Mutually Exclusive Projects
Project	Cost now ($)	Sale price in one year ($)	IRR (% pa)
Petrol station	9,000,000	11,000,000	22.22
Car wash	800,000	1,100,000	37.50
Car park	70,000	110,000	57.14

Which project should the investor accept?

(a) Petrol station.

(b) Car wash.

(c) Car park.

(d) None of the projects.

(e) All of the projects.

Question 532  mutually exclusive projects, NPV, IRR

An investor owns a whole level of an old office building which is currently worth $1 million. There are three mutually exclusive projects that can be started by the investor. The office building level can be:

• Rented out to a tenant for one year at $0.1m paid immediately, and then sold for $0.99m in one year.
• Refurbished into more modern commercial office rooms at a cost of $1m now, and then sold for $2.4m when the refurbishment is finished in one year.
• Converted into residential apartments at a cost of $2m now, and then sold for $3.4m when the conversion is finished in one year.

All of the development projects have the same risk so the required return of each is 10% pa. The table below shows the estimated cash flows and internal rates of returns (IRR's).

Mutually Exclusive Projects
Project	Cash flow now ($)	Cash flow in one year ($)	IRR (% pa)
Rent then sell as is	-900,000	990,000	10
Refurbishment into modern offices	-2,000,000	2,400,000	20
Conversion into residential apartments	-3,000,000	3,400,000	13.33

Which project should the investor accept?

(a) Rent then sell as is.

(b) Refurbishment into modern offices.

(c) Conversion into residential apartments.

(d) All of the above.

(e) Any of the above.

Question 579  price gains and returns over time, time calculation, effective rate

How many years will it take for an asset's price to double if the price grows by 10% pa?

(a) 1.8182 years

(b) 3.3219 years

(c) 7.2725 years

(d) 11.5267 years

(e) 13.7504 years

Question 580  price gains and returns over time, time calculation, effective rate

How many years will it take for an asset's price to quadruple (be four times as big, say from $1 to $4) if the price grows by 15% pa?

(a) 1.3685 years

(b) 3.4783 years

(c) 4.4808 years

(d) 9.919 years

(e) 11.5156 years

Question 476  income and capital returns, idiom

The saying "buy low, sell high" suggests that investors should make a:

(a) Positive income return.

(b) Positive capital return.

(c) Negative income return.

(d) Negative capital return.

(e) Positive total return.

Question 478  income and capital returns

Total cash flows can be broken into income and capital cash flows. What is the name given to the income cash flow from owning shares?

(a) Dividends.

(b) Rent.

(c) Coupons.

(d) Loan payments.

(e) Capital gains.

Question 477  income and capital returns

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

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

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

Which of the following is the expected capital return?

(a) ##c_1##

(b) ##p_1-p_0##

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

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

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

Question 151  income and capital returns

A share was bought for $30 (at t=0) and paid its annual dividend of $6 one year later (at t=1).

Just after the dividend was paid, the share price fell to $27 (at t=1). What were the total, capital and income returns given as effective annual rates?

The choices are given in the same order:

##r_\text{total}## , ##r_\text{capital}## , ##r_\text{dividend}##.

(a) -0.1, -0.3, 0.2.

(b) -0.1, 0.1, -0.2.

(c) 0.1, -0.1, 0.2.

(d) 0.1, 0.2, -0.1.

(e) 0.2, 0.1, -0.1.

Question 278  inflation, real and nominal returns and cash flows

Imagine that the interest rate on your savings account was 1% per year and inflation was 2% per year.

After one year, would you be able to buy , exactly the as or than today with the money in this account?

Question 542  price gains and returns over time, IRR, NPV, income and capital returns, effective return

For an asset price to double every 10 years, what must be the expected future capital return, given as an effective annual rate?

(a) 0.2

(b) 0.116123

(c) 0.082037

(d) 0.071773

(e) 0.06054

Question 993  inflation, real and nominal returns and cash flows

In February 2020, the RBA cash rate was 0.75% pa and the Australian CPI inflation rate was 1.8% pa.

You currently have $100 in the bank which pays a 0.75% pa interest rate.

Apples currently cost $1 each at the shop and inflation is 1.8% pa which is the expected growth rate in the apple price.

This information is summarised in the table below, with some parts missing that correspond to the answer options. All rates are given as effective annual rates. Note that when payments are not specified as real, as in this question, they're conventionally assumed to be nominal.

Wealth in Dollars and Apples
Time (year)	Bank account wealth ($)	Apple price ($)	Wealth in apples
0	100	1	100
1	100.75	1.018	(a)
2	(b)	(c)	(d)

 

Which of the following statements is NOT correct? Your:

(a) Real wealth at t=1 is $98.96856582 or 98.96856582 apples.

(b) Nominal wealth at t=2 is $101.505625.

(c) Apple price t=2 is $1.036324.

(d) Real wealth at t=2 is $102.0952287 or 102.0952287 apples.

(e) Real interest rate is exactly -1.0314342% pa.

Question 508  income and capital returns

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

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

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

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

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

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

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

Question 527  income and capital returns

Total cash flows can be broken into income and capital cash flows.

What is the name given to the cash flow generated from selling shares at a higher price than they were bought?

(a) Dividends.

(b) Rent.

(c) Coupons.

(d) Loan payments.

(e) Capital gains.

Question 543  price gains and returns over time, IRR, NPV, income and capital returns, effective return

For an asset price to triple every 5 years, what must be the expected future capital return, given as an effective annual rate?

(a) 0.6

(b) 0.319508

(c) 0.269705

(d) 0.245731

(e) 0.219755

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 452  limited liability, expected and historical returns

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

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

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

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

(a) ##0≤p<∞## and ##0≤r< 1##

(b) ##0≤p<∞## and ##-1≤r< ∞##

(c) ##0≤p<∞## and ##0≤r< ∞##

(d) ##0≤p<∞## and ##-∞≤r< ∞##

(e) ##-∞<p<∞## and ##-∞<r< ∞##

Question 482  market capitalisation of equity

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

What was MSFT's market capitalisation of equity?

(a) $395.11 million

(b) $21.01 billion

(c) $121.92 billion

(d) $393.95 billion

(e) $1.02935 trillion

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 992  inflation, real and nominal returns and cash flows

You currently have $100 in the bank which pays a 10% pa interest rate.

Oranges currently cost $1 each at the shop and inflation is 5% pa which is the expected growth rate in the orange price.

This information is summarised in the table below, with some parts missing that correspond to the answer options. All rates are given as effective annual rates. Note that when payments are not specified as real, as in this question, they're conventionally assumed to be nominal.

Wealth in Dollars and Oranges
Time (year)	Bank account wealth ($)	Orange price ($)	Wealth in oranges
0	100	1	100
1	110	1.05	(a)
2	(b)	(c)	(d)

 

Which of the following statements is NOT correct? Your:

(a) Real wealth at t=1 is $104.7619048 or 104.7619048 oranges.

(b) Nominal wealth at t=2 is $121.

(c) Orange price t=2 is $1.1025.

(d) Real wealth at t=2 is $109.7505669 or 109.7505669 oranges.

(e) Real interest rate is exactly 5% pa.

Question 578  inflation, real and nominal returns and cash flows

Which of the following statements about inflation is NOT correct?

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

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

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

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

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

Question 522  income and capital returns, real and nominal returns and cash flows, inflation, real estate

A residential investment property has an expected nominal total return of 6% pa and nominal capital return of 2.5% pa. Inflation is expected to be 2.5% pa.

All of the above are effective nominal rates and investors believe that they will stay the same in perpetuity.

What are the property's expected real total, capital and income returns?

The answer choices below are given in the same order.

(a) 3.4146%,   3.4146%,   0%.

(b) 3.4146%,   0.4878%,   0.4878%.

(c) 3.4146%,   0%,   3.4146%.

(d) 0.9878%,   0.5%,   0.4878%.

(e) 0.9756%,   0.4878%,   0.4878%.

Question 523  income and capital returns, real and nominal returns and cash flows, inflation

A low-growth mature stock has an expected nominal total return of 6% pa and nominal capital return of 2% pa. Inflation is expected to be 3% pa.

All of the above are effective nominal rates and investors believe that they will stay the same in perpetuity.

What are the stock's expected real total, capital and income returns?

The answer choices below are given in the same order.

(a) 2.9126%, 3.8835%, -0.9709%.

(b) 2.9126%, -0.9709%, 3.8835%.

(c) 2.9126%, -0.9709%, 0.9709%.

(d) -0.0291%, -1%, 0.9709%.

(e) 0%, -0.9709%, 0.9709%.

Question 727  inflation, real and nominal returns and cash flows

The Australian Federal Government lends money to domestic students to pay for their university education. This is known as the Higher Education Contribution Scheme (HECS). The nominal interest rate on the HECS loan is set equal to the consumer price index (CPI) inflation rate. The interest is capitalised every year, which means that the interest is added to the principal. The interest and principal does not need to be repaid by students until they finish study and begin working.

Which of the following statements about HECS loans is NOT correct?

(a) The real interest rate is zero.

(b) The nominal amount owing on the loan will increase at the inflation rate over time, if there are no extra payments or borrowings.

(c) The real amount owing on the loan in today's money will remain the same over time, if there are no extra payments or borrowings.

(d) The interest rate on the HECS loan advantages rich domestic students because they are able to pay off their debt sooner and avoid paying as much HECS interest.

(e) The interest rate on the HECS loan advantages all domestic students because the alternative of borrowing from the bank to pay for education would usually attract a higher interest rate.

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

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

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

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

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

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

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

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

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

Question 295  inflation, real and nominal returns and cash flows, NPV

When valuing assets using discounted cash flow (net present value) methods, it is important to consider inflation. To properly deal with inflation:

(I) Discount nominal cash flows by nominal discount rates.

(II) Discount nominal cash flows by real discount rates.

(III) Discount real cash flows by nominal discount rates.

(IV) Discount real cash flows by real discount rates.

Which of the above statements is or are correct?

(a) I only.

(b) III only.

(c) IV only.

(d) I and IV only.

(e) II and III only.

Question 554  inflation, real and nominal returns and cash flows

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

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

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

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

(a) $21,600,     $95,035.46

(b) $21,600,     $49,515.44

(c) $21,600,     $4,909.33

(d) $21,600,     $2,557.86

(e) $11,254.05,     $2,557.86

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

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

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

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

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

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

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

Question 732  real and nominal returns and cash flows, inflation, income and capital returns

An investor bought a bond for $100 (at t=0) and one year later it paid its annual coupon of $1 (at t=1). Just after the coupon was paid, the bond price was $100.50 (at t=1). Inflation over the past year (from t=0 to t=1) was 3% pa, given as an effective annual rate.

Which of the following statements is NOT correct? The bond investment produced a:

(a) Nominal income return of 1% pa ##\left( =\dfrac{1}{100} \right)##.

(b) Nominal capital return of 0.5% pa ##\left( =\dfrac{100.5-100}{100} \right)##.

(c) Nominal total return of 1.5% pa ##\left( =\dfrac{100.5-100+1}{100} \right)##.

(d) Real income return of 0.9708738% pa##\left( =\dfrac{ 1/(1+0.03)^1}{100} \right)##.

(e) Real capital return of 0.4854369% pa ##\left( =\dfrac{ (100.5-100)/(1+0.03)^1}{100} \right) ##.

Question 221  credit risk

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

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

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

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

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

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

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

Question 466  limited liability, business structure

Which business structure or structures have the advantage of limited liability for equity investors?

(a) Sole traders.

(b) Partnerships.

(c) Corporations.

(d) All of the above.

(e) None of the above

Question 531  bankruptcy or insolvency, capital structure, risk, limited liability

Who is most in danger of being personally bankrupt? Assume that all of their businesses' assets are highly liquid and can therefore be sold immediately.

(a) Alice has $6,000 cash, owes $10,000 credit card debt due immediately and 100% owns a sole tradership business with assets worth $10,000 and liabilities of $3,000.

(b) Billy has $10,000 cash, owes $6,000 credit card debt due immediately and 100% owns a corporate business with assets worth $3,000 and liabilities of $10,000.

(c) Carla has $6,000 cash, owes $10,000 credit card debt due immediately and 100% owns a corporate business with assets worth $10,000 and liabilities of $3,000.

(d) Darren has $10,000 cash, owes $6,000 credit card debt due immediately and 100% owns a sole tradership business with assets worth $3,000 and liabilities of $10,000.

(e) Ernie has $1,000 cash, lent $3,000 to his friend, and doesn't have any personal debt or own any businesses.

Question 473  market capitalisation of equity

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

What was CBA's market capitalisation of equity?

(a) $431.18 billion

(b) $429 billion

(c) $134.07 billion

(d) $8.44 billion

(e) $3.21 billion

Question 445  financing decision, corporate financial decision theory

The financing decision primarily affects which part of a business?

(a) Assets.

(b) Liabilities and owner's equity.

(c) Current assets and current liabilities.

(d) Dividends and buy backs.

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

Question 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 2  NPV, Annuity

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

Will you or politely Katya's deal?

Question 356  NPV, Annuity

Your friend overheard that you need some cash and asks if you would like to borrow some money. She can lend you $5,000 now (t=0), and in return she wants you to pay her back $1,000 in two years (t=2) and every year after that for the next 5 years, so there will be 6 payments of $1,000 from t=2 to t=7 inclusive.

What is the net present value (NPV) of borrowing from your friend?

Assume that banks loan funds at interest rates of 10% pa, given as an effective annual rate.

(a) -$1,000

(b) $209.2132

(c) $644.7393

(d) $1,040.6721

(e) $1,400.611

Question 499  NPV, Annuity

Some countries' interest rates are so low that they're zero.

If interest rates are 0% pa and are expected to stay at that level for the foreseeable future, what is the most that you would be prepared to pay a bank now if it offered to pay you $10 at the end of every year for the next 5 years?

In other words, what is the present value of five $10 payments at time 1, 2, 3, 4 and 5 if interest rates are 0% pa?

(a) $0

(b) $10

(c) $50

(d) Positive infinity

(e) Priceless

Question 479  perpetuity with growth, DDM, NPV

Discounted cash flow (DCF) valuation prices assets by finding the present value of the asset's future cash flows. The single cash flow, annuity, and perpetuity equations are very useful for this.

Which of the following equations is the 'perpetuity with growth' equation?

(a) ##V_0=\dfrac{C_t}{(1+r)^t} ##

(b) ##V_0=\dfrac{C_1}{r}.\left(1-\dfrac{1}{(1+r)^T} \right)= \sum\limits_{t=1}^T \left( \dfrac{C_t}{(1+r)^t} \right) ##

(c) ##V_0=\dfrac{C_1}{r-g}.\left(1-\left(\dfrac{1+g}{1+r}\right)^T \right)= \sum\limits_{t=1}^T \left( \dfrac{C_t.(1+g)^t}{(1+r)^t} \right) ##

(d) ##V_0=\dfrac{C_1}{r} = \sum\limits_{t=1}^\infty \left( \dfrac{C_t}{(1+r)^t} \right) ##

(e) ##V_0=\dfrac{C_1}{r-g} = \sum\limits_{t=1}^\infty \left( \dfrac{C_t.(1+g)^t}{(1+r)^t} \right) ##

Question 517  DDM

A stock is expected to pay its next dividend of $1 in one year. Future annual dividends are expected to grow by 2% pa. So the first dividend of $1 will be in one year, the year after that $1.02 (=1*(1+0.02)^1), and a year later $1.0404 (=1*(1+0.02)^2) and so on forever.

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

Calculate the current stock price.

(a) $10

(b) $12.254902

(c) $12.5

(d) $12.75

(e) $13.75

Question 518  DDM

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

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

Calculate the current stock price.

(a) $10

(b) $12.254902

(c) $12.5

(d) $12.75

(e) $13.75

Question 4  DDM

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

Would you like to Carla's share or politely ?

Question 7  DDM

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

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

The required return of the stock is 15% pa.

Would you like to the share or politely ?

Question 528  DDM, income and capital returns

The perpetuity with growth formula, also known as the dividend discount model (DDM) or Gordon growth model, is appropriate for valuing a company's shares. ##P_0## is the current share price, ##C_1## is next year's expected dividend, ##r## is the total required return and ##g## is the expected growth rate of the dividend.

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

The below graph shows the expected future price path of the company's shares. Which of the following statements about the graph is NOT correct?

(a) Between points A and B, the share price is expected to grow by ##r##.

(b) Between points B and C, the share price is expected to instantaneously fall by ##C_1##.

(c) Between points A and C, the share price is expected to grow by ##g##.

(d) Between points B and D, the share price is expected to grow by ##g##.

(e) Between points D and E, the share price is expected to instantaneously fall by ##C_1.(1+r)^1##.

Question 264  DDM

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

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

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

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

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

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

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

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

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

Question 28  DDM, income and capital returns

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

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

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

(a) The expected total return of the stock.

(b) The expected income return of the stock.

(c) The expected capital return of the stock.

(d) The expected growth rate of the dividend.

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

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

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

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

(a) $200 today and $210 tomorrow.

(b) $210 today and $220 tomorrow.

(c) $220 today and $230 tomorrow.

(d) $210 today and $200 tomorrow.

(e) $220 today and $210 tomorrow.

Question 289  DDM, expected and historical returns, ROE

In the dividend discount model:

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

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

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

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

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

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

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

Question 36  DDM, perpetuity with growth

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

(a) $127.5

(b) $125

(c) $102

(d) $101.98

(e) $100

Question 40  DDM, perpetuity with growth

A stock is expected to pay the following dividends:

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

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

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

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

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

(a) $27.7567

(b) $24.1226

(c) $23.5680

(d) $22.4457

(e) $3.6341

Question 535  DDM, real and nominal returns and cash flows, stock pricing

You are an equities analyst trying to value the equity of the Australian telecoms company Telstra, with ticker TLS. In Australia, listed companies like Telstra tend to pay dividends every 6 months. The payment around August is called the final dividend and the payment around February is called the interim dividend. Both occur annually.

• Today is mid-March 2015.
• TLS's last interim dividend of $0.15 was one month ago in mid-February 2015.
• TLS's last final dividend of $0.15 was seven months ago in mid-August 2014.

Judging by TLS's dividend history and prospects, you estimate that the nominal dividend growth rate will be 1% pa. Assume that TLS's total nominal cost of equity is 6% pa. The dividends are nominal cash flows and the inflation rate is 2.5% pa. All rates are quoted as nominal effective annual rates. Assume that each month is exactly one twelfth (1/12) of a year, so you can ignore the number of days in each month.

Calculate the current TLS share price.

(a) $6.06

(b) $6.080152

(c) $6.149576

(d) $6.179509

(e) $6.300707

Question 217  NPV, DDM, multi stage growth model

A stock is expected to pay a dividend of $15 in one year (t=1), then $25 for 9 years after that (payments at t=2 ,3,...10), and on the 11th year (t=11) the dividend will be 2% less than at t=10, and will continue to shrink at the same rate every year after that forever. The required return of the stock is 10%. All rates are effective annual rates.

What is the price of the stock now?

(a) $361.78

(b) $236.33

(c) $237.93

(d) $348.69

(e) $223.24

Question 348  PE ratio, Multiples valuation

Estimate the US bank JP Morgan's share price using a price earnings (PE) multiples approach with the following assumptions and figures only:

• The major US banks JP Morgan Chase (JPM), Citi Group (C) and Wells Fargo (WFC) are comparable companies;
• JP Morgan Chase's historical earnings per share (EPS) is $4.37;
• Citi Group's share price is $50.05 and historical EPS is $4.26;
• Wells Fargo's share price is $48.98 and historical EPS is $3.89.

Note: Figures sourced from Google Finance on 24 March 2014.

(a) $53.2353

(b) $53.1831

(c) $53.0995

(d) $26.5498

(e) $2.7849

Question 341  Multiples valuation, PE ratio

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

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

Source: Google Finance 28 Feb 2014.

(a) $63.15

(b) $61.67

(c) $30.83

(d) $28.25

(e) $8.60

Question 299  equivalent annual cash flow

Carlos and Edwin are brothers and they both love Holden Commodore cars.

Carlos likes to buy the latest Holden Commodore car for $40,000 every 4 years as soon as the new model is released. As soon as he buys the new car, he sells the old one on the second hand car market for $20,000. Carlos never has to bother with paying for repairs since his cars are brand new.

Edwin also likes Commodores, but prefers to buy 4-year old cars for $20,000 and keep them for 11 years until the end of their life (new ones last for 15 years in total but the 4-year old ones only last for another 11 years). Then he sells the old car for $2,000 and buys another 4-year old second hand car, and so on.

Every time Edwin buys a second hand 4 year old car he immediately has to spend $1,000 on repairs, and then $1,000 every year after that for the next 10 years. So there are 11 payments in total from when the second hand car is bought at t=0 to the last payment at t=10. One year later (t=11) the old car is at the end of its total 15 year life and can be scrapped for $2,000.

Assuming that Carlos and Edwin maintain their love of Commodores and keep up their habits of buying new ones and second hand ones respectively, how much larger is Carlos' equivalent annual cost of car ownership compared with Edwin's?

The real discount rate is 10% pa. All cash flows are real and are expected to remain constant. Inflation is forecast to be 3% pa. All rates are effective annual. Ignore capital gains tax and tax savings from depreciation since cars are tax-exempt for individuals.

(a) $13,848.99

(b) $13,106.61

(c) $8,547.50

(d) $4,238.08

(e) -$103.85

Question 288  Annuity

There are many ways to write the ordinary annuity formula.

Which of the following is NOT equal to the ordinary annuity formula?

(a) ##V_0 = \dfrac{C_1}{r} \left(1-\dfrac{1}{(1+r)^T} \right) ##

(b) ##V_0 = \dfrac{C_1 \left(1-\dfrac{1}{(1+r)^T} \right)}{r}##

(c) ##V_0 = C_1\dfrac{\left(1-(1+r)^{-T} \right)}{r}##

(d) ##V_0 = C_1 \left(1-(1+r)^{-T} \right) r^{-1}##

(e) ##V_0 = C_1 \left(r^{-1}-(1+r)^{-T-1} \right)##

Question 137  NPV, Annuity

The following cash flows are expected:

• 10 yearly payments of $60, with the first payment in 3 years from now (first payment at t=3 and last at t=12).
• 1 payment of $400 in 5 years and 6 months (t=5.5) from now.

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

(a) $513.80

(b) $525.36

(c) $541.50

(d) $605.48

(e) $704.69

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

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

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

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

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

The Net Present Value is:

(a) -$112,496,484

(b) -$32,260,693

(c) -$19,645,987

(d) $5,222,533

(e) $200,000,000

Question 451  DDM

The first payment of a constant perpetual annual cash flow is received at time 5. Let this cash flow be ##C_5## and the required return be ##r##.

So there will be equal annual cash flows at time 5, 6, 7 and so on forever, and all of the cash flows will be equal so ##C_5 = C_6 = C_7 = ...##

When the perpetuity formula is used to value this stream of cash flows, it will give a value (V) at time:

(a) 0, so ##V_0=\dfrac{C_5}{r}##

(b) 1, so ##V_1=\dfrac{C_5}{r}##

(c) 4, so ##V_4=\dfrac{C_5}{r}##

(d) 5, so ##V_5=\dfrac{C_5}{r}##

(e) 6, so ##V_6=\dfrac{C_5}{r}##

Question 216  DDM

A stock just paid its annual dividend of $9. The share price is $60. The required return of the stock is 10% pa as an effective annual rate.

What is the implied growth rate of the dividend per year?

(a) -0.8565

(b) -0.0500

(c) -0.0435

(d) 0.0000

(e) 0.1500

Question 352  income and capital returns, DDM, real estate

Two years ago Fred bought a house for $300,000.

Now it's worth $500,000, based on recent similar sales in the area.

Fred's residential property has an expected total return of 8% pa.

He rents his house out for $2,000 per month, paid in advance. Every 12 months he plans to increase the rental payments.

The present value of 12 months of rental payments is $23,173.86.

The future value of 12 months of rental payments one year ahead is $25,027.77.

What is the expected annual growth rate of the rental payments? In other words, by what percentage increase will Fred have to raise the monthly rent by each year to sustain the expected annual total return of 8%?

(a) -0.3426%

(b) 0%

(c) 0.2754%

(d) 2.9944%

(e) 3.3652%

Question 41  DDM, income and capital returns

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

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

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

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

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

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

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

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

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

Question 498  NPV, Annuity, perpetuity with growth, multi stage growth model

A business project is expected to cost $100 now (t=0), then pay $10 at the end of the third (t=3), fourth, fifth and sixth years, and then grow by 5% pa every year forever. So the cash flow will be $10.5 at the end of the seventh year (t=7), then $11.025 at the end of the eighth year (t=8) and so on perpetually. The total required return is 10℅ pa.

Which of the following formulas will NOT give the correct net present value of the project?

(a) ##-100+ \dfrac{ \dfrac{10}{0.1} \left(1-\dfrac{1}{(1+0.1)^3} \right)}{(1+0.1)^2} +\dfrac{\left(\dfrac{10}{0.1-0.05}\right)}{(1+0.1)^5} ##

(b) ##-100+ \dfrac{10}{(1+0.1)^3} +\dfrac{10}{(1+0.1)^4} +\dfrac{10}{(1+0.1)^5} +\dfrac{\left(\dfrac{10}{0.1-0.05}\right)}{(1+0.1)^5} ##

(c) ##-100+ \dfrac{ \dfrac{10}{0.1} \left(1-\dfrac{1}{(1+0.1)^4} \right)}{(1+0.1)^2} +\dfrac{\left(\dfrac{10.5}{0.1-0.05}\right)}{(1+0.1)^6} ##

(d) ##-100+ \dfrac{10}{(1+0.1)^3} +\dfrac{10}{(1+0.1)^4} +\dfrac{10}{(1+0.1)^5} +\dfrac{10}{(1+0.1)^6} +\dfrac{\left(\dfrac{10.5}{0.1-0.05}\right)}{(1+0.1)^6} ##

(e) ##-100+ \dfrac{ \dfrac{10}{0.1} \left(1-\dfrac{1}{(1+0.1)^3} \right)}{(1+0.1)^3} +\dfrac{\left(\dfrac{10}{0.1-0.05}\right)}{(1+0.1)^5} ##

Question 358  PE ratio, Multiples valuation

Estimate the Chinese bank ICBC's share price using a backward-looking price earnings (PE) multiples approach with the following assumptions and figures only. Note that the renminbi (RMB) is the Chinese currency, also known as the yuan (CNY).

• The 4 major Chinese banks ICBC, China Construction Bank (CCB), Bank of China (BOC) and Agricultural Bank of China (ABC) are comparable companies;
• ICBC 's historical earnings per share (EPS) is RMB 0.74;
• CCB's backward-looking PE ratio is 4.59;
• BOC 's backward-looking PE ratio is 4.78;
• ABC's backward-looking PE ratio is also 4.78;

Note: Figures sourced from Google Finance on 25 March 2014. Share prices are from the Shanghai stock exchange.

(a) RMB 6.4595

(b) RMB 6.3739

(c) RMB 6.3311

(d) RMB 3.4903

(e) RMB 3.3966

Question 505  equivalent annual cash flow

A low-quality second-hand car can be bought now for $1,000 and will last for 1 year before it will be scrapped for nothing.

A high-quality second-hand car can be bought now for $4,900 and it will last for 5 years before it will be scrapped for nothing.

What is the equivalent annual cost of each car? Assume a discount rate of 10% pa, given as an effective annual rate.

The answer choices are given as the equivalent annual cost of the low-quality car and then the high quality car.

(a) $100,   $490

(b) $909.09,   $608.5

(c) $1,000,   $980

(d) $1,000,   $1578.3

(e) $1,100,   $1,292.61

Question 333  DDM, time calculation

When using the dividend discount model, care must be taken to avoid using a nominal dividend growth rate that exceeds the country's nominal GDP growth rate. Otherwise the firm is forecast to take over the country since it grows faster than the average business forever.

Suppose a firm's nominal dividend grows at 10% pa forever, and nominal GDP growth is 5% pa forever. The firm's total dividends are currently $1 billion (t=0). The country's GDP is currently $1,000 billion (t=0).

In approximately how many years will the company's total dividends be as large as the country's GDP?

(a) 1,443 years

(b) 1,199 years

(c) 955 years

(d) 674 years

(e) 148 years

Question 463  PE ratio, industry roll up, Multiples valuation

Private equity firms are known to buy medium sized private companies operating in the same industry, merge them together into a larger company, and then sell it off in a public float (initial public offering, IPO).

If medium-sized private companies trade at PE ratios of 5 and larger listed companies trade at PE ratios of 15, what return can be achieved from this strategy?

Assume that:

• The medium-sized companies can be bought, merged and sold in an IPO instantaneously.
• There are no costs of finding, valuing, merging and restructuring the medium sized companies. Also, there is no competition to buy the medium-sized companies from other private equity firms.
• The large merged firm's earnings are the sum of the medium firms' earnings.
• The only reason for the difference in medium and large firm's PE ratios is due to the illiquidity of the medium firms' shares.
• Return is defined as: ##r_{0→1} = (p_1-p_0+c_1)/p_0## , where time zero is just before the merger and time one is just after.

(a) 300%.

(b) 200%

(c) 33.33%

(d) 30%

(e) 20%

Question 281  equivalent annual cash flow

You just bought a nice dress which you plan to wear once per month on nights out. You bought it a moment ago for $600 (at t=0). In your experience, dresses used once per month last for 6 years.

Your younger sister is a student with no money and wants to borrow your dress once a month when she hits the town. With the increased use, your dress will only last for another 3 years rather than 6.

What is the present value of the cost of letting your sister use your current dress for the next 3 years?

Assume: that bank interest rates are 10% pa, given as an effective annual rate; you will buy a new dress when your current one wears out; your sister will only use the current dress, not the next one that you will buy; and the price of a new dress never changes.

(a) 300

(b) 283.1403

(c) 282.2849

(d) 257.4003

(e) 225.3944

Question 128  debt terminology, needs refinement

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

Question 129  debt terminology

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

Question 130  debt terminology

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

Question 374  debt terminology

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

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

(a) Debt coupon rate.

(b) Required return on debt.

(c) Total return on debt.

(d) Opportunity cost of debt.

(e) Cost of debt capital.

Question 234  debt terminology

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

(a) Discount loan

(b) Par loan

(c) Premium loan

(d) Deferred repayment loan

(e) Fully amortising loan.

Question 372  debt terminology

Which of the following statements is NOT correct? Borrowers:

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

(b) Are debtors.

(c) Owe money.

(d) Are funded by debt.

(e) Buy debt.

Question 373  debt terminology

Which of the following statements is NOT correct? Lenders:

(a) Are long debt.

(b) Invest in debt.

(c) Are owed money.

(d) Provide debt funding.

(e) Have debt liabilities.

Question 290  APR, effective rate, debt terminology

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

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

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

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

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

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

Question 16  credit card, APR, effective rate

A credit card offers an interest rate of 18% pa, compounding monthly.

Find the effective monthly rate, effective annual rate and the effective daily rate. Assume that there are 365 days in a year.

All answers are given in the same order:

### r_\text{eff monthly} , r_\text{eff yearly} , r_\text{eff daily} ###

(a) 0.0072, 0.09, 0.0002.

(b) 0.0139, 0.18, 0.0005.

(c) 0.0139, 6.2876, 0.0055.

(d) 0.015, 0.1956, 0.0005.

(e) 0.015, 0.1956, 0.006.

Question 26  APR, effective rate

A European bond paying annual coupons of 6% offers a yield of 10% pa.

Convert the yield into an effective monthly rate, an effective annual rate and an effective daily rate. Assume that there are 365 days in a year.

All answers are given in the same order:

### r_\text{eff, monthly} , r_\text{eff, yearly} , r_\text{eff, daily} ###

(a) 0.0041, 0.05, 0.0001.

(b) 0.0080, 0.1, 0.0003.

(c) 0.0083, 0.1, 0.0003.

(d) 0.0083, 2.1384, 0.0031.

(e) 0.0083, 0.1047, 0.0033.

Question 131  APR, effective rate

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

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

All answers are given in the same order:

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

(a) 0.1956, 0.0609, 0.1.

(b) 0.015, 0.09, 0.1.

(c) 0.1881, 0.0609, 0.1025.

(d) 0.1956, 0.0617, 0.1047.

(e) 6.2876, 0.1236, 0.1.

Question 19  fully amortising loan, APR

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

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

(a) 900

(b) 2,700

(c) 2,722.1

(d) 2,843.71

(e) 34,424.99

Question 87  fully amortising loan, APR

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

What will be your monthly payments?

(a) 1,500.00

(b) 2,250.00

(c) 2,855.79

(d) 2,899.36

(e) 35,202.02

Question 134  fully amortising loan, APR

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

(a) $888.89

(b) $1,600.00

(c) $1,885.99

(d) $1,918.56

(e) $23,247.65

Question 149  fully amortising loan, APR

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

(a) $32,692.01

(b) $2,697.98

(c) $2,652.17

(d) $2,250.00

(e) $1,250.00

Question 172  fully amortising loan, APR

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

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

(a) 246,567.70,   93,351.63

(b) 246,567.70,   235,741.91

(c) 248,563.73,   96,346.75

(d) 248,563.73,   238,323.24

(e) 256,580.38,   245,314.97

Question 187  fully amortising loan, APR

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

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

(a) 169,672.58,     90,724.32

(b) 166,791.61,     90,073.45

(c) 166,791.61,     139,580.77

(d) 165,177.97,     88,321.04

(e) 165,177.97,     137,639.05

Question 203  fully amortising loan, APR

You just signed up for a 30 year fully amortising mortgage loan with monthly payments of $1,500 per month. The interest rate is 9% pa which is not expected to change.

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

(a) 184,925.77,     164,313.82

(b) 184,925.77,     115,517.84

(c) 186,422.80,     166,717.43

(d) 186,422.80,     118,412.54

(e) 192,435.28,     170,986.32

Question 222  fully amortising loan, APR

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

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

(a) $320,725.47,     $284,977.19

(b) $310,704.66,     $277,862.39

(c) $310,704.66,     $197,354.23

(d) $308,209.62,     $273,856.37

(e) $308,209.62,     $192,529.73

Question 259  fully amortising loan, APR

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

What will be your monthly payments?

(a) $1,000

(b) $1,106.6497

(c) $2,400

(d) $2,571.8327

(e) $2,641.5525

Question 29  interest only loan

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

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

(a) 900

(b) 2,700

(c) 2,722.1

(d) 2,843.71

(e) 34,424.99

Question 107  interest only loan

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

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

(a) 17,435.74

(b) 1,438.92

(c) 1,414.49

(d) 1,200.00

(e) 666.67

Question 160  interest only loan

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

(a) $ 1,250.00

(b) $ 2,250.00

(c) $ 2,652.17

(d) $ 2,697.98

(e) $ 32,692.01

Question 459  interest only loan, inflation

In Australia in the 1980's, inflation was around 8% pa, and residential mortgage loan interest rates were around 14%.

In 2013, inflation was around 2.5% pa, and residential mortgage loan interest rates were around 4.5%.

If a person can afford constant mortgage loan payments of $2,000 per month, how much more can they borrow when interest rates are 4.5% pa compared with 14.0% pa?

Give your answer as a proportional increase over the amount you could borrow when interest rates were high ##(V_\text{high rates})##, so:

###\text{Proportional increase} = \dfrac{V_\text{low rates}-V_\text{high rates}}{V_\text{high rates}} ###

Assume that:

• Interest rates are expected to be constant over the life of the loan.
• Loans are interest-only and have a life of 30 years.
• Mortgage loan payments are made every month in arrears and all interest rates are given as annualised percentage rates (APR's) compounding per month.

(a) 0.095

(b) 0.265775

(c) 1.326099

(d) 1.338477

(e) 2.111111

Question 509  bond pricing

Calculate the price of a newly issued ten year bond with a face value of $100, a yield of 8% pa and a fixed coupon rate of 6% pa, paid annually. So there's only one coupon per year, paid in arrears every year.

(a) $114.8775

(b) $114.7202

(c) $86.5798

(d) $86.4097

(e) $40.2605

Question 510  bond pricing

Calculate the price of a newly issued ten year bond with a face value of $100, a yield of 8% pa and a fixed coupon rate of 6% pa, paid semi-annually. So there are two coupons per year, paid in arrears every six months.

(a) $114.8775

(b) $114.7202

(c) $86.5798

(d) $86.4097

(e) $40.2605

Question 11  bond pricing

For a price of $100, Vera will sell you a 2 year bond paying semi-annual coupons of 10% pa. The face value of the bond is $100. Other bonds with similar risk, maturity and coupon characteristics trade at a yield of 8% pa.

Would you like to her bond or politely ?

Question 23  bond pricing, premium par and discount bonds

Bonds X and Y are issued by the same US company. Both bonds yield 10% pa, and they have the same face value ($100), maturity, seniority, and payment frequency.

The only difference is that bond X and Y's coupon rates are 8 and 12% pa respectively. Which of the following statements is true?

(a) Bonds X and Y are premium bonds.

(b) Bonds X and Y are discount bonds.

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

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

(e) Bonds X and Y are par bonds.

Question 33  bond pricing, premium par and discount bonds

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

Which bond would have the higher current price?

(a) Bond A will have a higher price.

(b) Bond B will have a higher price.

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

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

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

Question 38  bond pricing

A two year Government bond has a face value of $100, a yield of 0.5% and a fixed coupon rate of 0.5%, paid semi-annually. What is its price?

(a) $100.0000

(b) $98.0346

(c) $99.0062

(d) $99.0087

(e) $99.0124

Question 48  IRR, NPV, bond pricing, premium par and discount bonds, market efficiency

The theory of fixed interest bond pricing is an application of the theory of Net Present Value (NPV). Also, a 'fairly priced' asset is not over- or under-priced. Buying or selling a fairly priced asset has an NPV of zero.

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

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

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

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

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

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

Question 53  bond pricing

A two year Government bond has a face value of $100, a yield of 2.5% pa and a fixed coupon rate of 0.5% pa, paid semi-annually. What is its price?

(a) 90.6421

(b) 95.1524

(c) 95.2055

(d) 96.1219

(e) 103.9751

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

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

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

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

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

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

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

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

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

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

Question 63  bond pricing, NPV, market efficiency

The theory of fixed interest bond pricing is an application of the theory of Net Present Value (NPV). Also, a 'fairly priced' asset is not over- or under-priced. Buying or selling a fairly priced asset has an NPV of zero.

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

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

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

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

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

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

Question 133  bond pricing

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

(a) $33.93

(b) $55.37

(c) $57.61

(d) $68.28

(e) $85.12

Question 138  bond pricing, premium par and discount bonds

Bonds A and B are issued by the same Australian company. Both bonds yield 7% pa, and they have the same face value ($100), maturity, seniority, and payment frequency.

The only difference is that bond A pays coupons of 10% pa and bond B pays coupons of 5% pa. Which of the following statements is true about the bonds' prices?

(a) The prices of bonds A and B will be more than $100.

(b) The prices of bonds A and B will be less than $100.

(c) Bond A will have a price more than $100, and bond B will have a price less than $100.

(d) Bond A will have a price less than $100, and bond B will have a price more than $100.

(e) Bonds A and B will both have a price of $100.

Question 159  bond pricing

A three year bond has a fixed coupon rate of 12% pa, paid semi-annually. The bond's yield is currently 6% pa. The face value is $100. What is its price?

(a) $116.25

(b) $74.04

(c) $85.89

(d) $83.75

(e) $71.38

Question 163  bond pricing, premium par and discount bonds

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

Which of the following statements is true?

(a) Bonds X and Y are premium bonds.

(b) Bonds X and Y are discount bonds.

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

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

(e) Bonds X and Y are par bonds.

Question 168  bond pricing

A four year bond has a face value of $100, a yield of 6% and a fixed coupon rate of 12%, paid semi-annually. What is its price?

(a) 67.2123

(b) 78.9409

(c) 81.7042

(d) 111.1513

(e) 121.0591

Question 178  bond pricing, premium par and discount bonds

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

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

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

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

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

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

Question 179  bond pricing, capital raising

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

How many bonds should the firm issue?

(a) 140,202

(b) 184,280

(c) 184,460

(d) 186,881

(e) 200,000

Question 183  bond pricing

A five year bond has a face value of $100, a yield of 12% and a fixed coupon rate of 6%, paid semi-annually.

What is the bond's price?

(a) 36.2655

(b) 55.8395

(c) 59.3381

(d) 77.9197

(e) 87.3629

Question 193  bond pricing, premium par and discount bonds

Which one of the following bonds is trading at par?

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

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

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

(d) a two-year bond with a $50,000 face value whose yield to maturity is 5.2% compounding semi-annually which has a price of $50,000.

(e) None of the above bonds are trading at par.

Question 194  bond pricing, capital raising

A firm wishes to raise $8 million now. They will issue 7% pa semi-annual coupon bonds that will mature in 10 years and have a face value of $100 each. Bond yields are 10% pa, given as an APR compounding every 6 months, and the yield curve is flat.

How many bonds should the firm issue?

(a) 107,441

(b) 98,393

(c) 90,480

(d) 80,000

(e) 64,039

Question 227  bond pricing, premium par and discount bonds

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

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

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

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

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

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

Question 230  bond pricing, capital raising

A firm wishes to raise $10 million now. They will issue 6% pa semi-annual coupon bonds that will mature in 8 years and have a face value of $1,000 each. Bond yields are 10% pa, given as an APR compounding every 6 months, and the yield curve is flat.

How many bonds should the firm issue? All numbers are rounded up.

(a) 9,023 bonds

(b) 10,000 bonds

(c) 11,485 bonds

(d) 12,713 bonds

(e) 12,768 bonds

Question 233  bond pricing

A four year bond has a face value of $100, a yield of 9% and a fixed coupon rate of 6%, paid semi-annually. What is its price?

(a) $94.6187

(b) $90.1062

(c) $72.592

(d) $70.3185

(e) $53.1754

Question 255  bond pricing

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

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

(a) 94.20452353

(b) 100

(c) 106

(d) 112

(e) The bond is priceless.

Question 257  bond pricing

A 10 year bond has a face value of $100, a yield of 6% pa and a fixed coupon rate of 8% pa, paid semi-annually. What is its price?

(a) $114.7202

(b) $114.8775

(c) $122.9398

(d) $126.628

(e) $174.3874

Question 287  bond pricing

A 30 year Japanese government bond was just issued at par with a yield of 1.7% pa. The fixed coupon payments are semi-annual. The bond has a face value of $100.

Six months later, just after the first coupon is paid, the yield of the bond increases to 2% pa. What is the bond's new price?

(a) $89.5717

(b) $89.6632

(c) $90.5598

(d) $93.3393

(e) $100.0000

Question 328  bond pricing, APR

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

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

(a) $1,000

(b) $1,019.9181

(c) $1,033.8330

(d) $1,052.7005

(e) $1,060.5226

Question 332  bond pricing, premium par and discount bonds

Bonds X and Y are issued by the same US company. Both bonds yield 6% pa, and they have the same face value ($100), maturity, seniority, and payment frequency.

The only difference is that bond X pays coupons of 8% pa and bond Y pays coupons of 12% pa. Which of the following statements is true?

(a) Bonds X and Y are premium bonds.

(b) Bonds X and Y are discount bonds.

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

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

(e) Bonds X and Y are par bonds.

Question 460  bond pricing, premium par and discount bonds

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

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

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

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

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

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

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

Question 607  debt terminology

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

Question 609  debt terminology

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

Question 610  debt terminology

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

Question 611  debt terminology

You owe money. Are you a or a ?

Question 612  debt terminology

You are owed money. Are you a or a ?

Question 613  debt terminology

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

Question 582  APR, effective rate, effective rate conversion

A credit card company advertises an interest rate of 18% pa, payable monthly. Which of the following statements about the interest rate is NOT correct? All rates are given to four decimal places.

(a) The APR compounding monthly is 18.0000% per annum.

(b) The effective monthly rate is 1.5000% per month.

(c) The effective annual rate is 19.5618% per annum.

(d) The effective quarterly rate is 4.5678% per quarter.

(e) The APR compounding quarterly is 13.7035% per annum.

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

A European company just issued two bonds, a

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

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

(a) 0.0374

(b) 0.0604

(c) 0.1204

(d) 0.1250

(e) 0.1411

Question 581  APR, effective rate, effective rate conversion

A home loan company advertises an interest rate of 6% pa, payable monthly. Which of the following statements about the interest rate is NOT correct? All rates are given to four decimal places.

(a) The APR compounding monthly is 6.0000% per annum.

(b) The effective monthly rate is 0.5000% per month.

(c) The effective annual rate is 6.1678% per annum.

(d) The effective 6 month rate is 3.0000% per six months.

(e) The APR compounding semi-annually is 6.0755% per annum.

Question 583  APR, effective rate, effective rate conversion

A semi-annual coupon bond has a yield of 3% pa. Which of the following statements about the yield is NOT correct? All rates are given to four decimal places.

(a) The APR compounding semi-annually is 3.0000% per annum.

(b) The effective 6 month rate is 1.5000% per six months.

(c) The effective annual rate is 3.0225% per annum.

(d) The effective monthly rate is 0.2500% per month.

(e) The APR compounding monthly is 2.9814% per annum.

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 620  bond pricing, income and capital returns

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

(a) Less than its expected total return.

(b) Equal to its expected total return.

(c) More than its expected total return.

(d) More than its coupon rate.

(e) Equal to its coupon rate.

Question 35  bond pricing, zero coupon bond, term structure of interest rates, forward interest rate

A European company just issued two bonds, a

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

What is the company's forward rate over the second year (from t=1 to t=2)? Give your answer as an effective annual rate, which is how the above bond yields are quoted.

(a) 0.0185

(b) 0.0374

(c) 0.0604

(d) 0.1204

(e) 0.1250

Question 96  bond pricing, zero coupon bond, term structure of interest rates, forward interest rate

An Australian company just issued two bonds paying semi-annual coupons:

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

What is the forward rate on the company's debt from years 1 to 2? Give your answer as an APR compounding every 6 months, which is how the above bond yields are quoted.

(a) 6.01%

(b) 6.02%

(c) 9.20%

(d) 12.02%

(e) 18.40%

Question 32  time calculation, APR

You really want to go on a back packing trip to Europe when you finish university. Currently you have $1,500 in the bank. Bank interest rates are 8% pa, given as an APR compounding per month. If the holiday will cost $2,000, how long will it take for your bank account to reach that amount?

(a) -3.74 years

(b) 1.81 years

(c) 3.33 years

(d) 3.61 years

(e) 3.74 years

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 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 176  CFFA

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

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

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

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

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

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

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

Question 224  CFFA

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

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

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

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

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

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

Question 225  CFFA

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

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

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

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

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

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

Question 349  CFFA, depreciation tax shield

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

Remember:

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

(a) An increase in revenue (Rev).

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

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

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

(e) An increase in dividends.

Question 361  CFFA

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

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

Assume that:

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

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

(a) $2m

(b) $1m

(c) $0.4m

(d) $0.3m

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

Question 504  CFFA

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

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

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

 

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

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

(a) $51

(b) $52

(c) $58

(d) $61

(e) $62

Question 188  CFFA

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

Trademark Corp
Income Statement for
year ending 30th June 2013
	$m
Sales	100
COGS	25
Operating expense	5
Depreciation	20
Interest expense	20
Income before tax	30
Tax at 30%	9
Net income	21

Trademark Corp
Balance Sheet
as at 30th June	2013	2012
	$m	$m
Assets
Current assets	120	80
PPE
Cost	150	140
Accumul. depr.	60	40
Carrying amount	90	100
Total assets	210	180
Liabilities
Current liabilities	75	65
Non-current liabilities	75	55
Owners' equity
Retained earnings	10	10
Contributed equity	50	50
Total L and OE	210	180

 

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

(a) -19

(b) 21

(c) 41

(d) 61

(e) 121

Question 208  CFFA

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

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

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

 

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

(a) 12

(b) 2

(c) -8

(d) -18

(e) 48

Question 291  CFFA

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

Scubar Corp
Income Statement for
year ending 30th June 2013
	$m
Sales	200
COGS	60
Depreciation	20
Rent expense	11
Interest expense	19
Taxable Income	90
Taxes at 30%	27
Net income	63

Scubar Corp
Balance Sheet
as at 30th June	2013	2012
	$m	$m
Inventory	60	50
Trade debtors	19	6
Rent paid in advance	3	2
PPE	420	400
Total assets	502	458
Trade creditors	10	8
Bond liabilities	200	190
Contributed equity	130	130
Retained profits	162	130
Total L and OE	502	458

 

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

The cash flow from assets was:

(a) $40m

(b) $41m

(c) $54m

(d) $60m

(e) $74m

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 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 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 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 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 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 67  CFFA, interest tax shield

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

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

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

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

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

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

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

(c) ##D.r_D ##

(d) ##D / r_D##

(e) ##NI.r_D##

Question 223  CFFA, interest tax shield

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

(a) An increase in net capital spending.

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

(c) An increase in interest expense.

(d) An increase in net working capital.

(e) A decrease in dividends paid.

Question 296  CFFA, interest tax shield

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

Remember:

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

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

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

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

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

(e) An increase in dividends.

Question 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 368  interest tax shield, CFFA

A method commonly seen in textbooks for calculating a levered firm's free cash flow (FFCF, or CFFA) is the following:

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

Does this annual FFCF or the annual interest tax shield?

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 371  interest tax shield, CFFA

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

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

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

Question 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 413  CFFA, interest tax shield, depreciation tax shield

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

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

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

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

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

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

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

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

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

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

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

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

Question 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 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 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 507  leverage, accounting ratio

A firm has a debt-to-equity ratio of 60%. What is its debt-to-assets ratio?

(a) 64%

(b) 40%

(c) 37.5%

(d) 25%

(e) 6.25%

Question 799  LVR, leverage, accounting ratio

In the home loan market, the acronym LVR stands for Loan to Valuation Ratio. If you bought a house worth one million dollars, partly funded by an $800,000 home loan, then your LVR was 80%. The LVR is equivalent to which of the following ratios?

(a) Debt to equity ratio.

(b) Debt to assets ratio.

(c) Book to market ratio.

(d) Price to earnings ratio.

(e) Interest coverage ratio.

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 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 241  Miller and Modigliani, leverage, payout policy, diversification, NPV

One of Miller and Modigliani's (M&M's) important insights is that a firm's managers should not try to achieve a particular level of leverage in a world with zero taxes and perfect information since investors can make their own leverage. Therefore corporate capital structure policy is irrelevant since investors can achieve their own desired leverage at the personal level by borrowing or lending on their own.

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

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

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

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

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

Which of the above statement(s) are true?

(a) I only.

(b) I and II only.

(c) I and III only.

(d) III only.

(e) All are true.

Question 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 663  leverage, accounting ratio

A firm has a debt-to-assets ratio of 20%. What is its debt-to-equity ratio?

(a) 20%

(b) 25%

(c) 60%

(d) 75%

(e) 80%

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 766  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}##	$100m	Operating free cash flow
##\text{FFCF or CFFA}##	$112m	Firm free cash flow or cash flow from assets (includes interest tax shields)
##g##	0% pa	Growth rate of OFCF and FFCF
##\text{WACC}_\text{BeforeTax}##	7% pa	Weighted average cost of capital before tax
##\text{WACC}_\text{AfterTax}##	6.25% pa	Weighted average cost of capital after tax
##r_\text{D}##	5% pa	Cost of debt
##r_\text{EL}##	9% pa	Cost of levered equity
##D/V_L##	50% 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) $431.111m

(b) $444.444m

(c) $485m

(d) $515.464m

(e) $1600m

Question 804  CFFA, WACC, interest tax shield, DDM

Use the below information to value a levered company with annual perpetual cash flows from assets that grow. The next cash flow will be generated in one year from now. Note that ‘k’ means kilo or 1,000. So the $30k is $30,000.

Data on a Levered Firm with Perpetual Cash Flows
Item abbreviation	Value	Item full name
##\text{OFCF}##	$30k	Operating free cash flow
##g##	1.5% pa	Growth rate of OFCF
##r_\text{D}##	4% pa	Cost of debt
##r_\text{EL}##	16.3% pa	Cost of levered equity
##D/V_L##	80% pa	Debt to assets ratio, where the asset value includes tax shields
##t_c##	30%	Corporate tax rate
##n_\text{shares}##	100k	Number of shares

 

Which of the following statements is NOT correct?

(a) The WACC before tax is 6.46% pa.

(b) The WACC after tax is 5.50% pa.

(c) The current levered asset value including tax shields is $603.839k.

(d) The current debt value is $600k and the interest tax shield benefit over the first year is $7.2k (at t=1).

(e) The current share price is $1.50.

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 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 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 236  diversification, correlation, risk

Diversification in a portfolio of two assets works best when the correlation between their returns is:

(a) -1

(b) -0.5

(c) 0

(d) 0.5

(e) 1

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 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 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 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 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 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 565  correlation

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

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

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

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

(c) 1

(d) 0

(e) Mathematically undefined

Question 561  covariance, correlation

The covariance and correlation of two stocks X and Y's annual returns are calculated over a number of years. The units of the returns are in percent per annum ##(\% pa)##.

What are the units of the covariance ##(\sigma_{X,Y})## and correlation ##(\rho_{X,Y})## of returns respectively?

(a) Percentage points per annum ##(\text{pp pa})## and percentage points per annum ##(\text{pp pa})##.

(b) Percentage points per annum ##(\text{pp pa})## and percentage points per annum all squared ##\left( (\text{pp pa})^2 \right)##.

(c) Percentage points per annum all squared ##\left( (\text{pp pa})^2 \right)## and percentage points per annum ##(\text{pp pa})##.

(d) Percentage points per annum all squared ##\left( (\text{pp pa})^2 \right)## and percentage points per annum all squared ##\left( (\text{pp pa})^2 \right)##.

(e) Percentage points per annum all squared ##\left( (\text{pp pa})^2 \right)## and a pure number with no units.

Hint: Visit Wikipedia to understand the difference between percentage points ##(\text{pp})## and percent ##(\%)##.

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 294  short selling, portfolio weights

Which of the following statements about short-selling is NOT true?

(a) Short sellers benefit from price falls.

(b) To short sell, you must borrow the asset from person A and sell it to person B, then later on buy an identical asset from person C and return it to person A.

(c) Short selling only works for assets that are 'fungible' which means that there are many that are identical and substitutable, such as shares and bonds and unlike real estate.

(d) An investor who short-sells an asset has a negative weight in that asset.

(e) An investor who short-sells an asset is said to be 'long' that asset.

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 562  covariance

What is the covariance of a variable X with itself?

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

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

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

(c) 1

(d) 0

(e) Mathematically undefined

Question 560  standard deviation, variance, needs refinement

The standard deviation and variance of a stock's annual returns are calculated over a number of years. The units of the returns are percent per annum ##(\% pa)##.

What are the units of the standard deviation ##(\sigma)## and variance ##(\sigma^2)## of returns respectively?

(a) Percentage points per annum ##(\text{pp pa})## and percentage points per annum ##(\text{pp pa})##.

(b) Percentage points per annum ##(\text{pp pa})## and percentage points per annum all squared ##\left( (\text{pp pa})^2 \right)##.

(c) Percentage points per annum all squared ##\left( (\text{pp pa})^2 \right)## and percentage points per annum ##(\text{pp pa})##.

(d) Percentage points per annum all squared ##\left( (\text{pp pa})^2 \right)## and percentage points per annum all squared ##\left( (\text{pp pa})^2 \right)##.

(e) Percent per annum ##(\% pa)## and percent per annum ##(\% pa)##.

Hint: Visit Wikipedia to understand the difference between percentage points ##(\text{pp})## and percent ##(\%)##.

Question 307  risk, variance

Let the variance of returns for a share per month be ##\sigma_\text{monthly}^2##.

What is the formula for the variance of the share's returns per year ##(\sigma_\text{yearly}^2)##?

Assume that returns are independently and identically distributed (iid) so they have zero auto correlation, meaning that if the return was higher than average today, it does not indicate that the return tomorrow will be higher or lower than average.

(a) ##\sigma_\text{yearly}^2 = \sigma_\text{monthly}^2##

(b) ##\sigma_\text{yearly}^2 = \sigma_\text{monthly}^2 \times 12##

(c) ##\sigma_\text{yearly}^2 = \sigma_\text{monthly}^2 \times 12^2##

(d) ##\sigma_\text{yearly}^2 = \sigma_\text{monthly}^2 \times \sqrt{12}##

(e) ##\sigma_\text{yearly}^2 = \sigma_\text{monthly}^2 \times {12}^{1/3}##

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 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 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 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 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 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 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 86  CAPM

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

(a) 5% pa

(b) 7.5% pa

(c) 10% pa

(d) 12.5% pa

(e) 20% pa

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

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

You estimate that:

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

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

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

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

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

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

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

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

Question 809  Markowitz portfolio theory, CAPM, Jensens alpha, CML, systematic and idiosyncratic risk

A graph of assets’ expected returns ##(\mu)## versus standard deviations ##(\sigma)## is given in the graph below. The CML is the capital market line.

Which of the following statements about this graph, Markowitz portfolio theory and the Capital Asset Pricing Model (CAPM) theory is NOT correct?

(a) The market portfolio M has systematic risk only. It’s a fully diversified portfolio comprised of all individual risky assets. The market portfolio is usually assumed to be the equity index, such as the ASX200 in Australia or the S&P500 in the US.

(b) The risk free security has no risk at all. Government bonds are usually assumed to be the risk-free security.

(c) Portfolio combinations of the market portfolio and risk free security will plot on the CML and will have systematic risk only. They will have no diversifiable risk.

(d) The portfolios on the CML with a return above ##r_f## have maximum return for any given level of risk.

(e) The individual assets and portfolios with returns less than the risk free rate are over-priced, have a negative Jensen’s alpha and should be sold.

Question 242  technical analysis, market efficiency

Select the most correct statement from the following.

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

(a) Markets are weak-form efficient.

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

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

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

(e) Stock prices reflect all publically available information.

Question 100  market efficiency, technical analysis, joint hypothesis problem

A company selling charting and technical analysis software claims that independent academic studies have shown that its software makes significantly positive abnormal returns. Assuming the claim is true, which statement(s) are correct?

(I) Weak form market efficiency is broken.

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

(III) Strong form market efficiency is broken.

(IV) The asset pricing model used to measure the abnormal returns (such as the CAPM) had mis-specification error so the returns may not be abnormal but rather fair for the level of risk.

Select the most correct response:

(a) Only III is true.

(b) Only II and III are true.

(c) Only I, II and III are true.

(d) Only IV is true.

(e) Either I, II and III are true, or IV is true, or they are all true.

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

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

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

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

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

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

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

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

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

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

Question 621  market efficiency, technical analysis

Technical traders:

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

(b) Believe that markets are weak form efficient

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

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

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

Question 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 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