Fight Finance

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 991  NPV

The required return of a building 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.

The building firm is just about to start the project and the client has signed the contract. Initially the firm will pay $100 to the sub-contractors to carry out the work and then will receive an $11 payment from the client in one year and $121 when the project is finished in 2 years. Ignore credit risk.

But the building company is considering selling the project to a competitor at different points in time and is pondering the minimum price that they should sell it for.

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

Which of the below statements is NOT correct? The project is worth:

(a) $10 at t=0, just before the $100 is paid.

(b) $110 at t=0, just after the $100 cost is paid.

(c) $121 at t=1, just before the $11 revenue is received.

(d) $110 at t=1, just after the $11 is received.

(e) $60.5 at t=1.5, one and a half years after commencing the project.

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 250  NPV, Loan, arbitrage table

Your neighbour asks you for a loan of $100 and offers to pay you back $120 in one year.

You don't actually have any money right now, but you can borrow and lend from the bank at a rate of 10% pa. Rates are given as effective annual rates.

Assume that your neighbour will definitely pay you back. Ignore interest tax shields and transaction costs.

The Net Present Value (NPV) of lending to your neighbour is $9.09. Describe what you would do to actually receive a $9.09 cash flow right now with zero net cash flows in the future.

(a) Borrow $109.09 from the bank and lend $100 of it to your neighbour now.

(b) Borrow $100 from the bank and lend it to your neighbour now.

(c) Borrow $209.09 from the bank and lend $100 to your neighbour now.

(d) Borrow $120 from the bank and lend $100 of it to your neighbour now.

(e) Borrow $90.91 from the bank and lend it to your neighbour now.

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

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

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

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

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

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

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

Question 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 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 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 481  Annuity

This annuity formula ##\dfrac{C_1}{r}\left(1-\dfrac{1}{(1+r)^3} \right)## is equivalent to which of the following formulas? Note the 3.

In the below formulas, ##C_t## is a cash flow at time t. All of the cash flows are equal, but paid at different times.

(a) ##C_0+C_1+C_2+C_3##

(b) ##\dfrac{C_0+C_1+C_2+C_3}{(1+r)^3} ##

(c) ##C_0+\dfrac{C_1}{(1+r)^1} +\dfrac{C_2}{(1+r)^2} + \dfrac{C_3}{(1+r)^3} ##

(d) ##\dfrac{C_1}{(1+r)^1} +\dfrac{C_2}{(1+r)^2} + \dfrac{C_3}{(1+r)^3} ##

(e) ##\dfrac{C_1}{(1+r)^1} + \dfrac{C_2}{(1+r)^2} ##

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 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 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 201  DDM, income and capital returns

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

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

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

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

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

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

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

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

Question 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 148  DDM, income and capital returns

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

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

Which expression is NOT equal to the expected dividend yield?

(a) ## r-g ##

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

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

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

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

Question 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 158  DDM, income and capital returns

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

###p_0=\frac{d_1}{r_\text{eff}-g_\text{eff}}###

Which expression is NOT equal to the expected capital return?

(a) ## g_\text{eff} ##

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

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

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

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

Question 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 463  PE ratio, 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 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 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 548  equivalent annual cash flow, time calculation, no explanation

An Apple iPhone 6 smart phone can be bought now for $999. An Android Kogan Agora 4G+ smart phone can be bought now for $240.

If the Kogan phone lasts for one year, approximately how long must the Apple phone last for to have the same equivalent annual cost?

Assume that both phones have equivalent features besides their lifetimes, that both are worthless once they've outlasted their life, the discount rate is 10% pa given as an effective annual rate, and there are no extra costs or benefits from either phone.

(a) 11 years

(b) 9 years

(c) 7 years

(d) 5 years

(e) 3 years

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

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

Notes and coins:

(a) Pay no income cash flow.

(b) Have a nominal total return of zero.

(c) Have a nominal capital return of zero.

(d) Have a nominal income return of zero.

(e) Have a real total return of zero.

Question 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 575  inflation, real and nominal returns and cash flows

You expect a nominal payment of $100 in 5 years. The real discount rate is 10% pa and the inflation rate is 3% pa. Which of the following statements is NOT correct?

(a) The nominal cash flow of $100 in 5 years is equivalent to a real cash flow of $86.2609 in 5 years. This means that $86.2609 will buy the same amount of goods and services now as $100 will buy in 5 years.

(b) The real discount rate of 10% pa is equivalent to a nominal discount rate of 13.3333% pa.

(c) The nominal price of goods and services will increase by 3% every year.

(d) The real price of goods and services will increase by 3% every year.

(e) The present value of your payment will increase by the nominal discount rate every year.

Question 577  inflation, real and nominal returns and cash flows

What is the present value of a real payment of $500 in 2 years? The nominal discount rate is 7% pa and the inflation rate is 4% pa.

(a) $472.3557

(b) $471.298

(c) $436.7194

(d) $435.7415

(e) $405.8112

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 444  investment decision, corporate financial decision theory

The investment decision primarily affects which part of a business?

(a) Assets.

(b) Liabilities and owner's equity.

(c) Current assets and current liabilities.

(d) Dividends and buy backs.

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

Question 445  financing decision, corporate financial decision theory

The financing decision primarily affects which part of a business?

(a) Assets.

(b) Liabilities and owner's equity.

(c) Current assets and current liabilities.

(d) Dividends and buy backs.

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

Question 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 180  equivalent annual cash flow, inflation, real and nominal returns and cash flows

Details of two different types of light bulbs are given below:

• Low-energy light bulbs cost $3.50, have a life of nine years, and use about $1.60 of electricity a year, paid at the end of each year.
• Conventional light bulbs cost only $0.50, but last only about a year and use about $6.60 of energy a year, paid at the end of each year.

The real discount rate is 5%, given as an effective annual rate. Assume that all cash flows are real. The inflation rate is 3% given as an effective annual rate.

Find the Equivalent Annual Cost (EAC) of the low-energy and conventional light bulbs. The below choices are listed in that order.

(a) 1.4873, 6.7857

(b) 1.6525, 6.7857

(c) 2.1415, 7.1250

(d) 14.8725, 6.7857

(e) 2.0924, 7.1250

Question 462  equivalent annual cash flow

You own some nice shoes which you use once per week on date nights. You bought them 2 years ago for $500. In your experience, shoes used once per week last for 6 years. So you expect yours to last for another 4 years.

Your younger sister said that she wants to borrow your shoes once per week. With the increased use, your shoes will only last for another 2 years rather than 4.

What is the present value of the cost of letting your sister use your current shoes for the next 2 years?

Assume: that bank interest rates are 10% pa, given as an effective annual rate; you will buy a new pair of shoes when your current pair wears out and your sister will not use the new ones; your sister will only use your current shoes so she will only use it for the next 2 years; and the price of new shoes never changes.

(a) $164.6662

(b) $181.1328

(c) $199.2461

(d) $226.2443

(e) $301.1312

Question 576  inflation, real and nominal returns and cash flows

What is the present value of a nominal payment of $1,000 in 4 years? The nominal discount rate is 8% pa and the inflation rate is 2% pa.

(a) $795.62

(b) $792.0937

(c) $735.0299

(d) $731.7721

(e) $683.0135

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 739  real and nominal returns and cash flows, inflation

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

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

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

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

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

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

Question 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 607  debt terminology

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

Question 608  debt terminology

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

Question 609  debt terminology

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

Question 610  debt terminology

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

Question 611  debt terminology

You owe money. Are you a or a ?

Question 612  debt terminology

You are owed money. Are you a or a ?

Question 541  debt terminology

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

(a) Buy debt.

(b) Are debtors.

(c) Have debt assets.

(d) Provide debt funding.

(e) Are lenders.

Question 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 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 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 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 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 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 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 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 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 130  debt terminology

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

Question 128  debt terminology, needs refinement

An 'interest payment' is the same thing as a 'coupon payment'. 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 330  APR, effective rate, debt terminology

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

(a) Effective rates compound once over their time period. So an effective monthly rate compounds once per month.

(b) APR's compound more than once per year. So an APR compounding monthly compounds 12 times per year. The exception is an APR that compounds annually (once per year) which is the same thing as an effective annual rate.

(c) To convert an effective rate to an APR, multiply the effective rate by the number of time periods in one year. So an effective monthly rate multiplied by 12 is equal to an APR compounding monthly.

(d) To convert an APR compounding monthly to an effective monthly rate, divide the APR by the number of months in one year (12).

(e) To convert an APR compounding monthly to an effective weekly rate, divide the APR by the number of weeks in one year (approximately 52).

Question 49  inflation, real and nominal returns and cash flows, APR, effective rate

In Australia, nominal yields on semi-annual coupon paying Government Bonds with 2 years until maturity are currently 2.83% pa.

The inflation rate is currently 2.2% pa, given as an APR compounding per quarter. The inflation rate is not expected to change over the next 2 years.

What is the real yield on these bonds, given as an APR compounding every 6 months?

(a) 0.3086%

(b) 0.6171%

(c) 0.6181%

(d) 0.6239%

(e) 0.6300%

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 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 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 15  bond pricing

For a price of $95, Nicole will sell you a 10 year bond paying semi-annual coupons of 8% pa. The face value of the bond is $100. Other bonds with the same risk, maturity and coupon characteristics trade at a yield of 8% pa.

Would you like to the 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 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 491  capital budgeting, opportunity cost, sunk cost

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

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

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

(a) A sunk cost.

(b) An opportunity cost.

(c) A negative side effect.

(d) A capital expense.

(e) A depreciation expense.

Question 173  CFFA

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

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

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

 

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

(a) 242

(b) 182

(c) 112

(d) 92

(e) 52

Question 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 359  CFFA

Which one of the following will have no effect on net income (NI) but decrease cash flow from assets (CFFA or FFCF) 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 increase in rent expense (a type of recurring fixed cost, FC).

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

(d) An increase in inventories (a current asset).

(e) An decrease in interest expense (IntExp).

Question 360  CFFA

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

Ching-A-Lings Corp
Income Statement for
year ending 30th June 2013
	$m
Sales	100
COGS	20
Depreciation	20
Rent expense	11
Interest expense	19
Taxable Income	30
Taxes at 30%	9
Net income	21

Ching-A-Lings Corp
Balance Sheet
as at 30th June	2013	2012
	$m	$m
Inventory	49	38
Trade debtors	14	2
Rent paid in advance	5	5
PPE	400	400
Total assets	468	445
Trade creditors	4	10
Bond liabilities	200	190
Contributed equity	145	145
Retained profits	119	100
Total L and OE	468	445

 

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

The cash flow from assets was:

(a) $43m

(b) $31m

(c) $23m

(d) $11m

(e) $1m

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 226  CFFA

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

World Bar
Income Statement for
year ending 30th June 2013
	$m
Sales	300
COGS	150
Operating expense	50
Depreciation	40
Interest expense	10
Taxable income	50
Tax at 30%	15
Net income	35

World Bar
Balance Sheet
as at 30th June	2013	2012
	$m	$m
Assets
Current assets	200	230
PPE
Cost	400	400
Accumul. depr.	75	35
Carrying amount	325	365
Total assets	525	595
Liabilities
Current liabilities	150	205
Non-current liabilities	235	250
Owners' equity
Retained earnings	100	100
Contributed equity	40	40
Total L and OE	525	595

 

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

(a) 145

(b) 100

(c) 90

(d) 60

(e) -20

Question 350  CFFA

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

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

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

 

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

The cash flow from assets was:

(a) $138m

(b) $142m

(c) $143m

(d) $172m

(e) $176m

Question 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 512  capital budgeting, CFFA

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

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

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

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

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

(a) -6,   12.25,   16.68

(b) -6.8,   13.25,   14.05

(c) -6.8,   13.25,   15.88

(d) -6.8,   13.25,   18.51

(e) -6.8,   13.25,   17.71

Question 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 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 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 206  CFFA, interest expense, interest tax shield

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

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

Annual interest expense is equal to:

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

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

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

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

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

Question 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 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 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 69  interest tax shield, capital structure, leverage, WACC

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

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

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

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

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

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

Question 78  WACC, capital structure

A company issues a large amount of bonds to raise money for new projects of similar risk to the company's existing projects. The net present value (NPV) of the new projects is positive but small. Assume a classical tax system. Which statement is NOT correct?

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

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

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

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

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

Question 84  WACC, capital structure, capital budgeting

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

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

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

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

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

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

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

Question 91  WACC, capital structure

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

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

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

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

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

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

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

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

Assume that:

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

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

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

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

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

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

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

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

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

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

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

Assume that:

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

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

(a) $13.19m

(b) $12.36m

(c) $11.77m

(d) $11.53m

(e) $11.20m

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

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

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

(a) Approximately 6%.

(b) Approximately 4%.

(c) Approximately 2%.

(d) Approximately 0%.

(e) Approximately -2%.

Question 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 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 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 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 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 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 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 243  fundamental analysis, market efficiency

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

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

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

(c) Chartists make negative excess returns.

(d) Insiders make positive excess returns.

(e) Insiders make negative excess returns.

Question 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 71  CAPM, risk

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

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

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

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

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

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

Question 93  correlation, CAPM, systematic risk

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

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

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

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

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

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

Question 627  CAPM, SML, NPV, Jensens alpha

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

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

(b) Asset A is under-priced.

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

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

(e) Asset B is fairly priced.

Question 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 311  foreign exchange rate

When someone says that they're "buying American dollars" (USD), what type of asset are they probably buying? They're probably buying:

(a) Short term debt denominated in USD, for example lending to a US bank as a USD deposit.

(b) Long term debt denominated in USD, for example lending to a US company by buying their USD bonds.

(c) Shares denominated in USD, for example buying shares in Coca-Cola which is listed on the NYSE.

(d) Real estate denominated in USD, for example buying an apartment in Chicago.

(e) Commodities with USD, for example buying gold, wheat, or coal.

Question 601  foreign exchange rate, American and European terms

Australians usually quote the Australian dollar in USD per 1 AUD. For example, in October 2015 the Australian dollar was quoted as 0.72 USD per AUD. Is this an or terms quote?

Question 602  foreign exchange rate, American and European terms

Chinese people usually quote the Chinese Yuan or Renminbi in RMB per 1 USD. For example, in October 2015 the Chinese Renminbi was 6.35 RMB per USD. Is this an or terms quote?

Question 313  foreign exchange rate, American and European terms

If the AUD appreciates against the USD, the American terms quote of the AUD will or ?

Question 315  foreign exchange rate, American and European terms

If the current AUD exchange rate is USD 0.9686 = AUD 1, what is the European terms quote of the AUD against the USD?

(a) 0.9686 USD per AUD

(b) 0.9686 AUD per USD

(c) 1.0324 USD per AUD

(d) 1.0324 AUD per USD

(e) 1.0324 AUD per EUR

Question 317  foreign exchange rate, American and European terms

If the USD appreciates against the AUD, the European terms quote of the AUD will or ?

Question 626  cross currency interest rate parity, foreign exchange rate, forward foreign exchange rate

The Australian cash rate is expected to be 2% pa over the next one year, while the Japanese cash rate is expected to be 0% pa, both given as nominal effective annual rates. The current exchange rate is 100 JPY per AUD.

What is the implied 1 year forward foreign exchange rate?

(a) 98.04 JPY per AUD.

(b) 100 JPY per AUD.

(c) 102 JPY per AUD.

(d) 1.02 AUD per JPY.

(e) 0.9804 AUD per JPY.

Question 246  foreign exchange rate, forward foreign exchange rate, cross currency interest rate parity

Suppose the Australian cash rate is expected to be 8.15% pa and the US federal funds rate is expected to be 3.00% pa over the next 2 years, both given as nominal effective annual rates. The current exchange rate is at parity, so 1 USD = 1 AUD.

What is the implied 2 year forward foreign exchange rate?

(a) 1 USD = 1.1025 AUD

(b) 1.1025 USD = 1 AUD

(c) 1 USD = 1.05 AUD

(d) 1 USD = 1.1 AUD

(e) 1.1 USD = 1 AUD

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 302  WACC, CAPM

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

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

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

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

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

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

Question 114  WACC, capital structure, risk

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

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

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

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

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

(e) none of the above.

Question 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 449  personal tax on dividends, classical tax system

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

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

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

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

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

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

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

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

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

Question 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 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 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 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 111  portfolio risk, correlation

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

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

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

(c) The portfolio standard deviation declines.

(d) Both stocks' individual variances decline.

(e) Both stocks' individual standard deviations decline.

Question 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 306  risk, standard deviation

Let the standard deviation of returns for a share per month be ##\sigma_\text{monthly}##.

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

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} = \sigma_\text{monthly}##

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

(c) ##\sigma_\text{yearly} = \sigma_\text{monthly} \times 144##

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

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

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 569  personal tax

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

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

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

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

(a) $36,092.16

(b) $29,675.78

(c) $21,185.56

(d) $17,622.78

(e) $3,638.56

Question 454  NPV, capital structure, capital budgeting

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

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

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

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

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

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

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

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

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

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

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

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

Question 712  effective rate conversion

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

(a) 12.682503% pa

(b) 12.060201% pa

(c) 12% pa

(d) 11.940397% pa

(e) 3.464102% pa

Question 811  log-normal distribution, mean and median returns, return distribution, arithmetic and geometric averages

Which of the following statements about probability distributions is NOT correct?

(a) A normally distributed variable’s mean, median and mode are all expected to be equal.

(b) A log-normally distributed variable’s mean, median and mode are all expected to be different. Mean > median > mode.

(c) Future stock prices ##(P_t )## are often assumed to be log-normally distributed.

(d) Stocks’ annual net discrete returns ##(P_t/P_0-1)## must be normally distributed when stock prices ##(P_t)## are log-normally distributed.

(e) The total area under a probability density function (pdf) is always one.