Fight Finance

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 446  working capital decision, corporate financial decision theory

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

(a) Assets.

(b) Liabilities and owner's equity.

(c) Current assets and current liabilities.

(d) Dividends and buy backs.

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

Question 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 447  payout policy, corporate financial decision theory

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

(a) Assets.

(b) Liabilities and owner's equity.

(c) Current assets and current liabilities.

(d) Dividends and buy backs.

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

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

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

(a) Investment decision.

(b) Financing decision.

(c) Working capital decision.

(d) Payout policy decision.

(e) Capital or labour decision.

Question 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 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 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 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 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 136  income and capital returns

A stock was bought for $8 and paid a dividend of $0.50 one year later (at t=1 year). Just after the dividend was paid, the stock price was $7 (at t=1 year).

What were the total, capital and dividend returns given as effective annual rates? The choices are given in the same order:

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

(a) 0.0625, -0.0625, -0.125.

(b) 0.0625, 0.125, -0.0625.

(c) -0.0625, 0.0625, -0.125.

(d) -0.0625, -0.125, 0.0625.

(e) -0.125, -0.1875, 0.0625.

Question 527  income and capital returns

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

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

(a) Dividends.

(b) Rent.

(c) Coupons.

(d) Loan payments.

(e) Capital gains.

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

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

(a) 0.6

(b) 0.319508

(c) 0.269705

(d) 0.245731

(e) 0.219755

Question 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 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 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 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 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 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 211  equivalent annual cash flow

You're advising your superstar client 40-cent who is weighing up buying a private jet or a luxury yacht. 40-cent is just as happy with either, but he wants to go with the more cost-effective option. These are the cash flows of the two options:

• The private jet can be bought for $6m now, which will cost $12,000 per month in fuel, piloting and airport costs, payable at the end of each month. The jet will last for 12 years.
• Or the luxury yacht can be bought for $4m now, which will cost $20,000 per month in fuel, crew and berthing costs, payable at the end of each month. The yacht will last for 20 years.

What's unusual about 40-cent is that he is so famous that he will actually be able to sell his jet or yacht for the same price as it was bought since the next generation of superstar musicians will buy it from him as a status symbol.

Bank interest rates are 10% pa, given as an effective annual rate. You can assume that 40-cent will live for another 60 years and that when the jet or yacht's life is at an end, he will buy a new one with the same details as above.

Would you advise 40-cent to buy the or the ?

Note that the effective monthly rate is ##r_\text{eff monthly}=(1+0.1)^{1/12}-1=0.00797414##

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 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 174  profitability index

A project has the following cash flows:

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

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

(a) 0.9711

(b) 1.1750

(c) 1.3063

(d) 1.5537

(e) 1.8800

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

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

(a) The project should be rejected.

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

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

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

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

Question 219  profitability index

A project has the following cash flows:

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

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

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

(a) 1.0862

(b) 1.2672

(c) 1.3143

(d) 1.5333

(e) 1.7783

Question 182  NPV, IRR, pay back period

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

(a) The project should be rejected.

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

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

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

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

Question 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 781  NPV, IRR, pay back period

You're considering a business project which costs $11m now and is expected to pay a single cash flow of $11m in one year. So you pay $11m now, then one year later you receive $11m.

Assume that the initial $11m cost is funded using the your firm's existing cash so no new equity or debt will be raised. The cost of capital is 10% pa.

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

(a) The NPV is negative $1m.

(b) The IRR is 0% pa, less than the 10% cost of capital.

(c) The payback period is one year.

(d) The project should be rejected.

(e) If the project is accepted now then the market value of the firm's assets will fall by $11m.

Question 496  NPV, IRR, pay back period

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

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

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

(a) The NPV is zero.

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

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

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

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

Question 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 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 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 456  inflation, effective rate

In the 'Austin Powers' series of movies, the character Dr. Evil threatens to destroy the world unless the United Nations pays him a ransom (video 1, video 2). Dr. Evil makes the threat on two separate occasions:

• In 1969 he demands a ransom of $1 million (=10^6), and again;
• In 1997 he demands a ransom of $100 billion (=10^11).

If Dr. Evil's demands are equivalent in real terms, in other words $1 million will buy the same basket of goods in 1969 as $100 billion would in 1997, what was the implied inflation rate over the 28 years from 1969 to 1997?

The answer choices below are given as effective annual rates:

(a) 0.5086% pa

(b) 1.5086% pa

(c) 5.0859% pa

(d) 50.8591% pa

(e) 150.8591% pa

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 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 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 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 89  WACC, CFFA, interest tax shield

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

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

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

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

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

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

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

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

Question 224  CFFA

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

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

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

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

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

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

Question 492  capital budgeting, opportunity cost, sunk cost

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

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

(a) A sunk cost.

(b) An opportunity cost.

(c) A negative side effect.

(d) A capital expense.

(e) A depreciation expense.

Question 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 619  CFFA

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

(a) Net income, depreciation and interest expense.

(b) Depreciation and capital expenditure.

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

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

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

Question 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 176  CFFA

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

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

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

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

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

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

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

Question 128  debt terminology, needs refinement

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

Question 129  debt terminology

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

Question 130  debt terminology

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

Question 374  debt terminology

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

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

(a) Debt coupon rate.

(b) Required return on debt.

(c) Total return on debt.

(d) Opportunity cost of debt.

(e) Cost of debt capital.

Question 372  debt terminology

Which of the following statements is NOT correct? Borrowers:

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

(b) Are debtors.

(c) Owe money.

(d) Are funded by debt.

(e) Buy debt.

Question 373  debt terminology

Which of the following statements is NOT correct? Lenders:

(a) Are long debt.

(b) Invest in debt.

(c) Are owed money.

(d) Provide debt funding.

(e) Have debt liabilities.

Question 290  APR, effective rate, debt terminology

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

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

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

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

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

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

Question 16  credit card, APR, effective rate

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

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

All answers are given in the same order:

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

(a) 0.0072, 0.09, 0.0002.

(b) 0.0139, 0.18, 0.0005.

(c) 0.0139, 6.2876, 0.0055.

(d) 0.015, 0.1956, 0.0005.

(e) 0.015, 0.1956, 0.006.

Question 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 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 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 87  fully amortising loan, APR

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

What will be your monthly payments?

(a) 1,500.00

(b) 2,250.00

(c) 2,855.79

(d) 2,899.36

(e) 35,202.02

Question 134  fully amortising loan, APR

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

(a) $888.89

(b) $1,600.00

(c) $1,885.99

(d) $1,918.56

(e) $23,247.65

Question 149  fully amortising loan, APR

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

(a) $32,692.01

(b) $2,697.98

(c) $2,652.17

(d) $2,250.00

(e) $1,250.00

Question 172  fully amortising loan, APR

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

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

(a) 246,567.70,   93,351.63

(b) 246,567.70,   235,741.91

(c) 248,563.73,   96,346.75

(d) 248,563.73,   238,323.24

(e) 256,580.38,   245,314.97

Question 259  fully amortising loan, APR

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

What will be your monthly payments?

(a) $1,000

(b) $1,106.6497

(c) $2,400

(d) $2,571.8327

(e) $2,641.5525

Question 29  interest only loan

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

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

(a) 900

(b) 2,700

(c) 2,722.1

(d) 2,843.71

(e) 34,424.99

Question 223  CFFA, interest tax shield

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

(a) An increase in net capital spending.

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

(c) An increase in interest expense.

(d) An increase in net working capital.

(e) A decrease in dividends paid.

Question 296  CFFA, interest tax shield

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

Remember:

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

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

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

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

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

(e) An increase in dividends.

Question 291  CFFA

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

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

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

 

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

The cash flow from assets was:

(a) $40m

(b) $41m

(c) $54m

(d) $60m

(e) $74m

Question 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 209  CFFA

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

Piano Bar
Income Statement for
year ending 30th June 2013
	$m
Sales	310
COGS	185
Operating expense	20
Depreciation	15
Interest expense	10
Income before tax	80
Tax at 30%	24
Net income	56

Piano Bar
Balance Sheet
as at 30th June	2013	2012
	$m	$m
Assets
Current assets	240	230
PPE
Cost	420	400
Accumul. depr.	50	35
Carrying amount	370	365
Total assets	610	595
Liabilities
Current liabilities	180	190
Non-current liabilities	290	265
Owners' equity
Retained earnings	90	90
Contributed equity	50	50
Total L and OE	610	595

 

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

(a) 116

(b) 61

(c) 56

(d) 41

(e) 11

Question 208  CFFA

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

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

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

 

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

(a) 12

(b) 2

(c) -8

(d) -18

(e) 48

Question 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 351  CFFA

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

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

Assume that:

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

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

(a) $2.1m

(b) $1.3m

(c) $0.8m

(d) $0.3m

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

Question 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 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 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 379  leverage, capital structure, payout policy

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

Question 559  variance, standard deviation, covariance, correlation

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

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

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

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

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

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

Question 236  diversification, correlation, risk

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

(a) -1

(b) -0.5

(c) 0

(d) 0.5

(e) 1

Question 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 83  portfolio risk, standard deviation

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

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

(a) 0.4368

(b) 0.4911

(c) 0.6331

(d) 0.6564

(e) 0.7348

Question 293  covariance, correlation, portfolio risk

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

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

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

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

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

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

Question 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 565  correlation

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

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

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

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

(c) 1

(d) 0

(e) Mathematically undefined

Question 562  covariance

What is the covariance of a variable X with itself?

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

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

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

(c) 1

(d) 0

(e) Mathematically undefined

Question 564  covariance

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

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

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

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

(c) 1

(d) 0

(e) Mathematically undefined

Question 560  standard deviation, variance, needs refinement

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

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

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

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

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

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

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

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

Question 307  risk, variance

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

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

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

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

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

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

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

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

Question 90  CAPM, risk

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

(a) Global economic recession.

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

(c) An increase in corporate tax rates.

(d) The outbreak of world war.

(e) A company's poor earnings announcement.

Question 86  CAPM

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

(a) 5% pa

(b) 7.5% pa

(c) 10% pa

(d) 12.5% pa

(e) 20% pa

Question 232  CAPM, DDM

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

What is the price of the stock now?

(a) $55.6364

(b) $54.5455

(c) $40.8

(d) $40

(e) $37.5

Question 235  SML, NPV, CAPM, risk

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

Investment projects that plot on the SML would have:

(a) A positive NPV and should be accepted.

(b) A zero NPV.

(c) A negative NPV and should be rejected.

(d) A large amount of diversifiable risk.

(e) Zero diversifiable risk.

Question 244  CAPM, SML, NPV, risk

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

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

(a) Asset A is underpriced.

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

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

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

(e) Asset E is fairly priced.

Question 72  CAPM, portfolio beta, portfolio risk

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

What is the beta of the above portfolio?

(a) 0.75

(b) 0.833333333

(c) 1

(d) 1.166666667

(e) 1.4

Question 92  CAPM, SML, CML

Which statement(s) are correct?

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

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

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

Select the most correct response:

(a) Only (i) is true.

(b) Only (ii) is true.

(c) Only (iii) is true.

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

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

Question 98  capital structure, CAPM

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

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

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

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

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

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

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

Question 248  CAPM, DDM, income and capital returns

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Which of the equations are correct?

(a) I, IV and V only.

(b) II, III and V only.

(c) V only.

(d) All are true.

(e) None are true.

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

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

You estimate that:

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

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

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

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

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

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

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

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

Question 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 100  market efficiency, technical analysis, joint hypothesis problem

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

(I) Weak form market efficiency is broken.

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

(III) Strong form market efficiency is broken.

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

Select the most correct response:

(a) Only III is true.

(b) Only II and III are true.

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

(d) Only IV is true.

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

Question 633  personal tax

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

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

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

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

(a) $6,042

(b) $7,797

(c) $9,614

(d) $18,500

(e) $22,500

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

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

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

(a) -$21.4286

(b) -$7.563

(c) $15

(d) $21.4286

(e) $78.5714

Question 707  continuously compounding rate, continuously compounding rate conversion

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

(a) 230.258509% pa

(b) 10.536052% pa

(c) 10.517092% pa

(d) 10.468982% pa

(e) 9.531018% pa

Question 724  return distribution, mean and median returns

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

Question 726  return distribution, mean and median returns

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

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

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

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

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

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

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

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

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

Question 242  technical analysis, market efficiency

Select the most correct statement from the following.

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

(a) Markets are weak-form efficient.

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

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

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

(e) Stock prices reflect all publically available information.

Question 243  fundamental analysis, market efficiency

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

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

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

(c) Chartists make negative excess returns.

(d) Insiders make positive excess returns.

(e) Insiders make negative excess returns.

Question 105  NPV, risk, market efficiency

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

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

(a) $10

(b) $3

(c) $2.8037

(d) $2.7273

(e) $0

Question 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 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 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 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 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 252  NPV

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

You wish to consume an equal amount now (t=0), in one year (t=1) and in two years (t=2), and still have $50,000 in the bank after that (t=2).

How much can you consume at each time?

(a) $36,555.8912

(b) $23,666.6667

(c) $21,450.1511

(d) $18,277.9456

(e) $16,666.6667

Question 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 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 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 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 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 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 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 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 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 21  income and capital returns, bond pricing

A fixed coupon bond was bought for $90 and paid its annual coupon of $3 one year later (at t=1 year). Just after the coupon was paid, the bond price was $92 (at t=1 year). What was the total return, capital return and income return? Calculate your answers as effective annual rates.

The choices are given in the same order: ## r_\text{total},r_\text{capital},r_\text{income} ##.

(a) -0.0556, -0.0222, -0.0333

(b) 0.0222, -0.0111, 0.0333.

(c) 0.0333, 0.0556, 0.0222.

(d) 0.0556, 0.0222, 0.0333.

(e) 0.0556, 0.0333, 0.0222.

Question 353  income and capital returns, inflation, real and nominal returns and cash flows, real estate

A residential investment property has an expected nominal total return of 6% pa and nominal capital return of 3% pa.

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

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

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

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

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

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

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

Question 363  income and capital returns, inflation, real and nominal returns and cash flows, real estate

A residential investment property has an expected nominal total return of 8% pa and nominal capital return of 3% pa.

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

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

(a) 5.8824%, 0.9804%, 4.902%.

(b) 5.8824%, 0.9804%, 2.9412%.

(c) 4.0000%, 1.0000%, 3.0000%.

(d) 3.9412%, 1.0000%, 2.9412%.

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

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

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

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

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

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

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

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

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

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

Question 155  inflation, real and nominal returns and cash flows, Loan, effective rate conversion

You are a banker about to grant a 2 year loan to a customer. The loan's principal and interest will be repaid in a single payment at maturity, sometimes called a zero-coupon loan, discount loan or bullet loan.

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

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

(a) $838,907.00

(b) $838,986.09

(c) $841,754.97

(d) $889,996.44

(e) $944,108.22

Question 467  book and market values

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

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

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

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

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

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

Question 461  book and market values, ROE, ROA, market efficiency

One year ago a pharmaceutical firm floated by selling its 1 million shares for $100 each. Its book and market values of equity were both $100m. Its debt totalled $50m. The required return on the firm's assets was 15%, equity 20% and debt 5% pa.

In the year since then, the firm:

• Earned net income of $29m.
• Paid dividends totaling $10m.
• Discovered a valuable new drug that will lead to a massive 1,000 times increase in the firm's net income in 10 years after the research is commercialised. News of the discovery was publicly announced. The firm's systematic risk remains unchanged.

Which of the following statements is NOT correct? All statements are about current figures, not figures one year ago.

(a) The book value of equity would be larger than the market value of equity.

(b) The book ROA from accounting would be larger than the required return on assets from finance.

(c) The book ROE from accounting would be larger than the required return on equity from finance.

(d) The book ROE would be larger than the book ROA.

(e) The required return on equity would be larger than the required return on assets.

Hint: Book return on assets (ROA) and book return on equity (ROE) are ratios that accountants like to use to measure a business's past performance.

###\text{ROA}= \dfrac{\text{Net income}}{\text{Book value of assets}}###

###\text{ROE}= \dfrac{\text{Net income}}{\text{Book value of equity}}###

The required return on assets ##r_V## is a return that financiers like to use to estimate a business's future required performance which compensates them for the firm's assets' risks. If the business were to achieve realised historical returns equal to its required returns, then investment into the business's assets would have been a zero-NPV decision, which is neither good nor bad but fair.

###r_\text{V, 0 to 1}= \dfrac{\text{Cash flow from assets}_\text{1}}{\text{Market value of assets}_\text{0}} = \dfrac{CFFA_\text{1}}{V_\text{0}}###

Similarly for equity and debt.

Question 59  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	11
2	121

(a) -100

(b) 0

(c) 10

(d) 21

(e) 132

Question 533  NPV, no explanation

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

You wish to consume twice as much now (t=0) as in one year (t=1) and have nothing left in the bank at the end.

How much can you consume at time zero and one? The answer choices are given in the same order.

(a) $52,380.95,   $52,380.95

(b) $62,500,   $31,250

(c) $66,666.67,   $33,333.33

(d) $68,750,   $34,375

(e) $70,967.74,   $35,483.87

Question 534  NPV, no explanation

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

You wish to consume half as much now (t=0) as in one year (t=1) and have nothing left in the bank at the end.

How much can you consume at time zero and one? The answer choices are given in the same order.

(a) $26,190.48,   $52380.95

(b) $31,250,   $62,500

(c) $33,333.33,   $66,666.67

(d) $34,375,   $68,750

(e) $35,483.87,   $70,967.74

Question 2  NPV, Annuity

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

Will you or politely Katya's deal?

Question 356  NPV, Annuity

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

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

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

(a) -$1,000

(b) $209.2132

(c) $644.7393

(d) $1,040.6721

(e) $1,400.611

Question 499  NPV, Annuity

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

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

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

(a) $0

(b) $10

(c) $50

(d) Positive infinity

(e) Priceless

Question 479  perpetuity with growth, DDM, NPV

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

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

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

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

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

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

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

Question 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 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 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 289  DDM, expected and historical returns, ROE

In the dividend discount model:

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

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

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

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

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

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

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

Question 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 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 567  stock split, capital structure

A company conducts a 4 for 3 stock split. What is the percentage change in the stock price and the number of shares outstanding? The answers are given in the same order.

(a) -33.33%, 50%

(b) -25%, 33.33%

(c) -25%, 25%

(d) -20%, 25%

(e) 33.33%, -25%

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

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

Which one of the following corporate events may have happened?

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

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

(c) 5 for 4 stock split.

(d) 1 for 5 bonus issue.

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

Question 713  effective rate conversion

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

(a) 30% pa

(b) 26.236426% pa

(c) 10.254219% pa

(d) 10.25% pa

(e) 10% pa

Question 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 634  continuously compounding rate

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

(a) $112.749685

(b) $110.517092

(c) $110

(d) $108.328707

(e) $108

Question 652  future, continuously compounding rate

An equity index is currently at 5,200 points. The 6 month futures price is 5,300 points and the total required return is 6% pa with continuous compounding. Each index point is worth $25.

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

(a) 5.7145% pa

(b) 4.0952% pa

(c) 3.8096% pa

(d) 2.1904% pa

(e) 1.9048% pa

Question 653  future, continuously compounding rate

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

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

(a) -0.0625% pa

(b) 1.9584% pa

(c) 3.0937% pa

(d) 4.0416% pa

(e) 6.0625% pa

Question 708  continuously compounding rate, continuously compounding rate conversion

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

(a) 230.258509% pa

(b) 10.536052% pa

(c) 10.517092% pa

(d) 10.468982% pa

(e) 9.531018% pa

Question 710  continuously compounding rate, continuously compounding rate conversion

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

(a) 12.682503% pa

(b) 12.060201% pa

(c) 12% pa

(d) 11.940397% pa

(e) 3.464102% pa

Question 596  future, continuously compounding rate

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

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

(a) 0.3039% pa

(b) 3.8481% pa

(c) 4.1519% pa

(d) 7.3922% pa

(e) 7.6961% pa

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

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

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

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

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

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

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

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

Question 665  stock split

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

(a) -76.92%,   333.33%

(b) -70%,   333.33%

(c) -70%, 233.33%

(d) -57.14%,   233.33%

(e) 233.33%,   -70%

Question 944  stock split, bonus issue, stock dividend

A 2-for-1 stock split is equivalent to a 1-for-1 bonus issue or a 100% stock dividend. or ?

Question 945  stock split, bonus issue, stock dividend

A 3-for-2 stock split is equivalent to a 1-for-2 bonus issue or a 200% stock dividend. or ?

Question 946  stock split, bonus issue, stock dividend

A 1-for-4 bonus issue is equivalent to a 4-for-1 stock split or a 25% stock dividend. or ?

Question 961  stock split, bonus issue

Which one of the following statements is NOT correct? A 1-for-4 bonus issue:

(a) Will increase the number of shares by 25%.

(b) Will decrease the share price by 25%.

(c) Is equivalent to a 5-for-4 stock split.

(d) Is equivalent to a 25% stock dividend.

(e) Has no effect on the firm's cash flow.

Question 666  rights issue, capital raising

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

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

(a) -60%,   150%

(b) -42.22%,   150%

(c) -40%,   66.67%

(d) -22.22%,   66.67%

(e) -4.44%,   66.67%

Question 803  capital raising, rights issue, initial public offering, on market repurchase, no explanation

Which one of the following capital raisings or payouts involve the sale of shares to existing shareholders only?

(a) Rights issues.

(b) Private placements.

(c) Initial public offerings.

(d) Seasoned equity offerings.

(e) On-market buy backs.

Question 214  rights issue

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

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

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

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

• 29/10/2003. Shares trade ex-rights.

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

(a) 17.3492

(b) 17.2308

(c) 14.8418

(d) 13.7908

(e) 13.7692

Question 986  initial public offering, capital raising

In an initial public offering (IPO), a:

(a) Sole trader turns into a partnership.

(b) Partnership turns into a private company.

(c) Private company turns into a public company.

(d) Public company turns into a private company.

(e) Private company turns into a sole trader.

Question 1014  book build, initial public offering, capital raising, demand schedule

A firm is floating its stock in an IPO and its underwriter has received the following bids, listed in order from highest to lowest share price:

IPO Book Build Bids
Bidders	Share price	Number of shares
	$/share	millions
BidderA	2.5	2
BidderB	2	1.5
BidderC	1.5	4
BidderD	1	3
BidderE	0.5	2

 

Suppose that the firm's owner wishes to raise $6 million to expand the business by selling new stock in the initial public offering (IPO). The owner currently holds 8 million stock which are not for sale. Which of the following statements is NOT correct?

(a) The IPO share price will be $2 per share

(b) The pre-money equity market capitalisation is $16 million.

(c) The post-money equity market capitalisation is $22 million.

(d) Bidder A will be allocated their entire bid, while Bidders C, D and E will be unsuccessful.

(e) Bidder B will be allocated only 0.5m stock of their 1.5m stock bid.

Question 625  dividend re-investment plan, capital raising

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

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

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

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

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

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

Question 179  bond pricing, capital raising

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

How many bonds should the firm issue?

(a) 140,202

(b) 184,280

(c) 184,460

(d) 186,881

(e) 200,000

Question 194  bond pricing, capital raising

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

How many bonds should the firm issue?

(a) 107,441

(b) 98,393

(c) 90,480

(d) 80,000

(e) 64,039

Question 230  bond pricing, capital raising

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

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

(a) 9,023 bonds

(b) 10,000 bonds

(c) 11,485 bonds

(d) 12,713 bonds

(e) 12,768 bonds

Question 544  bond pricing, capital raising, no explanation

A firm wishes to raise $10 million now. They will issue 6% pa semi-annual coupon bonds that will mature in 3 years and have a face value of $100 each. Bond yields are 5% pa, given as an APR compounding every 6 months, and the yield curve is flat.

How many bonds should the firm issue?

(a) 102,755

(b) 100,000

(c) 97,349

(d) 97,320

(e) 86,548

Question 755  bond pricing, capital raising

A firm wishes to raise $50 million now. They will issue 7% pa semi-annual coupon bonds that will mature in 6 years and have a face value of $100 each. Bond yields are 5% pa, given as an APR compounding every 6 months, and the yield curve is flat.

How many bonds should the firm issue?

(a) 374,885

(b) 453,483

(c) 500,000

(d) 527,541

(e) 666,873

Question 756  bond pricing, capital raising, no explanation

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

How many bonds should the firm issue?

(a) 418,743

(b) 420,478

(c) 513,921

(d) 552,365

(e) 594,562

Question 757  bond pricing, capital raising, no explanation

A firm wishes to raise $50 million now. They will issue 5% pa semi-annual coupon bonds that will mature in 10 years and have a face value of $100 each. Bond yields are 5% pa, given as an APR compounding every 6 months, and the yield curve is flat.

How many bonds should the firm issue?

(a) 305,136

(b) 308,888

(c) 359,783

(d) 500,000

(e) 809,358

Question 789  rights issue, capital raising

A firm wishes to raise $30 million now. The firm's current market value of equity is $60m and the market price per share is $20. They estimate that they'll be able to issue shares in a rights issue at a subscription price of $15. Ignore the time value of money and assume that all shareholders exercise their rights. Which of the following statements is NOT correct?

(a) The firm currently has 3m shares on issue and will need to sell 2m new shares in the rights issue.

(b) The company should do a 2-for-3 rights issue.

(c) After the rights issue the market share price will be $17.

(d) The value of one right would be $3.

(e) If you don't take part in the rights issue and it is non-renounceable, you will lose $2 per share.

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

Fill in the missing words in the following sentence:

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

(a) Fall, fall.

(b) Fall, rises.

(c) Rise, fall.

(d) Rise, rise.

(e) Remain unchanged, remain unchanged.

Question 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 987  interest tax shield, capital structure, debt terminology

What creates interest tax shields for a company?

(a) Debt assets.

(b) Debt funding.

(c) Equity assets.

(d) Equity funding.

(e) None of the above.

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 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 77  interest tax shield

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

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

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

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

(a) ##IntExp.t_c##

(b) ##IntExp/t_c##

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

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

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

Question 240  negative gearing, interest tax shield

Unrestricted negative gearing is allowed in Australia, New Zealand and Japan. Negative gearing laws allow income losses on investment properties to be deducted from a tax-payer's pre-tax personal income. Negatively geared investors benefit from this tax advantage. They also hope to benefit from capital gains which exceed the income losses.

For example, a property investor buys an apartment funded by an interest only mortgage loan. Interest expense is $2,000 per month. The rental payments received from the tenant living on the property are $1,500 per month. The investor can deduct this income loss of $500 per month from his pre-tax personal income. If his personal marginal tax rate is 46.5%, this saves $232.5 per month in personal income tax.

The advantage of negative gearing is an example of the benefits of:

(a) Diversification.

(b) The time value of money.

(c) Interest tax shields.

(d) Depreciation tax shields.

(e) A 'buy and hold' investment strategy.

Question 413  CFFA, interest tax shield, depreciation tax shield

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Notes

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

Assumptions

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

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

(a) $7.33k

(b) $7.299k

(c) $6.946k

(d) $6.729k

(e) $6.667k

Question 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 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 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 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 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 571  foreign exchange rate

An Indonesian lady wishes to convert 1 million Indonesian rupiah (IDR) to Australian dollars (AUD). Exchange rates are 13,125 IDR per USD and 0.79 USD per AUD. How many AUD is the IDR 1 million worth?

(a) AUD 16,613,924,050.63

(b) AUD 10,368,750,000.00

(c) AUD 10,368.75

(d) AUD 96.44

(e) AUD 60.19