Fight Finance

Question 250  NPV, Loan, arbitrage table

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

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

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

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

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

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

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

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

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

Question 502  NPV, IRR, mutually exclusive projects

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

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

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

Which project should the investor accept?

(a) Petrol station.

(b) Car wash.

(c) Car park.

(d) None of the projects.

(e) All of the projects.

Question 404  income and capital returns, real estate

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

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

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

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

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

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

(a) 3.1029%

(b) 3.3201%

(c) 3.7235%

(d) 3.9841%

(e) 7%

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

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

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

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

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

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

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

Question 575  inflation, real and nominal returns and cash flows

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

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

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

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

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

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

Question 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 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 2  NPV, Annuity

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

Will you or politely Katya's deal?

Question 481  Annuity

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

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

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

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

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

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

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

Question 356  NPV, Annuity

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

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

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

(a) -$1,000

(b) $209.2132

(c) $644.7393

(d) $1,040.6721

(e) $1,400.611

Question 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 7  DDM

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

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

The required return of the stock is 15% pa.

Would you like to the share or politely ?

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

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

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

(a) $200 today and $210 tomorrow.

(b) $210 today and $220 tomorrow.

(c) $220 today and $230 tomorrow.

(d) $210 today and $200 tomorrow.

(e) $220 today and $210 tomorrow.

Question 217  NPV, DDM, multi stage growth model

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

What is the price of the stock now?

(a) $361.78

(b) $236.33

(c) $237.93

(d) $348.69

(e) $223.24

Question 39  DDM, perpetuity with growth

A stock is expected to pay the following dividends:

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

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

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

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

(a) $25.6033

(b) $20.7476

(c) $20.0000

(d) $19.8835

(e) $18.3126

Question 148  DDM, income and capital returns

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

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

Which expression is NOT equal to the expected dividend yield?

(a) ## r-g ##

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

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

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

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

Question 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 51  DDM

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

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

(a) $50.00

(b) $50.50

(c) $100.00

(d) $111.11

(e) $112.22

Question 270  real estate, DDM, effective rate conversion

You own an apartment which you rent out as an investment property.

What is the price of the apartment using discounted cash flow (DCF, same as NPV) valuation?

Assume that:

• You just signed a contract to rent the apartment out to a tenant for the next 12 months at $2,000 per month, payable in advance (at the start of the month, t=0). The tenant is just about to pay you the first $2,000 payment.
• The contract states that monthly rental payments are fixed for 12 months. After the contract ends, you plan to sign another contract but with rental payment increases of 3%. You intend to do this every year.
  So rental payments will increase at the start of the 13th month (t=12) to be $2,060 (=2,000(1+0.03)), and then they will be constant for the next 12 months.
  Rental payments will increase again at the start of the 25th month (t=24) to be $2,121.80 (=2,000(1+0.03)²), and then they will be constant for the next 12 months until the next year, and so on.
• The required return of the apartment is 8.732% pa, given as an effective annual rate.
• Ignore all taxes, maintenance, real estate agent, council and strata fees, periods of vacancy and other costs. Assume that the apartment will last forever and so will the rental payments.

(a) $415,149.4048

(b) $438,252.6707

(c) $441,067.7356

(d) $444,155.5276

(e) $455,263.0844

Question 488  income and capital returns, payout policy, payout ratio, DDM

Two companies BigDiv and ZeroDiv are exactly the same except for their dividend payouts.

BigDiv pays large dividends and ZeroDiv doesn't pay any dividends.

Currently the two firms have the same earnings, assets, number of shares, share price, expected total return and risk.

Assume a perfect world with no taxes, no transaction costs, no asymmetric information and that all assets including business projects are fairly priced and therefore zero-NPV.

All things remaining equal, which of the following statements is NOT correct?

(a) BigDiv is expected to have a lower capital return than ZeroDiv in the future.

(b) BigDiv is expected to have a lower total return than ZeroDiv in the future.

(c) ZeroDiv's assets are likely to grow faster than BigDiv's.

(d) ZeroDiv's share price will increase faster than BigDiv's.

(e) BigDiv currently has a higher payout ratio than ZeroDiv.

Question 465  NPV, perpetuity

The boss of WorkingForTheManCorp has a wicked (and unethical) idea. He plans to pay his poor workers one week late so that he can get more interest on his cash in the bank.

Every week he is supposed to pay his 1,000 employees $1,000 each. So $1 million is paid to employees every week.

The boss was just about to pay his employees today, until he thought of this idea so he will actually pay them one week (7 days) later for the work they did last week and every week in the future, forever.

Bank interest rates are 10% pa, given as a real effective annual rate. So ##r_\text{eff annual, real} = 0.1## and the real effective weekly rate is therefore ##r_\text{eff weekly, real} = (1+0.1)^{1/52}-1 = 0.001834569##

All rates and cash flows are real, the inflation rate is 3% pa and there are 52 weeks per year. The boss will always pay wages one week late. The business will operate forever with constant real wages and the same number of employees.

What is the net present value (NPV) of the boss's decision to pay later?

(a) $261.16

(b) $1,919.39

(c) $13,580.21

(d) $18,295.38

(e) $1,000,000.00

Question 347  PE ratio, Multiples valuation

Which of the following investable assets are NOT suitable for valuation using PE multiples techniques?

(a) Common equity in small private companies.

(b) Common equity in large private companies.

(c) Common equity in listed public companies.

(d) Fixed term bonds of listed public companies.

(e) Real estate.

Question 357  PE ratio, Multiples valuation

Which of the following investable assets are NOT suitable for valuation using PE multiples techniques?

(a) Common equity in a listed public mining extraction company that will cease operations, wind up, and return all capital to shareholders in one year when its sole gold mine becomes depleted.

(b) Common equity in a small private owner-operated mining services company whose main asset is its sole tanker truck which delivers fuel to mines. The firm's shares are 100% owned by Bob, the driver of the tanker truck.

(c) Common equity in a large listed public company in the banking industry.

(d) Residential apartment real estate.

(e) Commercial warehouse real estate.

Question 364  PE ratio, Multiples valuation

Which firms tend to have high forward-looking price-earnings (PE) ratios?

(a) Illiquid small private companies.

(b) Exchange-listed companies operating in stagnant industries with negative growth prospects.

(c) Exchange-listed companies expected to have temporarily high earnings over the next year, but with lower earnings later.

(d) Exchange-listed companies operating in high-risk industries with very high required returns on equity.

(e) Exchange-listed companies whose assets include a very large proportion of cash.

Question 463  PE ratio, Multiples valuation

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

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

Assume that:

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

(a) 300%.

(b) 200%

(c) 33.33%

(d) 30%

(e) 20%

Question 195  equivalent annual cash flow

An industrial chicken farmer grows chickens for their meat. Chickens:

1. Cost $0.50 each to buy as chicks. They are bought on the day they’re born, at t=0.
2. Grow at a rate of $0.70 worth of meat per chicken per week for the first 6 weeks (t=0 to t=6).
3. Grow at a rate of $0.40 worth of meat per chicken per week for the next 4 weeks (t=6 to t=10) since they’re older and grow more slowly.
4. Feed costs are $0.30 per chicken per week for their whole life. Chicken feed is bought and fed to the chickens once per week at the beginning of the week. So the first amount of feed bought for a chicken at t=0 costs $0.30, and so on.
5. Can be slaughtered (killed for their meat) and sold at no cost at the end of the week. The price received for the chicken is their total value of meat (note that the chicken grows fast then slow, see above).

The required return of the chicken farm is 0.5% given as an effective weekly rate.

Ignore taxes and the fixed costs of the factory. Ignore the chicken’s welfare and other environmental and ethical concerns.

Find the equivalent weekly cash flow of slaughtering a chicken at 6 weeks and at 10 weeks so the farmer can figure out the best time to slaughter his chickens. The choices below are given in the same order, 6 and 10 weeks.

(a) $0.3651, $0.2374

(b) $0.3172, $0.3506

(c) $0.3065, $0.2157

(d) $0.3050, $0.2142

(e) $0.0157, $0.0491

Question 299  equivalent annual cash flow

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

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

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

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

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

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

(a) $13,848.99

(b) $13,106.61

(c) $8,547.50

(d) $4,238.08

(e) -$103.85

Question 249  equivalent annual cash flow, effective rate conversion

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

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

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

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

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

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

(a) -$332.8709, -$68.2065

(b) -$327.595, -$62.9476

(c) -$828.9808, -$808.5709

(d) -$829.6304, -$810.2613

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

Question 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 462  equivalent annual cash flow

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

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

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

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

(a) $164.6662

(b) $181.1328

(c) $199.2461

(d) $226.2443

(e) $301.1312

Question 234  debt terminology

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

(a) Discount loan

(b) Par loan

(c) Premium loan

(d) Deferred repayment loan

(e) Fully amortising loan.

Question 330  APR, effective rate, debt terminology

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

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

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

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

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

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

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

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

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

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

(a) 0.3086%

(b) 0.6171%

(c) 0.6181%

(d) 0.6239%

(e) 0.6300%

Question 64  inflation, real and nominal returns and cash flows, APR, effective rate

In Germany, nominal yields on semi-annual coupon paying Government Bonds with 2 years until maturity are currently 0.04% pa.

The inflation rate is currently 1.4% 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) -1.3529627%

(b) -0.4977348%

(c) 0.4977348%

(d) 1.3529627%

(e) 1.3621776%

Question 187  fully amortising loan, APR

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

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

(a) 169,672.58,     90,724.32

(b) 166,791.61,     90,073.45

(c) 166,791.61,     139,580.77

(d) 165,177.97,     88,321.04

(e) 165,177.97,     137,639.05

Question 304  option

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

(a) Shares (ordinary and preference stocks).

(b) Real estate (land and buildings).

(c) Options (calls and puts).

(d) Human capital (education)

(e) Debt (bond and loan assets)

Question 57  interest only loan

You just borrowed $400,000 in the form of a 25 year interest-only mortgage with monthly payments of $3,000 per month. The interest rate is 9% pa which is not expected to change.

You actually plan to pay more than the required interest payment. You plan to pay $3,300 in mortgage payments every month, which your mortgage lender allows. These extra payments will reduce the principal and the minimum interest payment required each month.

At the maturity of the mortgage, what will be the principal? That is, after the last (300th) interest payment of $3,300 in 25 years, how much will be owing on the mortgage?

(a) $6,766.6469

(b) $35,748.4866

(c) $63,663.4188

(d) $90,000.0000

(e) Nothing, the mortgage will be fully paid off prior to maturity.

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

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

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

(a) Approximately 6%.

(b) Approximately 4%.

(c) Approximately 2%.

(d) Approximately 0%.

(e) Approximately -2%.

Question 509  bond pricing

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

(a) $114.8775

(b) $114.7202

(c) $86.5798

(d) $86.4097

(e) $40.2605

Question 33  bond pricing, premium par and discount bonds

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

Which bond would have the higher current price?

(a) Bond A will have a higher price.

(b) Bond B will have a higher price.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Question 63  bond pricing, NPV, market efficiency

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

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

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

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

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

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

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

Question 153  bond pricing, premium par and discount bonds

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

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

(a) Bonds X and Y are premium bonds.

(b) Bonds X and Y are discount bonds.

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

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

(e) Bonds X and Y have the same price.

Question 207  income and capital returns, bond pricing, coupon rate, no explanation

For a bond that pays fixed semi-annual coupons, how is the annual coupon rate defined, and how is the bond's annual income yield from time 0 to 1 defined mathematically?

Let: ##P_0## be the bond price now,

##F_T## be the bond's face value,

##T## be the bond's maturity in years,

##r_\text{total}## be the bond's total yield,

##r_\text{income}## be the bond's income yield,

##r_\text{capital}## be the bond's capital yield, and

##C_t## be the bond's coupon at time t in years. So ##C_{0.5}## is the coupon in 6 months, ##C_1## is the coupon in 1 year, and so on.

(a) coupon rate = ##\dfrac{C_{0.5}+C_{1}}{F_T}##, ##r_\text{income, 0 to 1}=\dfrac{C_{0.5}(1+r_\text{total})^{0.5}+C_{1}}{P_0}##

(b) coupon rate = ##\dfrac{2 \times C_{0.5}}{F_T}##, ##r_\text{income, 0 to 1}=\dfrac{C_{0.5}(1+r_\text{capital})^{0.5}+C_{1}}{P_0}##

(c) coupon rate = ##\dfrac{2 \times C_{1}}{P_0}##, ##r_\text{income, 0 to 1}=\dfrac{C_{0.5}+C_{1}}{P_0}##

(d) coupon rate = ##\dfrac{2 \times C_{1}}{P_0}##, ##r_\text{income, 0 to 1}=\dfrac{2 \times C_{1}}{P_0}##

(e) coupon rate = ##\dfrac{2 \times C_{1}}{F_T}##, ##r_\text{income, 0 to 1}=\dfrac{C_{0.5}(1+r_\text{total})^{0.5}+C_{1}}{F_T}##

Question 213  income and capital returns, bond pricing, premium par and discount bonds

The coupon rate of a fixed annual-coupon bond is constant (always the same).

What can you say about the income return (##r_\text{income}##) of a fixed annual coupon bond? Remember that:

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

###r_\text{total, 0 to 1} = \frac{c_1}{p_0} + \frac{p_1-p_0}{p_0}###

Assume that there is no change in the bond's total annual yield to maturity from when it is issued to when it matures.

Select the most correct statement.

From its date of issue until maturity, the income return of a fixed annual coupon:

(a) Premium bond will increase.

(b) Premium bond will decrease.

(c) Premium bond will remain constant.

(d) Par bond will increase.

(e) Par bond will decrease.

Question 229  bond pricing

An investor bought two fixed-coupon bonds issued by the same company, a zero-coupon bond and a 7% pa semi-annual coupon bond. Both bonds have a face value of $1,000, mature in 10 years, and had a yield at the time of purchase of 8% pa.

A few years later, yields fell to 6% pa. Which of the following statements is correct? Note that a capital gain is an increase in price.

(a) The zero-coupon bond and the 7% semi-annual coupon bond were both discount bonds but now they are both premium bonds.

(b) The zero-coupon bond and the 7% semi-annual coupon bond were both premium bonds but now they are both discount bonds.

(c) When yields fell, the investor made a capital loss on both bonds.

(d) When yields fell, the investor made a capital gain on both bonds.

(e) When yields fell, the investor made a capital gain on the zero coupon bond but a loss on the 7% semi-annual coupon bond.

Question 255  bond pricing

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

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

(a) 94.20452353

(b) 100

(c) 106

(d) 112

(e) The bond is priceless.

Question 366  opportunity cost, NPV, CFFA

Your friend is trying to find the net present value of an investment which:

• Costs $1 million initially (t=0); and
• Pays a single positive cash flow of $1.1 million in one year (t=1).

The investment has a total required return of 10% pa due to its moderate level of undiversifiable risk.

Your friend is aware of the importance of opportunity costs and the time value of money, but he is unsure of how to find the NPV of the project.

He knows that the opportunity cost of investing the $1m in the project is the expected gain from investing the money in shares instead. Like the project, shares also have an expected return of 10% since they have moderate undiversifiable risk. This opportunity cost is $0.1m ##(=1m \times 10\%)## which occurs in one year (t=1).

He knows that the time value of money should be accounted for, and this can be done by finding the present value of the cash flows in one year.

Your friend has listed a few different ways to find the NPV which are written down below.

Method 1: ##-1m + \dfrac{1.1m}{(1+0.1)^1} ##

Method 2: ##-1m + 1.1m - 1m \times 0.1 ##

Method 3: ##-1m + \dfrac{1.1m}{(1+0.1)^1} - 1m \times 0.1 ##

Which of the above calculations give the correct NPV? Select the most correct answer.

(a) Method 1 only.

(b) Method 2 only.

(c) Method 3 only.

(d) Methods 1 and 2 only.

(e) Methods 1 and 3 only.

Question 485  capital budgeting, opportunity cost, sunk cost

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

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

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

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

(a) A sunk cost.

(b) An opportunity cost.

(c) A negative side effect.

(d) A positive side effect.

(e) A depreciation expense.

Question 224  CFFA

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

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

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

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

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

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

Question 225  CFFA

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

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

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

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

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

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

Question 238  CFFA, leverage, interest tax shield

A company increases the proportion of debt funding it uses to finance its assets by issuing bonds and using the cash to repurchase stock, leaving assets unchanged.

Ignoring the costs of financial distress, which of the following statements is NOT correct:

(a) The company is increasing its debt-to-assets and debt-to-equity ratios. These are types of 'leverage' or 'gearing' ratios.

(b) The company will pay less tax to the government due to the benefit of interest tax shields.

(c) The company's net income, also known as earnings or net profit after tax, will fall.

(d) The company's expected levered firm free cash flow (FFCF or CFFA) will be higher due to tax shields.

(e) The company's expected levered equity free cash flow (EFCF) will not change.

Question 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 511  capital budgeting, CFFA

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

One Year Mining Project Data
Project life	1 year
Initial investment in building mine and equipment	$9m
Depreciation of mine and equipment over the year	$8m
Kilograms of gold mined at end of year	1,000
Sale price per kilogram	$0.05m
Variable cost per kilogram	$0.03m
Before-tax cost of closing mine at end of year	$4m
Tax rate	30%

Note 1: Due to the project, the firm also anticipates finding some rare diamonds which will give before-tax revenues of $1m at the end of the year.

Note 2: The land that will be mined actually has thermal springs and a family of koalas that could be sold to an eco-tourist resort for an after-tax amount of $3m right now. However, if the mine goes ahead then this natural beauty will be destroyed.

Note 3: The mining equipment will have a book value of $1m at the end of the year for tax purposes. However, the equipment is expected to fetch $2.5m when it is sold.

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

(a) -9,   15.65

(b) -9,   14.3

(c) -12,   16.8

(d) -12,   16.35

(e) -12,   14.3

Question 512  capital budgeting, CFFA

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

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

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

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

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

(a) -6,   12.25,   16.68

(b) -6.8,   13.25,   14.05

(c) -6.8,   13.25,   15.88

(d) -6.8,   13.25,   18.51

(e) -6.8,   13.25,   17.71

Question 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 68  WACC, CFFA, capital budgeting

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

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

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

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

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

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

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

Question 367  CFFA, interest tax shield

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

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

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

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

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

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

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

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

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

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

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

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

Assume that:

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

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

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

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

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

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

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

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

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

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

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

Assume that:

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

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

(a) $13.19m

(b) $12.36m

(c) $11.77m

(d) $11.53m

(e) $11.20m

Question 490  expected and historical returns, accounting ratio

Which of the following is NOT a synonym of 'required return'?

(a) total required yield

(b) cost of capital

(c) discount rate

(d) opportunity cost of capital

(e) accounting rate of return

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 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 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 561  covariance, correlation

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

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

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

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

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

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

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

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

Question 306  risk, standard deviation

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

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

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

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

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

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

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

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

Question 93  correlation, CAPM, systematic risk

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

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

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

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

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

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

Question 673  CAPM, beta, expected and historical returns

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

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

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

(a) -12.5%

(b) -4%

(c) -1.5%

(d) -1%

(e) 12.5%

Question 674  CAPM, beta, expected and historical returns

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

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

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

(a) -12.5% pa

(b) -4% pa

(c) -1.5% pa

(d) -1% pa

(e) 12.5% pa

Question 116  capital structure, CAPM

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

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

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

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

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

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

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

Question 114  WACC, capital structure, risk

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

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

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

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

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

(e) none of the above.

Question 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 119  market efficiency, fundamental analysis, joint hypothesis problem

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

(i) Weak form market efficiency is broken.

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

(iii) Strong form market efficiency is broken.

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

Select the most correct response:

(a) Only (iii) is true.

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

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

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

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

Question 338  market efficiency, CAPM, opportunity cost, technical analysis

A man inherits $500,000 worth of shares.

He believes that by learning the secrets of trading, keeping up with the financial news and doing complex trend analysis with charts that he can quit his job and become a self-employed day trader in the equities markets.

What is the expected gain from doing this over the first year? Measure the net gain in wealth received at the end of this first year due to the decision to become a day trader. Assume the following:

• He earns $60,000 pa in his current job, paid in a lump sum at the end of each year.
• He enjoys examining share price graphs and day trading just as much as he enjoys his current job.
• Stock markets are weak form and semi-strong form efficient.
• He has no inside information.
• He makes 1 trade every day and there are 250 trading days in the year. Trading costs are $20 per trade. His broker invoices him for the trading costs at the end of the year.
• The shares that he currently owns and the shares that he intends to trade have the same level of systematic risk as the market portfolio.
• The market portfolio's expected return is 10% pa.

Measure the net gain over the first year as an expected wealth increase at the end of the year.

(a) $110,000

(b) $50,000

(c) $45,000

(d) -$15,000

(e) -$65,000

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

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

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

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

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

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

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

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

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

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

Question 417  NPV, market efficiency, DDM

A managed fund charges fees based on the amount of money that you keep with them. The fee is 2% of the end-of-year amount, paid at the end of every year.

This fee is charged regardless of whether the fund makes gains or losses on your money.

The fund offers to invest your money in shares which have an expected return of 10% pa before fees.

You are thinking of investing $100,000 in the fund and keeping it there for 40 years when you plan to retire.

How much money do you expect to have in the fund in 40 years? Also, what is the future value of the fees that the fund expects to earn from you? Give both amounts as future values in 40 years. Assume that:

• The fund has no private information.
• Markets are weak and semi-strong form efficient.
• The fund's transaction costs are negligible.
• The cost and trouble of investing your money in shares by yourself, without the managed fund, is negligible.
• The fund invests its fees in the same companies as it invests your funds in, but with no fees.

The below answer choices list your expected wealth in 40 years and then the fund's expected wealth in 40 years.

(a) $4,462,125.27, $63,800.29

(b) $3,407,788.62, $1,118,136.94

(c) $3,316,736.53, $1,209,189.03

(d) $2,172,452.15, $2,353,473.41

(e) $2,017,206.85, $2,508,718.71

Question 464  mispriced asset, NPV, DDM, market efficiency

A company advertises an investment costing $1,000 which they say is underpriced. They say that it has an expected total return of 15% pa, but a required return of only 10% pa. Assume that there are no dividend payments so the entire 15% total return is all capital return.

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

In both cases, assume that the required return of 10% remains constant. All returns are given as effective annual rates.

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

(a)             $0,          $0

(b) $1,977.19,   $2,000

(c) $2,977.19,   $3,000

(d)    $499.96,      $500

(e) $84,214.9,   Infinite

Question 621  market efficiency, technical analysis

Technical traders:

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

(b) Believe that markets are weak form efficient

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

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

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

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

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

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

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

(a) $7,359.46, Infinite

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

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

(d) $1,471.89, $830.28

(e) $830.28, $3,000

Question 309  stock pricing, ex dividend date

A company announces that it will pay a dividend, as the market expected. The company's shares trade on the stock exchange which is open from 10am in the morning to 4pm in the afternoon each weekday. When would the share price be expected to fall by the amount of the dividend? Ignore taxes.

The share price is expected to fall during the:

(a) Day of the payment date, between the payment date's morning opening price and afternoon closing price.

(b) Night before the payment date, between the previous day's afternoon closing price and the payment date's morning opening price.

(c) Day of the ex-dividend date, between the ex-dividend date's morning opening price and afternoon closing price.

(d) Night before the ex-dividend date, between the last with-dividend date's afternoon closing price and the ex-dividend date's morning opening price.

(e) Day of the last with-dividend date, between the with-dividend date's morning opening price and afternoon closing price.

Question 202  DDM, payout policy

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

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

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

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

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

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

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

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

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

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

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

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

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

(a) 2.7% pa.

(b) 3.0% pa.

(c) 3.5% pa.

(d) 3.3% pa.

(e) 3.8% pa.

Question 630  mispriced asset, NPV, DDM, market efficiency

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

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

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

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

(a) 84,214.90,   Infinite

(b)  2,521.12,   3,000

(c)  2,100.93,   2,500

(d)  1,249.38,   1,333.33

(e)          0,               0

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 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 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 117  WACC

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

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

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

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

(a) 9.47%

(b) 8.93%

(c) 8.53%

(d) 7.80%

(e) 7.07%

Question 772  interest tax shield, capital structure, leverage

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

(a) Higher debt leads to higher interest expense.

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

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

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

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

Question 282  expected and historical returns, income and capital returns

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

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

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

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

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

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

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

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

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

Question 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 607  debt terminology

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

Question 608  debt terminology

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

Question 541  debt terminology

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

(a) Buy debt.

(b) Are debtors.

(c) Have debt assets.

(d) Provide debt funding.

(e) Are lenders.

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

A European company just issued two bonds, a

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

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

(a) 0.0374

(b) 0.0604

(c) 0.1204

(d) 0.1250

(e) 0.1411

Question 204  time calculation, fully amortising loan, APR

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

To your surprise, you can actually afford to pay $2,000 per month and your mortgage allows early repayments without fees. If you maintain these higher monthly payments, how long will it take to pay off your mortgage?

(a) 38.87 months, which is 3.24 yrs.

(b) 47.91 months, which is 3.99 yrs.

(c) 160.72 months, which is 13.39 yrs.

(d) 164.65 months, which is 13.72 yrs.

(e) None of the above.

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 709  continuously compounding rate, APR

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

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

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

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

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

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

Question 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 716  return distribution

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

Which of the below statements is NOT correct?

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

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

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

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

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

Question 721  mean and median returns, return distribution, arithmetic and geometric averages, continuously compounding rate

Fred owns some Commonwealth Bank (CBA) shares. He has calculated CBA’s monthly returns for each month in the past 20 years using this formula:

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

He then took the arithmetic average and found it to be 1% per month using this formula:

###\bar{r}_\text{monthly}= \dfrac{ \displaystyle\sum\limits_{t=1}^T{\left( r_\text{t monthly} \right)} }{T} =0.01=1\% \text{ per month}###

He also found the standard deviation of these monthly returns which was 5% per month:

###\sigma_\text{monthly} = \dfrac{ \displaystyle\sum\limits_{t=1}^T{\left( \left( r_\text{t monthly} - \bar{r}_\text{monthly} \right)^2 \right)} }{T} =0.05=5\%\text{ per month}###

Which of the below statements about Fred’s CBA shares is NOT correct? Assume that the past historical average return is the true population average of future expected returns.

(a) The returns ##r_\text{t monthly}## are continuously compounded monthly returns and are likely to be normally distributed, so the mean, median and mode of these continuously compounded returns are all equal to 1% per month.

(b) The annualised average continuously compounded return is ##\bar{r}_\text{cc annual}=12×0.01=0.1=12\%\text{ pa}##. The annualised standard deviation is ##\sigma_\text{annual} = \sqrt{12}×0.05=0.173205081=17.32\%\text{ pa}##.

(c) Over the next 10 years the mean, median and mode continuously compounded 10 year returns will all equal ##0.01 \times 12 \times 10 = 120\%##.

(d) Over the next 10 years the expected mean gross discrete 10 year return is ##e^{(0.01 - 0.05^2/2)×12×10} = 2.857651118## and the median gross discrete 10 year return is ##e^{(0.01 + 0.05^2/2)×12×10}=3.857425531##.

(e) If the current price of the CBA shares is $75, then in 10 years they’re expected to have a mean value of ##75×e^{(0.01 + 0.05^2/2)×12×10} = 289.3069148## and a median value of ##75×e^{0.01×12×10}=249.0087692##.

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

Question 321  foreign exchange rate, monetary policy, American and European terms

The market expects the Reserve Bank of Australia (RBA) to increase the policy rate by 25 basis points at their next meeting.

Then unexpectedly, the RBA announce that they will increase the policy rate by 50 basis points due to high future GDP and inflation forecasts.

What do you expect to happen to Australia's exchange rate in the short term? The Australian dollar will:

(a) Appreciate against the USD, so the 'American terms' quote of the AUD (USD per AUD) will increase.

(b) Depreciate against the USD, so the 'American terms' quote of the AUD (USD per AUD) will decrease.

(c) Appreciate against the USD, so the 'American terms' quote of the AUD (USD per AUD) will decrease.

(d) Depreciate against the USD, so the 'American terms' quote of the AUD (USD per AUD) will increase.

(e) Be unaffected by the change in the policy rate, so the exchange rate will remain the same.

Question 324  foreign exchange rate

The Chinese government attempts to fix its exchange rate against the US dollar and at the same time use monetary policy to fix its interest rate at a set level.

To be able to fix its exchange rate and interest rate in this way, what does the Chinese government actually do?

1. Adopts capital controls to prevent financial arbitrage by private firms and individuals.
2. Adopts the same interest rate (monetary policy) as the United States.
3. Fixes inflation so that the domestic real interest rate is equal to the United States' real interest rate.

Which of the above statements is or are true?

(a) I only.

(b) II only.

(c) III only.

(d) I and II.

(e) II and III.

Question 606  foreign exchange rate, American and European terms

Which of the following FX quotes (current in October 2015) is given in American terms?

(a) 1.55 USD per GBP

(b) 120.61 JPY per USD

(c) 6.32 RMB per USD

(d) 1 USD = 1.31 CAD

(e) 0.99 CHF = 1 USD

Question 318  foreign exchange rate, American and European terms

How is the AUD normally quoted in Australia? Using or terms?

Question 570  foreign exchange rate

An American wishes to convert USD 1 million to Australian dollars (AUD). The exchange rate is 0.8 USD per AUD. How much is the USD 1 million worth in AUD?

(a) AUD 0.2 million.

(b) AUD 0.8 million

(c) AUD 1 million

(d) AUD 1.25 million.

(e) AUD 1.8 million.

Question 603  foreign exchange rate, American and European terms

Vietnamese people usually quote the Vietnamese Dong in VND per 1 USD. For example, in October 2015 the Vietnamese Dong was 22,300 VND per USD. Is this an or terms quote?

Question 316  foreign exchange rate, American and European terms

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

Question 320  foreign exchange rate, monetary policy, American and European terms

Investors expect the Reserve Bank of Australia (RBA) to decrease the overnight cash rate at their next meeting.

Then unexpectedly, the RBA announce that they will keep the policy rate unchanged.

What do you expect to happen to Australia's exchange rate in the short term? The Australian dollar is likely to:

(a) Appreciate against the USD, so the 'European terms' quote of the AUD (AUD per USD) will increase.

(b) Depreciate against the USD, so the 'European terms' quote of the AUD (AUD per USD) will decrease.

(c) Appreciate against the USD, so the 'European terms' quote of the AUD (AUD per USD) will decrease.

(d) Depreciate against the USD, so the 'European terms' quote of the AUD (AUD per USD) will increase.

(e) Be unaffected by the change in the policy rate, so the exchange rate will remain the same.

Question 325  foreign exchange rate

In the 1997 Asian financial crisis many countries' exchange rates depreciated rapidly against the US dollar (USD). The Thai, Indonesian, Malaysian, Korean and Filipino currencies were severely affected. The below graph shows these Asian countries' currencies in USD per one unit of their currency, indexed to 100 in June 1997.

Of the statements below, which is NOT correct? The Asian countries':

(a) Exports denominated in domestic currency became cheaper to foreigners.

(b) Imports denominated in domestic currency became more expensive.

(c) Citizens would have to pay more in their own currency when holidaying in the US.

(d) USD interest payments on USD fixed-interest bonds became more expensive in their own currency.

(e) Domestic currency interest payments on fixed-interest bonds denominated in domestic currency became cheaper in their own currency.

Question 717  return distribution

The below three graphs show probability density functions (PDF) of three different random variables Red, Green and Blue. Let ##P_1## be the unknown price of a stock in one year. ##P_1## is a random variable. Let ##P_0 = 1##, so the share price now is $1. This one dollar is a constant, it is not a variable.

Which of the below statements is NOT correct? Financial practitioners commonly assume that the shape of the PDF represented in the colour:

(a) Green is a stock's continuously compounded rate of return, also called the log gross discrete return. ##r_\text{cc} = \ln(P_1/P_0)##

(b) Blue is a stock's future price, ##P_1##

(c) Blue is a stock's gross discrete return. ##\text{GDR} = P_1/P_0##

(d) Blue is a stock's effective rate of return. ##r_\text{eff} = (P_1-P_0)/P_0##

(e) Red is a stock's net discrete return. ##\text{NDR} = \text{GDR}-1##

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

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

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

 

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Question 661  systematic and idiosyncratic risk, CAPM

A stock's total standard deviation of returns is 20% pa. The market portfolio's total standard deviation of returns is 15% pa. The beta of the stock is 0.8.

What is the stock's diversifiable standard deviation?

(a) 16% pa

(b) 12% pa

(c) 8% pa

(d) 5% pa

(e) 4% pa