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Question 991  NPV

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

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

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

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

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



Question 251  NPV

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

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

How much can you consume at each time?



Question 252  NPV

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

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

How much can you consume at each time?



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.



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.



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

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



Question 278  inflation, real and nominal returns and cash flows

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

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


Question 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?



Question 444  investment decision, corporate financial decision theory

The investment decision primarily affects which part of a business?



Question 221  credit risk

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

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



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

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



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?



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.



Question 499  NPV, Annuity

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

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

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



Question 519  DDM

A stock is just about to pay a dividend of $1 tonight. Future annual dividends are expected to grow by 2% pa. The next dividend of $1 will be paid tonight, and the year after that the dividend will be $1.02 (=1*(1+0.02)^1), and a year later 1.0404 (=1*(1+0.04)^2) and so on forever.

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

Calculate the current stock price.



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 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?



Question 441  DDM, income and capital returns

A fairly valued share's current price is $4 and it has a total required return of 30%. Dividends are paid annually and next year's dividend is expected to be $1. After that, dividends are expected to grow by 5% pa in perpetuity. All rates are effective annual returns.

What is the expected dividend income paid at the end of the second year (t=2) and what is the expected capital gain from just after the first dividend (t=1) to just after the second dividend (t=2)? The answers are given in the same order, the dividend and then the capital gain.



Question 50  DDM, stock pricing, inflation, real and nominal returns and cash flows

Most listed Australian companies pay dividends twice per year, the 'interim' and 'final' dividends, which are roughly 6 months apart.

You are an equities analyst trying to value the company BHP. You decide to use the Dividend Discount Model (DDM) as a starting point, so you study BHP's dividend history and you find that BHP tends to pay the same interim and final dividend each year, and that both grow by the same rate.

You expect BHP will pay a $0.55 interim dividend in six months and a $0.55 final dividend in one year. You expect each to grow by 4% next year and forever, so the interim and final dividends next year will be $0.572 each, and so on in perpetuity.

Assume BHP's cost of equity is 8% pa. All rates are quoted as nominal effective rates. The dividends are nominal cash flows and the inflation rate is 2.5% pa.

What is the current price of a BHP share?



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

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

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

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

Calculate the current TLS share price.



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?



Question 280  equivalent annual cash flow

You own a nice suit which you wear once per week on nights out. You bought it one year ago for $600. In your experience, suits used once per week last for 6 years. So you expect yours to last for another 5 years.

Your younger brother said that retro is back in style so he wants to wants to borrow your suit once a week when he goes out. With the increased use, your suit will only last for another 4 years rather than 5.

What is the present value of the cost of letting your brother use your current suit for the next 4 years?

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



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.



Question 130  debt terminology

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


Question 234  debt terminology

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



Question 265  APR, Annuity

On his 20th birthday, a man makes a resolution. He will deposit $30 into a bank account at the end of every month starting from now, which is the start of the month. So the first payment will be in one month. He will write in his will that when he dies the money in the account should be given to charity.

The bank account pays interest at 6% pa compounding monthly, which is not expected to change.

If the man lives for another 60 years, how much money will be in the bank account if he dies just after making his last (720th) payment?



Question 583  APR, effective rate, effective rate conversion

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



Question 141  time calculation, APR, effective rate

You're trying to save enough money to buy your first car which costs $2,500. You can save $100 at the end of each month starting from now. You currently have no money at all. You just opened a bank account with an interest rate of 6% pa payable monthly.

How many months will it take to save enough money to buy the car? Assume that the price of the car will stay the same over time.



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?



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?



Question 300  NPV, opportunity cost

What is the net present value (NPV) of undertaking a full-time Australian undergraduate business degree as an Australian citizen? Only include the cash flows over the duration of the degree, ignore any benefits or costs of the degree after it's completed.

Assume the following:

  • The degree takes 3 years to complete and all students pass all subjects.
  • There are 2 semesters per year and 4 subjects per semester.
  • University fees per subject per semester are $1,277, paid at the start of each semester. Fees are expected to remain constant in real terms for the next 3 years.
  • There are 52 weeks per year.
  • The first semester is just about to start (t=0). The first semester lasts for 19 weeks (t=0 to 19).
  • The second semester starts immediately afterwards (t=19) and lasts for another 19 weeks (t=19 to 38).
  • The summer holidays begin after the second semester ends and last for 14 weeks (t=38 to 52). Then the first semester begins the next year, and so on.
  • Working full time at the grocery store instead of studying full-time pays $20/hr and you can work 35 hours per week. Wages are paid at the end of each week and are expected to remain constant in real terms.
  • Full-time students can work full-time during the summer holiday at the grocery store for the same rate of $20/hr for 35 hours per week.
  • The discount rate is 9.8% pa. All rates and cash flows are real. Inflation is expected to be 3% pa. All rates are effective annual.

The NPV of costs from undertaking the university degree is:



Question 350  CFFA

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

Sidebar Corp
Income Statement for
year ending 30th June 2013
  $m
Sales 405
COGS 100
Depreciation 34
Rent expense 22
Interest expense 39
Taxable Income 210
Taxes at 30% 63
Net income 147
 
Sidebar Corp
Balance Sheet
as at 30th June 2013 2012
  $m $m
Cash 0 0
Inventory 70 50
Trade debtors 11 16
Rent paid in advance 4 3
PPE 700 680
Total assets 785 749
 
Trade creditors 11 19
Bond liabilities 400 390
Contributed equity 220 220
Retained profits 154 120
Total L and OE 785 749
 

 

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

The cash flow from assets was:



Question 273  CFFA, capital budgeting

Value the following business project to manufacture a new product.

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

Notes

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

Assumptions

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

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



Question 507  leverage, accounting ratio

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



Question 406  leverage, WACC, margin loan, portfolio return

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

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

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

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

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


Question 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.



Question 113  WACC, CFFA, capital budgeting

The US firm Google operates in the online advertising business. In 2011 Google bought Motorola Mobility which manufactures mobile phones.

Assume the following:

  • Google had a 10% after-tax weighted average cost of capital (WACC) before it bought Motorola.
  • Motorola had a 20% after-tax WACC before it merged with Google.
  • Google and Motorola have the same level of gearing.
  • Both companies operate in a classical tax system.

You are a manager at Motorola. You must value a project for making mobile phones. Which method(s) will give the correct valuation of the mobile phone manufacturing project? Select the most correct answer.

The mobile phone manufacturing project's:



Question 371  interest tax shield, CFFA

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

###\begin{aligned} FFCF &= (Rev - COGS - Depr - FC - IntExp)(1-t_c) + Depr - CapEx -\Delta NWC + IntExp \\ &= (Rev - COGS - Depr - FC - 0)(1-t_c) + Depr - CapEx -\Delta NWC - 0\\ \end{aligned}###
Does this annual FFCF with zero interest expense or the annual interest tax shield?


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

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

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



Question 616  idiom, debt terminology, bond pricing

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

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



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?



Question 620  bond pricing, income and capital returns

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



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.



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?



Question 254  time calculation, APR

Your main expense is fuel for your car which costs $100 per month. You just refueled, so you won't need any more fuel for another month (first payment at t=1 month).

You have $2,500 in a bank account which pays interest at a rate of 6% pa, payable monthly. Interest rates are not expected to change.

Assuming that you have no income, in how many months time will you not have enough money to fully refuel your car?



Question 32  time calculation, APR

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



Question 765  bond pricing, no explanation

An investor bought a 5 year government bond with a 2% pa coupon rate at par. Coupons are paid semi-annually. The face value is $100.

Calculate the bond's new price 8 months later after yields have increased to 3% pa. Note that both yields are given as APR's compounding semi-annually. Assume that the yield curve was flat before the change in yields, and remained flat afterwards as well.



Question 804  CFFA, WACC, interest tax shield, DDM

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

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

 

Which of the following statements is NOT correct?



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?



Question 111  portfolio risk, correlation

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



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.



Question 307  risk, variance

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

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

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



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?

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


Question 556  portfolio risk, portfolio return, standard deviation

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

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

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

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



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?



Question 628  CAPM, SML, risk

Image of CML SML graph

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



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?



Question 410  CAPM, capital budgeting

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

###r_i=r_f+β_i (r_m-r_f)###

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



Question 418  capital budgeting, NPV, interest tax shield, WACC, CFFA, CAPM

Project Data
Project life 1 year
Initial investment in equipment $8m
Depreciation of equipment per year $8m
Expected sale price of equipment at end of project 0
Unit sales per year 4m
Sale price per unit $10
Variable cost per unit $5
Fixed costs per year, paid at the end of each year $2m
Interest expense in first year (at t=1) $0.562m
Corporate tax rate 30%
Government treasury bond yield 5%
Bank loan debt yield 9%
Market portfolio return 10%
Covariance of levered equity returns with market 0.32
Variance of market portfolio returns 0.16
Firm's and project's debt-to-equity ratio 50%
 

Notes

  1. Due to the project, current assets will increase by $6m now (t=0) and fall by $6m at the end (t=1). Current liabilities will not be affected.

Assumptions

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

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



Question 242  technical analysis, market efficiency

Select the most correct statement from the following.

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



Question 621  market efficiency, technical analysis

Technical traders:



Question 716  return distribution

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

PDF graph

Which of the below statements is NOT correct?



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:



Question 313  foreign exchange rate, American and European terms

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



Question 319  foreign exchange rate, monetary policy, American and European terms

Investors expect the Reserve Bank of Australia (RBA) to keep the policy rate steady at their next meeting.

Then unexpectedly, the RBA announce that they will increase the policy rate by 25 basis points due to fears that the economy is growing too fast and that inflation will be above their target rate of 2 to 3 per cent.

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



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?



Question 339  bond pricing, inflation, market efficiency, income and capital returns

Economic statistics released this morning were a surprise: they show a strong chance of consumer price inflation (CPI) reaching 5% pa over the next 2 years.

This is much higher than the previous forecast of 3% pa.

A vanilla fixed-coupon 2-year risk-free government bond was issued at par this morning, just before the economic news was released.

What is the expected change in bond price after the economic news this morning, and in the next 2 years? Assume that:

  • Inflation remains at 5% over the next 2 years.
  • Investors demand a constant real bond yield.
  • The bond price falls by the (after-tax) value of the coupon the night before the ex-coupon date, as in real life.



Question 623  market efficiency

The efficient markets hypothesis (EMH) and no-arbitrage pricing theory are most closely related to which of the following concepts?



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.



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):



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})##:


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 625  dividend re-investment plan, capital raising

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



Question 214  rights issue

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

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

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

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

  • 29/10/2003. Shares trade ex-rights.

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



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.



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:



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

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



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.



Question 609  debt terminology

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


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:



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.



Question 622  expected and historical returns, risk

An economy has only two investable assets: stocks and cash.

Stocks had a historical nominal average total return of negative two percent per annum (-2% pa) over the last 20 years. Stocks are liquid and actively traded. Stock returns are variable, they have risk.

Cash is riskless and has a nominal constant return of zero percent per annum (0% pa), which it had in the past and will have in the future. Cash can be kept safely at zero cost. Cash can be converted into shares and vice versa at zero cost.

The nominal total return of the shares over the next year is expected to be:



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##).



Question 390  real option, option

Some financially minded people insist on a prenuptial agreement before committing to marry their partner. This agreement states how the couple's assets should be divided in case they divorce. Prenuptial agreements are designed to give the richer partner more of the couples' assets if they divorce, thus maximising the richer partner's:



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: