Fight Finance

Courses  Tags  Random  All  Recent  Scores

Question 44  NPV

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

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

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



Question 126  IRR

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

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

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



Question 37  IRR

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



Question 60  pay back period

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

What is the payback period of the project in years?

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

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



Question 190  pay back period

A project has the following cash flows:

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

What is the payback period of the project in years?

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



Question 500  NPV, IRR

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

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

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



Question 489  NPV, IRR, pay back period, DDM

A firm is considering a business project which costs $11m now and is expected to pay a constant $1m at the end of every year forever.

Assume that the initial $11m 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?



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.

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 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?



Question 532  mutually exclusive projects, NPV, IRR

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

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

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

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

Which project should the investor accept?



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

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



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

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



Question 501  NPV, IRR, pay back period

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

Which of the following statements is NOT correct?



Question 478  income and capital returns

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



Question 477  income and capital returns

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

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

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

Which of the following is the expected capital return?



Question 151  income and capital returns

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

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

The choices are given in the same order:

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



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 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.



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

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

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

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



Question 577  inflation, real and nominal returns and cash flows

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



Question 554  inflation, real and nominal returns and cash flows

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

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

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

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



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 will give the highest returns?



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

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



Question 467  book and market values

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



Question 473  market capitalisation of equity

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

Image of CBA on Google finance on 7 Nov 2014

What was CBA's market capitalisation of equity?



Question 445  financing decision, corporate financial decision theory

The financing decision primarily affects which part of a business?



Question 444  investment decision, corporate financial decision theory

The investment decision primarily affects which part of a business?



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

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



Question 515  corporate financial decision theory, idiom

The expression 'you have to spend money to make money' relates to which business decision?



Question 466  limited liability

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



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?



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 Katya's deal?


Question 356  NPV, Annuity

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

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

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



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 479  perpetuity with growth, DDM, NPV

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

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



Question 517  DDM

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

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

Calculate the current stock price.



Question 518  DDM

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

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

Calculate the current stock price.



Question 4  DDM

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

Would you like to Carla's share or politely ?


Question 7  DDM

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

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

The required return of the stock is 15% pa.

Would you like to the share or politely ?


Question 152  NPV, Annuity

The following cash flows are expected:

  • 10 yearly payments of $80, with the first payment in 3 years from now (first payment at t=3).
  • 1 payment of $600 in 5 years and 6 months (t=5.5) from now.

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



Question 727  inflation, real and nominal returns and cash flows

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

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



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 729  book and market values, balance sheet, no explanation

If a firm makes a profit and pays no dividends, which of the following accounts will increase?



Question 730  DDM, income and capital returns, no explanation

A stock’s current price is $1. Its expected total return is 10% pa and its long term expected capital return is 4% pa. It pays an annual dividend and the next one will be paid in one year. All rates are given as effective annual rates. The dividend discount model is thought to be a suitable model for the stock. Ignore taxes. Which of the following statements about the stock is NOT correct?



Question 731  DDM, income and capital returns, no explanation

In the dividend discount model (DDM), share prices fall when dividends are paid. Let the high price before the fall be called the peak, and the low price after the fall be called the trough.

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

Which of the following statements about the DDM is NOT correct?



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 733  DDM, income and capital returns

A share’s current price is $60. It’s expected to pay a dividend of $1.50 in one year. The growth rate of the dividend is 0.5% pa and the stock’s required total return is 3% pa. The stock’s price can be modeled using the dividend discount model (DDM):

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

Which of the following methods is NOT equal to the stock’s expected price in one year and six months (t=1.5 years)? Note that the symbolic formulas shown in each line below do equal the formulas with numbers. The formula is just repeated with symbols and then numbers in case it helps you to identify the incorrect statement more quickly.



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 264  DDM

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

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

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

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



Question 503  DDM, NPV, stock pricing

A share currently worth $100 is expected to pay a constant dividend of $4 for the next 5 years with the first dividend in one year (t=1) and the last in 5 years (t=5).

The total required return is 10% pa.

What do you expected the share price to be in 5 years, just after the dividend at that time has been paid?



Question 28  DDM, income and capital returns

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

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

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



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, which one of the following statements is NOT correct? The long term expected:



Question 289  DDM, expected and historical returns, ROE

In the dividend discount model:

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

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



Question 36  DDM, perpetuity with growth

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



Question 40  DDM, perpetuity with growth

A stock is expected to pay the following dividends:

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

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

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

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

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



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 348  PE ratio, Multiples valuation

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

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

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



Question 341  Multiples valuation, PE ratio

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

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

Source: Google Finance 28 Feb 2014.



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

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

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

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

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



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 372  debt terminology

Which of the following statements is NOT correct? Borrowers:



Question 373  debt terminology

Which of the following statements is NOT correct? Lenders:



Question 581  APR, effective rate, effective rate conversion

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



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 16  credit card, APR, effective rate

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

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

All answers are given in the same order:

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



Question 131  APR, effective rate

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

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

All answers are given in the same order:

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



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 19  fully amortising loan, APR

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

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



Question 134  fully amortising loan, APR

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



Question 172  fully amortising loan, APR

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

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



Question 203  fully amortising loan, APR

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

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



Question 222  fully amortising loan, APR

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

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



Question 29  interest only loan

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

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



Question 107  interest only loan

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

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



Question 128  debt terminology, needs refinement

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


Question 129  debt terminology

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


Question 234  debt terminology

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



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.



Question 510  bond pricing

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



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 23  bond pricing, premium par and discount bonds

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

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



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?



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 133  bond pricing

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



Question 159  bond pricing

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



Question 178  bond pricing, premium par and discount bonds

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



Question 227  bond pricing, premium par and discount bonds

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



Question 257  bond pricing

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



Question 460  bond pricing, premium par and discount bonds

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

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



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

A European company just issued two bonds, a

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

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



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

An Australian company just issued two bonds:

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

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



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 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:



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
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 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).



Question 94  leverage, capital structure, real estate

Your friend just bought a house for $400,000. He financed it using a $320,000 mortgage loan and a deposit of $80,000.

In the context of residential housing and mortgages, the 'equity' tied up in the value of a person's house is the value of the house less the value of the mortgage. So the initial equity your friend has in his house is $80,000. Let this amount be E, let the value of the mortgage be D and the value of the house be V. So ##V=D+E##.

If house prices suddenly fall by 10%, what would be your friend's percentage change in equity (E)? Assume that the value of the mortgage is unchanged and that no income (rent) was received from the house during the short time over which house prices fell.

Remember:

### r_{0\rightarrow1}=\frac{p_1-p_0+c_1}{p_0} ###

where ##r_{0-1}## is the return (percentage change) of an asset with price ##p_0## initially, ##p_1## one period later, and paying a cash flow of ##c_1## at time ##t=1##.



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 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:



Question 506  leverage, accounting ratio

A firm has a debt-to-equity ratio of 25%. What is its debt-to-assets ratio?



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 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}###



Question 379  leverage, capital structure, payout policy

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


Question 301  leverage, capital structure, real estate

Your friend just bought a house for $1,000,000. He financed it using a $900,000 mortgage loan and a deposit of $100,000.

In the context of residential housing and mortgages, the 'equity' or 'net wealth' tied up in a house is the value of the house less the value of the mortgage loan. Assuming that your friend's only asset is his house, his net wealth is $100,000.

If house prices suddenly fall by 15%, what would be your friend's percentage change in net wealth?

Assume that:

  • No income (rent) was received from the house during the short time over which house prices fell.
  • Your friend will not declare bankruptcy, he will always pay off his debts.



Question 67  CFFA, interest tax shield

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

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

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

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

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



Question 296  CFFA, interest tax shield

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

Remember:

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



Question 507  leverage, accounting ratio

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



Question 89  WACC, CFFA, interest tax shield

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

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

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



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:



Question 368  interest tax shield, CFFA

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

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


Question 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 413  CFFA, interest tax shield, depreciation tax shield

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

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

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

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

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

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

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



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

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



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.



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?



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

Fill in the missing words in the following sentence:

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



Question 411  WACC, capital structure

A firm plans to issue equity and use the cash raised to pay off its debt. No assets will be bought or sold. Ignore the costs of financial distress.

Which of the following statements is NOT correct, all things remaining equal?



Question 137  NPV, Annuity

The following cash flows are expected:

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

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



Question 288  Annuity

There are many ways to write the ordinary annuity formula.

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



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:



Question 352  income and capital returns, DDM, real estate

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

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

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

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

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

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

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



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.



Question 505  equivalent annual cash flow

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

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

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

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



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.



Question 735  debt terminology

You deposit money into a bank. Which of the following statements is NOT correct? You:



Question 736  debt terminology

You bought a house, primarily funded using a home loan from a bank. Which of the following statements is NOT correct?



Question 737  financial statement, balance sheet, income statement

Where can a publicly listed firm's book value of equity be found? It can be sourced from the company's:



Question 739  real and nominal returns and cash flows, inflation

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



Question 741  APR, effective rate

A home loan company advertises an interest rate of 4.5% pa, payable monthly. Which of the following statements about the interest rate is NOT correct?



Question 743  price gains and returns over time, no explanation

How many years will it take for an asset's price to triple (increase from say $1 to $3) if it grows by 5% pa?



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 747  DDM, no explanation

A share will pay its next dividend of ##C_1## in one year, and will continue to pay a dividend every year after that forever, growing at a rate of ##g##. So the next dividend will be ##C_2=C_1 (1+g)^1##, then ##C_3=C_2 (1+g)^1##, and so on forever.

The current price of the share is ##P_0## and its required return is ##r##

Which of the following is NOT equal to the expected share price in 2 years ##(P_2)## just after the dividend at that time ##(C_2)## has been paid?



Question 748  income and capital returns, DDM, ex dividend date

A stock will pay you a dividend of $2 tonight if you buy it today.

Thereafter the annual dividend is expected to grow by 3% pa, so the next dividend after the $2 one tonight will be $2.06 in one year, then in two years it will be $2.1218 and so on. The stock's required return is 8% pa.

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



Question 750  PE ratio, Multiples valuation

Itau Unibanco is a major listed bank in Brazil with a market capitalisation of equity equal to BRL 85.744 billion, EPS of BRL 3.96 and 2.97 billion shares on issue.

Banco Bradesco is another major bank with total earnings of BRL 8.77 billion and 2.52 billion shares on issue.

Estimate Banco Bradesco's current share price using a price-earnings multiples approach assuming that Itau Unibanco is a comparable firm.

Note that BRL is the Brazilian Real, their currency. Figures sourced from Google Finance on the market close of the BVMF on 24/7/15.



Question 751  NPV, Annuity

Telsa Motors advertises that its Model S electric car saves $570 per month in fuel costs. Assume that Tesla cars last for 10 years, fuel and electricity costs remain the same, and savings are made at the end of each month with the first saving of $570 in one month from now.

The effective annual interest rate is 15.8%, and the effective monthly interest rate is 1.23%. What is the present value of the savings?



Question 753  NPV, perpetuity, DDM, no explanation

The following cash flows are expected:

  • A perpetuity of yearly payments of $30, with the first payment in 5 years (first payment at t=5, which continues every year after that forever).
  • One payment of $100 in 6 years and 3 months (t=6.25).

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



Question 754  fully amortising loan, interest only loan

How much more can you borrow using an interest-only loan compared to a 25-year fully amortising loan if interest rates are 4% pa compounding per month and are not expected to change? If it makes it easier, assume that you can afford to pay $2,000 per month on either loan. Express your answer as a proportional increase using the following formula:

###\text{Proportional Increase} = \dfrac{V_\text{0,interest only}}{V_\text{0,fully amortising}} - 1###



Question 755  bond pricing, capital raising, no explanation

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

How many bonds should the firm issue?



Question 756  bond pricing, capital raising, no explanation

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

How many bonds should the firm issue?



Question 757  bond pricing, capital raising, no explanation

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

How many bonds should the firm issue?



Question 758  time calculation, fully amortising loan, no explanation

Two years ago you entered into a fully amortising home loan with a principal of $1,000,000, an interest rate of 6% pa compounding monthly with a term of 25 years.

Then interest rates suddenly fall to 4.5% pa (t=0), but you continue to pay the same monthly home loan payments as you did before. How long will it now take to pay off your home loan? Measure the time taken to pay off the home loan from the current time which is 2 years after the home loan was first entered into.

Assume that the lower interest rate was given to you immediately after the loan repayment at the end of year 2, which was the 24th payment since the loan was granted. Also assume that rates were and are expected to remain constant.



Question 759  time calculation, fully amortising loan, no explanation

Five years ago you entered into a fully amortising home loan with a principal of $500,000, an interest rate of 4.5% pa compounding monthly with a term of 25 years.

Then interest rates suddenly fall to 3% pa (t=0), but you continue to pay the same monthly home loan payments as you did before. How long will it now take to pay off your home loan? Measure the time taken to pay off the home loan from the current time which is 5 years after the home loan was first entered into.

Assume that the lower interest rate was given to you immediately after the loan repayment at the end of year 5, which was the 60th payment since the loan was granted. Also assume that rates were and are expected to remain constant.



Question 760  time calculation, interest only loan, no explanation

Five years ago (##t=-5## years) you entered into an interest-only home loan with a principal of $500,000, an interest rate of 4.5% pa compounding monthly with a term of 25 years.

Then interest rates suddenly fall to 3% pa (##t=0##), but you continue to pay the same monthly home loan payments as you did before. Will your home loan be paid off by the end of its remaining term? If so, in how many years from now? Measure the time taken to pay off the home loan from the current time which is 5 years after the home loan was first entered into.

Assume that the lower interest rate was given to you immediately after the loan repayment at the end of year 5, which was the 60th payment since the loan was granted. Also assume that rates were and are expected to remain constant.



Question 762  equivalent annual cash flow, no explanation

Radio-Rentals.com offers the Apple iphone 5S smart phone for rent at $12.95 per week paid in advance on a 2 year contract. After renting the phone, you must return it to Radio-Rentals.

Kogan.com offers the Apple iphone 5S smart phone for sale at $699. You estimate that the phone will last for 3 years before it will break and be worthless.

Currently, the effective annual interest rate is 11.351%, the effective monthly interest rate 0.9% and the effective weekly interest rate is 0.207%. Assume that there are exactly 52 weeks per year and 12 months per year.

Find the equivalent annual cost of renting the phone and also buying the phone. The answers below are listed in the same order.



Question 59  NPV

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

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

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



Question 182  NPV, IRR, pay back period

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



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

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



Question 533  NPV, no explanation

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

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

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



Question 534  NPV, no explanation

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

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

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



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?



Question 508  income and capital returns

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

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



Question 527  income and capital returns

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

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



Question 120  credit risk, payout policy

A newly floated farming company is financed with senior bonds, junior bonds, cumulative non-voting preferred stock and common stock. The new company has no retained profits and due to floods it was unable to record any revenues this year, leading to a loss. The firm is not bankrupt yet since it still has substantial contributed equity (same as paid-up capital).

On which securities must it pay interest or dividend payments in this terrible financial year?



Question 482  market capitalisation of equity

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

Image of MSFT on Google finance on 28 Nov 2014

What was MSFT's market capitalisation of equity?



Question 524  risk, expected and historical returns, bankruptcy or insolvency, capital structure, corporate financial decision theory, limited liability

Which of the following statements is NOT correct?



Question 604  inflation, real and nominal returns and cash flows

Apples and oranges currently cost $1 each. Inflation is 5% pa, and apples and oranges are equally affected by this inflation rate. Note that when payments are not specified as real, as in this question, they're conventionally assumed to be nominal.

Which of the following statements is NOT correct?



Question 578  inflation, real and nominal returns and cash flows

Which of the following statements about inflation is NOT correct?



Question 576  inflation, real and nominal returns and cash flows

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



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

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

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

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

The answer choices below are given in the same order.



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

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

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

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

The answer choices below are given in the same order.



Question 41  DDM, income and capital returns

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

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

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

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



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?



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

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

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



Question 358  PE ratio, Multiples valuation

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

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

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



Question 333  DDM, time calculation

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

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

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



Question 608  debt terminology

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


Question 609  debt terminology

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


Question 610  debt terminology

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


Question 612  debt terminology

You are owed money. Are you a or a ?


Question 613  debt terminology

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


Question 541  debt terminology

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



Question 582  APR, effective rate, effective rate conversion

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



Question 330  APR, effective rate, debt terminology

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



Question 160  interest only loan

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



Question 149  fully amortising loan, APR

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



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?



Question 38  bond pricing

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



Question 230  bond pricing, capital raising

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

How many bonds should the firm issue?



Question 332  bond pricing, premium par and discount bonds

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

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



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.



Question 328  bond pricing, APR

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

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



Question 486  capital budgeting, opportunity cost, sunk cost

A young lady is trying to decide if she should attend university. Her friends say that she should go to university because she is more likely to meet a clever young man than if she begins full time work straight away.

What's the correct way to classify this item from a capital budgeting perspective when trying to find the Net Present Value of going to university rather than working?

The opportunity to meet a desirable future spouse should be classified as:



Question 491  capital budgeting, opportunity cost, sunk cost

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

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

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



Question 492  capital budgeting, opportunity cost, sunk cost

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

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



Question 173  CFFA

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

Candys Corp
Income Statement for
year ending 30th June 2013
  $m
Sales 200
COGS 50
Operating expense 10
Depreciation 20
Interest expense 10
Income before tax 110
Tax at 30% 33
Net income 77
 
Candys Corp
Balance Sheet
as at 30th June 2013 2012
  $m $m
Assets
Current assets 220 180
PPE    
    Cost 300 340
    Accumul. depr. 60 40
    Carrying amount 240 300
Total assets 460 480
 
Liabilities
Current liabilities 175 190
Non-current liabilities 135 130
Owners' equity
Retained earnings 50 60
Contributed equity 100 100
Total L and OE 460 480
 

 

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



Question 360  CFFA

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

Ching-A-Lings Corp
Income Statement for
year ending 30th June 2013
  $m
Sales 100
COGS 20
Depreciation 20
Rent expense 11
Interest expense 19
Taxable Income 30
Taxes at 30% 9
Net income 21
 
Ching-A-Lings Corp
Balance Sheet
as at 30th June 2013 2012
  $m $m
Inventory 49 38
Trade debtors 14 2
Rent paid in advance 5 5
PPE 400 400
Total assets 468 445
 
Trade creditors 4 10
Bond liabilities 200 190
Contributed equity 145 145
Retained profits 119 100
Total L and OE 468 445
 

 

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

The cash flow from assets was:



Question 224  CFFA

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



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###



Question 359  CFFA

Which one of the following will have no effect on net income (NI) but decrease cash flow from assets (CFFA or FFCF) in this year for a tax-paying firm, all else remaining constant?

Remember:

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



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.



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:



Question 559  variance, standard deviation, covariance, correlation

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



Question 236  diversification, correlation, risk

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



Question 111  portfolio risk, correlation

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



Question 83  portfolio risk, standard deviation

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

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



Question 285  covariance, portfolio risk

Two risky stocks A and B comprise an equal-weighted portfolio. The correlation between the stocks' returns is 70%.

If the variance of stock A increases but the:

  • Prices and expected returns of each stock stays the same,
  • Variance of stock B's returns stays the same,
  • Correlation of returns between the stocks stays the same.

Which of the following statements is NOT correct?



Question 293  covariance, correlation, portfolio risk

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



Question 557  portfolio weights, portfolio return

An investor wants to make a portfolio of two stocks A and B with a target expected portfolio return of 6% pa.

  • Stock A has an expected return of 5% pa.
  • Stock B has an expected return of 10% pa.

What portfolio weights should the investor have in stocks A and B respectively?



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 563  correlation

What is the correlation of a variable X with itself?

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



Question 565  correlation

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

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



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 706  utility, risk aversion, utility function

Mr Blue, Miss Red and Mrs Green are people with different utility functions.

Note that a fair gamble is a bet that has an expected value of zero, such as paying $0.50 to win $1 in a coin flip with heads or nothing if it lands tails. Fairly priced insurance is when the expected present value of the insurance premiums is equal to the expected loss from the disaster that the insurance protects against, such as the cost of rebuilding a home after a catastrophic fire.

Which of the following statements is NOT correct?

Utility curves



Question 80  CAPM, risk, diversification

Diversification is achieved by investing in a large amount of stocks. What type of risk is reduced by diversification?



Question 112  CAPM, risk

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



Question 326  CAPM

A fairly priced stock has an expected return equal to the market's. Treasury bonds yield 5% pa and the market portfolio's expected return is 10% pa. What is the stock's beta?



Question 110  CAPM, SML, NPV

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

Investment projects that plot above the SML would have:



Question 627  CAPM, SML, NPV, Jensens alpha

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. Which of the below statements is NOT correct?



Question 628  CAPM, SML, risk, no explanation

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 672  CAPM, beta

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

What do you think will be the stock's expected return over the next year, given as an effective annual rate?



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%. 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 302  WACC, CAPM

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



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:



Question 621  market efficiency, technical analysis, no explanation

Technical traders:



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 569  personal tax

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

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

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

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



Question 449  personal tax on dividends, classical tax system

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

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

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

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



Question 448  franking credit, personal tax on dividends, imputation tax system

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

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

The Australian imputation tax system applies because the company generates all of its income in Australia and pays corporate tax to the Australian Tax Office. Therefore all of the company's dividends are fully franked. The sole shareholder is an Australian for tax purposes and can therefore use the franking credits to offset his personal income tax liability.

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



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:



Question 454  NPV, capital structure, capital budgeting

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

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

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

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

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

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

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



Question 568  rights issue, capital raising, capital structure

A company conducts a 1 for 5 rights issue at a subscription price of $7 when the pre-announcement stock price was $10. What is the percentage change in the stock price and the number of shares outstanding? The answers are given in the same order. Ignore all taxes, transaction costs and signalling effects.



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 712  effective rate conversion

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



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 725  return distribution, mean and median returns

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


Question 718  arithmetic and geometric averages

The symbol ##\text{GDR}_{0\rightarrow 1}## represents a stock's gross discrete return per annum over the first year. ##\text{GDR}_{0\rightarrow 1} = P_1/P_0##. The subscript indicates the time period that the return is mentioned over. So for example, ##\text{AAGDR}_{1 \rightarrow 3}## is the arithmetic average GDR measured over the two year period from years 1 to 3, but it is expressed as a per annum rate.

Which of the below statements about the arithmetic and geometric average GDR is NOT correct?



Question 722  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 50 -0.6931 0.5 -0.5
2 100 0.6931 2 1
 
Arithmetic average 0 1.25 0.25
Arithmetic standard deviation -0.6931 0.75 0.75
 

 



Question 618  capital structure, no explanation

Who owns a company's shares? The:



Question 767  idiom, corporate financial decision theory, no explanation

The sayings "Don't cry over spilt milk", "Don't regret the things that you can't change" and "What's done is done" are most closely related to which financial concept?



Question 768  accounting terminology, book and market values, no explanation

Accountants and finance professionals have lots of names for the same things which can be quite confusing.

Which of the following groups of items are NOT synonyms?



Question 769  short selling, idiom, no explanation

"Buy low, sell high" is a well-known saying. It suggests that investors should buy low then sell high, in that order.

How would you re-phrase that saying to describe short selling?



Question 777  CAPM, beta

The market's expected total return is 10% pa and the risk free rate is 5% pa, both given as effective annual rates.

A stock has a beta of 0.5.

In the last 5 minutes, the federal government unexpectedly raised taxes. Over this time the share market fell by 3%. 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?



Question 770  expected and historical returns, income and capital returns, coupon rate, bond pricing, no explanation

Which of the following statements is NOT correct? Assume that all things remain equal. So for example, don't assume that just because a company's dividends and profit rise that its required return will also rise, assume the required return stays the same.



Question 771  debt terminology, interest expense, interest tax shield, credit risk, no explanation

You deposit money into a bank account. Which of the following statements about this deposit is NOT correct?



Question 773  CFFA, WACC, interest tax shield, DDM

Use the below information to value a levered company with constant annual perpetual cash flows from assets. The next cash flow will be generated in one year from now, so a perpetuity can be used to value this firm. Both the cash flow from assets including and excluding interest tax shields are constant (but not equal to each other).

Data on a Levered Firm with Perpetual Cash Flows
Item abbreviation Value Item full name
##\text{CFFA}_\text{U}## $48.5m Cash flow from assets excluding interest tax shields (unlevered)
##\text{CFFA}_\text{L}## $50m Cash flow from assets including interest tax shields (levered)
##g## 0% pa Growth rate of cash flow from assets, levered and unlevered
##\text{WACC}_\text{BeforeTax}## 10% pa Weighted average cost of capital before tax
##\text{WACC}_\text{AfterTax}## 9.7% pa Weighted average cost of capital after tax
##r_\text{D}## 5% pa Cost of debt
##r_\text{EL}## 11.25% pa Cost of levered equity
##D/V_L## 20% pa Debt to assets ratio, where the asset value includes tax shields
##t_c## 30% Corporate tax rate
 

 

What is the value of the levered firm including interest tax shields?



Question 774  leverage, WACC, real estate

One year ago you bought a $1,000,000 house partly funded using a mortgage loan. The loan size was $800,000 and the other $200,000 was your wealth or 'equity' in the house asset.

The interest rate on the home loan was 4% pa.

Over the year, the house produced a net rental yield of 2% pa and a capital gain of 2.5% pa.

Assuming that all cash flows (interest payments and net rental payments) were paid and received at the end of the year, and all rates are given as effective annual rates, what was the total return on your wealth over the past year?

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 657  systematic and idiosyncratic risk, CAPM, no explanation

A stock's required total return will decrease when its:



Question 658  CFFA, income statement, balance sheet, no explanation

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



Question 659  APR, effective rate, effective rate conversion, no explanation

A home loan company advertises an interest rate of 9% pa, payable monthly. Which of the following statements about the interest rate is NOT correct? All rates are given with an accuracy of 4 decimal places.



Question 660  fully amortising loan, interest only loan, APR

How much more can you borrow using an interest-only loan compared to a 25-year fully amortising loan if interest rates are 6% pa compounding per month and are not expected to change? If it makes it easier, assume that you can afford to pay $2,000 per month on either loan. Express your answer as a proportional increase using the following formula:

###\text{Proportional Increase} = \dfrac{V_\text{0,interest only}}{V_\text{0,fully amortising}} - 1###



Question 663  leverage, accounting ratio, no explanation

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



Question 664  real and nominal returns and cash flows, inflation, no explanation

What is the present value of real payments of $100 every year forever, with the first payment in one year? The nominal discount rate is 7% pa and the inflation rate is 4% pa.



Question 666  rights issue, capital raising

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

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



Question 667  forward foreign exchange rate, foreign exchange rate, cross currency interest rate parity, no explanation

The Australian cash rate is expected to be 2% pa over the next one year, while the US cash rate is expected to be 0% pa, both given as nominal effective annual rates. The current exchange rate is 0.73 USD per AUD.

What is the implied 1 year USD per AUD forward foreign exchange rate?



Question 668  buy and hold, market efficiency, idiom

A quote from the famous investor Warren Buffet: "Much success can be attributed to inactivity. Most investors cannot resist the temptation to constantly buy and sell."

Buffet is referring to the buy-and-hold strategy which is to buy and never sell shares. Which of the following is a disadvantage of a buy-and-hold strategy? Assume that share markets are semi-strong form efficient. Which of the following is NOT an advantage of the strict buy-and-hold strategy? A disadvantage of the buy-and-hold strategy is that it reduces:



Question 617  systematic and idiosyncratic risk, risk, CAPM

A stock's required total return will increase when its:



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

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

What is the implied 1 year forward foreign exchange rate?



Question 669  beta, CAPM, risk

Which of the following is NOT a valid method for estimating the beta of a company's stock? Assume that markets are efficient, a long history of past data is available, the stock possesses idiosyncratic and market risk. The variances and standard deviations below denote total risks.



Question 662  APR, effective rate, effective rate conversion, no explanation

Which of the following interest rate labels does NOT make sense?



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?



Question 284  covariance, correlation

The following table shows a sample of historical total returns of shares in two different companies A and B.

Stock Returns
Total effective annual returns
Year ##r_A## ##r_B##
2007 0.2 0.4
2008 0.04 -0.2
2009 -0.1 -0.3
2010 0.18 0.5
 

What is the historical sample covariance (##\hat{\sigma}_{A,B}##) and correlation (##\rho_{A,B}##) of stock A and B's total effective annual returns?



Question 81  risk, correlation, diversification

Stock A and B's returns have a correlation of 0.3. Which statement is NOT correct?



Question 82  portfolio return

Portfolio Details
Stock Expected
return
Standard
deviation
Correlation Dollars
invested
A 0.1 0.4 0.5 60
B 0.2 0.6 140
 

What is the expected return of the above portfolio?



Question 73  portfolio risk, standard deviation

Portfolio Details
Stock Expected
return
Standard
deviation
Covariance ##(\sigma_{A,B})## Beta Dollars
invested
A 0.2 0.4 0.12 0.5 40
B 0.3 0.8 1.5 80
 

What is the standard deviation (not variance) of the above portfolio? Note that the stocks' covariance is given, not correlation.



Question 294  short selling, portfolio weights

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



Question 558  portfolio weights, portfolio return, short selling

An investor wants to make a portfolio of two stocks A and B with a target expected portfolio return of 16% pa.

  • Stock A has an expected return of 8% pa.
  • Stock B has an expected return of 12% pa.

What portfolio weights should the investor have in stocks A and B respectively?



Question 564  covariance

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

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



Question 562  covariance

What is the covariance of a variable X with itself?

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



Question 694  utility

Which of the below statements about utility is NOT generally accepted by economists? Most people are thought to:



Question 695  utility, risk aversion, utility function

Mr Blue, Miss Red and Mrs Green are people with different utility functions. Which of the statements about the 3 utility functions is NOT correct?

Utility curves



Question 696  utility, risk aversion, utility function

Mr Blue, Miss Red and Mrs Green are people with different utility functions. Which of the statements about the 3 utility functions is NOT correct?

Utility curves



Question 90  CAPM, risk

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



Question 86  CAPM

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



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?



Question 235  SML, NPV, CAPM, risk

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

Investment projects that plot on the SML would have:



Question 244  CAPM, SML, NPV, risk

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

Image of CAPM SML graph

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



Question 72  CAPM, portfolio beta, portfolio risk

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

What is the beta of the above portfolio?



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:



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 633  personal tax

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

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

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

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



Question 513  stock split, reverse stock split, stock dividend, bonus issue, rights issue

Which of the following statements is NOT correct?



Question 567  stock split, capital structure

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



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

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

Which one of the following corporate events may have happened?



Question 212  rights issue

In mid 2009 the listed mining company Rio Tinto announced a 21-for-40 renounceable rights issue. Below is the chronology of events:

  • 04/06/2009. Share price opens at $69.00 and closes at $66.90.

  • 05/06/2009. 21-for-40 rights issue announced at a subscription price of $28.29.

  • 16/06/2009. Last day that shares trade cum-rights. Share price opens at $76.40 and closes at $75.50.

  • 17/06/2009. Shares trade ex-rights. Rights trading commences.

All things remaining equal, what would you expect Rio Tinto's stock price to open at on the first day that it trades ex-rights (17/6/2009)? Ignore the time value of money since time is negligibly short. Also ignore taxes.



Question 699  utility, risk aversion, utility function, gamble

Mr Blue, Miss Red and Mrs Green are people with different utility functions.

Each person has $50 of initial wealth. A coin toss game is offered to each person at a casino where the player can win or lose $50. Each player can flip a coin and if they flip heads, they receive $50. If they flip tails then they will lose $50. Which of the following statements is NOT correct?

Utility curves



Question 700  utility, risk aversion, utility function, gamble

Mr Blue, Miss Red and Mrs Green are people with different utility functions.

Each person has $50 of initial wealth. A coin toss game is offered to each person at a casino where the player can win or lose $50. Each player can flip a coin and if they flip heads, they receive $50. If they flip tails then they will lose $50. Which of the following statements is NOT correct?

Utility curves




Copyright © 2014 Keith Woodward