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?
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 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 469 franking credit, personal tax on dividends, imputation tax system, no explanation
A firm pays a fully franked cash dividend of $70 to one of its Australian shareholders who has a personal marginal tax rate of 45%. The corporate tax rate is 30%.
What will be the shareholder's personal tax payable due to the dividend payment?
Question 494 franking credit, personal tax on dividends, imputation tax system
A firm pays a fully franked cash dividend of $100 to one of its Australian shareholders who has a personal marginal tax rate of 15%. The corporate tax rate is 30%.
What will be the shareholder's personal tax payable due to the dividend payment?
Question 624 franking credit, personal tax on dividends, imputation tax system, no explanation
Which of the following statements about Australian franking credits is NOT correct? Franking credits:
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 444 investment decision, corporate financial decision theory
The investment decision primarily affects which part of a business?
Question 445 financing decision, corporate financial decision theory
The financing decision primarily affects which part of a business?
Question 446 working capital decision, corporate financial decision theory
The working capital decision primarily affects which part of a business?
Question 447 payout policy, corporate financial decision theory
Payout policy is most closely related to which part of a business?
The expression 'cash is king' emphasizes the importance of having enough cash to pay your short term debts to avoid bankruptcy. Which business decision is this expression most closely related to?
The expression 'you have to spend money to make money' relates to which business decision?
Which of the following decisions relates to the current assets and current liabilities of the firm?
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 729 book and market values, balance sheet, no explanation
If a firm makes a profit and pays no dividends, which of the firm’s accounts will increase?
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 738 financial statement, balance sheet, income statement
Where can a private firm's market value of equity be found? It can be sourced from the company's:
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 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?
Which of the following statements about book and market equity is NOT correct?
You deposit money into a bank. Which of the following statements is NOT correct? You:
You bought a house, primarily funded using a home loan from a bank. Which of the following statements is NOT correct?
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?
By convention, money market securities' yields are always quoted as:
Which of the following statements is NOT correct? Money market securities are:
A 180-day Bank Accepted Bill has a face value of $1,000,000. The interest rate is 8% pa and there are 365 days in the year. What is its price now?
A 90-day Bank Accepted Bill (BAB) has a face value of $1,000,000. The simple interest rate is 10% pa and there are 365 days in the year. What is its price now?
Question 327 bill pricing, simple interest rate, no explanation
On 27/09/13, three month Swiss government bills traded at a yield of -0.2%, given as a simple annual yield. That is, interest rates were negative.
If the face value of one of these 90 day bills is CHF1,000,000 (CHF represents Swiss Francs, the Swiss currency), what is the price of one of these bills?
A bank bill was bought for $99,000 and sold for $100,000 thirty (30) days later. There are 365 days in the year. Which of the following formulas gives the simple interest rate per annum over those 30 days?
Note: To help you identify which is the correct answer without doing any calculations yourself, the formulas used to calculate the numbers are given.
A 90 day bank bill has a face value of $100,000.
Investor A bought the bill when it was first issued at a simple yield to maturity of 3% pa and sold it 20 days later to Investor B who expected to earn a simple yield to maturity of 5% pa. Investor B held it until maturity.
Which of the following statements is NOT correct?
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).
You want to buy an apartment worth $500,000. You have saved a deposit of $50,000. The bank has agreed to lend you the $450,000 as a fully amortising mortgage loan with a term of 25 years. The interest rate is 6% pa and is not expected to change.
What will be your monthly payments?
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?
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?
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.
You just signed up for a 30 year fully amortising mortgage with monthly payments of $1,000 per month. The interest rate is 6% pa which is not expected to change.
How much did you borrow? After 20 years, how much will be owing on the mortgage? The interest rate is still 6% and is not expected to change.
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.
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.
You want to buy a house priced at $400,000. You have saved a deposit of $40,000. The bank has agreed to lend you $360,000 as a fully amortising loan with a term of 30 years. The interest rate is 8% pa payable monthly and is not expected to change.
What will be your monthly payments?
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).
You just signed up for a 30 year interest-only mortgage with monthly payments of $3,000 per month. The interest rate is 6% pa which is not expected to change.
How much did you borrow? After 15 years, just after the 180th payment at that time, how much will be owing on the mortgage? The interest rate is still 6% and is not expected to change. Remember that the mortgage is interest-only and that mortgage payments are paid in arrears (at the end of the month).
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?
You just borrowed $400,000 in the form of a 25 year interest-only mortgage with monthly payments of $3,000 per month. The interest rate is 9% pa which is not expected to change.
You actually plan to pay more than the required interest payment. You plan to pay $3,300 in mortgage payments every month, which your mortgage lender allows. These extra payments will reduce the principal and the minimum interest payment required each month.
At the maturity of the mortgage, what will be the principal? That is, after the last (300th) interest payment of $3,300 in 25 years, how much will be owing on the mortgage?
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?
Many Australian home loans that are interest-only actually require payments to be made on a fully amortising basis after a number of years.
You decide to borrow $600,000 from the bank at an interest rate of 4.25% pa for 25 years. The payments will be interest-only for the first 10 years (t=0 to 10 years), then they will have to be paid on a fully amortising basis for the last 15 years (t=10 to 25 years).
Assuming that interest rates will remain constant, what will be your monthly payments over the first 10 years from now, and then the next 15 years after that? The answer options are given in the same order.
The following cash flows are expected:
- 10 yearly payments of $80, with the first payment in 6.5 years from now (first payment at t=6.5).
- A single payment of $500 in 4 years and 3 months (t=4.25) from now.
What is the NPV of the cash flows if the discount rate is 10% given as an effective annual rate?
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?
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.
This annuity formula ##\dfrac{C_1}{r}\left(1-\dfrac{1}{(1+r)^3} \right)## is equivalent to which of the following formulas? Note the 3.
In the below formulas, ##C_t## is a cash flow at time t. All of the cash flows are equal, but paid at different times.
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?
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?
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?
There are many ways to write the ordinary annuity formula.
Which of the following is NOT equal to the ordinary annuity formula?
You are promised 20 payments of $100, where the first payment is immediate (t=0) and the last is at the end of the 19th year (t=19). The effective annual discount rate is ##r##.
Which of the following equations does NOT give the correct present value of these 20 payments?
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.
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.
Bonds X and Y are issued by the same US company. Both bonds yield 10% pa, and they have the same face value ($100), maturity, seniority, and payment frequency.
The only difference is that bond X and Y's coupon rates are 8 and 12% pa respectively. Which of the following statements is true?
A bond maturing in 10 years has a coupon rate of 4% pa, paid semi-annually. The bond's yield is currently 6% pa. The face value of the bond is $100. What is its price?
A three year bond has a fixed coupon rate of 12% pa, paid semi-annually. The bond's yield is currently 6% pa. The face value is $100. What is its price?
A two year Government bond has a face value of $100, a yield of 0.5% and a fixed coupon rate of 0.5%, paid semi-annually. What is its price?
A prospective home buyer can afford to pay $2,000 per month in mortgage loan repayments. The central bank recently lowered its policy rate by 0.25%, and residential home lenders cut their mortgage loan rates from 4.74% to 4.49%.
How much more can the prospective home buyer borrow now that interest rates are 4.49% rather than 4.74%? Give your answer as a proportional increase over the original amount he could borrow (##V_\text{before}##), so:
###\text{Proportional increase} = \frac{V_\text{after}-V_\text{before}}{V_\text{before}} ###Assume that:
- Interest rates are expected to be constant over the life of the loan.
- Loans are interest-only and have a life of 30 years.
- Mortgage loan payments are made every month in arrears and all interest rates are given as annualised percentage rates compounding per month.
In Australia in the 1980's, inflation was around 8% pa, and residential mortgage loan interest rates were around 14%.
In 2013, inflation was around 2.5% pa, and residential mortgage loan interest rates were around 4.5%.
If a person can afford constant mortgage loan payments of $2,000 per month, how much more can they borrow when interest rates are 4.5% pa compared with 14.0% pa?
Give your answer as a proportional increase over the amount you could borrow when interest rates were high ##(V_\text{high rates})##, so:
###\text{Proportional increase} = \dfrac{V_\text{low rates}-V_\text{high rates}}{V_\text{high rates}} ###
Assume that:
- Interest rates are expected to be constant over the life of the loan.
- Loans are interest-only and have a life of 30 years.
- Mortgage loan payments are made every month in arrears and all interest rates are given as annualised percentage rates (APR's) compounding per month.
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###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###Which one of the following bonds is trading at a discount?
Which one of the following bonds is trading at a premium?
An investor bought two fixed-coupon bonds issued by the same company, a zero-coupon bond and a 7% pa semi-annual coupon bond. Both bonds have a face value of $1,000, mature in 10 years, and had a yield at the time of purchase of 8% pa.
A few years later, yields fell to 6% pa. Which of the following statements is correct? Note that a capital gain is an increase in price.
"Buy low, sell high" is a phrase commonly heard in financial markets. It states that traders should try to buy assets at low prices and sell at high prices.
Traders in the fixed-coupon bond markets often quote promised bond yields rather than prices. Fixed-coupon bond traders should try to:
A firm wishes to raise $10 million now. They will issue 6% pa semi-annual coupon bonds that will mature in 8 years and have a face value of $1,000 each. Bond yields are 10% pa, given as an APR compounding every 6 months, and the yield curve is flat.
How many bonds should the firm issue? All numbers are rounded up.
A 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?
For a price of $100, Vera will sell you a 2 year bond paying semi-annual coupons of 10% pa. The face value of the bond is $100. Other bonds with similar risk, maturity and coupon characteristics trade at a yield of 8% pa.
For a price of $100, Carol will sell you a 5 year bond paying semi-annual coupons of 16% pa. The face value of the bond is $100. Other bonds with similar risk, maturity and coupon characteristics trade at a yield of 12% pa.
For a price of $100, Rad will sell you a 5 year bond paying semi-annual coupons of 16% pa. The face value of the bond is $100. Other bonds with the same risk, maturity and coupon characteristics trade at a yield of 6% pa.
For a price of $100, Andrea will sell you a 2 year bond paying annual coupons of 10% pa. The face value of the bond is $100. Other bonds with the same risk, maturity and coupon characteristics trade at a yield of 6% pa.
For a price of $95, Nicole will sell you a 10 year bond paying semi-annual coupons of 8% pa. The face value of the bond is $100. Other bonds with the same risk, maturity and coupon characteristics trade at a yield of 8% pa.
An investor bought a 10 year 2.5% pa fixed coupon government bond priced at par. The face value is $100. Coupons are paid semi-annually and the next one is in 6 months.
Six months later, just after the coupon at that time was paid, yields suddenly and unexpectedly fell to 2% pa. Note that all yields above are given as APR's compounding semi-annually.
What was the bond investors' historical total return over that first 6 month period, given as an effective semi-annual rate?
An investor bought a 20 year 5% pa fixed coupon government bond priced at par. The face value is $100. Coupons are paid semi-annually and the next one is in 6 months.
Six months later, just after the coupon at that time was paid, yields suddenly and unexpectedly rose to 5.5% pa. Note that all yields above are given as APR's compounding semi-annually.
What was the bond investors' historical total return over that first 6 month period, given as an effective semi-annual rate?
The below screenshot of Commonwealth Bank of Australia's (CBA) details were taken from the Google Finance website on 7 Nov 2014. Some information has been deliberately blanked out.
What was CBA's market capitalisation of equity?
Question 905 market capitalisation of equity, PE ratio, payout ratio
The below graph shows the computer software company Microsoft's stock price (MSFT) at the market close on the NASDAQ on Friday 1 June 2018.
Based on the screenshot above, which of the following statements about MSFT is NOT correct? MSFT's:
The first payment of a constant perpetual annual cash flow is received at time 5. Let this cash flow be ##C_5## and the required return be ##r##.
So there will be equal annual cash flows at time 5, 6, 7 and so on forever, and all of the cash flows will be equal so ##C_5 = C_6 = C_7 = ...##
When the perpetuity formula is used to value this stream of cash flows, it will give a value (V) at time:
A stock is expected to pay its next dividend of $1 in one year. Future annual dividends are expected to grow by 2% pa. So the first dividend of $1 will be in one year, the year after that $1.02 (=1*(1+0.02)^1), and a year later $1.0404 (=1*(1+0.02)^2) and so on forever.
Its required total return is 10% pa. The total required return and growth rate of dividends are given as effective annual rates.
Calculate the current stock price.
A stock just paid a dividend of $1. Future annual dividends are expected to grow by 2% pa. The next dividend of $1.02 (=1*(1+0.02)^1) will be in one year, and the year after that the dividend will be $1.0404 (=1*(1+0.02)^2), and so on forever.
Its required total return is 10% pa. The total required return and growth rate of dividends are given as effective annual rates.
Calculate the current stock price.
A stock is just about to pay a dividend of $1 tonight. Future annual dividends are expected to grow by 2% pa. The next dividend of $1 will be paid tonight, and the year after that the dividend will be $1.02 (=1*(1+0.02)^1), and a year later 1.0404 (=1*(1+0.04)^2) and so on forever.
Its required total return is 10% pa. The total required return and growth rate of dividends are given as effective annual rates.
Calculate the current stock price.
For a price of $13, Carla will sell you a share paying a dividend of $1 in one year and every year after that forever. The required return of the stock is 10% pa.
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.
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 ##?
The following is the Dividend Discount Model (DDM) used to price stocks:
###P_0=\dfrac{C_1}{r-g}###
If the assumptions of the DDM hold and the stock is fairly priced, which one of the following statements is NOT correct? The long term expected:
Question 497 income and capital returns, DDM, ex dividend date
A stock will pay you a dividend of $10 tonight if you buy it today. Thereafter the annual dividend is expected to grow by 5% pa, so the next dividend after the $10 one tonight will be $10.50 in one year, then in two years it will be $11.025 and so on. The stock's required return is 10% pa.
What is the stock price today and what do you expect the stock price to be tomorrow, approximately?
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?
The following equation is called the Dividend Discount Model (DDM), Gordon Growth Model or the perpetuity with growth formula: ### P_0 = \frac{ C_1 }{ r - g } ###
What is ##g##? The value ##g## is the long term expected:
For a price of $6, Carlos 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.
For a price of $102, Andrea will sell you a share which just paid a dividend of $10 yesterday, and is expected to pay dividends every year forever, growing at a rate of 5% pa.
So the next dividend will be ##10(1+0.05)^1=$10.50## in one year from now, and the year after it will be ##10(1+0.05)^2=11.025## and so on.
The required return of the stock is 15% pa.
For a price of $10.20 each, Renee will sell you 100 shares. Each share is expected to pay dividends in perpetuity, growing at a rate of 5% pa. The next dividend is one year away (t=1) and is expected to be $1 per share.
The required return of the stock is 15% pa.
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 is the discount rate '## r_\text{eff} ##' in this equation?
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?
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 539 debt terminology, fully amortising loan, bond pricing
A 'fully amortising' loan can also be called a:
Which of the below statements about effective rates and annualised percentage rates (APR's) is NOT correct?
Which of the following statements about effective rates and annualised percentage rates (APR's) is NOT correct?
Which of the following statements is NOT equivalent to the yield on debt?
Assume that the debt being referred to is fairly priced, but do not assume that it's priced at par.
Question 147 bill pricing, simple interest rate, no explanation
A 30-day Bank Accepted Bill has a face value of $1,000,000. The interest rate is 8% pa and there are 365 days in the year. What is its price now?
Question 157 bill pricing, simple interest rate, no explanation
A 90-day Bank Accepted Bill has a face value of $1,000,000. The interest rate is 6% pa and there are 365 days in the year. What is its price?
A 60-day Bank Accepted Bill has a face value of $1,000,000. The interest rate is 8% pa and there are 365 days in the year. What is its price now?
A 30-day Bank Accepted Bill has a face value of $1,000,000. The interest rate is 2.5% pa and there are 365 days in the year. What is its price now?
Question 862 yield curve, bond pricing, bill pricing, monetary policy, no explanation
Refer to the below graph when answering the questions.
Which of the following statements is NOT correct?
Question 906 effective rate, return types, net discrete return, return distribution, price gains and returns over time
For an asset's price to double from say $1 to $2 in one year, what must its effective annual return be? Note that an effective annual return is also called a net discrete return per annum. If the price now is ##P_0## and the price in one year is ##P_1## then the effective annul return over the next year is:
###r_\text{effective annual} = \dfrac{P_1 - P_0}{P_0} = \text{NDR}_\text{annual}###Question 907 continuously compounding rate, return types, return distribution, price gains and returns over time
For an asset's price to double from say $1 to $2 in one year, what must its continuously compounded return ##(r_{CC})## be? If the price now is ##P_0## and the price in one year is ##P_1## then the continuously compounded return over the next year is:
###r_\text{CC annual} = \ln{\left[ \dfrac{P_1}{P_0} \right]} = \text{LGDR}_\text{annual}###Question 908 effective rate, return types, gross discrete return, return distribution, price gains and returns over time
For an asset's price to double from say $1 to $2 in one year, what must its gross discrete return (GDR) be? If the price now is ##P_0## and the price in one year is ##P_1## then the gross discrete return over the next year is:
###\text{GDR}_\text{annual} = \dfrac{P_1}{P_0}###A three year bond has a face value of $100, a yield of 10% and a fixed coupon rate of 5%, paid semi-annually. What is its price?
Question 658 CFFA, income statement, balance sheet, no explanation
To value a business's assets, the free cash flow of the firm (FCFF, also called CFFA) needs to be calculated. This requires figures from the firm's income statement and balance sheet. For what figures is the income statement needed? Note that the income statement is sometimes also called the profit and loss, P&L, or statement of financial performance.
A 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} ###
Bonds X and Y are issued by different companies, but they both pay a semi-annual coupon of 10% pa and they have the same face value ($100), maturity (3 years) and yield (10%) as each other.
Which of the following statements is true?
A four year bond has a face value of $100, a yield of 6% and a fixed coupon rate of 12%, paid semi-annually. What is its price?
A five year bond has a face value of $100, a yield of 12% and a fixed coupon rate of 6%, paid semi-annually.
What is the bond's price?
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?
Bonds X and Y are issued by the same 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 pays coupons of 6% pa and bond Y pays coupons of 8% pa. Which of the following statements is true?
A four year bond has a face value of $100, a yield of 9% and a fixed coupon rate of 6%, paid semi-annually. What is its price?
In these tough economic times, central banks around the world have cut interest rates so low that they are practically zero. In some countries, government bond yields are also very close to zero.
A three year government bond with a face value of $100 and a coupon rate of 2% pa paid semi-annually was just issued at a yield of 0%. What is the price of the bond?
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?
Bonds A and B are issued by the same company. They have the same face value, maturity, seniority and coupon payment frequency. The only difference is that bond A has a 5% coupon rate, while bond B has a 10% coupon rate. The yield curve is flat, which means that yields are expected to stay the same.
Which bond would have the higher current price?
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 35 bond pricing, zero coupon bond, term structure of interest rates, forward interest rate
A European company just issued two bonds, a
- 1 year zero coupon bond at a yield of 8% pa, and a
- 2 year zero coupon bond at a yield of 10% pa.
What is the company's forward rate over the second year (from t=1 to t=2)? Give your answer as an effective annual rate, which is how the above bond yields are quoted.
A two year Government bond has a face value of $100, a yield of 2.5% pa and a fixed coupon rate of 0.5% pa, paid semi-annually. What is its price?
Question 96 bond pricing, zero coupon bond, term structure of interest rates, forward interest rate
An Australian company just issued two bonds paying semi-annual coupons:
- 1 year zero coupon bond at a yield of 8% pa, and a
- 2 year zero coupon bond at a yield of 10% pa.
What is the forward rate on the company's debt from years 1 to 2? Give your answer as an APR compounding every 6 months, which is how the above bond yields are quoted.
Question 108 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 10% pa, and
- A 2 year zero coupon bond at a yield of 8% 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 143 bond pricing, zero coupon bond, term structure of interest rates, forward interest rate
An Australian company just issued two bonds:
- A 6-month zero coupon bond at a yield of 6% pa, and
- A 12 month zero coupon bond at a yield of 7% pa.
What is the company's forward rate from 6 to 12 months? Give your answer as an APR compounding every 6 months, which is how the above bond yields are quoted.
Bonds X and Y are issued by different companies, but they both pay a semi-annual coupon of 10% pa and they have the same face value ($100) and maturity (3 years).
The only difference is that bond X and Y's yields are 8 and 12% pa respectively. Which of the following statements is true?
Which one of the following bonds is trading at par?
A firm wishes to raise $20 million now. They will issue 8% pa semi-annual coupon bonds that will mature in 5 years and have a face value of $100 each. Bond yields are 6% pa, given as an APR compounding every 6 months, and the yield curve is flat.
How many bonds should the firm issue?
The perpetuity with growth formula, also known as the dividend discount model (DDM) or Gordon growth model, is appropriate for valuing a company's shares. ##P_0## is the current share price, ##C_1## is next year's expected dividend, ##r## is the total required return and ##g## is the expected growth rate of the dividend.
###P_0=\dfrac{C_1}{r-g}###
The below graph shows the expected future price path of the company's shares. Which of the following statements about the graph is NOT correct?
Question 535 DDM, real and nominal returns and cash flows, stock pricing
You are an equities analyst trying to value the equity of the Australian telecoms company Telstra, with ticker TLS. In Australia, listed companies like Telstra tend to pay dividends every 6 months. The payment around August is called the final dividend and the payment around February is called the interim dividend. Both occur annually.
- Today is mid-March 2015.
- TLS's last interim dividend of $0.15 was one month ago in mid-February 2015.
- TLS's last final dividend of $0.15 was seven months ago in mid-August 2014.
Judging by TLS's dividend history and prospects, you estimate that the nominal dividend growth rate will be 1% pa. Assume that TLS's total nominal cost of equity is 6% pa. The dividends are nominal cash flows and the inflation rate is 2.5% pa. All rates are quoted as nominal effective annual rates. Assume that each month is exactly one twelfth (1/12) of a year, so you can ignore the number of days in each month.
Calculate the current TLS share price.
For a price of $129, Joanne will sell you a share which is expected to pay a $30 dividend in one year, and a $10 dividend every year after that forever. So the stock's dividends will be $30 at t=1, $10 at t=2, $10 at t=3, and $10 forever onwards.
The required return of the stock is 10% pa.
For a price of $95, Sherylanne will sell you a share which is expected to pay its first dividend of $10 in 7 years (t=7), and will continue to pay the same $10 dividend every year after that forever.
The required return of the stock is 10% pa.
Question 31 DDM, perpetuity with growth, effective rate conversion
What is the NPV of the following series of cash flows when the discount rate is 5% given as an effective annual rate?
The first payment of $10 is in 4 years, followed by payments every 6 months forever after that which shrink by 2% every 6 months. That is, the growth rate every 6 months is actually negative 2%, given as an effective 6 month rate. So the payment at ## t=4.5 ## years will be ## 10(1-0.02)^1=9.80 ##, and so on.
Question 22 NPV, perpetuity with growth, effective rate, effective rate conversion
What is the NPV of the following series of cash flows when the discount rate is 10% given as an effective annual rate?
The first payment of $90 is in 3 years, followed by payments every 6 months in perpetuity after that which shrink by 3% every 6 months. That is, the growth rate every 6 months is actually negative 3%, given as an effective 6 month rate. So the payment at ## t=3.5 ## years will be ## 90(1-0.03)^1=87.3 ##, and so on.
A European bond paying annual coupons of 6% offers a yield of 10% pa.
Convert the yield into an effective monthly rate, an effective annual rate and an 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} ###
Your friend wants to borrow $1,000 and offers to pay you back $100 in 6 months, with more $100 payments at the end of every month for another 11 months. So there will be twelve $100 payments in total. She says that 12 payments of $100 equals $1,200 so she's being generous.
If interest rates are 12% pa, given as an APR compounding monthly, what is the Net Present Value (NPV) of your friend's deal?
A young lady is trying to decide if she should attend university or not.
The young lady's parents say that she must attend university because otherwise all of her hard work studying and attending school during her childhood was a waste.
What's the correct way to classify this item from a capital budgeting perspective when trying to decide whether to attend university?
The hard work studying at school in her childhood should be classified as:
A 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:
A man is thinking about taking a day off from his casual painting job to relax.
He just woke up early in the morning and he's about to call his boss to say that he won't be coming in to work.
But he's thinking about the hours that he could work today (in the future) which are:
A young lady is trying to decide if she should attend university or begin working straight away in her home town.
The young lady's grandma says that she should not go to university because she is less likely to marry the local village boy whom she likes because she will spend less time with him if she attends university.
What's the correct way to classify this item from a capital budgeting perspective when trying to decide whether to attend university?
The cost of not marrying the local village boy should be classified as:
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:
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 |
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 |
If a project's net present value (NPV) is zero, then its internal rate of return (IRR) will be:
The required return of a project is 10%, given as an effective annual rate.
What is the payback period of the project in years?
Assume that the cash flows shown in the table are received smoothly over the year. So the $121 at time 2 is actually earned smoothly from t=1 to t=2.
| Project Cash Flows | |
| Time (yrs) | Cash flow ($) |
| 0 | -100 |
| 1 | 11 |
| 2 | 121 |
A project has the following cash flows. 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 $250 at time 2 is actually earned smoothly from t=1 to t=2:
| Project Cash Flows | |
| Time (yrs) | Cash flow ($) |
| 0 | -400 |
| 1 | 200 |
| 2 | 250 |
What is the payback period of the project in years?
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.
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.
The below graph shows a project's net present value (NPV) against its annual discount rate.
Which of the following statements is NOT correct?
You have $100,000 in the bank. The bank pays interest at 10% pa, given as an effective annual rate.
You wish to consume an equal amount now (t=0) and in one year (t=1) and have nothing left in the bank at the end (t=1).
How much can you consume at each time?
You have $100,000 in the bank. The bank pays interest at 10% pa, given as an effective annual rate.
You wish to consume an equal amount now (t=0), in one year (t=1) and in two years (t=2), and still have $50,000 in the bank after that (t=2).
How much can you consume at each time?
You're considering a business project which costs $11m now and is expected to pay a single cash flow of $11m in one year. So you pay $11m now, then one year later you receive $11m.
Assume that the initial $11m cost is funded using the your firm's existing cash so no new equity or debt will be raised. The cost of capital is 10% pa.
Which of the following statements about the net present value (NPV), internal rate of return (IRR) and payback period is NOT correct?
A 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?
Suppose you had $100 in a savings account and the interest rate was 2% per year.
After 5 years, how much do you think you would have in the account if you left the money to grow?
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.
Jan asks you for a loan. He wants $100 now and offers to pay you back $120 in 1 year. You can borrow and lend from the bank at an interest rate of 10% pa, given as an effective annual rate.
Ignore credit risk. Remember:
### V_0 = \frac{V_t}{(1+r_\text{eff})^t} ###
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.
Question 49 inflation, real and nominal returns and cash flows, APR, effective rate
In Australia, nominal yields on semi-annual coupon paying Government Bonds with 2 years until maturity are currently 2.83% pa.
The inflation rate is currently 2.2% pa, given as an APR compounding per quarter. The inflation rate is not expected to change over the next 2 years.
What is the real yield on these bonds, given as an APR compounding every 6 months?
Question 50 DDM, stock pricing, inflation, real and nominal returns and cash flows
Most listed Australian companies pay dividends twice per year, the 'interim' and 'final' dividends, which are roughly 6 months apart.
You are an equities analyst trying to value the company BHP. You decide to use the Dividend Discount Model (DDM) as a starting point, so you study BHP's dividend history and you find that BHP tends to pay the same interim and final dividend each year, and that both grow by the same rate.
You expect BHP will pay a $0.55 interim dividend in six months and a $0.55 final dividend in one year. You expect each to grow by 4% next year and forever, so the interim and final dividends next year will be $0.572 each, and so on in perpetuity.
Assume BHP's cost of equity is 8% pa. All rates are quoted as nominal effective rates. The dividends are nominal cash flows and the inflation rate is 2.5% pa.
What is the current price of a BHP share?
A European company just issued two bonds, a
- 3 year zero coupon bond at a yield of 6% pa, and a
- 4 year zero coupon bond at a yield of 6.5% pa.
What is the company's forward rate over the fourth year (from t=3 to t=4)? Give your answer as an effective annual rate, which is how the above bond yields are quoted.
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}##
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.
To receive the dividend you must own the stock when the market closes on which date?
On which date would the stock price increase if the dividend and earnings are higher than expected?
A company announces that it will pay a dividend, as the market expected. The company's shares trade on the stock exchange which is open from 10am in the morning to 4pm in the afternoon each weekday. When would the share price be expected to fall by the amount of the dividend? Ignore taxes.
The share price is expected to fall during the:
A pharmaceutical firm has just discovered a valuable new drug. So far the news has been kept a secret.
The net present value of making and commercialising the drug is $200 million, but $600 million of 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 bond raising to shareholders simultaneously in the same announcement. The bonds will be issued shortly after.
Once the announcement is made and the bonds are issued, what is the expected increase in the value of the firm's assets (ΔV), market capitalisation of debt (ΔD) and market cap of equity (ΔE)?
The triangle symbol 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: ##ΔV = ΔD+ΔE##
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 $300 million of new bonds will need to be issued to fund the project and buy the necessary plant and equipment.
The firm will release the news of the discovery and equity and bond raising to shareholders simultaneously in the same announcement. The shares and bonds will be issued shortly after.
Once the announcement is made and the new shares and bonds are issued, what is the expected increase in the value of the firm's assets ##(\Delta V)##, market capitalisation of debt ##(\Delta D)## and market cap of equity ##(\Delta E)##? Assume that markets are semi-strong form efficient.
The triangle symbol ##\Delta## is the Greek letter capital delta which means change or increase in mathematics.
Ignore the benefit of interest tax shields from having more debt.
Remember: ##\Delta V = \Delta D+ \Delta E##
An investor owns an empty block of land that has local government approval to be developed into a petrol station, car wash or car park. The council will only allow a single development so the projects are mutually exclusive.
All of the development projects have the same risk and the required return of each is 10% pa. Each project has an immediate cost and once construction is finished in one year the land and development will be sold. The table below shows the estimated costs payable now, expected sale prices in one year and the internal rates of returns (IRR's).
| Mutually Exclusive Projects | |||
| Project | Cost now ($) |
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?
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?
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 $75.50.
- 17/06/2009. Shares trade ex-rights. Rights trading commences.
All things remaining equal, what would you expect Rio Tinto's stock price to open at on the first day that it trades ex-rights (17/6/2009)? Ignore the time value of money since time is negligibly short. Also ignore taxes.
Question 572 bond pricing, zero coupon bond, term structure of interest rates, expectations hypothesis, forward interest rate, yield curve
In the below term structure of interest rates equation, all rates are effective annual yields and the numbers in subscript represent the years that the yields are measured over:
###(1+r_{0-3})^3 = (1+r_{0-1})(1+r_{1-2})(1+r_{2-3}) ###
Which of the following statements is NOT correct?
Question 573 bond pricing, zero coupon bond, term structure of interest rates, expectations hypothesis, liquidity premium theory, forward interest rate, yield curve
In the below term structure of interest rates equation, all rates are effective annual yields and the numbers in subscript represent the years that the yields are measured over:
###(1+r_{0-3})^3 = (1+r_{0-1})(1+r_{1-2})(1+r_{2-3}) ###
Which of the following statements is NOT correct?
Question 693 boot strapping zero coupon yield, forward interest rate, term structure of interest rates
Information about three risk free Government bonds is given in the table below.
| Federal Treasury Bond Data | ||||
| Maturity | Yield to maturity | Coupon rate | Face value | Price |
| (years) | (pa, compounding semi-annually) | (pa, paid semi-annually) | ($) | ($) |
| 0.5 | 3% | 4% | 100 | 100.4926 |
| 1 | 4% | 4% | 100 | 100.0000 |
| 1.5 | 5% | 4% | 100 | 98.5720 |
Based on the above government bonds' yields to maturity, which of the below statements about the spot zero rates and forward zero rates is NOT correct?
Question 784 boot strapping zero coupon yield, forward interest rate, term structure of interest rates
Information about three risk free Government bonds is given in the table below.
| Federal Treasury Bond Data | ||||
| Maturity | Yield to maturity | Coupon rate | Face value | Price |
| (years) | (pa, compounding annually) | (pa, paid annually) | ($) | ($) |
| 1 | 0% | 2% | 100 | 102 |
| 2 | 1% | 2% | 100 | 101.9703951 |
| 3 | 2% | 2% | 100 | 100 |
Based on the above government bonds' yields to maturity, which of the below statements about the spot zero rates and forward zero rates is NOT correct?
A share was bought for $20 (at t=0) and paid its annual dividend of $3 one year later (at t=1). Just after the dividend was paid, the share price was $16 (at t=1). What was the total return, capital return and income return? Calculate your answers as effective annual rates.
The choices are given in the same order: ## r_\text{total},r_\text{capital},r_\text{income} ##.
Which of the following statements about an asset’s standard deviation of returns is NOT correct? All other things remaining equal, the higher the asset’s standard deviation of returns:
Stock A and B's returns have a correlation of 0.3. Which statement is NOT correct?
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?
| 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?
All things remaining equal, the variance of a portfolio of two positively-weighted stocks rises as:
Diversification in a portfolio of two assets works best when the correlation between their returns is:
| 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 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?
The standard deviation and variance of a stock's annual returns are calculated over a number of years. The units of the returns are percent per annum ##(\% pa)##.
What are the units of the standard deviation ##(\sigma)## and variance ##(\sigma^2)## of returns respectively?
Hint: Visit Wikipedia to understand the difference between percentage points ##(\text{pp})## and percent ##(\%)##.
A stock's returns are normally distributed with a mean of 10% pa and a standard deviation of 20 percentage points pa. What is the 90% confidence interval of returns over the next year? Note that the Z-statistic corresponding to a one-tail:
- 90% normal probability density function is 1.282.
- 95% normal probability density function is 1.645.
- 97.5% normal probability density function is 1.960.
The 90% confidence interval of annual returns is between:
A stock's returns are normally distributed with a mean of 10% pa and a standard deviation of 20 percentage points pa. What is the 95% confidence interval of returns over the next year? Note that the Z-statistic corresponding to a one-tail:
- 90% normal probability density function is 1.282.
- 95% normal probability density function is 1.645.
- 97.5% normal probability density function is 1.960.
The 95% confidence interval of annual returns is between:
A stock has an expected return of 10% pa and you're 90% sure that over the next year, the return will be between -15% and 35%. The stock's returns are normally distributed. Note that the Z-statistic corresponding to a one-tail:
- 90% normal probability density function is 1.282.
- 95% normal probability density function is 1.645.
- 97.5% normal probability density function is 1.960.
What is the stock’s standard deviation of returns in percentage points per annum (pp pa)?
Question 282 expected and historical returns, income and capital returns
You're the boss of an investment bank's equities research team. Your five analysts are each trying to find the expected total return over the next year of shares in a mining company. The mining firm:
- Is regarded as a mature company since it's quite stable in size and was floated around 30 years ago. It is not a high-growth company;
- Share price is very sensitive to changes in the price of the market portfolio, economic growth, the exchange rate and commodities prices. Due to this, its standard deviation of total returns is much higher than that of the market index;
- Experienced tough times in the last 10 years due to unexpected falls in commodity prices.
- Shares are traded in an active liquid market.
- The analysts' source data is correct and true, but their inferences might be wrong;
- All returns and yields are given as effective annual nominal rates.
Question 559 variance, standard deviation, covariance, correlation
Which of the following statements about standard statistical mathematics notation is NOT correct?
What is the covariance of a variable X with itself?
The cov(X, X) or ##\sigma_{X,X}## equals:
What is the correlation of a variable X with itself?
The corr(X, X) or ##\rho_{X,X}## equals:
What is the covariance of a variable X with a constant C?
The cov(X, C) or ##\sigma_{X,C}## equals:
What is the correlation of a variable X with a constant C?
The corr(X, C) or ##\rho_{X,C}## equals:
Treasury bonds currently have a return of 5% pa. A stock has a beta of 0.5 and the market return is 10% pa. What is the expected return of the stock?
A 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?
According to the theory of the Capital Asset Pricing Model (CAPM), total variance can be broken into two components, systematic variance and idiosyncratic variance. Which of the following events would be considered the most diversifiable according to the theory of the CAPM?
A stock's required total return will increase when its:
A stock has a beta of 1.5. The market's expected total return is 10% pa and the risk free rate is 5% pa, both given as effective annual rates.
What do you think will be the stock's expected return over the next year, given as an effective annual rate?
A stock has a beta of 1.5. The market's expected total return is 10% pa and the risk free rate is 5% pa, both given as effective annual rates.
In the last 5 minutes, bad economic news was released showing a higher chance of recession. Over this time the share market fell by 1%. The risk free rate was unchanged.
What do you think was the stock's historical return over the last 5 minutes, given as an effective 5 minute rate?
A stock has a beta of 1.5. The market's expected total return is 10% pa and the risk free rate is 5% pa, both given as effective annual rates.
Over the last year, bad economic news was released showing a higher chance of recession. Over this time the share market fell by 1%. So ##r_{m} = (P_{0} - P_{-1})/P_{-1} = -0.01##, where the current time is zero and one year ago is time -1. The risk free rate was unchanged.
What do you think was the stock's historical return over the last year, given as an effective annual rate?
Question 807 market efficiency, expected and historical returns, CAPM, beta, systematic risk, no explanation
You work in Asia and just woke up. It looked like a nice day but then you read the news and found out that last night the American share market fell by 10% while you were asleep due to surprisingly poor macro-economic world news. You own a portfolio of liquid stocks listed in Asia with a beta of 1.6. When the Asian equity markets open, what do you expect to happen to your share portfolio? Assume that the capital asset pricing model (CAPM) is correct and that the market portfolio contains all shares in the world, of which American shares are a big part. Your portfolio beta is measured against this world market portfolio.
When the Asian equity market opens for trade, you would expect your portfolio value to:
Diversification is achieved by investing in a large amount of stocks. What type of risk is reduced by diversification?
Question 657 systematic and idiosyncratic risk, CAPM, no explanation
A stock's required total return will decrease when its:
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 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 778 CML, systematic and idiosyncratic risk, portfolio risk, CAPM
The capital market line (CML) is shown in the graph below. The total standard deviation is denoted by σ and the expected return is μ. Assume that markets are efficient so all assets are fairly priced.
Which of the below statements is NOT correct?
Question 809 Markowitz portfolio theory, CAPM, Jensens alpha, CML, systematic and idiosyncratic risk
A graph of assets’ expected returns ##(\mu)## versus standard deviations ##(\sigma)## is given in the graph below. The CML is the capital market line.
Which of the following statements about this graph, Markowitz portfolio theory and the Capital Asset Pricing Model (CAPM) theory is NOT correct?
Question 810 CAPM, systematic and idiosyncratic risk, market efficiency
Examine the graphs below. Assume that asset A is a single stock. Which of the following statements is NOT correct? Asset A:
Question 244 CAPM, SML, NPV, risk
Examine the following graph which shows stocks' betas ##(\beta)## and expected returns ##(\mu)##:
Assume that the CAPM holds and that future expectations of stocks' returns and betas are correctly measured. Which statement is NOT correct?
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:
The security market line (SML) shows the relationship between beta and expected return.
Buying investment projects that plot above the SML would lead to:
Stock A has a beta of 0.5 and stock B has a beta of 1. Which statement is NOT correct?
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?
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?
Government bonds currently have a return of 5% pa. A stock has an expected return of 6% pa and the market return is 7% pa. What is the beta of the stock?
| 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?
Government bonds currently have a return of 5%. A stock has a beta of 2 and the market return is 7%. What is the expected return of the stock?
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:
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 0.7.
What do you think will be the stock's expected return over the next year, given as an effective annual rate?
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 0.7.
In the last 5 minutes, bad economic news was released showing a higher chance of recession. Over this time the share market fell by 2%. The risk free rate was unchanged. What do you think was the stock's historical return over the last 5 minutes, given as an effective 5 minute rate?
A stock's correlation with the market portfolio increases while its total risk is unchanged. What will happen to the stock's expected return and systematic risk?
A fairly priced stock has an expected return of 15% pa. Treasury bonds yield 5% pa and the market portfolio's expected return is 10% pa. What is the beta of the stock?
According to the theory of the Capital Asset Pricing Model (CAPM), total risk can be broken into two components, systematic risk and idiosyncratic risk. Which of the following events would be considered a systematic, undiversifiable event according to the theory of the CAPM?
A fairly priced stock has a beta that is the same as the market portfolio's beta. Treasury bonds yield 5% pa and the market portfolio's expected return is 10% pa. What is the expected return of the stock?
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.
A firm has a debt-to-equity ratio of 25%. What is its debt-to-assets ratio?
Your friend just bought a house for $400,000. He financed it using a $320,000 mortgage loan and a deposit of $80,000.
In the context of residential housing and mortgages, the 'equity' tied up in the value of a person's house is the value of the house less the value of the mortgage. So the initial equity your friend has in his house is $80,000. Let this amount be E, let the value of the mortgage be D and the value of the house be V. So ##V=D+E##.
If house prices suddenly fall by 10%, what would be your friend's percentage change in equity (E)? Assume that the value of the mortgage is unchanged and that no income (rent) was received from the house during the short time over which house prices fell.
Remember:
### r_{0\rightarrow1}=\frac{p_1-p_0+c_1}{p_0} ###
where ##r_{0-1}## is the return (percentage change) of an asset with price ##p_0## initially, ##p_1## one period later, and paying a cash flow of ##c_1## at time ##t=1##.
A firm has a debt-to-equity ratio of 60%. What is its debt-to-assets ratio?
A firm has a debt-to-assets ratio of 20%. What is its debt-to-equity ratio?
A firm can issue 3 year annual coupon bonds at a yield of 10% pa and a coupon rate of 8% pa.
The beta of its levered equity is 2. The market's expected return is 10% pa and 3 year government bonds yield 6% pa with a coupon rate of 4% pa.
The market value of equity is $1 million and the market value of debt is $1 million. The corporate tax rate is 30%.
What is the firm's after-tax WACC? Assume a classical tax system.
A firm can issue 5 year annual coupon bonds at a yield of 8% pa and a coupon rate of 12% pa.
The beta of its levered equity is 1. Five year government bonds yield 5% pa with a coupon rate of 6% pa. The market's expected dividend return is 4% pa and its expected capital return is 6% pa.
The firm's debt-to-equity ratio is 2:1. The corporate tax rate is 30%.
What is the firm's after-tax WACC? Assume a classical tax system.
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.
The equations for Net Income (NI, also known as Earnings or Net Profit After Tax) and Cash Flow From Assets (CFFA, also known as Free Cash Flow to the Firm) per year are:
###NI=(Rev-COGS-FC-Depr-IntExp).(1-t_c)###
###CFFA=NI+Depr-CapEx - \varDelta NWC+IntExp###
For a firm with debt, what is the amount of the interest tax shield per year?
The equations for Net Income (NI, also known as Earnings or Net Profit After Tax) and Cash Flow From Assets (CFFA, also known as Free Cash Flow to the Firm) per year are:
###NI=(Rev-COGS-FC-Depr-IntExp).(1-t_c)###
###CFFA=NI+Depr-CapEx - \varDelta NWC+IntExp###
For a firm with debt, what is the formula for the present value of interest tax shields if the tax shields occur in perpetuity?
You may assume:
- the value of debt (D) is constant through time,
- The cost of debt and the yield on debt are equal and given by ##r_D##.
- the appropriate rate to discount interest tax shields is ##r_D##.
- ##\text{IntExp}=D.r_D##
A common phrase heard in financial markets is that ‘high risk investments deserve high returns’. To make this statement consistent with the Capital Asset Pricing Model (CAPM), a high amount of what specific type of risk deserves a high return?
Investors deserve high returns when they buy assets with high:
A stock has a beta of 1.2. Its next dividend is expected to be $20, paid one year from now.
Dividends are expected to be paid annually and grow by 1.5% pa forever.
Treasury bonds yield 3% pa and the market portfolio's expected return is 7% pa. All returns are effective annual rates.
What is the price of the stock now?
You work for XYZ company and you’ve been asked to evaluate a new project which has double the systematic risk of the company’s other projects.
You use the Capital Asset Pricing Model (CAPM) formula and input the treasury yield ##(r_f )##, market risk premium ##(r_m-r_f )## and the company’s asset beta risk factor ##(\beta_{XYZ} )## into the CAPM formula which outputs a return.
This return that you’ve just found is:
Question 772 interest tax shield, capital structure, leverage
A firm issues debt and uses the funds to buy back equity. Assume that there are no costs of financial distress or transactions costs. Which of the following statements about interest tax shields is NOT correct?
Use the below information to value a levered company with annual perpetual cash flows from assets that grow. The next cash flow will be generated in one year from now. Note that ‘k’ means kilo or 1,000. So the $30k is $30,000.
| Data on a Levered Firm with Perpetual Cash Flows | ||
| Item abbreviation | Value | Item full name |
| ##\text{OFCF}## | $30k | Operating free cash flow |
| ##g## | 1.5% pa | Growth rate of OFCF |
| ##r_\text{D}## | 4% pa | Cost of debt |
| ##r_\text{EL}## | 16.3% pa | Cost of levered equity |
| ##D/V_L## | 80% pa | Debt to assets ratio, where the asset value includes tax shields |
| ##t_c## | 30% | Corporate tax rate |
| ##n_\text{shares}## | 100k | Number of shares |
Which of the following statements is NOT correct?
Use the below information to value a levered company with constant annual perpetual cash flows from assets. The next cash flow will be generated in one year from now, so a perpetuity can be used to value this firm. Both the operating and firm free cash flows are constant (but not equal to each other).
| Data on a Levered Firm with Perpetual Cash Flows | ||
| Item abbreviation | Value | Item full name |
| ##\text{OFCF}## | $48.5m | Operating free cash flow |
| ##\text{FFCF or CFFA}## | $50m | Firm free cash flow or cash flow from assets |
| ##g## | 0% pa | Growth rate of OFCF and FFCF |
| ##\text{WACC}_\text{BeforeTax}## | 10% pa | Weighted average cost of capital before tax |
| ##\text{WACC}_\text{AfterTax}## | 9.7% pa | Weighted average cost of capital after tax |
| ##r_\text{D}## | 5% pa | Cost of debt |
| ##r_\text{EL}## | 11.25% pa | Cost of levered equity |
| ##D/V_L## | 20% pa | Debt to assets ratio, where the asset value includes tax shields |
| ##t_c## | 30% | Corporate tax rate |
What is the value of the levered firm including interest tax shields?
Use the below information to value a levered company with constant annual perpetual cash flows from assets. The next cash flow will be generated in one year from now, so a perpetuity can be used to value this firm. Both the operating and firm free cash flows are constant (but not equal to each other).
| Data on a Levered Firm with Perpetual Cash Flows | ||
| Item abbreviation | Value | Item full name |
| ##\text{OFCF}## | $100m | Operating free cash flow |
| ##\text{FFCF or CFFA}## | $112m | Firm free cash flow or cash flow from assets (includes interest tax shields) |
| ##g## | 0% pa | Growth rate of OFCF and FFCF |
| ##\text{WACC}_\text{BeforeTax}## | 7% pa | Weighted average cost of capital before tax |
| ##\text{WACC}_\text{AfterTax}## | 6.25% pa | Weighted average cost of capital after tax |
| ##r_\text{D}## | 5% pa | Cost of debt |
| ##r_\text{EL}## | 9% pa | Cost of levered equity |
| ##D/V_L## | 50% pa | Debt to assets ratio, where the asset value includes tax shields |
| ##t_c## | 30% | Corporate tax rate |
What is the value of the levered firm including interest tax shields?
Question 800 leverage, portfolio return, risk, portfolio risk, capital structure, no explanation
Which of the following assets would you expect to have the highest required rate of return? All values are current market values.
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###Unrestricted negative gearing is allowed in Australia, New Zealand and Japan. Negative gearing laws allow income losses on investment properties to be deducted from a tax-payer's pre-tax personal income. Negatively geared investors benefit from this tax advantage. They also hope to benefit from capital gains which exceed the income losses.
For example, a property investor buys an apartment funded by an interest only mortgage loan. Interest expense is $2,000 per month. The rental payments received from the tenant living on the property are $1,500 per month. The investor can deduct this income loss of $500 per month from his pre-tax personal income. If his personal marginal tax rate is 46.5%, this saves $232.5 per month in personal income tax.
The advantage of negative gearing is an example of the benefits of:
Question 941 negative gearing, leverage, capital structure, interest tax shield, real estate
Last year, two friends Lev and Nolev each bought similar investment properties for $1 million. Both earned net rents of $30,000 pa over the past year. They funded their purchases in different ways:
- Lev used $200,000 of his own money and borrowed $800,000 from the bank in the form of an interest-only loan with an interest rate of 5% pa.
- Nolev used $1,000,000 of his own money, he has no mortgage loan on his property.
Both Lev and Nolev also work in high-paying jobs and are subject personal marginal tax rates of 45%.
Which of the below statements about the past year is NOT correct?
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 455 income and capital returns, payout policy, DDM, market efficiency
A fairly priced unlevered firm plans to pay a dividend of $1 next year (t=1) which is expected to grow by 3% pa every year after that. The firm's required return on equity is 8% pa.
The firm is thinking about reducing its future dividend payments by 10% so that it can use the extra cash to invest in more projects which are expected to return 8% pa, and have the same risk as the existing projects. Therefore, next year's dividend will be $0.90. No new equity or debt will be issued to fund the new projects, they'll all be funded by the cut in dividends.
What will be the stock's new annual capital return (proportional increase in price per year) if the change in payout policy goes ahead?
Assume that payout policy is irrelevant to firm value (so there's no signalling effects) and that all rates are effective annual rates.
A company conducts a 4 for 3 stock split. What is the percentage change in the stock price and the number of shares outstanding? The answers are given in the same order.
A company conducts a 10 for 3 stock split. What is the percentage increase in the stock price and the number of shares outstanding? The answers are given in the same order.
A firm conducts a two-for-one stock split. Which of the following consequences would NOT be expected?
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 513 stock split, reverse stock split, stock dividend, bonus issue, rights issue
Which of the following statements is NOT correct?
Question 566 capital structure, capital raising, rights issue, on market repurchase, dividend, stock split, bonus issue
A company's share price fell by 20% and its number of shares rose by 25%. Assume that there are no taxes, no signalling effects and no transaction costs.
Which one of the following corporate events may have happened?
A 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 785 fixed for floating interest rate swap, non-intermediated swap
The below table summarises the borrowing costs confronting two companies A and B.
| Bond Market Yields | ||||
| Fixed Yield to Maturity (%pa) | Floating Yield (%pa) | |||
| Firm A | 3 | L - 0.4 | ||
| Firm B | 5 | L + 1 | ||
Firm A wishes to borrow at a floating rate and Firm B wishes to borrow at a fixed rate. Design a non-intermediated swap that benefits firm A only. What will be the swap rate?
In general, stock prices tend to rise. What does this mean for futures on equity?
Which of the following statements about futures contracts on shares is NOT correct, assuming that markets are efficient?
When an equity future is first negotiated (at t=0):
After doing extensive fundamental analysis of a company, you believe that their shares are overpriced and will soon fall significantly. The market believes that there will be no such fall.
Which of the following strategies is NOT a good idea, assuming that your prediction is true?
A trader buys one December futures contract on orange juice. Each contract is for the delivery of 10,000 pounds. The current futures price is $1.20 per pound. The initial margin is $5,000 per contract, and the maintenance margin is $4,000 per contract.
What is the smallest price change would that would lead to a margin call for the buyer?
The price of gold is currently $700 per ounce. The forward price for delivery in 1 year is $800. An arbitrageur can borrow money at 10% per annum given as an effective discrete annual rate. Assume that gold is fairly priced and the cost of storing gold is zero.
What is the best way to conduct an arbitrage in this situation? The best arbitrage strategy requires zero capital, has zero risk and makes money straight away. An arbitrageur should sell 1 forward on gold and:
The current gold price is $700, gold storage costs are 2% pa and the risk free rate is 10% pa, both with continuous compounding.
What should be the 3 year gold futures price?
A 2-year futures contract on a stock paying a continuous dividend yield of 3% pa was bought when the underlying stock price was $10 and the risk free rate was 10% per annum with continuous compounding. Assume that investors are risk-neutral, so the stock's total required return is the risk free rate.
Find the forward price ##(F_2)## and value of the contract ##(V_0)## initially. Also find the value of the contract in 6 months ##(V_{0.5})## if the stock price rose to $12.
An equity index is currently at 5,000 points. The 2 year futures price is 5,400 points and the total required return is 8% pa with continuous compounding. Each index point is worth $25.
What is the implied continuous dividend yield as a continuously compounded rate per annum?
A stock is expected to pay a dividend of $5 per share in 1 month and $5 again in 7 months.
The stock price is $100, and the risk-free rate of interest is 10% per annum with continuous compounding. The yield curve is flat. Assume that investors are risk-neutral.
An investor has just taken a short position in a one year forward contract on the stock.
Find the forward price ##(F_1)## and value of the contract ##(V_0)## initially. Also find the value of the short futures contract in 6 months ##(V_\text{0.5, SF})## if the stock price fell to $90.
Question 598 future, tailing the hedge, cross hedging
The standard deviation of monthly changes in the spot price of lamb is $0.015 per pound. The standard deviation of monthly changes in the futures price of live cattle is $0.012 per pound. The correlation between the spot price of lamb and the futures price of cattle is 0.4.
It is now January. A lamb producer is committed to selling 1,000,000 pounds of lamb in May. The spot price of live cattle is $0.30 per pound and the June futures price is $0.32 per pound. The spot price of lamb is $0.60 per pound.
The producer wants to use the June live cattle futures contracts to hedge his risk. Each futures contract is for the delivery of 50,000 pounds of cattle.
How many live cattle futures should the lamb farmer sell to hedge his risk? Round your answer to the nearest whole number of contracts.
Which one of the below option and futures contracts gives the possibility of potentially unlimited gains?
Which of the below formulas gives the payoff at maturity ##(f_T)## from being long a future? Let the underlying asset price at maturity be ##S_T## and the locked-in futures price be ##K_T##.
Which of the below formulas gives the payoff at maturity ##(f_T)## from being short a future? Let the underlying asset price at maturity be ##S_T## and the locked-in futures price be ##K_T##.
A trader buys one crude oil futures contract on the CME expiring in one year with a locked-in futures price of $38.94 per barrel. If the trader doesn’t close out her contract before expiry then in one year she will have the:
A trader sells one crude oil futures contract on the CME expiring in one year with a locked-in futures price of $38.94 per barrel. The crude oil spot price is $40.33. If the trader doesn’t close out her contract before expiry then in one year she will have the:
Alice, Bob, Chris and Delta are traders in the futures market. The following trades occur over a single day in a newly-opened equity index future that matures in one year which the exchange just made available.
1. Alice buys a future from Bob.
2. Chris buys a future from Delta.
3. Delta buys a future from Alice.
These were the only trades made in this equity index future. What was the trading volume and what is the open interest?
Alice, Bob, Chris and Delta are traders in the futures market. The following trades occur over a single day in a newly-opened equity index future that matures in one year which the exchange just made available.
1. Alice buys a future from Bob.
2. Chris buys a future from Delta.
3. Delta buys a future from Bob.
These were the only trades made in this equity index future. What was the trading volume and what is the open interest?
A trader buys a one year futures contract on crude oil. The contract is for the delivery of 1,000 barrels. The current futures price is $38.94 per barrel. The initial margin is $3,410 per contract, and the maintenance margin is $3,100 per contract.
What is the smallest price change that would lead to a margin call for the buyer?
A trader sells a one year futures contract on crude oil. The contract is for the delivery of 1,000 barrels. The current futures price is $38.94 per barrel. The initial margin is $3,410 per contract, and the maintenance margin is $3,100 per contract.
What is the smallest price change that would lead to a margin call for the seller?
In February a company sold one December 40,000 pound (about 18 metric tons) lean hog futures contract. It closed out its position in May.
The spot price was $0.68 per pound in February. The December futures price was $0.70 per pound when the trader entered into the contract in February, $0.60 when he closed out his position in May, and $0.55 when the contract matured in December.
What was the total profit?
An equity index is currently at 5,200 points. The 6 month futures price is 5,300 points and the total required return is 6% pa with continuous compounding. Each index point is worth $25.
What is the implied dividend yield as a continuously compounded rate per annum?
An equity index is currently at 4,800 points. The 1.5 year futures price is 5,100 points and the total required return is 6% pa with continuous compounding. Each index point is worth $25.
What is the implied dividend yield as a continuously compounded rate per annum?
Which of the following statements about futures and forward contracts is NOT correct?
Alice, Bob, Chris and Delta are traders in the futures market. The following trades occur over a single day in a newly-opened equity index future that matures in one year which the exchange just made available.
1. Alice buys a future from Bob.
2. Chris buys a future from Delta.
3. Bob buys a future from Chris.
These were the only trades made in this equity index future. What was the trading volume and what is the open interest?
Alice, Bob, Chris and Delta are traders in the futures market. The following trades occur over a single day in a newly-opened equity index future that matures in one year which the exchange just made available.
1. Alice buys a future from Bob.
2. Chris buys a future from Delta.
3. Alice buys a future from Chris.
These were the only trades made in this equity index future. What was the trading volume and what is the open interest?
An equity index stands at 100 points and the one year equity futures price is 102.
The equity index is expected to have a dividend yield of 4% pa. Assume that investors are risk-neutral so their total required return on the shares is the same as the risk free Treasury bond yield which is 10% pa. Both are given as discrete effective annual rates.
Assuming that the equity index is fairly priced, an arbitrageur would recognise that the equity futures are:
An equity index stands at 100 points and the one year equity futures price is 107.
The equity index is expected to have a dividend yield of 3% pa. Assume that investors are risk-neutral so their total required return on the shares is the same as the risk free Treasury bond yield which is 10% pa. Both are given as discrete effective annual rates.
Assuming that the equity index is fairly priced, an arbitrageur would recognise that the equity futures are:
A pig farmer in the US is worried about the price of hogs falling and wants to lock in a price now. In one year the pig farmer intends to sell 1,000,000 pounds of hogs. Luckily, one year CME lean hog futures expire on the exact day that he wishes to sell his pigs. The futures have a notional principal of 40,000 pounds (about 18 metric tons) and currently trade at a price of 63.85 cents per pound. The underlying lean hogs spot price is 77.15 cents per pound. The correlation between the futures price and the underlying hogs price is one and the standard deviations are both 4 cents per pound. The initial margin is USD1,500 and the maintenance margin is USD1,200 per futures contract.
Which of the below statements is NOT correct?
An equity index fund manager controls a USD1 billion diversified equity portfolio with a beta of 1.3. The equity manager fears that a global recession will begin in the next year, causing equity prices to tumble. The market does not think that this will happen. If the fund manager wishes to reduce her portfolio beta to 0.5, how many S&P500 futures should she sell?
The US market equity index is the S&P500. One year CME futures on the S&P500 currently trade at 2,062 points and the spot price is 2,091 points. Each point is worth $250. How many one year S&P500 futures contracts should the fund manager sell?
The standard deviation of monthly changes in the spot price of corn is 50 cents per bushel. The standard deviation of monthly changes in the futures price of corn is 40 cents per bushel. The correlation between the spot price of corn and the futures price of corn is 0.9.
It is now March. A corn chip manufacturer is committed to buying 250,000 bushels of corn in May. The spot price of corn is 381 cents per bushel and the June futures price is 399 cents per bushel.
The corn chip manufacturer wants to use the June corn futures contracts to hedge his risk. Each futures contract is for the delivery of 5,000 bushels of corn. One bushel is about 127 metric tons.
How many corn futures should the corn chip manufacturer buy to hedge his risk? Round your answer to the nearest whole number of contracts. Remember to tail the hedge.
Alice, Bob, Chris and Delta are traders in the futures market. The following trades occur over a single day in a newly-opened equity index future that matures in one year which the exchange just made available.
1. Alice buys 2 futures from Bob.
2. Chris buys 3 futures from Delta.
3. Delta buys 5 futures from Alice.
Which of the following statements is NOT correct?
Which derivatives position has the possibility of unlimited potential gains?
What derivative position are you exposed to if you have the obligation to sell the underlying asset at maturity, so you will definitely be forced to sell the underlying asset?
Question 825 future, hedging, tailing the hedge, speculation, no explanation
An equity index fund manager controls a USD500 million diversified equity portfolio with a beta of 0.9. The equity manager expects a significant rally in equity prices next year. The market does not think that this will happen. If the fund manager wishes to increase his portfolio beta to 1.5, how many S&P500 futures should he buy?
The US market equity index is the S&P500. One year CME futures on the S&P500 currently trade at 2,155 points and the spot price is 2,180 points. Each point is worth $250.
The number of one year S&P500 futures contracts that the fund manager should buy is:
On 1 February 2016 you were told that your refinery company will need to purchase oil on 1 July 2016. You were afraid of the oil price rising between now and then so you bought some August 2016 futures contracts on 1 February 2016 to hedge against changes in the oil price. On 1 February 2016 the oil price was $40 and the August 2016 futures price was $43.
It's now 1 July 2016 and oil price is $45 and the August 2016 futures price is $46. You bought the spot oil and closed out your futures position on 1 July 2016.
What was the effective price paid for the oil, taking into account basis risk? All spot and futures oil prices quoted above and below are per barrel.
You intend to use futures on oil to hedge the risk of purchasing oil. There is no cross-hedging risk. Oil pays no dividends but it’s costly to store. Which of the following statements about basis risk in this scenario is NOT correct?
You bought a 1.5 year (18 month) futures contract on oil. Oil storage costs are 4% pa continuously compounded and oil pays no dividends. The futures contract is entered into when the oil price is $40 per barrel and the risk-free rate of interest is 10% per annum with continuous compounding.
Which of the following statements is NOT correct?
Question 829 option, future, delta, gamma, theta, no explanation
Below are some statements about futures and European-style options on non-dividend paying stocks. Assume that the risk free rate is always positive. Which of these statements is NOT correct? All other things remaining equal:
A stock is expected to pay its semi-annual dividend of $1 per share for the foreseeable future. The current stock price is $40 and the continuously compounded risk free rate is 3% pa for all maturities. An investor has just taken a long position in a 12-month futures contract on the stock. The last dividend payment was exactly 4 months ago. Therefore the next $1 dividend is in 2 months, and the $1 dividend after is 8 months from now. Which of the following statements about this scenario is NOT correct?
A non-dividend paying stock has a current price of $20.
The risk free rate is 5% pa given as a continuously compounded rate.
A 2 year futures contract on the stock has a futures price of $24.
You suspect that the futures contract is mis-priced and would like to conduct a risk-free arbitrage that requires zero capital. Which of the following steps about arbitraging the situation is NOT correct?
Question 950 future, backwardation
A company runs a number of slaughterhouses which supply hamburger meat to McDonalds. The company is afraid that live cattle prices will increase over the next year, even though there is widespread belief in the market that they will be stable. What can the company do to hedge against the risk of increasing live cattle prices? Which statement(s) are correct?
(i) buy call options on live cattle.
(ii) buy put options on live cattle.
(iii) sell call options on live cattle.
Select the most correct response:
Below are 4 option graphs. Note that the y-axis is payoff at maturity (T). What options do they depict? List them in the order that they are numbered.
You have just sold an 'in the money' 6 month European put option on the mining company BHP at an exercise price of $40 for a premium of $3.
Which of the following statements best describes your situation?
Below are 4 option graphs. Note that the y-axis is payoff at maturity (T). What options do they depict? List them in the order that they are numbered
You operate a cattle farm that supplies hamburger meat to the big fast food chains. You buy a lot of grain to feed your cattle, and you sell the fully grown cattle on the livestock market.
You're afraid of adverse movements in grain and livestock prices. What options should you buy to hedge your exposures in the grain and cattle livestock markets?
Select the most correct response:
Question 271 CAPM, option, risk, systematic risk, systematic and idiosyncratic risk
All things remaining equal, according to the capital asset pricing model, if the systematic variance of an asset increases, its required return will increase and its price will decrease.
If the idiosyncratic variance of an asset increases, its price will be unchanged.
What is the relationship between the price of a call or put option and the total, systematic and idiosyncratic variance of the underlying asset that the option is based on? Select the most correct answer.
Call and put option prices increase when the:
Which one of the following is NOT usually considered an 'investable' asset for long-term wealth creation?
You believe that the price of a share will fall significantly very soon, but the rest of the market does not. The market thinks that the share price will remain the same. Assuming that your prediction will soon be true, which of the following trades is a bad idea? In other words, which trade will NOT make money or prevent losses?
A European call option will mature in ##T## years with a strike price of ##K## dollars. The underlying asset has a price of ##S## dollars.
What is an expression for the payoff at maturity ##(f_T)## in dollars from owning (being long) the call option?
A European put option will mature in ##T## years with a strike price of ##K## dollars. The underlying asset has a price of ##S## dollars.
What is an expression for the payoff at maturity ##(f_T)## in dollars from owning (being long) the put option?
A European call option will mature in ##T## years with a strike price of ##K## dollars. The underlying asset has a price of ##S## dollars.
What is an expression for the payoff at maturity ##(f_T)## in dollars from having written (being short) the call option?
Question 432 option, option intrinsic value, no explanation
An American style call option with a strike price of ##K## dollars will mature in ##T## years. The underlying asset has a price of ##S## dollars.
What is an expression for the current intrinsic value in dollars from owning (being long) the American style call option? Note that the intrinsic value of an option does not subtract the premium paid to buy the option.
A European put option will mature in ##T## years with a strike price of ##K## dollars. The underlying asset has a price of ##S## dollars.
What is an expression for the payoff at maturity ##(f_T)## in dollars from having written (being short) the put option?
Question 584 option, option payoff at maturity, option profit
Which of the following statements about European call options on non-dividend paying stocks is NOT correct?
A man just sold a call option to his counterparty, a lady. The man has just now:
Which of the following statements about option contracts is NOT correct? For every:
If trader A has sold the right that allows counterparty B to buy the underlying asset from him at maturity if counterparty B wants then trader A is:
Question 636 option, option payoff at maturity, no explanation
Which of the below formulas gives the payoff ##(f)## at maturity ##(T)## from being long a call option? Let the underlying asset price at maturity be ##S_T## and the exercise price be ##X_T##.
Question 637 option, option payoff at maturity, no explanation
Which of the below formulas gives the payoff ##(f)## at maturity ##(T)## from being short a call option? Let the underlying asset price at maturity be ##S_T## and the exercise price be ##X_T##.
Question 639 option, option payoff at maturity, no explanation
Which of the below formulas gives the payoff ##(f)## at maturity ##(T)## from being short a put option? Let the underlying asset price at maturity be ##S_T## and the exercise price be ##X_T##.
Question 638 option, option payoff at maturity, no explanation
Which of the below formulas gives the payoff ##(f)## at maturity ##(T)## from being long a put option? Let the underlying asset price at maturity be ##S_T## and the exercise price be ##X_T##.
A trader buys one crude oil European style call option contract on the CME expiring in one year with an exercise price of $44 per barrel for a price of $6.64. The crude oil spot price is $40.33. If the trader doesn’t close out her contract before maturity, then at maturity she will have the:
Which of the below formulas gives the profit ##(\pi)## from being long a call option? Let the underlying asset price at maturity be ##S_T##, the exercise price be ##X_T## and the option price be ##f_{LC,0}##. Note that ##S_T##, ##X_T## and ##f_{LC,0}## are all positive numbers.
Which of the below formulas gives the profit ##(\pi)## from being short a call option? Let the underlying asset price at maturity be ##S_T##, the exercise price be ##X_T## and the option price be ##f_{LC,0}##. Note that ##S_T##, ##X_T## and ##f_{LC,0}## are all positive numbers.
Which of the below formulas gives the profit ##(\pi)## from being long a put option? Let the underlying asset price at maturity be ##S_T##, the exercise price be ##X_T## and the option price be ##f_{LP,0}##. Note that ##S_T##, ##X_T## and ##f_{LP,0}## are all positive numbers.
Which of the below formulas gives the profit ##(\pi)## from being short a put option? Let the underlying asset price at maturity be ##S_T##, the exercise price be ##X_T## and the option price be ##f_{LP,0}##. Note that ##S_T##, ##X_T## and ##f_{LP,0}## are all positive numbers.
A trader sells one crude oil European style call option contract on the CME expiring in one year with an exercise price of $44 per barrel for a price of $6.64. The crude oil spot price is $40.33. If the trader doesn’t close out her contract before maturity, then at maturity she will have the:
A trader buys one crude oil European style put option contract on the CME expiring in one year with an exercise price of $44 per barrel for a price of $6.64. The crude oil spot price is $40.33. If the trader doesn’t close out her contract before maturity, then at maturity she will have the:
Which of the following statements about call options is NOT correct?
A trader just bought a European style put option on CBA stock. The current option premium is $2, the exercise price is $75, the option matures in one year and the spot CBA stock price is $74.
Which of the following statements is NOT correct?
Question 793 option, hedging, delta hedging, gamma hedging, gamma, Black-Scholes-Merton option pricing
A bank buys 1000 European put options on a $10 non-dividend paying stock at a strike of $12. The bank wishes to hedge this exposure. The bank can trade the underlying stocks and European call options with a strike price of 7 on the same stock with the same maturity. Details of the call and put options are given in the table below. Each call and put option is on a single stock.
| European Options on a Non-dividend Paying Stock | |||
| Description | Symbol | Put Values | Call Values |
| Spot price ($) | ##S_0## | 10 | 10 |
| Strike price ($) | ##K_T## | 12 | 7 |
| Risk free cont. comp. rate (pa) | ##r## | 0.05 | 0.05 |
| Standard deviation of the stock's cont. comp. returns (pa) | ##\sigma## | 0.4 | 0.4 |
| Option maturity (years) | ##T## | 1 | 1 |
| Option price ($) | ##p_0## or ##c_0## | 2.495350486 | 3.601466138 |
| ##N[d_1]## | ##\partial c/\partial S## | 0.888138405 | |
| ##N[d_2]## | ##N[d_2]## | 0.792946442 | |
| ##-N[-d_1]## | ##\partial p/\partial S## | -0.552034778 | |
| ##N[-d_2]## | ##N[-d_2]## | 0.207053558 | |
| Gamma | ##\Gamma = \partial^2 c/\partial S^2## or ##\partial^2 p/\partial S^2## | 0.098885989 | 0.047577422 |
| Theta | ##\Theta = \partial c/\partial T## or ##\partial p/\partial T## | 0.348152078 | 0.672379961 |
Which of the following statements is NOT correct?
Question 794 option, Black-Scholes-Merton option pricing, option delta, no explanation
Which of the following quantities from the Black-Scholes-Merton option pricing formula gives the Delta of a European call option?
Where:
###d_1=\dfrac{\ln[S_0/K]+(r+\sigma^2/2).T)}{\sigma.\sqrt{T}}### ###d_2=d_1-\sigma.\sqrt{T}=\dfrac{\ln[S_0/K]+(r-\sigma^2/2).T)}{\sigma.\sqrt{T}}###Question 795 option, Black-Scholes-Merton option pricing, option delta, no explanation
Which of the following quantities from the Black-Scholes-Merton option pricing formula gives the Delta of a European put option?
Question 796 option, Black-Scholes-Merton option pricing, option delta, no explanation
Which of the following quantities from the Black-Scholes-Merton option pricing formula gives the risk-neutral probability that a European call option will be exercised?
Question 797 option, Black-Scholes-Merton option pricing, option delta, no explanation
Which of the following quantities from the Black-Scholes-Merton option pricing formula gives the risk-neutral probability that a European put option will be exercised?
Which of the following terms about options are NOT synonyms?
Question 821 option, option profit, option payoff at maturity, no explanation
You just paid $4 for a 3 month European style call option on a stock currently priced at $47 with a strike price of $50. The stock’s next dividend will be $1 in 4 months’ time. Note that the dividend is paid after the option matures. Which of the below statements is NOT correct?
When does a European option's last-traded market price become a sunk cost?
Question 823 option, option payoff at maturity, option profit, no explanation
A European call option should only be exercised if:
A put option written on a risky non-dividend paying stock will mature in one month. As is normal, assume that the option's exercise price is non-zero and positive ##(K>0)## and the stock has limited liability ##(S>0)##.
Which of the following statements is NOT correct? The put option's:
Below are some statements about European-style options on non-dividend paying stocks. Assume that the risk free rate is always positive. Which of these statements is NOT correct?
Question 834 option, delta, theta, gamma, standard deviation, Black-Scholes-Merton option pricing
Which of the following statements about an option (either a call or put) and its underlying stock is NOT correct?
| European Call Option | ||
| on a non-dividend paying stock | ||
| Description | Symbol | Quantity |
| Spot price ($) | ##S_0## | 20 |
| Strike price ($) | ##K_T## | 18 |
| Risk free cont. comp. rate (pa) | ##r## | 0.05 |
| Standard deviation of the stock's cont. comp. returns (pa) | ##\sigma## | 0.3 |
| Option maturity (years) | ##T## | 1 |
| Call option price ($) | ##c_0## | 3.939488 |
| Delta | ##\Delta = N[d_1]## | 0.747891 |
| ##N[d_2]## | ##N[d_2]## | 0.643514 |
| Gamma | ##\Gamma## | 0.053199 |
| Theta ($/year) | ##\Theta = \partial c / \partial T## | 1.566433 |