A home loan company advertises an interest rate of 6% pa, payable monthly. Which of the following statements about the interest rate is NOT correct? All rates are given to four decimal places.
A credit card company advertises an interest rate of 18% pa, payable monthly. Which of the following statements about the interest rate is NOT correct? All rates are given to four decimal places.
A semiannual coupon bond has a yield of 3% pa. Which of the following statements about the yield is NOT correct? All rates are given to four decimal places.
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?
A credit card offers an interest rate of 18% pa, compounding monthly.
Find the effective monthly rate, effective annual rate and the effective daily rate. Assume that there are 365 days in a year.
All answers are given in the same order:
### r_\text{eff monthly} , r_\text{eff yearly} , r_\text{eff daily} ###
A 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} ###
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 semiannually.
 An annual dividendpaying stock offering a return of 10% pa compounding annually.
All answers are given in the same order:
##r_\text{credit card, eff yrly}##, ##r_\text{bond, eff yrly}##, ##r_\text{stock, eff yrly}##
Question 49 inflation, real and nominal returns and cash flows, APR, effective rate
In Australia, nominal yields on semiannual 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?
On his 20th birthday, a man makes a resolution. He will deposit $30 into a bank account at the end of every month starting from now, which is the start of the month. So the first payment will be in one month. He will write in his will that when he dies the money in the account should be given to charity.
The bank account pays interest at 6% pa compounding monthly, which is not expected to change.
If the man lives for another 60 years, how much money will be in the bank account if he dies just after making his last (720th) payment?
Question 64 inflation, real and nominal returns and cash flows, APR, effective rate
In Germany, nominal yields on semiannual coupon paying Government Bonds with 2 years until maturity are currently 0.04% pa.
The inflation rate is currently 1.4% pa, given as an APR compounding per quarter. The inflation rate is not expected to change over the next 2 years.
What is the real yield on these bonds, given as an APR compounding every 6 months?
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 signed up for a 30 year fully amortising mortgage loan with monthly payments of $1,500 per month. The interest rate is 9% pa which is not expected to change.
To your surprise, you can actually afford to pay $2,000 per month and your mortgage allows early repayments without fees. If you maintain these higher monthly payments, how long will it take to pay off your mortgage?
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 interestonly 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 interestonly and that mortgage payments are paid in arrears (at the end of the month).
You just borrowed $400,000 in the form of a 25 year interestonly 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 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 want to buy an apartment priced at $500,000. You have saved a deposit of $50,000. The bank has agreed to lend you the $450,000 as an interest only loan with a term of 30 years. The interest rate is 6% pa and is not expected to change. What will be your monthly payments?
Question 239 income and capital returns, inflation, real and nominal returns and cash flows, interest only loan
A bank grants a borrower an interestonly residential mortgage loan with a very large 50% deposit and a nominal interest rate of 6% that is not expected to change. Assume that inflation is expected to be a constant 2% pa over the life of the loan. Ignore credit risk.
From the bank's point of view, what is the long term expected nominal capital return of the loan asset?
A 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 interestonly 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.
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.
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.
"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 fixedcoupon bond markets often quote promised bond yields rather than prices. Fixedcoupon bond traders should try to:
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 semiannually. So there are two coupons per year, paid in arrears every six months.
For a price of $100, Vera will sell you a 2 year bond paying semiannual 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 $95, Nicole will sell you a 10 year bond paying semiannual 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.
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?
Bonds A and B are issued by the same company. They have the same face value, maturity, seniority and coupon payment frequency. The only difference is that bond A has a 5% coupon rate, while bond B has a 10% coupon rate. The yield curve is flat, which means that yields are expected to stay the same.
Which bond would have the higher current price?
A two year Government bond has a face value of $100, a yield of 0.5% and a fixed coupon rate of 0.5%, paid semiannually. What is its price?
Question 48 IRR, NPV, bond pricing, premium par and discount bonds, market efficiency
The theory of fixed interest bond pricing is an application of the theory of Net Present Value (NPV). Also, a 'fairly priced' asset is not over or underpriced. Buying or selling a fairly priced asset has an NPV of zero.
Considering this, which of the following statements is NOT correct?
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 semiannually. What is its price?
Question 56 income and capital returns, bond pricing, premium par and discount bonds
Which of the following statements about risk free government bonds is NOT correct?
Hint: Total return can be broken into income and capital returns as follows:
###\begin{aligned} r_\text{total} &= \frac{c_1}{p_0} + \frac{p_1p_0}{p_0} \\ &= r_\text{income} + r_\text{capital} \end{aligned} ###
The capital return is the growth rate of the price.
The income return is the periodic cash flow. For a bond this is the coupon payment.
The theory of fixed interest bond pricing is an application of the theory of Net Present Value (NPV). Also, a 'fairly priced' asset is not over or underpriced. Buying or selling a fairly priced asset has an NPV of zero.
Considering this, which of the following statements is NOT correct?
A bond maturing in 10 years has a coupon rate of 4% pa, paid semiannually. The bond's yield is currently 6% pa. The face value of the bond is $100. What is its price?
Bonds A and B are issued by the same Australian company. Both bonds yield 7% pa, and they have the same face value ($100), maturity, seniority, and payment frequency.
The only difference is that bond A pays coupons of 10% pa and bond B pays coupons of 5% pa. Which of the following statements is true about the bonds' prices?
Bonds X and Y are issued by different companies, but they both pay a semiannual coupon of 10% pa and they have the same face value ($100) and maturity (3 years).
The only difference is that bond X and Y's yields are 8 and 12% pa respectively. Which of the following statements is true?
A three year bond has a fixed coupon rate of 12% pa, paid semiannually. The bond's yield is currently 6% pa. The face value is $100. What is its price?
Bonds X and Y are issued by different companies, but they both pay a semiannual 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 semiannually. What is its price?
Which one of the following bonds is trading at a discount?
A firm wishes to raise $20 million now. They will issue 8% pa semiannual coupon bonds that will mature in 5 years and have a face value of $100 each. Bond yields are 6% pa, given as an APR compounding every 6 months, and the yield curve is flat.
How many bonds should the firm issue?
A five year bond has a face value of $100, a yield of 12% and a fixed coupon rate of 6%, paid semiannually.
What is the bond's price?
Which one of the following bonds is trading at par?
A firm wishes to raise $8 million now. They will issue 7% pa semiannual coupon bonds that will mature in 10 years and have a face value of $100 each. Bond yields are 10% pa, given as an APR compounding every 6 months, and the yield curve is flat.
How many bonds should the firm issue?
Let the 'income return' of a bond be the coupon at the end of the period divided by the market price now at the start of the period ##(C_1/P_0)##. The expected income return of a premium fixed coupon bond is:
Question 213 income and capital returns, bond pricing, premium par and discount bonds
The coupon rate of a fixed annualcoupon bond is constant (always the same).
What can you say about the income return (##r_\text{income}##) of a fixed annual coupon bond? Remember that:
###r_\text{total} = r_\text{income} + r_\text{capital}###
###r_\text{total, 0 to 1} = \frac{c_1}{p_0} + \frac{p_1p_0}{p_0}###
Assume that there is no change in the bond's total annual yield to maturity from when it is issued to when it matures.
Select the most correct statement.
From its date of issue until maturity, the income return of a fixed annual coupon:
Which one of the following bonds is trading at a premium?
An investor bought two fixedcoupon bonds issued by the same company, a zerocoupon bond and a 7% pa semiannual coupon bond. Both bonds have a face value of $1,000, mature in 10 years, and had a yield at the time of purchase of 8% pa.
A few years later, yields fell to 6% pa. Which of the following statements is correct? Note that a capital gain is an increase in price.
A firm wishes to raise $10 million now. They will issue 6% pa semiannual 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?
A four year bond has a face value of $100, a yield of 9% and a fixed coupon rate of 6%, paid semiannually. 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 semiannually was just issued at a yield of 0%. What is the price of the bond?
A 10 year bond has a face value of $100, a yield of 6% pa and a fixed coupon rate of 8% pa, paid semiannually. 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 30 year Japanese government bond was just issued at par with a yield of 1.7% pa. The fixed coupon payments are semiannual. The bond has a face value of $100.
Six months later, just after the first coupon is paid, the yield of the bond increases to 2% pa. What is the bond's new price?
A 10 year Australian government bond was just issued at par with a yield of 3.9% pa. The fixed coupon payments are semiannual. 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?
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?
Below are some statements about loans and bonds. The first descriptive sentence is correct. But one of the second sentences about the loans' or bonds' prices is not correct. Which statement is NOT correct? Assume that interest rates are positive.
Note that coupons or interest payments are the periodic payments made throughout a bond or loan's life. The face or par value of a bond or loan is the amount paid at the end when the debt matures.
Question 35 bond pricing, zero coupon bond, term structure of interest rates, forward interest rate
A European company just issued two bonds, a
 1 year zero coupon bond at a yield of 8% pa, and a
 2 year zero coupon bond at a yield of 10% pa.
What is the company's forward rate over the second year (from t=1 to t=2)? Give your answer as an effective annual rate, which is how the above bond yields are quoted.
Question 25 bond pricing, zero coupon bond, term structure of interest rates, forward interest rate
A European company just issued two bonds, a
 2 year zero coupon bond at a yield of 8% pa, and a
 3 year zero coupon bond at a yield of 10% pa.
What is the company's forward rate over the third year (from t=2 to t=3)? Give your answer as an effective annual rate, which is how the above bond yields are quoted.
A 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.
Question 143 bond pricing, zero coupon bond, term structure of interest rates, forward interest rate
An Australian company just issued two bonds:
 A 6month 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.
Question 96 bond pricing, zero coupon bond, term structure of interest rates, forward interest rate
An Australian company just issued two bonds:
 A 1 year zero coupon bond at a yield of 8% pa, and
 A 2 year zero coupon bond at a yield of 10% pa.
What is the forward rate on the company's debt from years 1 to 2? Give your answer as an APR compounding every 6 months, which is how the above bond yields are quoted.
Question 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 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_{03})^3 = (1+r_{01})(1+r_{12})(1+r_{23}) ###
Which of the following statements is NOT correct?
Which of the following statements about yield curves 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_{03})^3 = (1+r_{01})(1+r_{12})(1+r_{23}) ###
Which of the following statements is NOT correct?
You're trying to save enough money to buy your first car which costs $2,500. You can save $100 at the end of each month starting from now. You currently have no money at all. You just opened a bank account with an interest rate of 6% pa payable monthly.
How many months will it take to save enough money to buy the car? Assume that the price of the car will stay the same over time.
Your main expense is fuel for your car which costs $100 per month. You just refueled, so you won't need any more fuel for another month (first payment at t=1 month).
You have $2,500 in a bank account which pays interest at a rate of 6% pa, payable monthly. Interest rates are not expected to change.
Assuming that you have no income, in how many months time will you not have enough money to fully refuel your car?
You really want to go on a back packing trip to Europe when you finish university. Currently you have $1,500 in the bank. Bank interest rates are 8% pa, given as an APR compounding per month. If the holiday will cost $2,000, how long will it take for your bank account to reach that amount?
You're trying to save enough money for a deposit to buy a house. You want to buy a house worth $400,000 and the bank requires a 20% deposit ($80,000) before it will give you a loan for the other $320,000 that you need.
You currently have no savings, but you just started working and can save $2,000 per month, with the first payment in one month from now. Bank interest rates on savings accounts are 4.8% pa with interest paid monthly and interest rates are not expected to change.
How long will it take to save the $80,000 deposit? Round your answer up to the nearest month.
A student won $1m in a lottery. Currently the money is in a bank account which pays interest at 6% pa, given as an APR compounding per month.
She plans to spend $20,000 at the beginning of every month from now on (so the first withdrawal will be at t=0). After each withdrawal, she will check how much money is left in the account. When there is less than $500,000 left, she will donate that remaining amount to charity.
In how many months will she make her last withdrawal and donate the remainder to charity?
The saying "buy low, sell high" suggests that investors should make a:
Question 490 expected and historical returns, accounting ratio
Which of the following is NOT a synonym of 'required return'?
Total cash flows can be broken into income and capital cash flows. What is the name given to the income cash flow from owning shares?
Total cash flows can be broken into income and capital cash flows.
What is the name given to the cash flow generated from selling shares at a higher price than they were bought?
Which of the following equations is NOT equal to the total return of an asset?
Let ##p_0## be the current price, ##p_1## the expected price in one year and ##c_1## the expected income in one year.
An asset's total expected return over the next year is given by:
###r_\text{total} = \dfrac{c_1+p_1p_0}{p_0} ###
Where ##p_0## is the current price, ##c_1## is the expected income in one year and ##p_1## is the expected price in one year. The total return can be split into the income return and the capital return.
Which of the following is the expected capital return?
A stock was bought for $8 and paid a dividend of $0.50 one year later (at t=1 year). Just after the dividend was paid, the stock price was $7 (at t=1 year).
What were the total, capital and dividend returns given as effective annual rates? The choices are given in the same order:
##r_\text{total}##, ##r_\text{capital}##, ##r_\text{dividend}##.
A share was bought for $30 (at t=0) and paid its annual dividend of $6 one year later (at t=1).
Just after the dividend was paid, the share price fell to $27 (at t=1). What were the total, capital and income returns given as effective annual rates?
The choices are given in the same order:
##r_\text{total}## , ##r_\text{capital}## , ##r_\text{dividend}##.
A fixed coupon bond was bought for $90 and paid its annual coupon of $3 one year later (at t=1 year). Just after the coupon was paid, the bond price was $92 (at t=1 year). What was the total return, capital return and income return? Calculate your answers as effective annual rates.
The choices are given in the same order: ## r_\text{total},r_\text{capital},r_\text{income} ##.
One and a half years ago Frank bought a house for $600,000. Now it's worth only $500,000, based on recent similar sales in the area.
The expected total return on Frank's residential property is 7% pa.
He rents his house out for $1,600 per month, paid in advance. Every 12 months he plans to increase the rental payments.
The present value of 12 months of rental payments is $18,617.27.
The future value of 12 months of rental payments one year in the future is $19,920.48.
What is the expected annual rental yield of the property? Ignore the costs of renting such as maintenance, real estate agent fees and so on.
Question 542 price gains and returns over time, IRR, NPV, income and capital returns, effective return
For an asset price to double every 10 years, what must be the expected future capital return, given as an effective annual rate?
Question 543 price gains and returns over time, IRR, NPV, income and capital returns, effective return
For an asset price to triple every 5 years, what must be the expected future capital return, given as an effective annual rate?
Question 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.
Question 604 inflation, real and nominal returns and cash flows
Apples and oranges currently cost $1 each. Inflation is 5% pa, and apples and oranges are equally affected by this inflation rate. Note that when payments are not specified as real, as in this question, they're conventionally assumed to be nominal.
Which of the following statements is NOT correct?
In the 'Austin Powers' series of movies, the character Dr. Evil threatens to destroy the world unless the United Nations pays him a ransom (video 1, video 2). Dr. Evil makes the threat on two separate occasions:
 In 1969 he demands a ransom of $1 million (=10^6), and again;
 In 1997 he demands a ransom of $100 billion (=10^11).
If Dr. Evil's demands are equivalent in real terms, in other words $1 million will buy the same basket of goods in 1969 as $100 billion would in 1997, what was the implied inflation rate over the 28 years from 1969 to 1997?
The answer choices below are given as effective annual rates:
Question 353 income and capital returns, inflation, real and nominal returns and cash flows, real estate
A residential investment property has an expected nominal total return of 6% pa and nominal capital return of 3% pa.
Inflation is expected to be 2% pa. All rates are given as effective annual rates.
What are the property's expected real total, capital and income returns? The answer choices below are given in the same order.
Question 363 income and capital returns, inflation, real and nominal returns and cash flows, real estate
A residential investment property has an expected nominal total return of 8% pa and nominal capital return of 3% pa.
Inflation is expected to be 2% pa. All rates are given as effective annual rates.
What are the property's expected real total, capital and income returns? The answer choices below are given in the same order.
Question 407 income and capital returns, inflation, real and nominal returns and cash flows
A stock has a real expected total return of 7% pa and a real expected capital return of 2% pa.
Inflation is expected to be 2% pa. All rates are given as effective annual rates.
What is the nominal expected total return, capital return and dividend yield? The answers below are given in the same order.
Question 525 income and capital returns, real and nominal returns and cash flows, inflation
Which of the following statements about cash in the form of notes and coins is NOT correct? Assume that inflation is positive.
Notes and coins:
Question 295 inflation, real and nominal returns and cash flows, NPV
When valuing assets using discounted cash flow (net present value) methods, it is important to consider inflation. To properly deal with inflation:
(I) Discount nominal cash flows by nominal discount rates.
(II) Discount nominal cash flows by real discount rates.
(III) Discount real cash flows by nominal discount rates.
(IV) Discount real cash flows by real discount rates.
Which of the above statements is or are correct?
Question 526 real and nominal returns and cash flows, inflation, no explanation
How can a nominal cash flow be precisely converted into a real cash flow?
Question 574 inflation, real and nominal returns and cash flows, NPV
What is the present value of a nominal payment of $100 in 5 years? The real discount rate is 10% pa and the inflation rate is 3% pa.
Question 575 inflation, real and nominal returns and cash flows
You expect a nominal payment of $100 in 5 years. The real discount rate is 10% pa and the inflation rate is 3% pa. Which of the following statements is NOT correct?
Question 576 inflation, real and nominal returns and cash flows
What is the present value of a nominal payment of $1,000 in 4 years? The nominal discount rate is 8% pa and the inflation rate is 2% pa.
Question 577 inflation, real and nominal returns and cash flows
What is the present value of a real payment of $500 in 2 years? The nominal discount rate is 7% pa and the inflation rate is 4% pa.
Question 578 inflation, real and nominal returns and cash flows
Which of the following statements about inflation is NOT correct?
Question 554 inflation, real and nominal returns and cash flows
On his 20th birthday, a man makes a resolution. He will put $30 cash under his bed at the end of every month starting from today. His birthday today is the first day of the month. So the first addition to his cash stash will be in one month. He will write in his will that when he dies the cash under the bed should be given to charity.
If the man lives for another 60 years, how much money will be under his bed if he dies just after making his last (720th) addition?
Also, what will be the real value of that cash in today's prices if inflation is expected to 2.5% pa? Assume that the inflation rate is an effective annual rate and is not expected to change.
The answers are given in the same order, the amount of money under his bed in 60 years, and the real value of that money in today's prices.
You're considering making an investment in a particular company. They have preference shares, ordinary shares, senior debt and junior debt.
Which is the safest investment? Which will give the highest returns?
Which business structure or structures have the advantage of limited liability for equity investors?
A newly floated farming company is financed with senior bonds, junior bonds, cumulative nonvoting preferred stock and common stock. The new company has no retained profits and due to floods it was unable to record any revenues this year, leading to a loss. The firm is not bankrupt yet since it still has substantial contributed equity (same as paidup capital).
On which securities must it pay interest or dividend payments in this terrible financial year?
Question 452 limited liability, expected and historical returns
What is the lowest and highest expected share price and expected return from owning shares in a company over a finite period of time?
Let the current share price be ##p_0##, the expected future share price be ##p_1##, the expected future dividend be ##d_1## and the expected return be ##r##. Define the expected return as:
##r=\dfrac{p_1p_0+d_1}{p_0} ##
The answer choices are stated using inequalities. As an example, the first answer choice "(a) ##0≤p<∞## and ##0≤r< 1##", states that the share price must be larger than or equal to zero and less than positive infinity, and that the return must be larger than or equal to zero and less than one.
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.
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?
The below screenshot of Microsoft's (MSFT) details were taken from the Google Finance website on 28 Nov 2014. Some information has been deliberately blanked out.
What was MSFT's market capitalisation of equity?
Which of the following statements about book and market equity is NOT correct?
Question 461 book and market values, ROE, ROA, market efficiency
One year ago a pharmaceutical firm floated by selling its 1 million shares for $100 each. Its book and market values of equity were both $100m. Its debt totalled $50m. The required return on the firm's assets was 15%, equity 20% and debt 5% pa.
In the year since then, the firm:
 Earned net income of $29m.
 Paid dividends totaling $10m.
 Discovered a valuable new drug that will lead to a massive 1,000 times increase in the firm's net income in 10 years after the research is commercialised. News of the discovery was publicly announced. The firm's systematic risk remains unchanged.
Which of the following statements is NOT correct? All statements are about current figures, not figures one year ago.
Hint: Book return on assets (ROA) and book return on equity (ROE) are ratios that accountants like to use to measure a business's past performance.
###\text{ROA}= \dfrac{\text{Net income}}{\text{Book value of assets}}###
###\text{ROE}= \dfrac{\text{Net income}}{\text{Book value of equity}}###
The required return on assets ##r_V## is a return that financiers like to use to estimate a business's future required performance which compensates them for the firm's assets' risks. If the business were to achieve realised historical returns equal to its required returns, then investment into the business's assets would have been a zeroNPV decision, which is neither good nor bad but fair.
###r_\text{V, 0 to 1}= \dfrac{\text{Cash flow from assets}_\text{1}}{\text{Market value of assets}_\text{0}} = \dfrac{CFFA_\text{1}}{V_\text{0}}###
Similarly for equity and debt.
Question 444 investment decision, corporate financial decision theory
The investment 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 445 financing decision, corporate financial decision theory
The financing 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?
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?
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?
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 
The required return of a project is 10%, given as an effective annual rate. Assume that the cash flows shown in the table are paid all at once at the given point in time.
What is the Net Present Value (NPV) of the project?
Project Cash Flows  
Time (yrs)  Cash flow ($) 
0  100 
1  11 
2  121 
What is the Internal Rate of Return (IRR) of the project detailed in the table below?
Assume that the cash flows shown in the table are paid all at once at the given point in time. All answers are given as effective annual rates.
Project Cash Flows  
Time (yrs)  Cash flow ($) 
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:
A project's NPV is positive. Select the most correct statement:
You have $100,000 in the bank. The bank pays interest at 10% pa, given as an effective annual rate.
You wish to consume twice as much now (t=0) as in one year (t=1) and have nothing left in the bank at the end.
How much can you consume at time zero and one? The answer choices are given in the same order.
You have $100,000 in the bank. The bank pays interest at 10% pa, given as an effective annual rate.
You wish to consume half as much now (t=0) as in one year (t=1) and have nothing left in the bank at the end.
How much can you consume at time zero and one? The answer choices are given in the same order.
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?
A firm is considering a business project which costs $11m now and is expected to pay a constant $1m at the end of every year forever.
Assume that the initial $11m cost is funded using the firm's existing cash so no new equity or debt will be raised. The cost of capital is 10% pa.
Which of the following statements about net present value (NPV), internal rate of return (IRR) and payback period is NOT correct?
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?
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 $50,000 in the bank after that (t=2).
How much can you consume at each time?
An investor owns an empty block of land that has local government approval to be developed into a petrol station, car wash or car park. The council will only allow a single development so the projects are mutually exclusive.
All of the development projects have the same risk and the required return of each is 10% pa. Each project has an immediate cost and once construction is finished in one year the land and development will be sold. The table below shows the estimated costs payable now, expected sale prices in one year and the internal rates of returns (IRR's).
Mutually Exclusive Projects  
Project  Cost now ($) 
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?
The phone company Telstra have 2 mobile service plans on offer which both have the same amount of phone call, text message and internet data credit. Both plans have a contract length of 24 months and the monthly cost is payable in advance. The only difference between the two plans is that one is a:
 'Bring Your Own' (BYO) mobile service plan, costing $50 per month. There is no phone included in this plan. The other plan is a:
 'Bundled' mobile service plan that comes with the latest smart phone, costing $71 per month. This plan includes the latest smart phone.
Neither plan has any additional payments at the start or end.
The only difference between the plans is the phone, so what is the implied cost of the phone as a present value?
Assume that the discount rate is 2% per month given as an effective monthly rate, the same high interest rate on credit cards.
The boss of WorkingForTheManCorp has a wicked (and unethical) idea. He plans to pay his poor workers one week late so that he can get more interest on his cash in the bank.
Every week he is supposed to pay his 1,000 employees $1,000 each. So $1 million is paid to employees every week.
The boss was just about to pay his employees today, until he thought of this idea so he will actually pay them one week (7 days) later for the work they did last week and every week in the future, forever.
Bank interest rates are 10% pa, given as a real effective annual rate. So ##r_\text{eff annual, real} = 0.1## and the real effective weekly rate is therefore ##r_\text{eff weekly, real} = (1+0.1)^{1/52}1 = 0.001834569##
All rates and cash flows are real, the inflation rate is 3% pa and there are 52 weeks per year. The boss will always pay wages one week late. The business will operate forever with constant real wages and the same number of employees.
What is the net present value (NPV) of the boss's decision to pay later?
Question 579 price gains and returns over time, time calculation, effective rate
How many years will it take for an asset's price to double if the price grows by 10% pa?
Question 580 price gains and returns over time, time calculation, effective rate
How many years will it take for an asset's price to quadruple (be four times as big, say from $1 to $4) if the price grows by 15% pa?
When using the dividend discount model, care must be taken to avoid using a nominal dividend growth rate that exceeds the country's nominal GDP growth rate. Otherwise the firm is forecast to take over the country since it grows faster than the average business forever.
Suppose a firm's nominal dividend grows at 10% pa forever, and nominal GDP growth is 5% pa forever. The firm's total dividends are currently $1 billion (t=0). The country's GDP is currently $1,000 billion (t=0).
In approximately how many years will the company's total dividends be as large as the country's GDP?
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:
Project Cash Flows  
Time (yrs)  Cash flow ($) 
0  400 
1  0 
2  500 
What is the payback period of the project in years?
Normally cash flows are assumed to happen at the given time. But here, assume that the cash flows are received smoothly over the year. So the $500 at time 2 is actually earned smoothly from t=1 to t=2.
A project to build a toll road will take 3 years to complete, costing three payments of $50 million, paid at the start of each year (at times 0, 1, and 2).
After completion, the toll road will yield a constant $10 million at the end of each year forever with no costs. So the first payment will be at t=4.
The required return of the project is 10% pa given as an effective nominal rate. All cash flows are nominal.
What is the payback period?
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.
There are many ways to write the ordinary annuity formula.
Which of the following is NOT equal to the ordinary annuity formula?
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.
The following cash flows are expected:
 10 yearly payments of $60, with the first payment in 3 years from now (first payment at t=3).
 1 payment of $400 in 5 years and 6 months (t=5.5) from now.
What is the NPV of the cash flows if the discount rate is 10% given as an effective annual rate?
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?
Your friend overheard that you need some cash and asks if you would like to borrow some money. She can lend you $5,000 now (t=0), and in return she wants you to pay her back $1,000 in two years (t=2) and every year after that for the next 5 years, so there will be 6 payments of $1,000 from t=2 to t=7 inclusive.
What is the net present value (NPV) of borrowing from your friend?
Assume that banks loan funds at interest rates of 10% pa, given as an effective annual rate.
Question 58 NPV, inflation, real and nominal returns and cash flows, Annuity
A project to build a toll bridge will take two years to complete, costing three payments of $100 million at the start of each year for the next three years, that is at t=0, 1 and 2.
After completion, the toll bridge will yield a constant $50 million at the end of each year for the next 10 years. So the first payment will be at t=3 and the last at t=12. After the last payment at t=12, the bridge will be given to the government.
The required return of the project is 21% pa given as an effective annual nominal rate.
All cash flows are real and the expected inflation rate is 10% pa given as an effective annual rate. Ignore taxes.
The Net Present Value is:
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?
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?
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.
Discounted cash flow (DCF) valuation prices assets by finding the present value of the asset's future cash flows. The single cash flow, annuity, and perpetuity equations are very useful for this.
Which of the following equations is the 'perpetuity with growth' equation?
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 $13, Carla will sell you a share which will pay a dividend of $1 in one year and every year after that forever. The required return of the stock is 10% pa.
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:
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 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}{rg}###
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?
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}{rg}###
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?
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}{rg}###
If the assumptions of the DDM hold, which one of the following statements is NOT correct? The long term expected:
A stock just paid its annual dividend of $9. The share price is $60. The required return of the stock is 10% pa as an effective annual rate.
What is the implied growth rate of the dividend per year?
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?
In the dividend discount model:
###P_0 = \dfrac{C_1}{rg}###
The return ##r## is supposed to be the:
Two years ago Fred bought a house for $300,000.
Now it's worth $500,000, based on recent similar sales in the area.
Fred's residential property has an expected total return of 8% pa.
He rents his house out for $2,000 per month, paid in advance. Every 12 months he plans to increase the rental payments.
The present value of 12 months of rental payments is $23,173.86.
The future value of 12 months of rental payments one year ahead is $25,027.77.
What is the expected annual growth rate of the rental payments? In other words, by what percentage increase will Fred have to raise the monthly rent by each year to sustain the expected annual total return of 8%?
A stock pays annual dividends which are expected to continue forever. It just paid a dividend of $10. The growth rate in the dividend is 2% pa. You estimate that the stock's required return is 10% pa. Both the discount rate and growth rate are given as effective annual rates. Using the dividend discount model, what will be the share price?
A stock is expected to pay the following dividends:
Cash Flows of a Stock  
Time (yrs)  0  1  2  3  4  ... 
Dividend ($)  0.00  1.00  1.05  1.10  1.15  ... 
After year 4, the annual dividend will grow in perpetuity at 5% pa, so;
 the dividend at t=5 will be $1.15(1+0.05),
 the dividend at t=6 will be $1.15(1+0.05)^2, and so on.
The required return on the stock is 10% pa. Both the growth rate and required return are given as effective annual rates.
What will be the price of the stock in three and a half years (t = 3.5)?
The following is the Dividend Discount Model (DDM) used to price stocks:
### P_0 = \frac{d_1}{rg} ###Assume that the assumptions of the DDM hold and that the time period is measured in years.
Which of the following is equal to the expected dividend in 3 years, ## d_3 ##?
The following equation is the Dividend Discount Model, also known as the 'Gordon Growth Model' or the 'Perpetuity with growth' equation.
### p_0 = \frac{d_1}{r  g} ###
Which expression is NOT equal to the expected dividend yield?
The following equation is the Dividend Discount Model, also known as the 'Gordon Growth Model' or the 'Perpetuity with growth' equation.
###p_0=\frac{d_1}{r_\text{eff}g_\text{eff}}###
Which expression is NOT equal to the expected capital return?
A fairly valued share's current price is $4 and it has a total required return of 30%. Dividends are paid annually and next year's dividend is expected to be $1. After that, dividends are expected to grow by 5% pa in perpetuity. All rates are effective annual returns.
What is the expected dividend income paid at the end of the second year (t=2) and what is the expected capital gain from just after the first dividend (t=1) to just after the second dividend (t=2)? The answers are given in the same order, the dividend and then the capital gain.
Question 488 income and capital returns, payout policy, payout ratio, DDM
Two companies BigDiv and ZeroDiv are exactly the same except for their dividend payouts.
BigDiv pays large dividends and ZeroDiv doesn't pay any dividends.
Currently the two firms have the same earnings, assets, number of shares, share price, expected total return and risk.
Assume a perfect world with no taxes, no transaction costs, no asymmetric information and that all assets including business projects are fairly priced and therefore zeroNPV.
All things remaining equal, which of the following statements is NOT correct?
Question 50 DDM, stock pricing, inflation, real and nominal returns and cash flows
Most listed Australian companies pay dividends twice per year, the 'interim' and 'final' dividends, which are roughly 6 months apart.
You are an equities analyst trying to value the company BHP. You decide to use the Dividend Discount Model (DDM) as a starting point, so you study BHP's dividend history and you find that BHP tends to pay the same interim and final dividend each year, and that both grow by the same rate.
You expect BHP will pay a $0.55 interim dividend in six months and a $0.55 final dividend in one year. You expect each to grow by 4% next year and forever, so the interim and final dividends next year will be $0.572 each, and so on in perpetuity.
Assume BHP's cost of equity is 8% pa. All rates are quoted as nominal effective rates. The dividends are nominal cash flows and the inflation rate is 2.5% pa.
What is the current price of a BHP share?
Question 535 DDM, real and nominal returns and cash flows, stock pricing
You are an equities analyst trying to value the equity of the Australian telecoms company Telstra, with ticker TLS. In Australia, listed companies like Telstra tend to pay dividends every 6 months. The payment around August is called the final dividend and the payment around February is called the interim dividend. Both occur annually.
 Today is midMarch 2015.
 TLS's last interim dividend of $0.15 was one month ago in midFebruary 2015.
 TLS's last final dividend of $0.15 was seven months ago in midAugust 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.
A stock is expected to pay a dividend of $15 in one year (t=1), then $25 for 9 years after that (payments at t=2 ,3,...10), and on the 11th year (t=11) the dividend will be 2% less than at t=10, and will continue to shrink at the same rate every year after that forever. The required return of the stock is 10%. All rates are effective annual rates.
What is the price of the stock now?
Estimate the US bank JP Morgan's share price using a price earnings (PE) multiples approach with the following assumptions and figures only:
 The major US banks JP Morgan Chase (JPM), Citi Group (C) and Wells Fargo (WFC) are comparable companies;
 JP Morgan Chase's historical earnings per share (EPS) is $4.37;
 Citi Group's share price is $50.05 and historical EPS is $4.26;
 Wells Fargo's share price is $48.98 and historical EPS is $3.89.
Note: Figures sourced from Google Finance on 24 March 2014.
Estimate the Chinese bank ICBC's share price using a backwardlooking price earnings (PE) multiples approach with the following assumptions and figures only. Note that the renminbi (RMB) is the Chinese currency, also known as the yuan (CNY).
 The 4 major Chinese banks ICBC, China Construction Bank (CCB), Bank of China (BOC) and Agricultural Bank of China (ABC) are comparable companies;
 ICBC 's historical earnings per share (EPS) is RMB 0.74;
 CCB's backwardlooking PE ratio is 4.59;
 BOC 's backwardlooking PE ratio is 4.78;
 ABC's backwardlooking PE ratio is also 4.78;
Note: Figures sourced from Google Finance on 25 March 2014. Share prices are from the Shanghai stock exchange.
Estimate Microsoft's (MSFT) share price using a price earnings (PE) multiples approach with the following assumptions and figures only:
 Apple, Google and Microsoft are comparable companies,
 Apple's (AAPL) share price is $526.24 and historical EPS is $40.32.
 Google's (GOOG) share price is $1,215.65 and historical EPS is $36.23.
 Micrsoft's (MSFT) historical earnings per share (EPS) is $2.71.
Source: Google Finance 28 Feb 2014.
Estimate the French bank Societe Generale's share price using a backwardlooking price earnings (PE) multiples approach with the following assumptions and figures only. Note that EUR is the euro, the European monetary union's currency.
 The 4 major European banks Credit Agricole (ACA), Deutsche Bank AG (DBK), UniCredit (UCG) and Banco Santander (SAN) are comparable companies to Societe Generale (GLE);
 Societe Generale's (GLE's) historical earnings per share (EPS) is EUR 2.92;
 ACA's backwardlooking PE ratio is 16.29 and historical EPS is EUR 0.84;
 DBK's backwardlooking PE ratio is 25.01 and historical EPS is EUR 1.26;
 SAN's backwardlooking PE ratio is 14.71 and historical EPS is EUR 0.47;
 UCG's backwardlooking PE ratio is 15.78 and historical EPS is EUR 0.40;
Note: Figures sourced from Google Finance on 27 March 2015.
Private equity firms are known to buy medium sized private companies operating in the same industry, merge them together into a larger company, and then sell it off in a public float (initial public offering, IPO).
If mediumsized private companies trade at PE ratios of 5 and larger listed companies trade at PE ratios of 15, what return can be achieved from this strategy?
Assume that:
 The mediumsized companies can be bought, merged and sold in an IPO instantaneously.
 There are no costs of finding, valuing, merging and restructuring the medium sized companies. Also, there is no competition to buy the mediumsized companies from other private equity firms.
 The large merged firm's earnings are the sum of the medium firms' earnings.
 The only reason for the difference in medium and large firm's PE ratios is due to the illiquidity of the medium firms' shares.
 Return is defined as: ##r_{0→1} = (p_1p_0+c_1)/p_0## , where time zero is just before the merger and time one is just after.
A lowquality secondhand car can be bought now for $1,000 and will last for 1 year before it will be scrapped for nothing.
A highquality secondhand car can be bought now for $4,900 and it will last for 5 years before it will be scrapped for nothing.
What is the equivalent annual cost of each car? Assume a discount rate of 10% pa, given as an effective annual rate.
The answer choices are given as the equivalent annual cost of the lowquality car and then the high quality car.
You're advising your superstar client 40cent who is weighing up buying a private jet or a luxury yacht. 40cent is just as happy with either, but he wants to go with the more costeffective option. These are the cash flows of the two options:
 The private jet can be bought for $6m now, which will cost $12,000 per month in fuel, piloting and airport costs, payable at the end of each month. The jet will last for 12 years.
 Or the luxury yacht can be bought for $4m now, which will cost $20,000 per month in fuel, crew and berthing costs, payable at the end of each month. The yacht will last for 20 years.
What's unusual about 40cent is that he is so famous that he will actually be able to sell his jet or yacht for the same price as it was bought since the next generation of superstar musicians will buy it from him as a status symbol.
Bank interest rates are 10% pa, given as an effective annual rate. You can assume that 40cent will live for another 60 years and that when the jet or yacht's life is at an end, he will buy a new one with the same details as above.
Would you advise 40cent to buy the or the ?
Note that the effective monthly rate is ##r_\text{eff monthly}=(1+0.1)^{1/12}1=0.00797414##
Question 180 equivalent annual cash flow, inflation, real and nominal returns and cash flows
Details of two different types of light bulbs are given below:
 Lowenergy light bulbs cost $3.50, have a life of nine years, and use about $1.60 of electricity a year, paid at the end of each year.
 Conventional light bulbs cost only $0.50, but last only about a year and use about $6.60 of energy a year, paid at the end of each year.
The real discount rate is 5%, given as an effective annual rate. Assume that all cash flows are real. The inflation rate is 3% given as an effective annual rate.
Find the Equivalent Annual Cost (EAC) of the lowenergy and conventional light bulbs. The below choices are listed in that order.
Carlos and Edwin are brothers and they both love Holden Commodore cars.
Carlos likes to buy the latest Holden Commodore car for $40,000 every 4 years as soon as the new model is released. As soon as he buys the new car, he sells the old one on the second hand car market for $20,000. Carlos never has to bother with paying for repairs since his cars are brand new.
Edwin also likes Commodores, but prefers to buy 4year old cars for $20,000 and keep them for 11 years until the end of their life (new ones last for 15 years in total but the 4year old ones only last for another 11 years). Then he sells the old car for $2,000 and buys another 4year old second hand car, and so on.
Every time Edwin buys a second hand 4 year old car he immediately has to spend $1,000 on repairs, and then $1,000 every year after that for the next 10 years. So there are 11 payments in total from when the second hand car is bought at t=0 to the last payment at t=10. One year later (t=11) the old car is at the end of its total 15 year life and can be scrapped for $2,000.
Assuming that Carlos and Edwin maintain their love of Commodores and keep up their habits of buying new ones and second hand ones respectively, how much larger is Carlos' equivalent annual cost of car ownership compared with Edwin's?
The real discount rate is 10% pa. All cash flows are real and are expected to remain constant. Inflation is forecast to be 3% pa. All rates are effective annual. Ignore capital gains tax and tax savings from depreciation since cars are taxexempt for individuals.
You just bought a nice dress which you plan to wear once per month on nights out. You bought it a moment ago for $600 (at t=0). In your experience, dresses used once per month last for 6 years.
Your younger sister is a student with no money and wants to borrow your dress once a month when she hits the town. With the increased use, your dress will only last for another 3 years rather than 6.
What is the present value of the cost of letting your sister use your current dress for the next 3 years?
Assume: that bank interest rates are 10% pa, given as an effective annual rate; you will buy a new dress when your current one wears out; your sister will only use the current dress, not the next one that you will buy; and the price of a new dress never changes.
You own a nice suit which you wear once per week on nights out. You bought it one year ago for $600. In your experience, suits used once per week last for 6 years. So you expect yours to last for another 5 years.
Your younger brother said that retro is back in style so he wants to wants to borrow your suit once a week when he goes out. With the increased use, your suit will only last for another 4 years rather than 5.
What is the present value of the cost of letting your brother use your current suit for the next 4 years?
Assume: that bank interest rates are 10% pa, given as an effective annual rate; you will buy a new suit when your current one wears out and your brother will not use the new one; your brother will only use your current suit so he will only use it for the next four years; and the price of a new suit never changes.
You own some nice shoes which you use once per week on date nights. You bought them 2 years ago for $500. In your experience, shoes used once per week last for 6 years. So you expect yours to last for another 4 years.
Your younger sister said that she wants to borrow your shoes once per week. With the increased use, your shoes will only last for another 2 years rather than 4.
What is the present value of the cost of letting your sister use your current shoes for the next 2 years?
Assume: that bank interest rates are 10% pa, given as an effective annual rate; you will buy a new pair of shoes when your current pair wears out and your sister will not use the new ones; your sister will only use your current shoes so she will only use it for the next 2 years; and the price of new shoes never changes.
An industrial chicken farmer grows chickens for their meat. Chickens:
 Cost $0.50 each to buy as chicks. They are bought on the day they’re born, at t=0.
 Grow at a rate of $0.70 worth of meat per chicken per week for the first 6 weeks (t=0 to t=6).
 Grow at a rate of $0.40 worth of meat per chicken per week for the next 4 weeks (t=6 to t=10) since they’re older and grow more slowly.
 Feed costs are $0.30 per chicken per week for their whole life. Chicken feed is bought and fed to the chickens once per week at the beginning of the week. So the first amount of feed bought for a chicken at t=0 costs $0.30, and so on.
 Can be slaughtered (killed for their meat) and sold at no cost at the end of the week. The price received for the chicken is their total value of meat (note that the chicken grows fast then slow, see above).
The required return of the chicken farm is 0.5% given as an effective weekly rate.
Ignore taxes and the fixed costs of the factory. Ignore the chicken’s welfare and other environmental and ethical concerns.
Find the equivalent weekly cash flow of slaughtering a chicken at 6 weeks and at 10 weeks so the farmer can figure out the best time to slaughter his chickens. The choices below are given in the same order, 6 and 10 weeks.
Question 548 equivalent annual cash flow, time calculation, no explanation
An Apple iPhone 6 smart phone can be bought now for $999. An Android Kogan Agora 4G+ smart phone can be bought now for $240.
If the Kogan phone lasts for one year, approximately how long must the Apple phone last for to have the same equivalent annual cost?
Assume that both phones have equivalent features besides their lifetimes, that both are worthless once they've outlasted their life, the discount rate is 10% pa given as an effective annual rate, and there are no extra costs or benefits from either phone.
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(10.02)^1=9.80 ##, and so on.
A share just paid its semiannual dividend of $10. The dividend is expected to grow at 2% every 6 months forever. This 2% growth rate is an effective 6 month rate. Therefore the next dividend will be $10.20 in six months. The required return of the stock 10% pa, given as an effective annual rate.
What is the price of the share now?
A stock is expected to pay the following dividends:
Cash Flows of a Stock  
Time (yrs)  0  1  2  3  4  ... 
Dividend ($)  0.00  1.00  1.05  1.10  1.15  ... 
After year 4, the annual dividend will grow in perpetuity at 5% pa, so;
 the dividend at t=5 will be $1.15(1+0.05),
 the dividend at t=6 will be $1.15(1+0.05)^2, and so on.
The required return on the stock is 10% pa. Both the growth rate and required return are given as effective annual rates. What is the current price of the stock?
A stock pays semiannual dividends. It just paid a dividend of $10. The growth rate in the dividend is 1% every 6 months, given as an effective 6 month rate. You estimate that the stock's required return is 21% pa, as an effective annual rate.
Using the dividend discount model, what will be the share price?
You own an apartment which you rent out as an investment property.
What is the price of the apartment using discounted cash flow (DCF, same as NPV) valuation?
Assume that:
 You just signed a contract to rent the apartment out to a tenant for the next 12 months at $2,000 per month, payable in advance (at the start of the month, t=0). The tenant is just about to pay you the first $2,000 payment.
 The contract states that monthly rental payments are fixed for 12 months. After the contract ends, you plan to sign another contract but with rental payment increases of 3%. You intend to do this every year.
So rental payments will increase at the start of the 13th month (t=12) to be $2,060 (=2,000(1+0.03)), and then they will be constant for the next 12 months.
Rental payments will increase again at the start of the 25th month (t=24) to be $2,121.80 (=2,000(1+0.03)^{2}), and then they will be constant for the next 12 months until the next year, and so on.  The required return of the apartment is 8.732% pa, given as an effective annual rate.
 Ignore all taxes, maintenance, real estate agent, council and strata fees, periods of vacancy and other costs. Assume that the apartment will last forever and so will the rental payments.
Question 498 NPV, Annuity, perpetuity with growth, multi stage growth model
A business project is expected to cost $100 now (t=0), then pay $10 at the end of the third (t=3), fourth, fifth and sixth years, and then grow by 5% pa every year forever. So the cash flow will be $10.5 at the end of the seventh year (t=7), then $11.025 at the end of the eighth year (t=8) and so on perpetually. The total required return is 10℅ pa.
Which of the following formulas will NOT give the correct net present value of the project?
Question 215 equivalent annual cash flow, effective rate conversion
You're about to buy a car. These are the cash flows of the two different cars that you can buy:
 You can buy an old car for $5,000 now, for which you will have to buy $90 of fuel at the end of each week from the date of purchase. The old car will last for 3 years, at which point you will sell the old car for $500.
 Or you can buy a new car for $14,000 now for which you will have to buy $50 of fuel at the end of each week from the date of purchase. The new car will last for 4 years, at which point you will sell the new car for $1,000.
Bank interest rates are 10% pa, given as an effective annual rate. Assume that there are exactly 52 weeks in a year. Ignore taxes and environmental and pollution factors.
Should you buy the or the ?
Question 249 equivalent annual cash flow, effective rate conversion
Details of two different types of desserts or edible treats are given below:
 Highsugar treats like candy, chocolate and ice cream make a person very happy. High sugar treats are cheap at only $2 per day.
 Lowsugar treats like nuts, cheese and fruit make a person equally happy if these foods are of high quality. Low sugar treats are more expensive at $4 per day.
The advantage of lowsugar treats is that a person only needs to pay the dentist $2,000 for fillings and root canal therapy once every 15 years. Whereas with highsugar treats, that treatment needs to be done every 5 years.
The real discount rate is 10%, given as an effective annual rate. Assume that there are 365 days in every year and that all cash flows are real. The inflation rate is 3% given as an effective annual rate.
Find the equivalent annual cash flow (EAC) of the highsugar treats and lowsugar treats, including dental costs. The below choices are listed in that order.
Ignore the pain of dental therapy, personal preferences and other factors.
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_1p_0+c_1}{p_0} ###
where ##r_{01}## 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##.
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.
One year ago you bought $100,000 of shares partly funded using a margin loan. The margin loan size was $70,000 and the other $30,000 was your own wealth or 'equity' in the share assets.
The interest rate on the margin loan was 7.84% pa.
Over the year, the shares produced a dividend yield of 4% pa and a capital gain of 5% pa.
What was the total return on your wealth? Ignore taxes, assume that all cash flows (interest payments and dividends) were paid and received at the end of the year, and all rates above are effective annual rates.
Hint: Remember that wealth in this context is your equity (E) in the house asset (V = D+E) which is funded by the loan (D) and your deposit or equity (E).
Here are the Net Income (NI) and Cash Flow From Assets (CFFA) equations:
###NI=(RevCOGSFCDeprIntExp).(1t_c)###
###CFFA=NI+DeprCapEx  \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.
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 fixedcoupon bond that has a liquid secondary market? Select the most correct answer:
Annual interest expense is equal to:
Which one of the following will decrease net income (NI) but increase cash flow from assets (CFFA) in this year for a taxpaying firm, all else remaining constant?
Remember:
###NI=(RevCOGSFCDeprIntExp).(1t_c )### ###CFFA=NI+DeprCapEx  ΔNWC+IntExp###Which one of the following will increase the Cash Flow From Assets in this year for a taxpaying firm, all else remaining constant?
A manufacturing company is considering a new project in the more risky services industry. The cash flows from assets (CFFA) are estimated for the new project, with interest expense excluded from the calculations. To get the levered value of the project, what should these unlevered cash flows be discounted by?
Assume that the manufacturing firm has a target debttoassets ratio that it sticks to.
A retail furniture company buys furniture wholesale and distributes it through its retail stores. The owner believes that she has some good ideas for making stylish new furniture. She is considering a project to buy a factory and employ workers to manufacture the new furniture she's designed. Furniture manufacturing has more systematic risk than furniture retailing.
Her furniture retailing firm's aftertax WACC is 20%. Furniture manufacturing firms have an aftertax WACC of 30%. Both firms are optimally geared. Assume a classical tax system.
Which method(s) will give the correct valuation of the new furnituremaking project? Select the most correct answer.
The US firm Google operates in the online advertising business. In 2011 Google bought Motorola Mobility which manufactures mobile phones.
Assume the following:
 Google had a 10% aftertax weighted average cost of capital (WACC) before it bought Motorola.
 Motorola had a 20% aftertax WACC before it merged with Google.
 Google and Motorola have the same level of gearing.
 Both companies operate in a classical tax system.
You are a manager at Motorola. You must value a project for making mobile phones. Which method(s) will give the correct valuation of the mobile phone manufacturing project? Select the most correct answer.
The mobile phone manufacturing project's:
A company increases the proportion of debt funding it uses to finance its assets by issuing bonds and using the cash to repurchase stock, leaving assets unchanged.
Ignoring the costs of financial distress, which of the following statements is NOT correct:
Value the following business project to manufacture a new product.
Project Data  
Project life  2 yrs  
Initial investment in equipment  $6m  
Depreciation of equipment per year  $3m  
Expected sale price of equipment at end of project  $0.6m  
Unit sales per year  4m  
Sale price per unit  $8  
Variable cost per unit  $5  
Fixed costs per year, paid at the end of each year  $1m  
Interest expense per year  0  
Tax rate  30%  
Weighted average cost of capital after tax per annum  10%  
Notes
 The firm's current assets and current liabilities are $3m and $2m respectively right now. This net working capital will not be used in this project, it will be used in other unrelated projects.
Due to the project, current assets (mostly inventory) will grow by $2m initially (at t = 0), and then by $0.2m at the end of the first year (t=1).
Current liabilities (mostly trade creditors) will increase by $0.1m at the end of the first year (t=1).
At the end of the project, the net working capital accumulated due to the project can be sold for the same price that it was bought.  The project cost $0.5m to research which was incurred one year ago.
Assumptions
 All cash flows occur at the start or end of the year as appropriate, not in the middle or throughout the year.
 All rates and cash flows are real. The inflation rate is 3% pa.
 All rates are given as effective annual rates.
 The business considering the project is run as a 'sole tradership' (run by an individual without a company) and is therefore eligible for a 50% capital gains tax discount when the equipment is sold, as permitted by the Australian Tax Office.
What is the expected net present value (NPV) of the project?
A method commonly seen in textbooks for calculating a levered firm's free cash flow (FFCF, or CFFA) is the following:
###\begin{aligned} FFCF &= (Rev  COGS  Depr  FC  IntExp)(1t_c) + \\ &\space\space\space+ Depr  CapEx \Delta NWC + IntExp(1t_c) \\ \end{aligned}###
Question 370 capital budgeting, NPV, interest tax shield, WACC, CFFA
Project Data  
Project life  2 yrs  
Initial investment in equipment  $600k  
Depreciation of equipment per year  $250k  
Expected sale price of equipment at end of project  $200k  
Revenue per job  $12k  
Variable cost per job  $4k  
Quantity of jobs per year  120  
Fixed costs per year, paid at the end of each year  $100k  
Interest expense in first year (at t=1)  $16.091k  
Interest expense in second year (at t=2)  $9.711k  
Tax rate  30%  
Government treasury bond yield  5%  
Bank loan debt yield  6%  
Levered cost of equity  12.5%  
Market portfolio return  10%  
Beta of assets  1.24  
Beta of levered equity  1.5  
Firm's and project's debttoequity ratio  25%  
Notes
 The project will require an immediate purchase of $50k of inventory, which will all be sold at cost when the project ends. Current liabilities are negligible so they can be ignored.
Assumptions
 The debttoequity ratio will be kept constant throughout the life of the project. The amount of interest expense at the end of each period has been correctly calculated to maintain this constant debttoequity ratio. Note that interest expense is different in each year.
 Thousands are represented by 'k' (kilo).
 All cash flows occur at the start or end of the year as appropriate, not in the middle or throughout the year.
 All rates and cash flows are nominal. The inflation rate is 2% pa.
 All rates are given as effective annual rates.
 The 50% capital gains tax discount is not available since the project is undertaken by a firm, not an individual.
What is the net present value (NPV) of the project?
A firm has a debttoequity ratio of 25%. What is its debttoassets ratio?
There are many ways to calculate a firm's free cash flow (FFCF), also called cash flow from assets (CFFA). Some include the annual interest tax shield in the cash flow and some do not.
Which of the below FFCF formulas include the interest tax shield in the cash flow?
###(1) \quad FFCF=NI + Depr  CapEx ΔNWC + IntExp### ###(2) \quad FFCF=NI + Depr  CapEx ΔNWC + IntExp.(1t_c)### ###(3) \quad FFCF=EBIT.(1t_c )+ Depr CapEx ΔNWC+IntExp.t_c### ###(4) \quad FFCF=EBIT.(1t_c) + Depr CapEx ΔNWC### ###(5) \quad FFCF=EBITDA.(1t_c )+Depr.t_c CapEx ΔNWC+IntExp.t_c### ###(6) \quad FFCF=EBITDA.(1t_c )+Depr.t_c CapEx ΔNWC### ###(7) \quad FFCF=EBITTax + Depr  CapEx ΔNWC### ###(8) \quad FFCF=EBITTax + Depr  CapEx ΔNWCIntExp.t_c### ###(9) \quad FFCF=EBITDATax  CapEx ΔNWC### ###(10) \quad FFCF=EBITDATax  CapEx ΔNWCIntExp.t_c###The formulas for net income (NI also called earnings), EBIT and EBITDA are given below. Assume that depreciation and amortisation are both represented by 'Depr' and that 'FC' represents fixed costs such as rent.
###NI=(Rev  COGS  Depr  FC  IntExp).(1t_c )### ###EBIT=Rev  COGS  FCDepr### ###EBITDA=Rev  COGS  FC### ###Tax =(Rev  COGS  Depr  FC  IntExp).t_c= \dfrac{NI.t_c}{1t_c}###One formula for calculating a levered firm's free cash flow (FFCF, or CFFA) is to use earnings before interest and tax (EBIT).
###\begin{aligned} FFCF &= (EBIT)(1t_c) + Depr  CapEx \Delta NWC + IntExp.t_c \\ &= (Rev  COGS  Depr  FC)(1t_c) + Depr  CapEx \Delta NWC + IntExp.t_c \\ \end{aligned} \\###
One formula for calculating a levered firm's free cash flow (FFCF, or CFFA) is to use net operating profit after tax (NOPAT).
###\begin{aligned} FFCF &= NOPAT + Depr  CapEx \Delta NWC \\ &= (Rev  COGS  Depr  FC)(1t_c) + Depr  CapEx \Delta NWC \\ \end{aligned} \\###
A company issues a large amount of bonds to raise money for new projects of similar risk to the company's existing projects. The net present value (NPV) of the new projects is positive but small. Assume a classical tax system. Which statement is NOT correct?
A firm has a debttoassets ratio of 50%. The firm then issues a large amount of equity to raise money for new projects of similar systematic risk to the company's existing projects. Assume a classical tax system. Which statement is correct?
A firm has a debttoassets ratio of 50%. The firm then issues a large amount of debt to raise money for new projects of similar risk to the company's existing projects. Assume a classical tax system. Which statement is correct?
Question 337 capital structure, interest tax shield, leverage, real and nominal returns and cash flows, multi stage growth model
A fastgrowing firm is suitable for valuation using a multistage growth model.
It's nominal unlevered cash flow from assets (##CFFA_U##) at the end of this year (t=1) is expected to be $1 million. After that it is expected to grow at a rate of:
 12% pa for the next two years (from t=1 to 3),
 5% over the fourth year (from t=3 to 4), and
 1% forever after that (from t=4 onwards). Note that this is a negative one percent growth rate.
Assume that:
 The nominal WACC after tax is 9.5% pa and is not expected to change.
 The nominal WACC before tax is 10% pa and is not expected to change.
 The firm has a target debttoequity ratio that it plans to maintain.
 The inflation rate is 3% pa.
 All rates are given as nominal effective annual rates.
What is the levered value of this fast growing firm's assets?
Question 559 variance, standard deviation, covariance, correlation
Which of the following statements about standard statistical mathematics notation is NOT correct?
Diversification in a portfolio of two assets works best when the correlation between their returns is:
Portfolio Details  
Stock  Expected return 
Standard deviation 
Correlation ##(\rho_{A,B})##  Dollars invested 

A  0.1  0.4  0.5  60  
B  0.2  0.6  140  
What is the standard deviation (not variance) of the above portfolio?
All things remaining equal, the variance of a portfolio of two positivelyweighted stocks rises as:
Two risky stocks A and B comprise an equalweighted portfolio. The correlation between the stocks' returns is 70%.
If the variance of stock A increases but the:
 Prices and expected returns of each stock stays the same,
 Variance of stock B's returns stays the same,
 Correlation of returns between the stocks stays the same.
Which of the following statements is NOT correct?
All things remaining equal, the higher the correlation of returns between two stocks:
An investor wants to make a portfolio of two stocks A and B with a target expected portfolio return of 6% pa.
 Stock A has an expected return of 5% pa.
 Stock B has an expected return of 10% pa.
What portfolio weights should the investor have in stocks A and B respectively?
Question 556 portfolio risk, portfolio return, standard deviation
An investor wants to make a portfolio of two stocks A and B with a target expected portfolio return of 12% pa.
 Stock A has an expected return of 10% pa and a standard deviation of 20% pa.
 Stock B has an expected return of 15% pa and a standard deviation of 30% pa.
The correlation coefficient between stock A and B's expected returns is 70%.
What will be the annual standard deviation of the portfolio with this 12% pa target return?
What is the correlation of a variable X with itself?
The corr(X, X) or ##\rho_{X,X}## equals:
What is the correlation of a variable X with a constant C?
The corr(X, C) or ##\rho_{X,C}## equals:
The covariance and correlation of two stocks X and Y's annual returns are calculated over a number of years. The units of the returns are in percent per annum ##(\% pa)##.
What are the units of the covariance ##(\sigma_{X,Y})## and correlation ##(\rho_{X,Y})## of returns respectively?
Hint: Visit Wikipedia to understand the difference between percentage points ##(\text{pp})## and percent ##(\%)##.
Let the standard deviation of returns for a share per month be ##\sigma_\text{monthly}##.
What is the formula for the standard deviation of the share's returns per year ##(\sigma_\text{yearly})##?
Assume that returns are independently and identically distributed (iid) so they have zero auto correlation, meaning that if the return was higher than average today, it does not indicate that the return tomorrow will be higher or lower than average.
Mr Blue, Miss Red and Mrs Green are people with different utility functions.
Note that a fair gamble is a bet that has an expected value of zero, such as paying $0.50 to win $1 in a coin flip with heads or nothing if it lands tails. Fairly priced insurance is when the expected present value of the insurance premiums is equal to the expected loss from the disaster that the insurance protects against, such as the cost of rebuilding a home after a catastrophic fire.
Which of the following statements is NOT correct?
Question 703 utility, risk aversion, utility function, gamble
Mr Blue, Miss Red and Mrs Green are people with different utility functions.
Each person has $500 of initial wealth. A coin toss game is offered to each person at a casino where the player can win or lose $500. Each player can flip a coin and if they flip heads, they receive $500. If they flip tails then they will lose $500. Which of the following statements is NOT correct?
Question 704 utility, risk aversion, utility function, gamble
Mr Blue, Miss Red and Mrs Green are people with different utility functions.
Each person has $256 of initial wealth. A coin toss game is offered to each person at a casino where the player can win or lose $256. Each player can flip a coin and if they flip heads, they receive $256. If they flip tails then they will lose $256. Which of the following statements is NOT correct?
Mr Blue, Miss Red and Mrs Green are people with different utility functions.
Which of the following statements is NOT correct?
Diversification is achieved by investing in a large amount of stocks. What type of risk is reduced by diversification?
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 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?
The security market line (SML) shows the relationship between beta and expected return.
Investment projects that plot above the SML would have:
Stock A has a beta of 0.5 and stock B has a beta of 1. Which statement is NOT correct?
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?
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?
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?
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?
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%. 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?
The CAPM can be used to find a business's expected opportunity cost of capital:
###r_i=r_f+β_i (r_mr_f)###
What should be used as the risk free rate ##r_f##?
A firm changes its capital structure by issuing a large amount of equity and using the funds to repay debt. Its assets are unchanged. Ignore interest tax shields.
According to the Capital Asset Pricing Model (CAPM), which statement is correct?
Which of the following statements about the weighted average cost of capital (WACC) is NOT correct?
Question 418 capital budgeting, NPV, interest tax shield, WACC, CFFA, CAPM
Project Data  
Project life  1 year  
Initial investment in equipment  $8m  
Depreciation of equipment per year  $8m  
Expected sale price of equipment at end of project  0  
Unit sales per year  4m  
Sale price per unit  $10  
Variable cost per unit  $5  
Fixed costs per year, paid at the end of each year  $2m  
Interest expense in first year (at t=1)  $0.562m  
Corporate tax rate  30%  
Government treasury bond yield  5%  
Bank loan debt yield  9%  
Market portfolio return  10%  
Covariance of levered equity returns with market  0.32  
Variance of market portfolio returns  0.16  
Firm's and project's debttoequity ratio  50%  
Notes
 Due to the project, current assets will increase by $6m now (t=0) and fall by $6m at the end (t=1). Current liabilities will not be affected.
Assumptions
 The debttoequity ratio will be kept constant throughout the life of the project. The amount of interest expense at the end of each period has been correctly calculated to maintain this constant debttoequity ratio.
 Millions are represented by 'm'.
 All cash flows occur at the start or end of the year as appropriate, not in the middle or throughout the year.
 All rates and cash flows are real. The inflation rate is 2% pa. All rates are given as effective annual rates.
 The project is undertaken by a firm, not an individual.
What is the net present value (NPV) of the project?
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?
A firm's weighted average cost of capital before tax (##r_\text{WACC before tax}##) would increase due to:
A company has:
 50 million shares outstanding.
 The market price of one share is currently $6.
 The riskfree rate is 5% and the market return is 10%.
 Market analysts believe that the company's ordinary shares have a beta of 2.
 The company has 1 million preferred stock which have a face (or par) value of $100 and pay a constant dividend of 10% of par. They currently trade for $80 each.
 The company's debentures are publicly traded and their market price is equal to 90% of their face value.
 The debentures have a total face value of $60,000,000 and the current yield to maturity of corporate debentures is 10% per annum. The corporate tax rate is 30%.
What is the company's aftertax weighted average cost of capital (WACC)? Assume a classical tax system.
A company has:
 140 million shares outstanding.
 The market price of one share is currently $2.
 The company's debentures are publicly traded and their market price is equal to 93% of the face value.
 The debentures have a total face value of $50,000,000 and the current yield to maturity of corporate debentures is 12% per annum.
 The riskfree rate is 8.50% and the market return is 13.7%.
 Market analysts estimated that the company's stock has a beta of 0.90.
 The corporate tax rate is 30%.
What is the company's aftertax weighted average cost of capital (WACC) in a classical tax system?
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 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 aftertax WACC? Assume a classical tax system.
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?
Which statement(s) are correct?
(i) All stocks that plot on the Security Market Line (SML) are fairly priced.
(ii) All stocks that plot above the Security Market Line (SML) are overpriced.
(iii) All fairly priced stocks that plot on the Capital Market Line (CML) have zero idiosyncratic risk.
Select the most correct response:
A firm changes its capital structure by issuing a large amount of debt and using the funds to repurchase shares. Its assets are unchanged. Ignore interest tax shields.
According to the Capital Asset Pricing Model (CAPM), which statement is correct?
Question 104 CAPM, payout policy, capital structure, Miller and Modigliani, risk
Assume that there exists a perfect world with no transaction costs, no asymmetric information, no taxes, no agency costs, equal borrowing rates for corporations and individual investors, the ability to short the risk free asset, semistrong form efficient markets, the CAPM holds, investors are rational and riskaverse and there are no other market frictions.
For a firm operating in this perfect world, which statement(s) are correct?
(i) When a firm changes its capital structure and/or payout policy, share holders' wealth is unaffected.
(ii) When the idiosyncratic risk of a firm's assets increases, share holders do not expect higher returns.
(iii) When the systematic risk of a firm's assets increases, share holders do not expect higher returns.
Select the most correct response:
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?
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?
A stock has a beta of 0.5. Its next dividend is expected to be $3, paid one year from now. Dividends are expected to be paid annually and grow by 2% pa forever. Treasury bonds yield 5% pa and the market portfolio's expected return is 10% pa. All returns are effective annual rates.
What is the price of the stock now?
Question 235 SML, NPV, CAPM, risk
The security market line (SML) shows the relationship between beta and expected return.
Investment projects that plot on the SML would have:
Question 244 CAPM, SML, NPV, risk
Examine the following graph which shows stocks' betas ##(\beta)## and expected returns ##(\mu)##:
Assume that the CAPM holds and that future expectations of stocks' returns and betas are correctly measured. Which statement is NOT correct?
The total return of any asset can be broken down in different ways. One possible way is to use the dividend discount model (or Gordon growth model):
###p_0 = \frac{c_1}{r_\text{total}r_\text{capital}}###
Which, since ##c_1/p_0## is the income return (##r_\text{income}##), can be expressed as:
###r_\text{total}=r_\text{income}+r_\text{capital}###
So the total return of an asset is the income component plus the capital or price growth component.
Another way to break up total return is to use the Capital Asset Pricing Model:
###r_\text{total}=r_\text{f}+β(r_\text{m} r_\text{f})###
###r_\text{total}=r_\text{time value}+r_\text{risk premium}###
So the risk free rate is the time value of money and the term ##β(r_\text{m} r_\text{f})## is the compensation for taking on systematic risk.
Using the above theory and your general knowledge, which of the below equations, if any, are correct?
(I) ##r_\text{income}=r_\text{time value}##
(II) ##r_\text{income}=r_\text{risk premium}##
(III) ##r_\text{capital}=r_\text{time value}##
(IV) ##r_\text{capital}=r_\text{risk premium}##
(V) ##r_\text{income}+r_\text{capital}=r_\text{time value}+r_\text{risk premium}##
Which of the equations are correct?
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 419 capital budgeting, NPV, interest tax shield, WACC, CFFA, CAPM, no explanation
Project Data  
Project life  1 year  
Initial investment in equipment  $6m  
Depreciation of equipment per year  $6m  
Expected sale price of equipment at end of project  0  
Unit sales per year  9m  
Sale price per unit  $8  
Variable cost per unit  $6  
Fixed costs per year, paid at the end of each year  $1m  
Interest expense in first year (at t=1)  $0.53m  
Tax rate  30%  
Government treasury bond yield  5%  
Bank loan debt yield  6%  
Market portfolio return  10%  
Covariance of levered equity returns with market  0.08  
Variance of market portfolio returns  0.16  
Firm's and project's debttoassets ratio  50%  
Notes
 Due to the project, current assets will increase by $5m now (t=0) and fall by $5m at the end (t=1). Current liabilities will not be affected.
Assumptions
 The debttoassets ratio will be kept constant throughout the life of the project. The amount of interest expense at the end of each period has been correctly calculated to maintain this constant debttoequity ratio.
 Millions are represented by 'm'.
 All cash flows occur at the start or end of the year as appropriate, not in the middle or throughout the year.
 All rates and cash flows are real. The inflation rate is 2% pa.
 All rates are given as effective annual rates.
 The 50% capital gains tax discount is not available since the project is undertaken by a firm, not an individual.
What is the net present value (NPV) of the project?
Question 657 systematic and idiosyncratic risk, CAPM, no explanation
A stock's required total return will decrease when its:
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 119 market efficiency, fundamental analysis, joint hypothesis problem
Your friend claims that by reading 'The Economist' magazine's economic news articles, she can identify shares that will have positive abnormal expected returns over the next 2 years. Assuming that her claim is true, which statement(s) are correct?
(i) Weak form market efficiency is broken.
(ii) Semistrong form market efficiency is broken.
(iii) Strong form market efficiency is broken.
(iv) The asset pricing model used to measure the abnormal returns (such as the CAPM) is either wrong (misspecification error) or is measured using the wrong inputs (data errors) so the returns may not be abnormal but rather fair for the level of risk.
Select the most correct response:
Fundamentalists who analyse company financial reports and news announcements (but who don't have inside information) will make positive abnormal returns if:
The efficient markets hypothesis (EMH) and noarbitrage pricing theory is most closely related to which of the following concepts?
Question 339 bond pricing, inflation, market efficiency, income and capital returns
Economic statistics released this morning were a surprise: they show a strong chance of consumer price inflation (CPI) reaching 5% pa over the next 2 years.
This is much higher than the previous forecast of 3% pa.
A vanilla fixedcoupon 2year riskfree government bond was issued at par this morning, just before the economic news was released.
What is the expected change in bond price after the economic news this morning, and in the next 2 years? Assume that:
 Inflation remains at 5% over the next 2 years.
 Investors demand a constant real bond yield.
 The bond price falls by the (aftertax) value of the coupon the night before the excoupon date, as in real life.
Question 338 market efficiency, CAPM, opportunity cost, technical analysis
A man inherits $500,000 worth of shares.
He believes that by learning the secrets of trading, keeping up with the financial news and doing complex trend analysis with charts that he can quit his job and become a selfemployed day trader in the equities markets.
What is the expected gain from doing this over the first year? Measure the net gain in wealth received at the end of this first year due to the decision to become a day trader. Assume the following:
 He earns $60,000 pa in his current job, paid in a lump sum at the end of each year.
 He enjoys examining share price graphs and day trading just as much as he enjoys his current job.
 Stock markets are weak form and semistrong form efficient.
 He has no inside information.
 He makes 1 trade every day and there are 250 trading days in the year. Trading costs are $20 per trade. His broker invoices him for the trading costs at the end of the year.
 The shares that he currently owns and the shares that he intends to trade have the same level of systematic risk as the market portfolio.
 The market portfolio's expected return is 10% pa.
Measure the net gain over the first year as an expected wealth increase at the end of the year.
A company advertises an investment costing $1,000 which they say is underpriced. They say that it has an expected total return of 15% pa, but a required return of only 10% pa. Assume that there are no dividend payments so the entire 15% total return is all capital return.
Assuming that the company's statements are correct, what is the NPV of buying the investment if the 15% return lasts for the next 100 years (t=0 to 100), then reverts to 10% pa after that time? Also, what is the NPV of the investment if the 15% return lasts forever?
In both cases, assume that the required return of 10% remains constant. All returns are given as effective annual rates.
The answer choices below are given in the same order (15% for 100 years, and 15% forever):
Question 100 market efficiency, technical analysis, joint hypothesis problem
A company selling charting and technical analysis software claims that independent academic studies have shown that its software makes significantly positive abnormal returns. Assuming the claim is true, which statement(s) are correct?
(I) Weak form market efficiency is broken.
(II) Semistrong form market efficiency is broken.
(III) Strong form market efficiency is broken.
(IV) The asset pricing model used to measure the abnormal returns (such as the CAPM) had misspecification error so the returns may not be abnormal but rather fair for the level of risk.
Select the most correct response:
A person is thinking about borrowing $100 from the bank at 7% pa and investing it in shares with an expected return of 10% pa. One year later the person will sell the shares and pay back the loan in full. Both the loan and the shares are fairly priced.
What is the Net Present Value (NPV) of this one year investment? Note that you are asked to find the present value (##V_0##), not the value in one year (##V_1##).
Select the most correct statement from the following.
'Chartists', also known as 'technical traders', believe that:
Question 668 buy and hold, market efficiency, idiom
A quote from the famous investor Warren Buffet: "Much success can be attributed to inactivity. Most investors cannot resist the temptation to constantly buy and sell."
Buffet is referring to the buyandhold strategy which is to buy and never sell shares. Which of the following is a disadvantage of a buyandhold strategy? Assume that share markets are semistrong form efficient. Which of the following is NOT an advantage of the strict buyandhold strategy? A disadvantage of the buyandhold strategy is that it reduces:
A managed fund charges fees based on the amount of money that you keep with them. The fee is 2% of the startofyear amount, but it is paid at the end of every year.
This fee is charged regardless of whether the fund makes gains or losses on your money.
The fund offers to invest your money in shares which have an expected return of 10% pa before fees.
You are thinking of investing $100,000 in the fund and keeping it there for 40 years when you plan to retire.
What is the Net Present Value (NPV) of investing your money in the fund? Note that the question is not asking how much money you will have in 40 years, it is asking: what is the NPV of investing in the fund? Assume that:
 The fund has no private information.
 Markets are weak and semistrong form efficient.
 The fund's transaction costs are negligible.
 The cost and trouble of investing your money in shares by yourself, without the managed fund, is negligible.
Question 416 real estate, market efficiency, income and capital returns, DDM, CAPM
A residential real estate investor believes that house prices will grow at a rate of 5% pa and that rents will grow by 2% pa forever.
All rates are given as nominal effective annual returns. Assume that:
 His forecast is true.
 Real estate is and always will be fairly priced and the capital asset pricing model (CAPM) is true.
 Ignore all costs such as taxes, agent fees, maintenance and so on.
 All rental income cash flow is paid out to the owner, so there is no reinvestment and therefore no additions or improvements made to the property.
 The nonmonetary benefits of owning real estate and renting remain constant.
Which one of the following statements is NOT correct? Over time:
A managed fund charges fees based on the amount of money that you keep with them. The fee is 2% of the endofyear amount, paid at the end of every year.
This fee is charged regardless of whether the fund makes gains or losses on your money.
The fund offers to invest your money in shares which have an expected return of 10% pa before fees.
You are thinking of investing $100,000 in the fund and keeping it there for 40 years when you plan to retire.
How much money do you expect to have in the fund in 40 years? Also, what is the future value of the fees that the fund expects to earn from you? Give both amounts as future values in 40 years. Assume that:
 The fund has no private information.
 Markets are weak and semistrong form efficient.
 The fund's transaction costs are negligible.
 The cost and trouble of investing your money in shares by yourself, without the managed fund, is negligible.
 The fund invests its fees in the same companies as it invests your funds in, but with no fees.
The below answer choices list your expected wealth in 40 years and then the fund's expected wealth in 40 years.