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 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 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 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 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.
In Australia in the 1980's, inflation was around 8% pa, and residential mortgage loan interest rates were around 14%.
In 2013, inflation was around 2.5% pa, and residential mortgage loan interest rates were around 4.5%.
If a person can afford constant mortgage loan payments of $2,000 per month, how much more can they borrow when interest rates are 4.5% pa compared with 14.0% pa?
Give your answer as a proportional increase over the amount you could borrow when interest rates were high ##(V_\text{high rates})##, so:
###\text{Proportional increase} = \dfrac{V_\text{low rates}V_\text{high rates}}{V_\text{high rates}} ###
Assume that:
 Interest rates are expected to be constant over the life of the loan.
 Loans are 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 (APR's) compounding per month.
Calculate the price of a newly issued ten year bond with a face value of $100, a yield of 8% pa and a fixed coupon rate of 6% pa, paid annually. So there's only one coupon per year, paid in arrears every year.
Calculate the price of a newly issued ten year bond with a face value of $100, a yield of 8% pa and a fixed coupon rate of 6% pa, paid 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?
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?
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?
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?
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.
"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:
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.
Find Candys Corporation's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.
Candys Corp  
Income Statement for  
year ending 30th June 2013  
$m  
Sales  200  
COGS  50  
Operating expense  10  
Depreciation  20  
Interest expense  10  
Income before tax  110  
Tax at 30%  33  
Net income  77  
Candys Corp  
Balance Sheet  
as at 30th June  2013  2012 
$m  $m  
Assets  
Current assets  220  180 
PPE  
Cost  300  340 
Accumul. depr.  60  40 
Carrying amount  240  300 
Total assets  460  480 
Liabilities  
Current liabilities  175  190 
Noncurrent liabilities  135  130 
Owners' equity  
Retained earnings  50  60 
Contributed equity  100  100 
Total L and OE  460  480 
Note: all figures are given in millions of dollars ($m).
Why is Capital Expenditure (CapEx) subtracted in the Cash Flow From Assets (CFFA) formula?
###CFFA=NI+DeprCapEx  \Delta NWC+IntExp###
A firm has forecast its Cash Flow From Assets (CFFA) for this year and management is worried that it is too low. Which one of the following actions will lead to a higher CFFA for this year (t=0 to 1)? Only consider cash flows this year. Do not consider cash flows after one year, or the change in the NPV of the firm. Consider each action in isolation.
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  \Delta NWC+IntExp###Which one of the following will have no effect on net income (NI) but decrease cash flow from assets (CFFA or FFCF) in this year for a taxpaying firm, all else remaining constant?
Remember:
###NI=(RevCOGSFCDeprIntExp).(1t_c )### ###CFFA=NI+DeprCapEx  ΔNWC+IntExp###Find ChingALings Corporation's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.
ChingALings Corp  
Income Statement for  
year ending 30th June 2013  
$m  
Sales  100  
COGS  20  
Depreciation  20  
Rent expense  11  
Interest expense  19  
Taxable Income  30  
Taxes at 30%  9  
Net income  21  
ChingALings Corp  
Balance Sheet  
as at 30th June  2013  2012 
$m  $m  
Inventory  49  38 
Trade debtors  14  2 
Rent paid in advance  5  5 
PPE  400  400 
Total assets  468  445 
Trade creditors  4  10 
Bond liabilities  200  190 
Contributed equity  145  145 
Retained profits  119  100 
Total L and OE  468  445 
Note: All figures are given in millions of dollars ($m).
The cash flow from assets was:
Over the next year, the management of an unlevered company plans to:
 Make $5m in sales, $1.9m in net income and $2m in equity free cash flow (EFCF).
 Pay dividends of $1m.
 Complete a $1.3m share buyback.
Assume that:
 All amounts are received and paid at the end of the year so you can ignore the time value of money.
 The firm has sufficient retained profits to legally pay the dividend and complete the buy back.
 The firm plans to run a very tight ship, with no excess cash above operating requirements currently or over the next year.
How much new equity financing will the company need? In other words, what is the value of new shares that will need to be issued?
Read the following financial statements and calculate the firm's free cash flow over the 2014 financial year.
UBar Corp  
Income Statement for  
year ending 30th June 2014  
$m  
Sales  293  
COGS  200  
Rent expense  15  
Gas expense  8  
Depreciation  10  
EBIT  60  
Interest expense  0  
Taxable income  60  
Taxes  18  
Net income  42  
UBar Corp  
Balance Sheet  
as at 30th June  2014  2013 
$m  $m  
Assets  
Cash  30  29 
Accounts receivable  5  7 
Prepaid rent expense  1  0 
Inventory  50  46 
PPE  290  300 
Total assets  376  382 
Liabilities  
Trade payables  20  18 
Accrued gas expense  3  2 
Noncurrent liabilities  0  0 
Contributed equity  212  212 
Retained profits  136  150 
Asset revaluation reserve  5  0 
Total L and OE  376  382 
Note: all figures are given in millions of dollars ($m).
The firm's free cash flow over the 2014 financial year was:
Find Trademark Corporation's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.
Trademark Corp  
Income Statement for  
year ending 30th June 2013  
$m  
Sales  100  
COGS  25  
Operating expense  5  
Depreciation  20  
Interest expense  20  
Income before tax  30  
Tax at 30%  9  
Net income  21  
Trademark Corp  
Balance Sheet  
as at 30th June  2013  2012 
$m  $m  
Assets  
Current assets  120  80 
PPE  
Cost  150  140 
Accumul. depr.  60  40 
Carrying amount  90  100 
Total assets  210  180 
Liabilities  
Current liabilities  75  65 
Noncurrent liabilities  75  55 
Owners' equity  
Retained earnings  10  10 
Contributed equity  50  50 
Total L and OE  210  180 
Note: all figures are given in millions of dollars ($m).
Find UniBar Corp's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.
UniBar Corp  
Income Statement for  
year ending 30th June 2013  
$m  
Sales  80  
COGS  40  
Operating expense  15  
Depreciation  10  
Interest expense  5  
Income before tax  10  
Tax at 30%  3  
Net income  7  
UniBar Corp  
Balance Sheet  
as at 30th June  2013  2012 
$m  $m  
Assets  
Current assets  120  90 
PPE  
Cost  360  320 
Accumul. depr.  40  30 
Carrying amount  320  290 
Total assets  440  380 
Liabilities  
Current liabilities  110  60 
Noncurrent liabilities  190  180 
Owners' equity  
Retained earnings  95  95 
Contributed equity  45  45 
Total L and OE  440  380 
Note: all figures are given in millions of dollars ($m).
Find Piano Bar's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.
Piano Bar  
Income Statement for  
year ending 30th June 2013  
$m  
Sales  310  
COGS  185  
Operating expense  20  
Depreciation  15  
Interest expense  10  
Income before tax  80  
Tax at 30%  24  
Net income  56  
Piano Bar  
Balance Sheet  
as at 30th June  2013  2012 
$m  $m  
Assets  
Current assets  240  230 
PPE  
Cost  420  400 
Accumul. depr.  50  35 
Carrying amount  370  365 
Total assets  610  595 
Liabilities  
Current liabilities  180  190 
Noncurrent liabilities  290  265 
Owners' equity  
Retained earnings  90  90 
Contributed equity  50  50 
Total L and OE  610  595 
Note: all figures are given in millions of dollars ($m).
Find World Bar's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.
World Bar  
Income Statement for  
year ending 30th June 2013  
$m  
Sales  300  
COGS  150  
Operating expense  50  
Depreciation  40  
Interest expense  10  
Taxable income  50  
Tax at 30%  15  
Net income  35  
World Bar  
Balance Sheet  
as at 30th June  2013  2012 
$m  $m  
Assets  
Current assets  200  230 
PPE  
Cost  400  400 
Accumul. depr.  75  35 
Carrying amount  325  365 
Total assets  525  595 
Liabilities  
Current liabilities  150  205 
Noncurrent liabilities  235  250 
Owners' equity  
Retained earnings  100  100 
Contributed equity  40  40 
Total L and OE  525  595 
Note: all figures above and below are given in millions of dollars ($m).
Find Scubar Corporation's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.
Scubar Corp  
Income Statement for  
year ending 30th June 2013  
$m  
Sales  200  
COGS  60  
Depreciation  20  
Rent expense  11  
Interest expense  19  
Taxable Income  90  
Taxes at 30%  27  
Net income  63  
Scubar Corp  
Balance Sheet  
as at 30th June  2013  2012 
$m  $m  
Inventory  60  50 
Trade debtors  19  6 
Rent paid in advance  3  2 
PPE  420  400 
Total assets  502  458 
Trade creditors  10  8 
Bond liabilities  200  190 
Contributed equity  130  130 
Retained profits  162  130 
Total L and OE  502  458 
Note: All figures are given in millions of dollars ($m).
The cash flow from assets was:
A young lady is trying to decide if she should attend university or not.
The young lady's parents say that she must attend university because otherwise all of her hard work studying and attending school during her childhood was a waste.
What's the correct way to classify this item from a capital budgeting perspective when trying to decide whether to attend university?
The hard work studying at school in her childhood should be classified as:
A young lady is trying to decide if she should attend university. Her friends say that she should go to university because she is more likely to meet a clever young man than if she begins full time work straight away.
What's the correct way to classify this item from a capital budgeting perspective when trying to find the Net Present Value of going to university rather than working?
The opportunity to meet a desirable future spouse should be classified as:
What is the net present value (NPV) of undertaking a fulltime Australian undergraduate business degree as an Australian citizen? Only include the cash flows over the duration of the degree, ignore any benefits or costs of the degree after it's completed.
Assume the following:
 The degree takes 3 years to complete and all students pass all subjects.
 There are 2 semesters per year and 4 subjects per semester.
 University fees per subject per semester are $1,277, paid at the start of each semester. Fees are expected to stay constant for the next 3 years.
 There are 52 weeks per year.
 The first semester is just about to start (t=0). The first semester lasts for 19 weeks (t=0 to 19).
 The second semester starts immediately afterwards (t=19) and lasts for another 19 weeks (t=19 to 38).
 The summer holidays begin after the second semester ends and last for 14 weeks (t=38 to 52). Then the first semester begins the next year, and so on.
 Working full time at the grocery store instead of studying fulltime pays $20/hr and you can work 35 hours per week. Wages are paid at the end of each week.
 Fulltime students can work fulltime during the summer holiday at the grocery store for the same rate of $20/hr for 35 hours per week. Wages are paid at the end of each week.
 The discount rate is 9.8% pa. All rates and cash flows are real. Inflation is expected to be 3% pa. All rates are effective annual.
The NPV of costs from undertaking the university degree is:
A firm plans to issue equity and use the cash raised to pay off its debt. No assets will be bought or sold. Ignore the costs of financial distress.
Which of the following statements is NOT correct, all things remaining equal?
Question 121 capital structure, leverage, financial distress, interest tax shield
Fill in the missing words in the following sentence:
All things remaining equal, as a firm's amount of debt funding falls, benefits of interest tax shields __________ and the costs of financial distress __________.
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 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?
Question 69 interest tax shield, capital structure, leverage, WACC
Which statement about risk, required return and capital structure is the most correct?
A firm is considering a new project of similar risk to the current risk of the firm. This project will expand its existing business. The cash flows of the project have been calculated assuming that there is no interest expense. In other words, the cash flows assume that the project is allequity financed.
In fact the firm has a target debttoequity ratio of 1, so the project will be financed with 50% debt and 50% equity. To find the levered value of the firm's assets, what discount rate should be applied to the project's unlevered cash flows? Assume a classical tax system.
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.
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.
Which one of the following will increase the Cash Flow From Assets in this year for a taxpaying firm, all else remaining constant?
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###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 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}###
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 method for calculating a firm's free cash flow (FFCF, or CFFA) is to ignore interest expense. That is, pretend that interest expense ##(IntExp)## is zero:
###\begin{aligned} FFCF &= (Rev  COGS  Depr  FC  IntExp)(1t_c) + Depr  CapEx \Delta NWC + IntExp \\ &= (Rev  COGS  Depr  FC  0)(1t_c) + Depr  CapEx \Delta NWC  0\\ \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 firm has a debttoassets ratio of 50%. The firm then issues a large amount of debt to raise money for new projects of similar market 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?
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?
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.
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} ###
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 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?
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?
A new company's Firm Free Cash Flow (FFCF, same as CFFA) is forecast in the graph below.
To value the firm's assets, the terminal value needs to be calculated using the perpetuity with growth formula:
###V_{\text{terminal, }t1} = \dfrac{FFCF_{\text{terminal, }t}}{rg}###
Which point corresponds to the best time to calculate the terminal value?
A young lady is trying to decide if she should attend university or begin working straight away in her home town.
The young lady's grandma says that she should not go to university because she is less likely to marry the local village boy whom she likes because she will spend less time with him if she attends university.
What's the correct way to classify this item from a capital budgeting perspective when trying to decide whether to attend university?
The cost of not marrying the local village boy should be classified as:
Find the cash flow from assets (CFFA) of the following project.
Project Data  
Project life  2 years 
Initial investment in equipment  $8m 
Depreciation of equipment per year for tax purposes  $3m 
Unit sales per year  10m 
Sale price per unit  $9 
Variable cost per unit  $4 
Fixed costs per year, paid at the end of each year  $2m 
Tax rate  30% 
Note 1: Due to the project, the firm will have to purchase $40m of inventory initially (at t=0). Half of this inventory will be sold at t=1 and the other half at t=2.
Note 2: The equipment will have a book value of $2m at the end of the project for tax purposes. However, the equipment is expected to fetch $1m when it is sold. Assume that the full capital loss is taxdeductible and taxed at the full corporate tax rate.
Note 3: The project will be fully funded by equity which investors will expect to pay dividends totaling $10m at the end of each year.
Find the project's CFFA at time zero, one and two. Answers are given in millions of dollars ($m).
The equations for Net Income (NI, also known as Earnings or Net Profit After Tax) and Cash Flow From Assets (CFFA, also known as Free Cash Flow to the Firm) per year are:
###NI=(RevCOGSFCDeprIntExp).(1t_c)###
###CFFA=NI+DeprCapEx  \varDelta NWC+IntExp###
For a firm with debt, what is the amount of the interest tax shield per year?
Question 237 WACC, Miller and Modigliani, interest tax shield
Which of the following discount rates should be the highest for a levered company? Ignore the costs of financial distress.
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 and last at t=12).
 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?
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?
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 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?
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?
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?
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 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 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 $1.15(1+0.05)^2, and so on.
The required return on the stock is 10% pa. Both the growth rate and required return are given as effective annual rates. What is the current price of the stock?
A stock is expected to pay the following dividends:
Cash Flows of a Stock  
Time (yrs)  0  1  2  3  4  ... 
Dividend ($)  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 equation is the Dividend Discount Model, also known as the 'Gordon Growth Model' or the 'Perpetuity with growth' equation.
### p_0 = \frac{d_1}{r  g} ###
Which expression is NOT equal to the expected dividend yield?
A 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.
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?
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?
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 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?
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?
The following equation is the Dividend Discount Model, also known as the 'Gordon Growth Model' or the 'Perpetuity with growth' equation.
### p_{0} = \frac{c_1}{r_{\text{eff}}  g_{\text{eff}}} ###
What is the discount rate '## r_\text{eff} ##' in this equation?
When using the dividend discount model to price a stock:
### p_{0} = \frac{d_1}{r  g} ###
The growth rate of dividends (g):
The following is the Dividend Discount Model used to price stocks:
### p_0=\frac{d_1}{rg} ###
Which of the following statements about the Dividend Discount Model is NOT correct?
A company's shares just paid their annual dividend of $2 each.
The stock price is now $40 (just after the dividend payment). The annual dividend is expected to grow by 3% every year forever. The assumptions of the dividend discount model are valid for this company.
What do you expect the effective annual dividend yield to be in 3 years (dividend yield from t=3 to t=4)?
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}{rg} ###
Which expression is equal to the expected dividend return?
Three years ago Frederika bought a house for $400,000.
Now it's worth $600,000, based on recent similar sales in the area.
Frederika's residential property has an expected total return of 7% pa.
She rents her house out for $2,500 per month, paid in advance. Every 12 months she plans to increase the rental payments.
The present value of 12 months of rental payments is $29,089.48.
The future value of 12 months of rental payments one year ahead is $31,125.74.
What is the expected annual capital yield of the property?
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 405 DDM, income and capital returns, no explanation
The perpetuity with growth formula is:
###P_0= \dfrac{C_1}{rg}###
Which of the following is NOT equal to the total required return (r)?
The perpetuity with growth equation is:
###P_0=\dfrac{C_1}{rg}###
Which of the following is NOT equal to the expected capital return as an effective annual rate?
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?
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?
Which of the following equations is NOT equal to the total return of an asset?
Let ##p_0## be the current price, ##p_1## the expected price in one year and ##c_1## the expected income in one year.
Question 748 income and capital returns, DDM, ex dividend date
A stock will pay you a dividend of $2 tonight if you buy it today.
Thereafter the annual dividend is expected to grow by 3% pa, so the next dividend after the $2 one tonight will be $2.06 in one year, then in two years it will be $2.1218 and so on. The stock's required return is 8% pa.
What is the stock price today and what do you expect the stock price to be tomorrow, approximately?
Question 731 DDM, income and capital returns, no explanation
In the dividend discount model (DDM), share prices fall when dividends are paid. Let the high price before the fall be called the peak, and the low price after the fall be called the trough.
###P_0=\dfrac{C_1}{rg}###
Which of the following statements about the DDM is NOT correct?
Question 730 DDM, income and capital returns, no explanation
A stock’s current price is $1. Its expected total return is 10% pa and its long term expected capital return is 4% pa. It pays an annual dividend and the next one will be paid in one year. All rates are given as effective annual rates. The dividend discount model is thought to be a suitable model for the stock. Ignore taxes. Which of the following statements about the stock is NOT correct?
Question 728 inflation, real and nominal returns and cash flows, income and capital returns, no explanation
Which of the following statements about gold is NOT correct? Assume that the gold price increases by inflation. Gold:
An investor bought a 20 year 5% pa fixed coupon government bond priced at par. The face value is $100. Coupons are paid semiannually and the next one is in 6 months.
Six months later, just after the coupon at that time was paid, yields suddenly and unexpectedly rose to 5.5% pa. Note that all yields above are given as APR's compounding semiannually.
What was the bond investors' historical total return over that first 6 month period, given as an effective semiannual rate?
A share’s current price is $60. It’s expected to pay a dividend of $1.50 in one year. The growth rate of the dividend is 0.5% pa and the stock’s required total return is 3% pa. The stock’s price can be modeled using the dividend discount model (DDM):
##P_0=\dfrac{C_1}{rg}##
Which of the following methods is NOT equal to the stock’s expected price in one year and six months (t=1.5 years)? Note that the symbolic formulas shown in each line below do equal the formulas with numbers. The formula is just repeated with symbols and then numbers in case it helps you to identify the incorrect statement more quickly.
Question 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?
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.
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.
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.
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.
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.
Which of the following investable assets are NOT suitable for valuation using PE multiples techniques?
Which firms tend to have low forwardlooking priceearnings (PE) ratios?
Only consider firms with positive earnings, disregard firms with negative earnings and therefore negative PE ratios.
Which of the following investable assets are NOT suitable for valuation using PE multiples techniques?
Which firms tend to have high forwardlooking priceearnings (PE) ratios?
Which firms tend to have low forwardlooking priceearnings (PE) ratios? Only consider firms with positive PE ratios.
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.
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'?
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} ##.
A share was bought for $20 (at t=0) and paid its annual dividend of $3 one year later (at t=1). Just after the dividend was paid, the share price was $16 (at t=1). What was the total return, capital return and income return? Calculate your answers as effective annual rates.
The choices are given in the same order: ## r_\text{total},r_\text{capital},r_\text{income} ##.
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 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?
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 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 155 inflation, real and nominal returns and cash flows, Loan, effective rate conversion
You are a banker about to grant a 2 year loan to a customer. The loan's principal and interest will be repaid in a single payment at maturity, sometimes called a zerocoupon loan, discount loan or bullet loan.
You require a real return of 6% pa over the two years, given as an effective annual rate. Inflation is expected to be 2% this year and 4% next year, both given as effective annual rates.
You judge that the customer can afford to pay back $1,000,000 in 2 years, given as a nominal cash flow. How much should you lend to her right now?
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 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?
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?
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?
Which business structure or structures have the advantage of limited liability for equity investors?
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.
If a project's net present value (NPV) is zero, then its internal rate of return (IRR) will be:
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 
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?
Your neighbour asks you for a loan of $100 and offers to pay you back $120 in one year.
You don't actually have any money right now, but you can borrow and lend from the bank at a rate of 10% pa. Rates are given as effective annual rates.
Assume that your neighbour will definitely pay you back. Ignore interest tax shields and transaction costs.
The Net Present Value (NPV) of lending to your neighbour is $9.09. Describe what you would do to actually receive a $9.09 cash flow right now with zero net cash flows in the future.
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?
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.
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.
You bought a house, primarily funded using a home loan from a bank. Which of the following statements is NOT correct?
Question 737 financial statement, balance sheet, income statement
Where can a publicly listed firm's book value of equity be found? It can be sourced from the company's:
Question 738 financial statement, balance sheet, income statement
Where can a private firm's market value of equity be found? It can be sourced from the company's:
Question 739 real and nominal returns and cash flows, inflation
There are a number of different formulas involving real and nominal returns and cash flows. Which one of the following formulas is NOT correct? All returns are effective annual rates. Note that the symbol ##\approx## means 'approximately equal to'.
Question 744 income and capital returns, real and nominal returns and cash flows, inflation
If someone says "my shares rose by 10% last year", what do you assume that they mean?
Question 734 real and nominal returns and cash flows, inflation, DDM, no explanation
An equities analyst is using the dividend discount model to price a company's shares. The company operates domestically and has no plans to expand overseas. It is part of a mature industry with stable positive growth prospects.
The analyst has estimated the real required return (r) of the stock and the value of the dividend that the stock just paid a moment before ##(C_\text{0 before})##.
What is the highest perpetual real growth rate of dividends (g) that can be justified? Select the most correct statement from the following choices. The highest perpetual real expected growth rate of dividends that can be justified is the country's expected:
Stocks in the United States usually pay quarterly dividends. For example, the software giant Microsoft paid a $0.23 dividend every quarter over the 2013 financial year and plans to pay a $0.28 dividend every quarter over the 2014 financial year.
Using the dividend discount model and net present value techniques, calculate the stock price of Microsoft assuming that:
 The time now is the beginning of July 2014. The next dividend of $0.28 will be received in 3 months (end of September 2014), with another 3 quarterly payments of $0.28 after this (end of December 2014, March 2015 and June 2015).
 The quarterly dividend will increase by 2.5% every year, but each quarterly dividend over the year will be equal. So each quarterly dividend paid in the financial year beginning in September 2015 will be $ 0.287 ##(=0.28×(1+0.025)^1)##, with the last at the end of June 2016. In the next financial year beginning in September 2016 each quarterly dividend will be $0.294175 ##(=0.28×(1+0.025)^2)##, with the last at the end of June 2017, and so on forever.
 The total required return on equity is 6% pa.
 The required return and growth rate are given as effective annual rates.
 Dividend payment dates and exdividend dates are at the same time.
 Remember that there are 4 quarters in a year and 3 months in a quarter.
What is the current stock price?
Stocks in the United States usually pay quarterly dividends. For example, the retailer WalMart Stores paid a $0.47 dividend every quarter over the 2013 calendar year and plans to pay a $0.48 dividend every quarter over the 2014 calendar year.
Using the dividend discount model and net present value techniques, calculate the stock price of WalMart Stores assuming that:
 The time now is the beginning of January 2014. The next dividend of $0.48 will be received in 3 months (end of March 2014), with another 3 quarterly payments of $0.48 after this (end of June, September and December 2014).
 The quarterly dividend will increase by 2% every year, but each quarterly dividend over the year will be equal. So each quarterly dividend paid in 2015 will be $0.4896 (##=0.48×(1+0.02)^1##), with the first at the end of March 2015 and the last at the end of December 2015. In 2016 each quarterly dividend will be $0.499392 (##=0.48×(1+0.02)^2##), with the first at the end of March 2016 and the last at the end of December 2016, and so on forever.
 The total required return on equity is 6% pa.
 The required return and growth rate are given as effective annual rates.
 All cash flows and rates are nominal. Inflation is 3% pa.
 Dividend payment dates and exdividend dates are at the same time.
 Remember that there are 4 quarters in a year and 3 months in a quarter.
What is the current stock price?
A home loan company advertises an interest rate of 4.5% pa, payable monthly. Which of the following statements about the interest rate is NOT correct?
Question 742 price gains and returns over time, no explanation
For an asset's price to quintuple every 5 years, what must be its effective annual capital return? Note that a stock's price quintuples when it increases from say $1 to $5.
Question 743 price gains and returns over time, no explanation
How many years will it take for an asset's price to triple (increase from say $1 to $3) if it grows by 5% pa?
Question 745 real and nominal returns and cash flows, inflation, income and capital returns
If the nominal gold price is expected to increase at the same rate as inflation which is 3% pa, which of the following statements is NOT correct?
A stock is expected to pay a dividend of $1 in one year. Its future annual dividends are expected to grow by 10% pa. So the first dividend of $1 is in one year, and the year after that the dividend will be $1.1 (=1*(1+0.1)^1), and a year later $1.21 (=1*(1+0.1)^2) and so on forever.
Its required total return is 30% pa. The total required return and growth rate of dividends are given as effective annual rates. The stock is fairly priced.
Calculate the pay back period of buying the stock and holding onto it forever, assuming that the dividends are received as at each time, not smoothly over each year.
Itau Unibanco is a major listed bank in Brazil with a market capitalisation of equity equal to BRL 85.744 billion, EPS of BRL 3.96 and 2.97 billion shares on issue.
Banco Bradesco is another major bank with total earnings of BRL 8.77 billion and 2.52 billion shares on issue.
Estimate Banco Bradesco's current share price using a priceearnings multiples approach assuming that Itau Unibanco is a comparable firm.
Note that BRL is the Brazilian Real, their currency. Figures sourced from Google Finance on the market close of the BVMF on 24/7/15.
Telsa Motors advertises that its Model S electric car saves $570 per month in fuel costs. Assume that Tesla cars last for 10 years, fuel and electricity costs remain the same, and savings are made at the end of each month with the first saving of $570 in one month from now.
The effective annual interest rate is 15.8%, and the effective monthly interest rate is 1.23%. What is the present value of the savings?
How much more can you borrow using an interestonly loan compared to a 25year fully amortising loan if interest rates are 4% pa compounding per month and are not expected to change? If it makes it easier, assume that you can afford to pay $2,000 per month on either loan. Express your answer as a proportional increase using the following formula:
###\text{Proportional Increase} = \dfrac{V_\text{0,interest only}}{V_\text{0,fully amortising}}  1###A firm wishes to raise $50 million now. They will issue 5% pa semiannual coupon bonds that will mature in 10 years and have a face value of $100 each. Bond yields are 5% pa, given as an APR compounding every 6 months, and the yield curve is flat.
How many bonds should the firm issue?
Question 760 time calculation, interest only loan, no explanation
Five years ago (##t=5## years) you entered into an interestonly home loan with a principal of $500,000, an interest rate of 4.5% pa compounding monthly with a term of 25 years.
Then interest rates suddenly fall to 3% pa (##t=0##), but you continue to pay the same monthly home loan payments as you did before. Will your home loan be paid off by the end of its remaining term? If so, in how many years from now? Measure the time taken to pay off the home loan from the current time which is 5 years after the home loan was first entered into.
Assume that the lower interest rate was given to you immediately after the loan repayment at the end of year 5, which was the 60th payment since the loan was granted. Also assume that rates were and are expected to remain constant.
The phone company Optus 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 $80 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 $100 per month. This plan includes the latest smart phone.
Neither plan has any additional payments at the start or end. Assume that the discount rate is 1% per month given as an effective monthly rate.
The only difference between the plans is the phone, so what is the implied cost of the phone as a present value? Given that the latest smart phone actually costs $600 to purchase outright from another retailer, should you commit to the BYO plan or the bundled plan?
A stock is expected to pay its first dividend of $20 in 3 years (t=3), which it will continue to pay for the next nine years, so there will be ten $20 payments altogether with the last payment in year 12 (t=12).
From the thirteenth year onward, the dividend is expected to be 4% more than the previous year, forever. So the dividend in the thirteenth year (t=13) will be $20.80, then $21.632 in year 14, and so on forever. The required return of the stock is 10% pa. All rates are effective annual rates. Calculate the current (t=0) stock price.
A 4.5% fixed coupon Australian Government bond was issued at par in midApril 2009. Coupons are paid semiannually in arrears in midApril and midOctober each year. The face value is $1,000. The bond will mature in midApril 2020, so the bond had an original tenor of 11 years.
Today is midSeptember 2015 and similar bonds now yield 1.9% pa.
What is the bond's new price? Note: there are 10 semiannual coupon payments remaining from now (midSeptember 2015) until maturity (midApril 2020); both yields are given as APR's compounding semiannually; assume that the yield curve was flat before the change in yields, and remained flat afterwards as well.
An investor bought a 5 year government bond with a 2% pa coupon rate at par. Coupons are paid semiannually. The face value is $100.
Calculate the bond's new price 8 months later after yields have increased to 3% pa. Note that both yields are given as APR's compounding semiannually. Assume that the yield curve was flat before the change in yields, and remained flat afterwards as well.
Use the below information to value a levered company with constant annual perpetual cash flows from assets. The next cash flow will be generated in one year from now, so a perpetuity can be used to value this firm. Both the operating and firm free cash flows are constant (but not equal to each other).
Data on a Levered Firm with Perpetual Cash Flows  
Item abbreviation  Value  Item full name 
##\text{OFCF}##  $100m  Operating free cash flow 
##\text{FFCF or CFFA}##  $112m  Firm free cash flow or cash flow from assets 
##g##  0% pa  Growth rate of OFCF and FFCF 
##\text{WACC}_\text{BeforeTax}##  7% pa  Weighted average cost of capital before tax 
##\text{WACC}_\text{AfterTax}##  6.25% pa  Weighted average cost of capital after tax 
##r_\text{D}##  5% pa  Cost of debt 
##r_\text{EL}##  9% pa  Cost of levered equity 
##D/V_L##  50% pa  Debt to assets ratio, where the asset value includes tax shields 
##t_c##  30%  Corporate tax rate 
What is the value of the levered firm including interest tax shields?
Which of the following companies is most suitable for valuation using PE multiples techniques?
A firm has 1 million shares which trade at a price of $30 each. The firm is expected to announce earnings of $3 million at the end of the year and pay an annual dividend of $1.50 per share.
What is the firm's (forward looking) price/earnings (PE) ratio?
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 backwardslooking priceearnings ratio?
A firm has 2m shares and a market capitalisation of equity of $30m. The firm just announced earnings of $5m and paid an annual dividend of $0.75 per share.
What is the firm's (backward looking) price/earnings (PE) ratio?
You are promised 20 payments of $100, where the first payment is immediate (t=0) and the last is at the end of the 19th year (t=19). The effective annual discount rate is ##r##.
Which of the following equations does NOT give the correct present value of these 20 payments?
The required return of a project is 10%, given as an effective annual rate. Assume that the cash flows shown in the table are paid all at once at the given point in time.
What is the Net Present Value (NPV) of the project?
Project Cash Flows  
Time (yrs)  Cash flow ($) 
0  100 
1  0 
2  121 
A project's net present value (NPV) is negative. Select the most correct statement.
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?
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 share currently worth $100 is expected to pay a constant dividend of $4 for the next 5 years with the first dividend in one year (t=1) and the last in 5 years (t=5).
The total required return is 10% pa.
What do you expected the share price to be in 5 years, just after the dividend at that time has been paid?
Question 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:
Let the variance of returns for a share per month be ##\sigma_\text{monthly}^2##.
What is the formula for the variance of the share's returns per year ##(\sigma_\text{yearly}^2)##?
Assume that returns are independently and identically distributed (iid) so they have zero auto correlation, meaning that if the return was higher than average today, it does not indicate that the return tomorrow will be higher or lower than average.
The standard deviation and variance of a stock's annual returns are calculated over a number of years. The units of the returns are percent per annum ##(\% pa)##.
What are the units of the standard deviation ##(\sigma)## and variance ##(\sigma^2)## of returns respectively?
Hint: Visit Wikipedia to understand the difference between percentage points ##(\text{pp})## and percent ##(\%)##.
All things remaining equal, the higher the correlation of returns between two stocks:
The following table shows a sample of historical total returns of shares in two different companies A and B.
Stock Returns  
Total effective annual returns  
Year  ##r_A##  ##r_B## 
2007  0.2  0.4 
2008  0.04  0.2 
2009  0.1  0.3 
2010  0.18  0.5 
What is the historical sample covariance (##\hat{\sigma}_{A,B}##) and correlation (##\rho_{A,B}##) of stock A and B's total effective annual returns?
What is the covariance of a variable X with itself?
The cov(X, X) or ##\sigma_{X,X}## equals:
Portfolio Details  
Stock  Expected return 
Standard deviation 
Covariance ##(\sigma_{A,B})##  Beta  Dollars invested 

A  0.2  0.4  0.12  0.5  40  
B  0.3  0.8  1.5  80  
What is the standard deviation (not variance) of the above portfolio? Note that the stocks' covariance is given, not correlation.
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?
Portfolio Details  
Stock  Expected return 
Standard deviation 
Correlation  Dollars invested 

A  0.1  0.4  0.5  60  
B  0.2  0.6  140  
What is the expected return of the above portfolio?
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 558 portfolio weights, portfolio return, short selling
An investor wants to make a portfolio of two stocks A and B with a target expected portfolio return of 16% pa.
 Stock A has an expected return of 8% pa.
 Stock B has an expected return of 12% pa.
What portfolio weights should the investor have in stocks A and B respectively?
Which of the following statements about shortselling is NOT true?
You believe that the price of a share will fall significantly very soon, but the rest of the market does not. The market thinks that the share price will remain the same. Assuming that your prediction will soon be true, which of the following trades is a bad idea? In other words, which trade will NOT make money or prevent losses?
After doing extensive fundamental analysis of a company, you believe that their shares are overpriced and will soon fall significantly. The market believes that there will be no such fall.
Which of the following strategies is NOT a good idea, assuming that your prediction is true?
Find the sample standard deviation of returns using the data in the table:
Stock Returns  
Year  Return pa 
2008  0.3 
2009  0.02 
2010  0.2 
2011  0.4 
The returns above and standard deviations below are given in decimal form.
Mr Blue, Miss Red and Mrs Green are people with different utility functions. Which of the statements about the 3 utility functions is NOT correct?
Mr Blue, Miss Red and Mrs Green are people with different utility functions. Which of the statements about the 3 utility functions is NOT correct?
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 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?
The security market line (SML) shows the relationship between beta and expected return.
Investment projects that plot above the SML would have:
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?
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 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.
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 firm changes its capital structure by issuing a large amount of equity and using the funds to repay debt. Its assets are unchanged. Ignore interest tax shields.
According to the Capital Asset Pricing Model (CAPM), which statement is correct?
A 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?
Which of the following is NOT a valid method for estimating the beta of a company's stock? Assume that markets are efficient, a long history of past data is available, the stock possesses idiosyncratic and market risk. The variances and standard deviations below denote total risks.
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?
There are many different ways to value a firm's assets. Which of the following will NOT give the correct market value of a levered firm's assets ##(V_L)##? Assume that:
 The firm is financed by listed common stock and vanilla annual fixed coupon bonds, which are both traded in a liquid market.
 The bonds' yield is equal to the coupon rate, so the bonds are issued at par. The yield curve is flat and yields are not expected to change. When bonds mature they will be rolled over by issuing the same number of new bonds with the same expected yield and coupon rate, and so on forever.
 Tax rates on the dividends and capital gains received by investors are equal, and capital gains tax is paid every year, even on unrealised gains regardless of when the asset is sold.
 There is no reinvestment of the firm's cash back into the business. All of the firm's excess cash flow is paid out as dividends so real growth is zero.
 The firm operates in a mature industry with zero real growth.
 All cash flows and rates in the below equations are real (not nominal) and are expected to be stable forever. Therefore the perpetuity equation with no growth is suitable for valuation.
Where:
###r_\text{WACC before tax} = r_D.\frac{D}{V_L} + r_{EL}.\frac{E_L}{V_L} = \text{Weighted average cost of capital before tax}### ###r_\text{WACC after tax} = r_D.(1t_c).\frac{D}{V_L} + r_{EL}.\frac{E_L}{V_L} = \text{Weighted average cost of capital after tax}### ###NI_L=(RevCOGSFCDepr\mathbf{IntExp}).(1t_c) = \text{Net Income Levered}### ###CFFA_L=NI_L+DeprCapEx  \varDelta NWC+\mathbf{IntExp} = \text{Cash Flow From Assets Levered}### ###NI_U=(RevCOGSFCDepr).(1t_c) = \text{Net Income Unlevered}### ###CFFA_U=NI_U+DeprCapEx  \varDelta NWC= \text{Cash Flow From Assets Unlevered}###A fairly priced stock has an expected return equal to the market's. Treasury bonds yield 5% pa and the market portfolio's expected return is 10% pa. What is the stock's beta?
Question 408 leverage, portfolio beta, portfolio risk, real estate, CAPM
You just bought a house worth $1,000,000. You financed it with an $800,000 mortgage loan and a deposit of $200,000.
You estimate that:
 The house has a beta of 1;
 The mortgage loan has a beta of 0.2.
What is the beta of the equity (the $200,000 deposit) that you have in your house?
Also, if the risk free rate is 5% pa and the market portfolio's return is 10% pa, what is the expected return on equity in your house? Ignore taxes, assume that all cash flows (interest payments and rent) were paid and received at the end of the year, and all rates are effective annual rates.
Assets A, B, M and ##r_f## are shown on the graphs above. Asset M is the market portfolio and ##r_f## is the risk free yield on government bonds. Which of the below statements is NOT correct?
Question 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?
A stock has a beta of 1.5. The market's expected total return is 10% pa and the risk free rate is 5% pa, both given as effective annual rates.
What do you think will be the stock's expected return over the next year, given as an effective annual rate?
Question 701 utility, risk aversion, utility function, gamble
Mr Blue, Miss Red and Mrs Green are people with different utility functions.
Each person has $50 of initial wealth. A coin toss game is offered to each person at a casino where the player can win or lose $50. Each player can flip a coin and if they flip heads, they receive $50. If they flip tails then they will lose $50. Which of the following statements is NOT correct?
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?
A company advertises an investment costing $1,000 which they say is underpriced. They say that it has an expected total return of 15% pa, but a required return of only 10% pa. Of the 15% pa total expected return, the dividend yield is expected to always be 7% pa and rest is the capital yield.
Assuming that the company's statements are correct, what is the NPV of buying the investment if the 15% total return lasts for the next 100 years (t=0 to 100), then reverts to 10% after that time? Also, what is the NPV of the investment if the 15% return lasts forever?
In both cases, assume that the required return of 10% remains constant, the dividends can only be reinvested at 10% pa and all returns are given as effective annual rates.
The answer choices below are given in the same order (15% for 100 years, and 15% forever):
A 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):
Select the most correct statement from the following.
'Chartists', also known as 'technical traders', believe that:
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 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.
The average weekly earnings of an Australian adult worker before tax was $1,542.40 per week in November 2014 according to the Australian Bureau of Statistics. Therefore average annual earnings before tax were $80,204.80 assuming 52 weeks per year. Personal income tax rates published by the Australian Tax Office are reproduced for the 20142015 financial year in the table below:
Taxable income  Tax on this income 

0 – $18,200  Nil 
$18,201 – $37,000  19c for each $1 over $18,200 
$37,001 – $80,000  $3,572 plus 32.5c for each $1 over $37,000 
$80,001 – $180,000  $17,547 plus 37c for each $1 over $80,000 
$180,001 and over  $54,547 plus 45c for each $1 over $180,000 
The above rates do not include the Medicare levy of 2%. Exclude the Medicare levy from your calculations
How much personal income tax would you have to pay per year if you earned $80,204.80 per annum beforetax?
In 2014 the median starting salaries of male and female Australian bachelor degree accounting graduates aged less than 25 years in their first fulltime industry job was $50,000 before tax, according to Graduate Careers Australia. See page 9 of this report. Personal income tax rates published by the Australian Tax Office are reproduced for the 20142015 financial year in the table below.
Taxable income  Tax on this income 

0 – $18,200  Nil 
$18,201 – $37,000  19c for each $1 over $18,200 
$37,001 – $80,000  $3,572 plus 32.5c for each $1 over $37,000 
$80,001 – $180,000  $17,547 plus 37c for each $1 over $80,000 
$180,001 and over  $54,547 plus 45c for each $1 over $180,000 
The above rates do not include the Medicare levy of 2%. Exclude the Medicare levy from your calculations
How much personal income tax would you have to pay per year if you earned $50,000 per annum beforetax?
Question 448 franking credit, personal tax on dividends, imputation tax system
A small private company has a single shareholder. This year the firm earned a $100 profit before tax. All of the firm's after tax profits will be paid out as dividends to the owner.
The corporate tax rate is 30% and the sole shareholder's personal marginal tax rate is 45%.
The Australian imputation tax system applies because the company generates all of its income in Australia and pays corporate tax to the Australian Tax Office. Therefore all of the company's dividends are fully franked. The sole shareholder is an Australian for tax purposes and can therefore use the franking credits to offset his personal income tax liability.
What will be the personal tax payable by the shareholder and the corporate tax payable by the company?
Question 449 personal tax on dividends, classical tax system
A small private company has a single shareholder. This year the firm earned a $100 profit before tax. All of the firm's after tax profits will be paid out as dividends to the owner.
The corporate tax rate is 30% and the sole shareholder's personal marginal tax rate is 45%.
The United States' classical tax system applies because the company generates all of its income in the US and pays corporate tax to the Internal Revenue Service. The shareholder is also an American for tax purposes.
What will be the personal tax payable by the shareholder and the corporate tax payable by the company?
Question 469 franking credit, personal tax on dividends, imputation tax system, no explanation
A firm pays a fully franked cash dividend of $70 to one of its Australian shareholders who has a personal marginal tax rate of 45%. The corporate tax rate is 30%.
What will be the shareholder's personal tax payable due to the dividend payment?
Question 494 franking credit, personal tax on dividends, imputation tax system
A firm pays a fully franked cash dividend of $100 to one of its Australian shareholders who has a personal marginal tax rate of 15%. The corporate tax rate is 30%.
What will be the shareholder's personal tax payable due to the dividend payment?
Currently, a mining company has a share price of $6 and pays constant annual dividends of $0.50. The next dividend will be paid in 1 year. Suddenly and unexpectedly the mining company announces that due to higher than expected profits, all of these windfall profits will be paid as a special dividend of $0.30 in 1 year.
If investors believe that the windfall profits and dividend is a oneoff event, what will be the new share price? If investors believe that the additional dividend is actually permanent and will continue to be paid, what will be the new share price? Assume that the required return on equity is unchanged. Choose from the following, where the first share price includes the oneoff increase in earnings and dividends for the first year only ##(P_\text{0 oneoff})## , and the second assumes that the increase is permanent ##(P_\text{0 permanent})##:
Note: When a firm makes excess profits they sometimes pay them out as special dividends. Special dividends are just like ordinary dividends but they are oneoff and investors do not expect them to continue, unlike ordinary dividends which are expected to persist.
Question 524 risk, expected and historical returns, bankruptcy or insolvency, capital structure, corporate financial decision theory, limited liability
Which of the following statements is NOT correct?
Question 536 idiom, bond pricing, capital structure, leverage
The expression 'my word is my bond' is often used in everyday language to make a serious promise.
Why do you think this expression uses the metaphor of a bond rather than a share?
A mining firm has just discovered a new mine. So far the news has been kept a secret.
The net present value of digging the mine and selling the minerals is $250 million, but $500 million of new equity and $300 million of new bonds will need to be issued to fund the project and buy the necessary plant and equipment.
The firm will release the news of the discovery and equity and bond raising to shareholders simultaneously in the same announcement. The shares and bonds will be issued shortly after.
Once the announcement is made and the new shares and bonds are issued, what is the expected increase in the value of the firm's assets ##(\Delta V)##, market capitalisation of debt ##(\Delta D)## and market cap of equity ##(\Delta E)##? Assume that markets are semistrong form efficient.
The triangle symbol ##\Delta## is the Greek letter capital delta which means change or increase in mathematics.
Ignore the benefit of interest tax shields from having more debt.
Remember: ##\Delta V = \Delta D+ \Delta E##
A company conducts a 4 for 3 stock split. What is the percentage change in the stock price and the number of shares outstanding? The answers are given in the same order.
Question 568 rights issue, capital raising, capital structure
A company conducts a 1 for 5 rights issue at a subscription price of $7 when the preannouncement stock price was $10. What is the percentage change in the stock price and the number of shares outstanding? The answers are given in the same order. Ignore all taxes, transaction costs and signalling effects.
A company conducts a 2 for 3 rights issue at a subscription price of $8 when the preannouncement stock price was $9. Assume that all investors use their rights to buy those extra shares.
What is the percentage increase in the stock price and the number of shares outstanding? The answers are given in the same order.
Question 513 stock split, reverse stock split, stock dividend, bonus issue, rights issue
Which of the following statements is NOT correct?
In late 2003 the listed bank ANZ announced a 2for11 rights issue to fund the takeover of New Zealand bank NBNZ. Below is the chronology of events:
 23/10/2003. Share price closes at $18.30.
 24/10/2003. 2for11 rights issue announced at a subscription price of $13. The proceeds of the rights issue will be used to acquire New Zealand bank NBNZ. Trading halt announced in morning before market opens.
 28/10/2003. Trading halt lifted. Last (and only) day that shares trade cumrights. Share price opens at $18.00 and closes at $18.14.
 29/10/2003. Shares trade exrights.
All things remaining equal, what would you expect ANZ's stock price to open at on the first day that it trades exrights (29/10/2003)? Ignore the time value of money since time is negligibly short. Also ignore taxes.
A $100 stock has a continuously compounded expected total return of 10% pa. Its dividend yield is 2% pa with continuous compounding. What do you expect its price to be in 2.5 years?
Question 691 continuously compounding rate, effective rate, continuously compounding rate conversion, no explanation
A bank quotes an interest rate of 6% pa with quarterly compounding. Note that another way of stating this rate is that it is an annual percentage rate (APR) compounding discretely every 3 months.
Which of the following statements about this rate is NOT correct? All percentages are given to 6 decimal places. The equivalent:
Question 707 continuously compounding rate, continuously compounding rate conversion
Convert a 10% effective annual rate ##(r_\text{eff annual})## into a continuously compounded annual rate ##(r_\text{cc annual})##. The equivalent continuously compounded annual rate is:
Question 708 continuously compounding rate, continuously compounding rate conversion
Convert a 10% continuously compounded annual rate ##(r_\text{cc annual})## into an effective annual rate ##(r_\text{eff annual})##. The equivalent effective annual rate is:
Question 710 continuously compounding rate, continuously compounding rate conversion
A continuously compounded monthly return of 1% ##(r_\text{cc monthly})## is equivalent to a continuously compounded annual return ##(r_\text{cc annual})## of:
Question 711 continuously compounding rate, continuously compounding rate conversion
A continuously compounded semiannual return of 5% ##(r_\text{cc 6mth})## is equivalent to a continuously compounded annual return ##(r_\text{cc annual})## of:
Question 719 mean and median returns, return distribution, arithmetic and geometric averages, continuously compounding rate
A stock has an arithmetic average continuously compounded return (AALGDR) of 10% pa, a standard deviation of continuously compounded returns (SDLGDR) of 80% pa and current stock price of $1. Assume that stock prices are lognormally distributed.
In one year, what do you expect the mean and median prices to be? The answer options are given in the same order.
Question 720 mean and median returns, return distribution, arithmetic and geometric averages, continuously compounding rate
A stock has an arithmetic average continuously compounded return (AALGDR) of 10% pa, a standard deviation of continuously compounded returns (SDLGDR) of 80% pa and current stock price of $1. Assume that stock prices are lognormally distributed.
In 5 years, what do you expect the mean and median prices to be? The answer options are given in the same order.
Question 721 mean and median returns, return distribution, arithmetic and geometric averages, continuously compounding rate
Fred owns some Commonwealth Bank (CBA) shares. He has calculated CBA’s monthly returns for each month in the past 20 years using this formula:
###r_\text{t monthly}=\ln \left( \dfrac{P_t}{P_{t1}} \right)###He then took the arithmetic average and found it to be 1% per month using this formula:
###\bar{r}_\text{monthly}= \dfrac{ \displaystyle\sum\limits_{t=1}^T{\left( r_\text{t monthly} \right)} }{T} =0.01=1\% \text{ per month}###He also found the standard deviation of these monthly returns which was 5% per month:
###\sigma_\text{monthly} = \dfrac{ \displaystyle\sum\limits_{t=1}^T{\left( \left( r_\text{t monthly}  \bar{r}_\text{monthly} \right)^2 \right)} }{T} =0.05=5\%\text{ per month}###Which of the below statements about Fred’s CBA shares is NOT correct? Assume that the past historical average return is the true population average of future expected returns.
Question 722 mean and median returns, return distribution, arithmetic and geometric averages, continuously compounding rate
Here is a table of stock prices and returns. Which of the statements below the table is NOT correct?
Price and Return Population Statistics  
Time  Prices  LGDR  GDR  NDR 
0  100  
1  50  0.6931  0.5  0.5 
2  100  0.6931  2  1 
Arithmetic average  0  1.25  0.25  
Arithmetic standard deviation  0.6931  0.75  0.75  
Question 723 mean and median returns, return distribution, arithmetic and geometric averages, continuously compounding rate
Here is a table of stock prices and returns. Which of the statements below the table is NOT correct?
Price and Return Population Statistics  
Time  Prices  LGDR  GDR  NDR 
0  100  
1  99  0.010050  0.990000  0.010000 
2  180.40  0.600057  1.822222  0.822222 
3  112.73  0.470181  0.624889  0.375111 
Arithmetic average  0.0399  1.1457  0.1457  
Arithmetic standard deviation  0.4384  0.5011  0.5011  
Question 779 mean and median returns, return distribution, arithmetic and geometric averages, continuously compounding rate
Fred owns some BHP shares. He has calculated BHP’s monthly returns for each month in the past 30 years using this formula:
###r_\text{t monthly}=\ln \left( \dfrac{P_t}{P_{t1}} \right)###He then took the arithmetic average and found it to be 0.8% per month using this formula:
###\bar{r}_\text{monthly}= \dfrac{ \displaystyle\sum\limits_{t=1}^T{\left( r_\text{t monthly} \right)} }{T} =0.008=0.8\% \text{ per month}###He also found the standard deviation of these monthly returns which was 15% per month:
###\sigma_\text{monthly} = \dfrac{ \displaystyle\sum\limits_{t=1}^T{\left( \left( r_\text{t monthly}  \bar{r}_\text{monthly} \right)^2 \right)} }{T} =0.15=15\%\text{ per month}###Assume that the past historical average return is the true population average of future expected returns and the stock's returns calculated above ##(r_\text{t monthly})## are normally distributed. Which of the below statements about Fred’s BHP shares is NOT correct?
Question 662 APR, effective rate, effective rate conversion, no explanation
Which of the following interest rate labels does NOT make sense?
Which of the following quantities is commonly assumed to be normally distributed?
If a variable, say X, is normally distributed with mean ##\mu## and variance ##\sigma^2## then mathematicians write ##X \sim \mathcal{N}(\mu, \sigma^2)##.
If a variable, say Y, is lognormally distributed and the underlying normal distribution has mean ##\mu## and variance ##\sigma^2## then mathematicians write ## Y \sim \mathbf{ln} \mathcal{N}(\mu, \sigma^2)##.
The below three graphs show probability density functions (PDF) of three different random variables Red, Green and Blue.
Select the most correct statement:
The below three graphs show probability density functions (PDF) of three different random variables Red, Green and Blue.
Which of the below statements is NOT correct?
The below three graphs show probability density functions (PDF) of three different random variables Red, Green and Blue. Let ##P_1## be the unknown price of a stock in one year. ##P_1## is a random variable. Let ##P_0 = 1##, so the share price now is $1. This one dollar is a constant, it is not a variable.
Which of the below statements is NOT correct? Financial practitioners commonly assume that the shape of the PDF represented in the colour:
Below is a graph of 3 peoples’ utility functions, Mr Blue (U=W^(1/2) ), Miss Red (U=W/10) and Mrs Green (U=W^2/1000). Assume that each of them currently have $50 of wealth.
Which of the following statements about them is NOT correct?
(a) Mr Blue would prefer to invest his wealth in a well diversified portfolio of stocks rather than a single stock, assuming that all stocks had the same total risk and return.
Question 767 idiom, corporate financial decision theory, no explanation
The sayings "Don't cry over spilt milk", "Don't regret the things that you can't change" and "What's done is done" are most closely related to which financial concept?
Question 768 accounting terminology, book and market values, no explanation
Accountants and finance professionals have lots of names for the same things which can be quite confusing.
Which of the following groups of items are NOT synonyms?
Suppose you had $100 in a savings account and the interest rate was 2% per year.
After 5 years, how much do you think you would have in the account if you left the money to grow?
Jan asks you for a loan. He wants $100 now and offers to pay you back $120 in 1 year. You can borrow and lend from the bank at an interest rate of 10% pa, given as an effective annual rate.
Ignore credit risk. Remember:
### V_0 = \frac{V_t}{(1+r_\text{eff})^t} ###
For a price of $6, Carlos will sell you a share which will pay a dividend of $1 in one year and every year after that forever. The required return of the stock is 10% pa.
Question 780 mispriced asset, NPV, DDM, market efficiency, no explanation
A company advertises an investment costing $1,000 which they say is under priced. They say that it has an expected total return of 15% pa, but a required return of only 10% pa. Of the 15% pa total expected return, the dividend yield is expected to be 4% pa and the capital yield 11% pa. Assume that the company's statements are correct.
What is the NPV of buying the investment if the 15% total return lasts for the next 100 years (t=0 to 100), then reverts to 10% after that time? Also, what is the NPV of the investment if the 15% return lasts forever?
In both cases, assume that the required return of 10% remains constant, the dividends can only be reinvested at 10% pa and all returns are given as effective annual rates. The answer choices below are given in the same order (15% for 100 years, and 15% forever):
Question 776 market efficiency, systematic and idiosyncratic risk, beta, income and capital returns
Which of the following statements about returns is NOT correct? A stock's:
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 backwardslooking priceearnings ratio?
Question 625 dividend reinvestment plan, capital raising
Which of the following statements about dividend reinvestment plans (DRP's) is NOT correct?
Question 771 debt terminology, interest expense, interest tax shield, credit risk, no explanation
You deposit money into a bank account. Which of the following statements about this deposit is NOT correct?
One year ago you bought a $1,000,000 house partly funded using a mortgage loan. The loan size was $800,000 and the other $200,000 was your wealth or 'equity' in the house asset.
The interest rate on the home loan was 4% pa.
Over the year, the house produced a net rental yield of 2% pa and a capital gain of 2.5% pa.
Assuming that all cash flows (interest payments and net rental payments) were paid and received at the end of the year, and all rates are given as effective annual rates, what was the total return on your wealth over the past year?
Hint: Remember that wealth in this context is your equity (E) in the house asset (V = D+E) which is funded by the loan (D) and your deposit or equity (E).
The hardest and most important aspect of business project valuation is the estimation of the:
The 'time value of money' is most closely related to which of the following concepts?
Question 770 expected and historical returns, income and capital returns, coupon rate, bond pricing, no explanation
Which of the following statements is NOT correct? Assume that all things remain equal. So for example, don't assume that just because a company's dividends and profit rise that its required return will also rise, assume the required return stays the same.
Question 778 CML, systematic and idiosyncratic risk, portfolio risk, CAPM, no explanation
The capital market line (CML) is shown in the graph below. The total standard deviation is denoted by σ and the expected return is μ. Assume that markets are efficient so all assets are fairly priced.
Which of the below statements is NOT correct?
The market's expected total return is 10% pa and the risk free rate is 5% pa, both given as effective annual rates.
A stock has a beta of 0.5.
In the last 5 minutes, the federal government unexpectedly raised taxes. Over this time the share market fell by 3%. The risk free rate was unchanged.
What do you think was the stock's historical return over the last 5 minutes, given as an effective 5 minute rate?
Use the below information to value a levered company with constant annual perpetual cash flows from assets. The next cash flow will be generated in one year from now, so a perpetuity can be used to value this firm. Both the operating and firm free cash flows are constant (but not equal to each other).
Data on a Levered Firm with Perpetual Cash Flows  
Item abbreviation  Value  Item full name 
##\text{OFCF}##  $48.5m  Operating free cash flow 
##\text{FFCF or CFFA}##  $50m  Firm free cash flow or cash flow from assets 
##g##  0% pa  Growth rate of OFCF and FFCF 
##\text{WACC}_\text{BeforeTax}##  10% pa  Weighted average cost of capital before tax 
##\text{WACC}_\text{AfterTax}##  9.7% pa  Weighted average cost of capital after tax 
##r_\text{D}##  5% pa  Cost of debt 
##r_\text{EL}##  11.25% pa  Cost of levered equity 
##D/V_L##  20% pa  Debt to assets ratio, where the asset value includes tax shields 
##t_c##  30%  Corporate tax rate 
What is the value of the levered firm including interest tax shields?
The following cash flows are expected:
 A perpetuity of yearly payments of $30, with the first payment in 5 years (first payment at t=5, which continues every year after that forever).
 One payment of $100 in 6 years and 3 months (t=6.25).
What is the NPV of the cash flows if the discount rate is 10% given as an effective annual rate?
An effective monthly return of 1% ##(r_\text{eff monthly})## is equivalent to an effective annual return ##(r_\text{eff annual})## of:
An effective semiannual return of 5% ##(r_\text{eff 6mth})## is equivalent to an effective annual return ##(r_\text{eff annual})## of:
An economy has only two investable assets: stocks and cash.
Stocks had a historical nominal average total return of negative two percent per annum (2% pa) over the last 20 years. Stocks are liquid and actively traded. Stock returns are variable, they have risk.
Cash is riskless and has a nominal constant return of zero percent per annum (0% pa), which it had in the past and will have in the future. Cash can be kept safely at zero cost. Cash can be converted into shares and vice versa at zero cost.
The nominal total return of the shares over the next year is expected to be:
In the dividend discount model:
### P_0= \frac{d_1}{rg} ###
The pronumeral ##g## is supposed to be the:
Question 772 interest tax shield, capital structure, leverage
A firm issues debt and uses the funds to buy back equity. Assume that there are no costs of financial distress or transactions costs. Which of the following statements about interest tax shields is NOT correct?