The market's expected total return is 10% pa and the risk free rate is 5% pa, both given as effective annual rates.
A stock has a beta of 0.7.
What do you think will be the stock's expected return over the next year, given as an effective annual rate?
The market's expected total return is 10% pa and the risk free rate is 5% pa, both given as effective annual rates.
A stock has a beta of 0.7.
In the last 5 minutes, bad economic news was released showing a higher chance of recession. Over this time the share market fell by 2%. The risk free rate was unchanged. What do you think was the stock's historical return over the last 5 minutes, given as an effective 5 minute rate?
A common phrase heard in financial markets is that ‘high risk investments deserve high returns’. To make this statement consistent with the Capital Asset Pricing Model (CAPM), a high amount of what specific type of risk deserves a high return?
Investors deserve high returns when they buy assets with high:
A stock has a beta of 1.2. Its next dividend is expected to be $20, paid one year from now.
Dividends are expected to be paid annually and grow by 1.5% pa forever.
Treasury bonds yield 3% pa and the market portfolio's expected return is 7% pa. All returns are effective annual rates.
What is the price of the stock now?
You work for XYZ company and you’ve been asked to evaluate a new project which has double the systematic risk of the company’s other projects.
You use the Capital Asset Pricing Model (CAPM) formula and input the treasury yield ##(r_f )##, market risk premium ##(r_mr_f )## and the company’s asset beta risk factor ##(\beta_{XYZ} )## into the CAPM formula which outputs a return.
This return that you’ve just found is:
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?
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?
Stock A has a beta of 0.5 and stock B has a beta of 1. Which statement is NOT correct?
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?
Question 810 CAPM, systematic and idiosyncratic risk, market efficiency
Examine the graphs below. Assume that asset A is a single stock. Which of the following statements is NOT correct? Asset A:
Question 809 Markowitz portfolio theory, CAPM, Jensens alpha, CML, systematic and idiosyncratic risk
A graph of assets’ expected returns ##(\mu)## versus standard deviations ##(\sigma)## is given in the graph below. The CML is the capital market line.
Which of the following statements about this graph, Markowitz portfolio theory and the Capital Asset Pricing Model (CAPM) theory is NOT correct?
Question 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?
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.
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 657 systematic and idiosyncratic risk, CAPM, no explanation
A stock's required total return will decrease when its:
Diversification is achieved by investing in a large amount of stocks. What type of risk is reduced by diversification?
Question 807 market efficiency, expected and historical returns, CAPM, beta, systematic risk, no explanation
You work in Asia and just woke up. It looked like a nice day but then you read the news and found out that last night the American share market fell by 10% while you were asleep due to surprisingly poor macroeconomic world news. You own a portfolio of liquid stocks listed in Asia with a beta of 1.6. When the Asian equity markets open, what do you expect to happen to your share portfolio? Assume that the capital asset pricing model (CAPM) is correct and that the market portfolio contains all shares in the world, of which American shares are a big part. Your portfolio beta is measured against this world market portfolio.
When the Asian equity market opens for trade, you would expect your portfolio value to:
To receive the dividend you must own the stock when the market closes on which date?
On which date would the stock price increase if the dividend and earnings are higher than expected?
A company announces that it will pay a dividend, as the market expected. The company's shares trade on the stock exchange which is open from 10am in the morning to 4pm in the afternoon each weekday. When would the share price be expected to fall by the amount of the dividend? Ignore taxes.
The share price is expected to fall during the:
A company conducts a 4 for 3 stock split. What is the percentage change in the stock price and the number of shares outstanding? The answers are given in the same order.
A company conducts a 10 for 3 stock split. What is the percentage increase in the stock price and the number of shares outstanding? The answers are given in the same order.
A firm conducts a twoforone stock split. Which of the following consequences would NOT be expected?
Question 625 dividend reinvestment plan, capital raising
Which of the following statements about dividend reinvestment plans (DRP's) is NOT correct?
Question 731 DDM, income and capital returns, no explanation
In the dividend discount model (DDM), share prices fall when dividends are paid. Let the high price before the fall be called the peak, and the low price after the fall be called the trough.
###P_0=\dfrac{C_1}{rg}###
Which of the following statements about the DDM is NOT correct?
For certain shares, the forwardlooking PriceEarnings Ratio (##P_0/EPS_1##) is equal to the inverse of the share's total expected return (##1/r_\text{total}##).
For what shares is this true?
Assume:
 The general accounting definition of 'payout ratio' which is dividends per share (DPS) divided by earnings per share (EPS).
 All cash flows, earnings and rates are real.
A mature firm has constant expected future earnings and dividends. Both amounts are equal. So earnings and dividends are expected to be equal and unchanging.
Which of the following statements is NOT correct?
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.
Question 455 income and capital returns, payout policy, DDM, market efficiency
A fairly priced unlevered firm plans to pay a dividend of $1 next year (t=1) which is expected to grow by 3% pa every year after that. The firm's required return on equity is 8% pa.
The firm is thinking about reducing its future dividend payments by 10% so that it can use the extra cash to invest in more projects which are expected to return 8% pa, and have the same risk as the existing projects. Therefore, next year's dividend will be $0.90. No new equity or debt will be issued to fund the new projects, they'll all be funded by the cut in dividends.
What will be the stock's new annual capital return (proportional increase in price per year) if the change in payout policy goes ahead?
Assume that payout policy is irrelevant to firm value (so there's no signalling effects) and that all rates are effective annual rates.
A company 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):
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):
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.
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##.
Question 800 leverage, portfolio return, risk, portfolio risk, capital structure, no explanation
Which of the following assets would you expect to have the highest required rate of return? All values are current market values.
A firm has a debttoequity ratio of 25%. What is its debttoassets ratio?
A firm has a debttoequity ratio of 60%. What is its debttoassets ratio?
A firm has a debttoassets ratio of 20%. What is its debttoequity ratio?
A firm can issue 3 year annual coupon bonds at a yield of 10% pa and a coupon rate of 8% pa.
The beta of its levered equity is 2. The market's expected return is 10% pa and 3 year government bonds yield 6% pa with a coupon rate of 4% pa.
The market value of equity is $1 million and the market value of debt is $1 million. The corporate tax rate is 30%.
What is the firm's aftertax WACC? Assume a classical tax system.
A firm can issue 5 year annual coupon bonds at a yield of 8% pa and a coupon rate of 12% pa.
The beta of its levered equity is 1. Five year government bonds yield 5% pa with a coupon rate of 6% pa. The market's expected dividend return is 4% pa and its expected capital return is 6% pa.
The firm's debttoequity ratio is 2:1. The corporate tax rate is 30%.
What is the firm's aftertax WACC? Assume a classical tax system.
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.
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?
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 formula for the present value of interest tax shields if the tax shields occur in perpetuity?
You may assume:
 the value of debt (D) is constant through time,
 The cost of debt and the yield on debt are equal and given by ##r_D##.
 the appropriate rate to discount interest tax shields is ##r_D##.
 ##\text{IntExp}=D.r_D##
Interest expense (IntExp) is an important part of a company's income statement (or 'profit and loss' or 'statement of financial performance').
How does an accountant calculate the annual interest expense of a fixedcoupon bond that has a liquid secondary market? Select the most correct answer:
Annual interest expense is equal to:
Unrestricted negative gearing is allowed in Australia, New Zealand and Japan. Negative gearing laws allow income losses on investment properties to be deducted from a taxpayer's pretax personal income. Negatively geared investors benefit from this tax advantage. They also hope to benefit from capital gains which exceed the income losses.
For example, a property investor buys an apartment funded by an interest only mortgage loan. Interest expense is $2,000 per month. The rental payments received from the tenant living on the property are $1,500 per month. The investor can deduct this income loss of $500 per month from his pretax personal income. If his personal marginal tax rate is 46.5%, this saves $232.5 per month in personal income tax.
The advantage of negative gearing is an example of the benefits of:
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###Question 941 negative gearing, leverage, capital structure, interest tax shield, real estate
Last year, two friends Lev and Nolev each bought similar investment properties for $1 million. Both earned net rents of $30,000 pa over the past year. They funded their purchases in different ways:
 Lev used $200,000 of his own money and borrowed $800,000 from the bank in the form of an interestonly loan with an interest rate of 5% pa.
 Nolev used $1,000,000 of his own money, he has no mortgage loan on his property.
Both Lev and Nolev also work in highpaying jobs and are subject personal marginal tax rates of 45%.
Which of the below statements about the past year is NOT correct?
Use the below information to value a levered company with constant annual perpetual cash flows from assets. The next cash flow will be generated in one year from now, so a perpetuity can be used to value this firm. Both the cash flow from assets including and excluding interest tax shields are constant (but not equal to each other).
Data on a Levered Firm with Perpetual Cash Flows  
Item abbreviation  Value  Item full name 
##\text{CFFA}_\text{U}##  $100m  Cash flow from assets excluding interest tax shields (unlevered) 
##\text{CFFA}_\text{L}##  $112m  Cash flow from assets including interest tax shields (levered) 
##g##  0% pa  Growth rate of cash flow from assets, levered and unlevered 
##\text{WACC}_\text{BeforeTax}##  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?
Use the below information to value a levered company with constant annual perpetual cash flows from assets. The next cash flow will be generated in one year from now, so a perpetuity can be used to value this firm. Both the cash flow from assets including and excluding interest tax shields are constant (but not equal to each other).
Data on a Levered Firm with Perpetual Cash Flows  
Item abbreviation  Value  Item full name 
##\text{CFFA}_\text{U}##  $48.5m  Cash flow from assets excluding interest tax shields (unlevered) 
##\text{CFFA}_\text{L}##  $50m  Cash flow from assets including interest tax shields (levered) 
##g##  0% pa  Growth rate of cash flow from assets, levered and unlevered 
##\text{WACC}_\text{BeforeTax}##  10% pa  Weighted average cost of capital before tax 
##\text{WACC}_\text{AfterTax}##  9.7% pa  Weighted average cost of capital after tax 
##r_\text{D}##  5% pa  Cost of debt 
##r_\text{EL}##  11.25% pa  Cost of levered equity 
##D/V_L##  20% pa  Debt to assets ratio, where the asset value includes tax shields 
##t_c##  30%  Corporate tax rate 
What is the value of the levered firm including interest tax shields?
Use the below information to value a levered company with annual perpetual cash flows from assets that grow. The next cash flow will be generated in one year from now, so a perpetuity can be used to value this firm. Note that ‘k’ means kilo or 1,000. So the $30k is $30,000.
Data on a Levered Firm with Perpetual Cash Flows  
Item abbreviation  Value  Item full name 
##\text{CFFA}_\text{U}##  $30k  Cash flow from assets excluding interest tax shields (unlevered) 
##g##  1.5% pa  Growth rate of cash flow from assets, levered and unlevered 
##r_\text{D}##  4% pa  Cost of debt 
##r_\text{EL}##  16.3% pa  Cost of levered equity 
##D/V_L##  80% pa  Debt to assets ratio, where the asset value includes tax shields 
##t_c##  30%  Corporate tax rate 
Which of the following statements is NOT correct?
Question 772 interest tax shield, capital structure, leverage
A firm issues debt and uses the funds to buy back equity. Assume that there are no costs of financial distress or transactions costs. Which of the following statements about interest tax shields is NOT correct?
Treasury bonds currently have a return of 5% pa. A stock has a beta of 0.5 and the market return is 10% pa. What is the expected return of the stock?
A stock has a beta of 0.5. Its next dividend is expected to be $3, paid one year from now. Dividends are expected to be paid annually and grow by 2% pa forever. Treasury bonds yield 5% pa and the market portfolio's expected return is 10% pa. All returns are effective annual rates.
What is the price of the stock now?
According to the theory of the Capital Asset Pricing Model (CAPM), total variance can be broken into two components, systematic variance and idiosyncratic variance. Which of the following events would be considered the most diversifiable according to the theory of the CAPM?
A stock's required total return will increase when its:
A stock has a beta of 1.5. The market's expected total return is 10% pa and the risk free rate is 5% pa, both given as effective annual rates.
What do you think will be the stock's expected return over the next year, given as an effective annual rate?
A stock has a beta of 1.5. The market's expected total return is 10% pa and the risk free rate is 5% pa, both given as effective annual rates.
In the last 5 minutes, bad economic news was released showing a higher chance of recession. Over this time the share market fell by 1%. The risk free rate was unchanged.
What do you think was the stock's historical return over the last 5 minutes, given as an effective 5 minute rate?
A stock has a beta of 1.5. The market's expected total return is 10% pa and the risk free rate is 5% pa, both given as effective annual rates.
Over the last year, bad economic news was released showing a higher chance of recession. Over this time the share market fell by 1%. The risk free rate was unchanged.
What do you think was the stock's historical return over the last year, given as an effective annual rate?
A share was bought for $20 (at t=0) and paid its annual dividend of $3 one year later (at t=1). Just after the dividend was paid, the share price was $16 (at t=1). What was the total return, capital return and income return? Calculate your answers as effective annual rates.
The choices are given in the same order: ## r_\text{total},r_\text{capital},r_\text{income} ##.
Which of the following statements about an asset’s standard deviation of returns is NOT correct? All other things remaining equal, the higher the asset’s standard deviation of returns:
Stock A and B's returns have a correlation of 0.3. Which statement is NOT correct?
The following table shows a sample of historical total returns of shares in two different companies A and B.
Stock Returns  
Total effective annual returns  
Year  ##r_A##  ##r_B## 
2007  0.2  0.4 
2008  0.04  0.2 
2009  0.1  0.3 
2010  0.18  0.5 
What is the historical sample covariance (##\hat{\sigma}_{A,B}##) and correlation (##\rho_{A,B}##) of stock A and B's total effective annual returns?
Portfolio Details  
Stock  Expected return 
Standard deviation 
Correlation  Dollars invested 

A  0.1  0.4  0.5  60  
B  0.2  0.6  140  
What is the expected return of the above portfolio?
All things remaining equal, the variance of a portfolio of two positivelyweighted stocks rises as:
Diversification in a portfolio of two assets works best when the correlation between their returns is:
Portfolio Details  
Stock  Expected return 
Standard deviation 
Covariance ##(\sigma_{A,B})##  Beta  Dollars invested 

A  0.2  0.4  0.12  0.5  40  
B  0.3  0.8  1.5  80  
What is the standard deviation (not variance) of the above portfolio? Note that the stocks' covariance is given, not correlation.
Question 558 portfolio weights, portfolio return, short selling
An investor wants to make a portfolio of two stocks A and B with a target expected portfolio return of 16% pa.
 Stock A has an expected return of 8% pa.
 Stock B has an expected return of 12% pa.
What portfolio weights should the investor have in stocks A and B respectively?
The standard deviation and variance of a stock's annual returns are calculated over a number of years. The units of the returns are percent per annum ##(\% pa)##.
What are the units of the standard deviation ##(\sigma)## and variance ##(\sigma^2)## of returns respectively?
Hint: Visit Wikipedia to understand the difference between percentage points ##(\text{pp})## and percent ##(\%)##.
A stock's returns are normally distributed with a mean of 10% pa and a standard deviation of 20 percentage points pa. What is the 90% confidence interval of returns over the next year? Note that the Zstatistic corresponding to a onetail:
 90% normal probability density function is 1.282.
 95% normal probability density function is 1.645.
 97.5% normal probability density function is 1.960.
The 90% confidence interval of annual returns is between:
A stock's returns are normally distributed with a mean of 10% pa and a standard deviation of 20 percentage points pa. What is the 95% confidence interval of returns over the next year? Note that the Zstatistic corresponding to a onetail:
 90% normal probability density function is 1.282.
 95% normal probability density function is 1.645.
 97.5% normal probability density function is 1.960.
The 95% confidence interval of annual returns is between:
A stock has an expected return of 10% pa and you're 90% sure that over the next year, the return will be between 15% and 35%. The stock's returns are normally distributed. Note that the Zstatistic corresponding to a onetail:
 90% normal probability density function is 1.282.
 95% normal probability density function is 1.645.
 97.5% normal probability density function is 1.960.
What is the stock’s standard deviation of returns in percentage points per annum (pp pa)?
Question 282 expected and historical returns, income and capital returns
You're the boss of an investment bank's equities research team. Your five analysts are each trying to find the expected total return over the next year of shares in a mining company. The mining firm:
 Is regarded as a mature company since it's quite stable in size and was floated around 30 years ago. It is not a highgrowth company;
 Share price is very sensitive to changes in the price of the market portfolio, economic growth, the exchange rate and commodities prices. Due to this, its standard deviation of total returns is much higher than that of the market index;
 Experienced tough times in the last 10 years due to unexpected falls in commodity prices.
 Shares are traded in an active liquid market.
Assume that:
 The analysts' source data is correct and true, but their inferences might be wrong;
 All returns and yields are given as effective annual nominal rates.
Question 559 variance, standard deviation, covariance, correlation
Which of the following statements about standard statistical mathematics notation is NOT correct?
What is the covariance of a variable X with itself?
The cov(X, X) or ##\sigma_{X,X}## equals:
What is the correlation of a variable X with itself?
The corr(X, X) or ##\rho_{X,X}## equals:
What is the covariance of a variable X with a constant C?
The cov(X, C) or ##\sigma_{X,C}## equals:
What is the correlation of a variable X with a constant C?
The corr(X, C) or ##\rho_{X,C}## equals:
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.
A European company just issued two bonds, a
 3 year zero coupon bond at a yield of 6% pa, and a
 4 year zero coupon bond at a yield of 6.5% pa.
What is the company's forward rate over the fourth year (from t=3 to t=4)? Give your answer as an effective annual rate, which is how the above bond yields are quoted.
Question 25 bond pricing, zero coupon bond, term structure of interest rates, forward interest rate
A European company just issued two bonds, a
 2 year zero coupon bond at a yield of 8% pa, and a
 3 year zero coupon bond at a yield of 10% pa.
What is the company's forward rate over the third year (from t=2 to t=3)? Give your answer as an effective annual rate, which is how the above bond yields are quoted.
Question 35 bond pricing, zero coupon bond, term structure of interest rates, forward interest rate
A European company just issued two bonds, a
 1 year zero coupon bond at a yield of 8% pa, and a
 2 year zero coupon bond at a yield of 10% pa.
What is the company's forward rate over the second year (from t=1 to t=2)? Give your answer as an effective annual rate, which is how the above bond yields are quoted.
Question 108 bond pricing, zero coupon bond, term structure of interest rates, forward interest rate
An Australian company just issued two bonds:
 A 1 year zero coupon bond at a yield of 10% pa, and
 A 2 year zero coupon bond at a yield of 8% pa.
What is the forward rate on the company's debt from years 1 to 2? Give your answer as an APR compounding every 6 months, which is how the above bond yields are quoted.
Question 143 bond pricing, zero coupon bond, term structure of interest rates, forward interest rate
An Australian company just issued two bonds:
 A 6month zero coupon bond at a yield of 6% pa, and
 A 12 month zero coupon bond at a yield of 7% pa.
What is the company's forward rate from 6 to 12 months? Give your answer as an APR compounding every 6 months, which is how the above bond yields are quoted.
Question 572 bond pricing, zero coupon bond, term structure of interest rates, expectations hypothesis, forward interest rate, yield curve
In the below term structure of interest rates equation, all rates are effective annual yields and the numbers in subscript represent the years that the yields are measured over:
###(1+r_{03})^3 = (1+r_{01})(1+r_{12})(1+r_{23}) ###
Which of the following statements is NOT correct?
Question 573 bond pricing, zero coupon bond, term structure of interest rates, expectations hypothesis, liquidity premium theory, forward interest rate, yield curve
In the below term structure of interest rates equation, all rates are effective annual yields and the numbers in subscript represent the years that the yields are measured over:
###(1+r_{03})^3 = (1+r_{01})(1+r_{12})(1+r_{23}) ###
Which of the following statements is NOT correct?
Question 693 boot strapping zero coupon yield, forward interest rate, term structure of interest rates
Information about three risk free Government bonds is given in the table below.
Federal Treasury Bond Data  
Maturity  Yield to maturity  Coupon rate  Face value  Price 
(years)  (pa, compounding semiannually)  (pa, paid semiannually)  ($)  ($) 
0.5  3%  4%  100  100.4926 
1  4%  4%  100  100.0000 
1.5  5%  4%  100  98.5720 
Based on the above government bonds' yields to maturity, which of the below statements about the spot zero rates and forward zero rates is NOT correct?
Question 784 boot strapping zero coupon yield, forward interest rate, term structure of interest rates
Information about three risk free Government bonds is given in the table below.
Federal Treasury Bond Data  
Maturity  Yield to maturity  Coupon rate  Face value  Price 
(years)  (pa, compounding annually)  (pa, paid annually)  ($)  ($) 
1  0%  2%  100  102 
2  1%  2%  100  101.9703951 
3  2%  2%  100  100 
Based on the above government bonds' yields to maturity, which of the below statements about the spot zero rates and forward zero rates is NOT correct?
A young lady is trying to decide if she should attend university or not.
The young lady's parents say that she must attend university because otherwise all of her hard work studying and attending school during her childhood was a waste.
What's the correct way to classify this item from a capital budgeting perspective when trying to decide whether to attend university?
The hard work studying at school in her childhood should be classified as:
A young lady is trying to decide if she should attend university. Her friends say that she should go to university because she is more likely to meet a clever young man than if she begins full time work straight away.
What's the correct way to classify this item from a capital budgeting perspective when trying to find the Net Present Value of going to university rather than working?
The opportunity to meet a desirable future spouse should be classified as:
A man is thinking about taking a day off from his casual painting job to relax.
He just woke up early in the morning and he's about to call his boss to say that he won't be coming in to work.
But he's thinking about the hours that he could work today (in the future) which are:
A man has taken a day off from his casual painting job to relax.
It's the end of the day and he's thinking about the hours that he could have spent working (in the past) which are now:
The required return of a project is 10%, given as an effective annual rate. Assume that the cash flows shown in the table are paid all at once at the given point in time.
What is the Net Present Value (NPV) of the project?
Project Cash Flows  
Time (yrs)  Cash flow ($) 
0  100 
1  0 
2  121 
What is the Internal Rate of Return (IRR) of the project detailed in the table below?
Assume that the cash flows shown in the table are paid all at once at the given point in time. All answers are given as effective annual rates.
Project Cash Flows  
Time (yrs)  Cash flow ($) 
0  100 
1  0 
2  121 
If a project's net present value (NPV) is zero, then its internal rate of return (IRR) will be:
The required return of a project is 10%, given as an effective annual rate.
What is the payback period of the project in years?
Assume that the cash flows shown in the table are received smoothly over the year. So the $121 at time 2 is actually earned smoothly from t=1 to t=2.
Project Cash Flows  
Time (yrs)  Cash flow ($) 
0  100 
1  11 
2  121 
A project has the following cash flows:
Project Cash Flows  
Time (yrs)  Cash flow ($) 
0  400 
1  0 
2  500 
What is the payback period of the project in years?
Normally cash flows are assumed to happen at the given time. But here, assume that the cash flows are received smoothly over the year. So the $500 at time 2 is actually earned smoothly from t=1 to t=2.
The below graph shows a project's net present value (NPV) against its annual discount rate.
For what discount rate or range of discount rates would you accept and commence the project?
All answer choices are given as approximations from reading off the graph.
The below graph shows a project's net present value (NPV) against its annual discount rate.
Which of the following statements is NOT correct?
You have $100,000 in the bank. The bank pays interest at 10% pa, given as an effective annual rate.
You wish to consume an equal amount now (t=0) and in one year (t=1) and have nothing left in the bank at the end (t=1).
How much can you consume at each time?
You have $100,000 in the bank. The bank pays interest at 10% pa, given as an effective annual rate.
You wish to consume an equal amount now (t=0), in one year (t=1) and in two years (t=2), and still have $50,000 in the bank after that (t=2).
How much can you consume at each time?
You're considering a business project which costs $11m now and is expected to pay a single cash flow of $11m in one year. So you pay $11m now, then one year later you receive $11m.
Assume that the initial $11m cost is funded using the your firm's existing cash so no new equity or debt will be raised. The cost of capital is 10% pa.
Which of the following statements about the net present value (NPV), internal rate of return (IRR) and payback period is NOT correct?
A firm is considering a business project which costs $10m now and is expected to pay a single cash flow of $12.1m in two years.
Assume that the initial $10m cost is funded using the firm's existing cash so no new equity or debt will be raised. The cost of capital is 10% pa.
Which of the following statements about net present value (NPV), internal rate of return (IRR) and payback period is NOT correct?
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.
A pharmaceutical firm has just discovered a valuable new drug. So far the news has been kept a secret.
The net present value of making and commercialising the drug is $200 million, but $600 million of bonds will need to be issued to fund the project and buy the necessary plant and equipment.
The firm will release the news of the discovery and bond raising to shareholders simultaneously in the same announcement. The bonds will be issued shortly after.
Once the announcement is made and the bonds are issued, what is the expected increase in the value of the firm's assets (ΔV), market capitalisation of debt (ΔD) and market cap of equity (ΔE)?
The triangle symbol is the Greek letter capital delta which means change or increase in mathematics.
Ignore the benefit of interest tax shields from having more debt.
Remember: ##ΔV = ΔD+ΔE##
A mining firm has just discovered a new mine. So far the news has been kept a secret.
The net present value of digging the mine and selling the minerals is $250 million, but $500 million of new equity and $300 million of new bonds will need to be issued to fund the project and buy the necessary plant and equipment.
The firm will release the news of the discovery and equity and bond raising to shareholders simultaneously in the same announcement. The shares and bonds will be issued shortly after.
Once the announcement is made and the new shares and bonds are issued, what is the expected increase in the value of the firm's assets ##(\Delta V)##, market capitalisation of debt ##(\Delta D)## and market cap of equity ##(\Delta E)##? Assume that markets are semistrong form efficient.
The triangle symbol ##\Delta## is the Greek letter capital delta which means change or increase in mathematics.
Ignore the benefit of interest tax shields from having more debt.
Remember: ##\Delta V = \Delta D+ \Delta E##
An investor owns an empty block of land that has local government approval to be developed into a petrol station, car wash or car park. The council will only allow a single development so the projects are mutually exclusive.
All of the development projects have the same risk and the required return of each is 10% pa. Each project has an immediate cost and once construction is finished in one year the land and development will be sold. The table below shows the estimated costs payable now, expected sale prices in one year and the internal rates of returns (IRR's).
Mutually Exclusive Projects  
Project  Cost now ($) 
Sale price in one year ($) 
IRR (% pa) 
Petrol station  9,000,000  11,000,000  22.22 
Car wash  800,000  1,100,000  37.50 
Car park  70,000  110,000  57.14 
Which project should the investor accept?
An investor owns a whole level of an old office building which is currently worth $1 million. There are three mutually exclusive projects that can be started by the investor. The office building level can be:
 Rented out to a tenant for one year at $0.1m paid immediately, and then sold for $0.99m in one year.
 Refurbished into more modern commercial office rooms at a cost of $1m now, and then sold for $2.4m when the refurbishment is finished in one year.
 Converted into residential apartments at a cost of $2m now, and then sold for $3.4m when the conversion is finished in one year.
All of the development projects have the same risk so the required return of each is 10% pa. The table below shows the estimated cash flows and internal rates of returns (IRR's).
Mutually Exclusive Projects  
Project  Cash flow now ($) 
Cash flow in one year ($) 
IRR (% pa) 
Rent then sell as is  900,000  990,000  10 
Refurbishment into modern offices  2,000,000  2,400,000  20 
Conversion into residential apartments  3,000,000  3,400,000  13.33 
Which project should the investor accept?
The below screenshot of Commonwealth Bank of Australia's (CBA) details were taken from the Google Finance website on 7 Nov 2014. Some information has been deliberately blanked out.
What was CBA's market capitalisation of equity?
Question 905 market capitalisation of equity, PE ratio, payout ratio
The below graph shows the computer software company Microsoft's stock price (MSFT) at the market close on the NASDAQ on Friday 1 June 2018.
Based on the screenshot above, which of the following statements about MSFT is NOT correct? MSFT's:
The first payment of a constant perpetual annual cash flow is received at time 5. Let this cash flow be ##C_5## and the required return be ##r##.
So there will be equal annual cash flows at time 5, 6, 7 and so on forever, and all of the cash flows will be equal so ##C_5 = C_6 = C_7 = ...##
When the perpetuity formula is used to value this stream of cash flows, it will give a value (V) at time:
A stock is expected to pay its next dividend of $1 in one year. Future annual dividends are expected to grow by 2% pa. So the first dividend of $1 will be in one year, the year after that $1.02 (=1*(1+0.02)^1), and a year later $1.0404 (=1*(1+0.02)^2) and so on forever.
Its required total return is 10% pa. The total required return and growth rate of dividends are given as effective annual rates.
Calculate the current stock price.
A stock just paid a dividend of $1. Future annual dividends are expected to grow by 2% pa. The next dividend of $1.02 (=1*(1+0.02)^1) will be in one year, and the year after that the dividend will be $1.0404 (=1*(1+0.02)^2), and so on forever.
Its required total return is 10% pa. The total required return and growth rate of dividends are given as effective annual rates.
Calculate the current stock price.
A stock is just about to pay a dividend of $1 tonight. Future annual dividends are expected to grow by 2% pa. The next dividend of $1 will be paid tonight, and the year after that the dividend will be $1.02 (=1*(1+0.02)^1), and a year later 1.0404 (=1*(1+0.04)^2) and so on forever.
Its required total return is 10% pa. The total required return and growth rate of dividends are given as effective annual rates.
Calculate the current stock price.
For a price of $13, Carla will sell you a share which will pay a dividend of $1 in one year and every year after that forever. The required return of the stock is 10% pa.
For a price of $1040, Camille will sell you a share which just paid a dividend of $100, and is expected to pay dividends every year forever, growing at a rate of 5% pa.
So the next dividend will be ##100(1+0.05)^1=$105.00##, and the year after it will be ##100(1+0.05)^2=110.25## and so on.
The required return of the stock is 15% pa.
The perpetuity with growth formula, also known as the dividend discount model (DDM) or Gordon growth model, is appropriate for valuing a company's shares. ##P_0## is the current share price, ##C_1## is next year's expected dividend, ##r## is the total required return and ##g## is the expected growth rate of the dividend.
###P_0=\dfrac{C_1}{rg}###
The below graph shows the expected future price path of the company's shares. Which of the following statements about the graph is NOT correct?
The following equation is the Dividend Discount Model, also known as the 'Gordon Growth Model' or the 'Perpetuity with growth' equation.
###P_0=\frac{d_1}{rg}###
A stock pays dividends annually. It just paid a dividend, but the next dividend (##d_1##) will be paid in one year.
According to the DDM, what is the correct formula for the expected price of the stock in 2.5 years?
The following equation is the Dividend Discount Model, also known as the 'Gordon Growth Model' or the 'Perpetuity with growth' equation.
### P_{0} = \frac{C_1}{r_{\text{eff}}  g_{\text{eff}}} ###
What would you call the expression ## C_1/P_0 ##?
The following is the Dividend Discount Model (DDM) used to price stocks:
###P_0=\dfrac{C_1}{rg}###
If the assumptions of the DDM hold, which one of the following statements is NOT correct? The long term expected:
Question 497 income and capital returns, DDM, ex dividend date
A stock will pay you a dividend of $10 tonight if you buy it today. Thereafter the annual dividend is expected to grow by 5% pa, so the next dividend after the $10 one tonight will be $10.50 in one year, then in two years it will be $11.025 and so on. The stock's required return is 10% pa.
What is the stock price today and what do you expect the stock price to be tomorrow, approximately?
Question 748 income and capital returns, DDM, ex dividend date
A stock will pay you a dividend of $2 tonight if you buy it today.
Thereafter the annual dividend is expected to grow by 3% pa, so the next dividend after the $2 one tonight will be $2.06 in one year, then in two years it will be $2.1218 and so on. The stock's required return is 8% pa.
What is the stock price today and what do you expect the stock price to be tomorrow, approximately?
In the dividend discount model:
###P_0 = \dfrac{C_1}{rg}###
The return ##r## is supposed to be the:
A stock pays annual dividends which are expected to continue forever. It just paid a dividend of $10. The growth rate in the dividend is 2% pa. You estimate that the stock's required return is 10% pa. Both the discount rate and growth rate are given as effective annual rates. Using the dividend discount model, what will be the share price?
A stock is expected to pay the following dividends:
Cash Flows of a Stock  
Time (yrs)  0  1  2  3  4  ... 
Dividend ($)  0.00  1.00  1.05  1.10  1.15  ... 
After year 4, the annual dividend will grow in perpetuity at 5% pa, so;
 the dividend at t=5 will be $1.15(1+0.05),
 the dividend at t=6 will be $1.15(1+0.05)^2, and so on.
The required return on the stock is 10% pa. Both the growth rate and required return are given as effective annual rates.
What will be the price of the stock in three and a half years (t = 3.5)?
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.
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:
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 stock is expected to pay a dividend of $15 in one year (t=1), then $25 for 9 years after that (payments at t=2 ,3,...10), and on the 11th year (t=11) the dividend will be 2% less than at t=10, and will continue to shrink at the same rate every year after that forever. The required return of the stock is 10%. All rates are effective annual rates.
What is the price of the stock now?
Question 50 DDM, stock pricing, inflation, real and nominal returns and cash flows
Most listed Australian companies pay dividends twice per year, the 'interim' and 'final' dividends, which are roughly 6 months apart.
You are an equities analyst trying to value the company BHP. You decide to use the Dividend Discount Model (DDM) as a starting point, so you study BHP's dividend history and you find that BHP tends to pay the same interim and final dividend each year, and that both grow by the same rate.
You expect BHP will pay a $0.55 interim dividend in six months and a $0.55 final dividend in one year. You expect each to grow by 4% next year and forever, so the interim and final dividends next year will be $0.572 each, and so on in perpetuity.
Assume BHP's cost of equity is 8% pa. All rates are quoted as nominal effective rates. The dividends are nominal cash flows and the inflation rate is 2.5% pa.
What is the current price of a BHP share?
Question 535 DDM, real and nominal returns and cash flows, stock pricing
You are an equities analyst trying to value the equity of the Australian telecoms company Telstra, with ticker TLS. In Australia, listed companies like Telstra tend to pay dividends every 6 months. The payment around August is called the final dividend and the payment around February is called the interim dividend. Both occur annually.
 Today is midMarch 2015.
 TLS's last interim dividend of $0.15 was one month ago in midFebruary 2015.
 TLS's last final dividend of $0.15 was seven months ago in midAugust 2014.
Judging by TLS's dividend history and prospects, you estimate that the nominal dividend growth rate will be 1% pa. Assume that TLS's total nominal cost of equity is 6% pa. The dividends are nominal cash flows and the inflation rate is 2.5% pa. All rates are quoted as nominal effective annual rates. Assume that each month is exactly one twelfth (1/12) of a year, so you can ignore the number of days in each month.
Calculate the current TLS share price.
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?
When using the dividend discount model, care must be taken to avoid using a nominal dividend growth rate that exceeds the country's nominal GDP growth rate. Otherwise the firm is forecast to take over the country since it grows faster than the average business forever.
Suppose a firm's nominal dividend grows at 10% pa forever, and nominal GDP growth is 5% pa forever. The firm's total dividends are currently $1 billion (t=0). The country's GDP is currently $1,000 billion (t=0).
In approximately how many years will the company's total dividends be as large as the country's GDP?
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 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 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.
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.
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.
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.
Bonds X and Y are issued by the same US company. Both bonds yield 10% pa, and they have the same face value ($100), maturity, seniority, and payment frequency.
The only difference is that bond X and Y's coupon rates are 8 and 12% pa respectively. Which of the following statements is true?
A bond maturing in 10 years has a coupon rate of 4% pa, paid semiannually. The bond's yield is currently 6% pa. The face value of the bond is $100. What is its price?
A three year bond has a fixed coupon rate of 12% pa, paid semiannually. The bond's yield is currently 6% pa. The face value is $100. What is its price?
Which one of the following bonds is trading at a discount?
Which one of the following bonds is trading at a premium?
An investor bought two 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.
In these tough economic times, central banks around the world have cut interest rates so low that they are practically zero. In some countries, government bond yields are also very close to zero.
A three year government bond with a face value of $100 and a coupon rate of 2% pa paid semiannually was just issued at a yield of 0%. What is the price of the bond?
"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:
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 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 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?
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 $100, Carol will sell you a 5 year bond paying semiannual coupons of 16% pa. The face value of the bond is $100. Other bonds with similar risk, maturity and coupon characteristics trade at a yield of 12% pa.
For a price of $100, Rad will sell you a 5 year bond paying semiannual coupons of 16% pa. The face value of the bond is $100. Other bonds with the same risk, maturity and coupon characteristics trade at a yield of 6% pa.
For a price of $100, Andrea will sell you a 2 year bond paying annual coupons of 10% pa. The face value of the bond is $100. Other bonds with the same risk, maturity and coupon characteristics trade at a yield of 6% pa.
For a price of $95, Nicole will sell you a 10 year bond paying 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.
An investor bought a 10 year 2.5% 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 fell to 2% 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?
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?
You want to buy an apartment priced at $300,000. You have saved a deposit of $30,000. The bank has agreed to lend you the $270,000 as a fully amortising loan with a term of 25 years. The interest rate is 12% pa and is not expected to change.
What will be your monthly payments? Remember that mortgage loan payments are paid in arrears (at the end of the month).
You want to buy an apartment worth $500,000. You have saved a deposit of $50,000. The bank has agreed to lend you the $450,000 as a fully amortising mortgage loan with a term of 25 years. The interest rate is 6% pa and is not expected to change.
What will be your monthly payments?
You want to buy an apartment worth $400,000. You have saved a deposit of $80,000. The bank has agreed to lend you the $320,000 as a fully amortising mortgage loan with a term of 30 years. The interest rate is 6% pa and is not expected to change. What will be your monthly payments?
You want to buy an apartment priced at $500,000. You have saved a deposit of $50,000. The bank has agreed to lend you the $450,000 as a fully amortising loan with a term of 30 years. The interest rate is 6% pa and is not expected to change. What will be your monthly payments?
You just signed up for a 30 year fully amortising mortgage loan with monthly payments of $2,000 per month. The interest rate is 9% pa which is not expected to change.
How much did you borrow? After 5 years, how much will be owing on the mortgage? The interest rate is still 9% and is not expected to change.
You just signed up for a 30 year fully amortising mortgage with monthly payments of $1,000 per month. The interest rate is 6% pa which is not expected to change.
How much did you borrow? After 20 years, how much will be owing on the mortgage? The interest rate is still 6% and is not expected to change.
You just signed up for a 30 year fully amortising mortgage loan with monthly payments of $1,500 per month. The interest rate is 9% pa which is not expected to change.
How much did you borrow? After 10 years, how much will be owing on the mortgage? The interest rate is still 9% and is not expected to change.
You just agreed to a 30 year fully amortising mortgage loan with monthly payments of $2,500. The interest rate is 9% pa which is not expected to change.
How much did you borrow? After 10 years, how much will be owing on the mortgage? The interest rate is still 9% and is not expected to change. The below choices are given in the same order.
You want to buy a house priced at $400,000. You have saved a deposit of $40,000. The bank has agreed to lend you $360,000 as a fully amortising loan with a term of 30 years. The interest rate is 8% pa payable monthly and is not expected to change.
What will be your monthly payments?
You want to buy an apartment priced at $300,000. You have saved a deposit of $30,000. The bank has agreed to lend you the $270,000 as an interest only loan with a term of 25 years. The interest rate is 12% pa and is not expected to change.
What will be your monthly payments? Remember that mortgage payments are paid in arrears (at the end of the month).
You just signed up for a 30 year interestonly mortgage with monthly payments of $3,000 per month. The interest rate is 6% pa which is not expected to change.
How much did you borrow? After 15 years, just after the 180th payment at that time, how much will be owing on the mortgage? The interest rate is still 6% and is not expected to change. Remember that the mortgage is interestonly and that mortgage payments are paid in arrears (at the end of the month).
You just borrowed $400,000 in the form of a 25 year interestonly mortgage with monthly payments of $3,000 per month. The interest rate is 9% pa which is not expected to change.
You actually plan to pay more than the required interest payment. You plan to pay $3,300 in mortgage payments every month, which your mortgage lender allows. These extra payments will reduce the principal and the minimum interest payment required each month.
At the maturity of the mortgage, what will be the principal? That is, after the last (300th) interest payment of $3,300 in 25 years, how much will be owing on the mortgage?
You want to buy an apartment worth $300,000. You have saved a deposit of $60,000.
The bank has agreed to lend you $240,000 as an interest only mortgage loan with a term of 30 years. The interest rate is 6% pa and is not expected to change. What will be your monthly payments?
You want to buy an apartment priced at $500,000. You have saved a deposit of $50,000. The bank has agreed to lend you the $450,000 as an interest only loan with a term of 30 years. The interest rate is 6% pa and is not expected to change. What will be your monthly payments?
Question 550 fully amortising loan, interest only loan, APR, no explanation
Many Australian home loans that are interestonly actually require payments to be made on a fully amortising basis after a number of years.
You decide to borrow $600,000 from the bank at an interest rate of 4.25% pa for 25 years. The payments will be interestonly for the first 10 years (t=0 to 10 years), then they will have to be paid on a fully amortising basis for the last 15 years (t=10 to 25 years).
Assuming that interest rates will remain constant, what will be your monthly payments over the first 10 years from now, and then the next 15 years after that? The answer options are given in the same order.
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.
How much more can you borrow using an interestonly loan compared to a 25year fully amortising loan if interest rates are 6% pa compounding per month and are not expected to change? If it makes it easier, assume that you can afford to pay $2,000 per month on either loan. Express your answer as a proportional increase using the following formula:
###\text{Proportional Increase} = \dfrac{V_\text{0,interest only}}{V_\text{0,fully amortising}}  1###How much more can you borrow using an 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###This annuity formula ##\dfrac{C_1}{r}\left(1\dfrac{1}{(1+r)^3} \right)## is equivalent to which of the following formulas? Note the 3.
In the below formulas, ##C_t## is a cash flow at time t. All of the cash flows are equal, but paid at different times.
Telsa Motors advertises that its Model S electric car saves $570 per month in fuel costs. Assume that Tesla cars last for 10 years, fuel and electricity costs remain the same, and savings are made at the end of each month with the first saving of $570 in one month from now.
The effective annual interest rate is 15.8%, and the effective monthly interest rate is 1.23%. What is the present value of the savings?
The following cash flows are expected:
 10 yearly payments of $80, with the first payment in 3 years from now (first payment at t=3).
 1 payment of $600 in 5 years and 6 months (t=5.5) from now.
What is the NPV of the cash flows if the discount rate is 10% given as an effective annual rate?
On his 20th birthday, a man makes a resolution. He will deposit $30 into a bank account at the end of every month starting from now, which is the start of the month. So the first payment will be in one month. He will write in his will that when he dies the money in the account should be given to charity.
The bank account pays interest at 6% pa compounding monthly, which is not expected to change.
If the man lives for another 60 years, how much money will be in the bank account if he dies just after making his last (720th) payment?
There are many ways to write the ordinary annuity formula.
Which of the following is NOT equal to the ordinary annuity formula?
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.
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?
The following cash flows are expected:
 10 yearly payments of $80, with the first payment in 6.5 years from now (first payment at t=6.5).
 A single payment of $500 in 4 years and 3 months (t=4.25) from now.
What is the NPV of the cash flows if the discount rate is 10% given as an effective annual rate?
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?
You deposit money into a bank. Which of the following statements is NOT correct? You:
You bought a house, primarily funded using a home loan from a bank. Which of the following statements is NOT correct?
Question 771 debt terminology, interest expense, interest tax shield, credit risk, no explanation
You deposit money into a bank account. Which of the following statements about this deposit is NOT correct?
Question 909 money market, bills
By convention, money market securities' yields are always quoted as:
Which of the following statements is NOT correct? Money market securities are:
A 180day Bank Accepted Bill has a face value of $1,000,000. The interest rate is 8% pa and there are 365 days in the year. What is its price now?
A 90day Bank Accepted Bill (BAB) has a face value of $1,000,000. The simple interest rate is 10% pa and there are 365 days in the year. What is its price now?
Question 327 bill pricing, simple interest rate, no explanation
On 27/09/13, three month Swiss government bills traded at a yield of 0.2%, given as a simple annual yield. That is, interest rates were negative.
If the face value of one of these 90 day bills is CHF1,000,000 (CHF represents Swiss Francs, the Swiss currency), what is the price of one of these bills?
A bank bill was bought for $99,000 and sold for $100,000 thirty (30) days later. There are 365 days in the year. Which of the following formulas gives the simple interest rate per annum over those 30 days?
Note: To help you identify which is the correct answer without doing any calculations yourself, the formulas used to calculate the numbers are given.
A 90 day bank bill has a face value of $100,000.
Investor A bought the bill when it was first issued at a simple yield to maturity of 3% pa and sold it 20 days later to Investor B who expected to earn a simple yield to maturity of 5% pa. Investor B held it until maturity.
Which of the following statements is NOT correct?
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 449 personal tax on dividends, classical tax system
A small private company has a single shareholder. This year the firm earned a $100 profit before tax. All of the firm's after tax profits will be paid out as dividends to the owner.
The corporate tax rate is 30% and the sole shareholder's personal marginal tax rate is 45%.
The United States' classical tax system applies because the company generates all of its income in the US and pays corporate tax to the Internal Revenue Service. The shareholder is also an American for tax purposes.
What will be the personal tax payable by the shareholder and the corporate tax payable by the company?
Question 448 franking credit, personal tax on dividends, imputation tax system
A small private company has a single shareholder. This year the firm earned a $100 profit before tax. All of the firm's after tax profits will be paid out as dividends to the owner.
The corporate tax rate is 30% and the sole shareholder's personal marginal tax rate is 45%.
The Australian imputation tax system applies because the company generates all of its income in Australia and pays corporate tax to the Australian Tax Office. Therefore all of the company's dividends are fully franked. The sole shareholder is an Australian for tax purposes and can therefore use the franking credits to offset his personal income tax liability.
What will be the personal tax payable by the shareholder and the corporate tax payable by the company?
Question 469 franking credit, personal tax on dividends, imputation tax system, no explanation
A firm pays a fully franked cash dividend of $70 to one of its Australian shareholders who has a personal marginal tax rate of 45%. The corporate tax rate is 30%.
What will be the shareholder's personal tax payable due to the dividend payment?
Question 494 franking credit, personal tax on dividends, imputation tax system
A firm pays a fully franked cash dividend of $100 to one of its Australian shareholders who has a personal marginal tax rate of 15%. The corporate tax rate is 30%.
What will be the shareholder's personal tax payable due to the dividend payment?
Question 624 franking credit, personal tax on dividends, imputation tax system, no explanation
Which of the following statements about Australian franking credits is NOT correct? Franking credits:
Question 443 corporate financial decision theory, investment decision, financing decision, working capital decision, payout policy
Business people make lots of important decisions. Which of the following is the most important long term decision?
Question 444 investment decision, corporate financial decision theory
The investment decision primarily affects which part of a business?
Question 445 financing decision, corporate financial decision theory
The financing decision primarily affects which part of a business?
Question 446 working capital decision, corporate financial decision theory
The working capital decision primarily affects which part of a business?
Question 447 payout policy, corporate financial decision theory
Payout policy is most closely related to which part of a business?
The expression 'cash is king' emphasizes the importance of having enough cash to pay your short term debts to avoid bankruptcy. Which business decision is this expression most closely related to?
The expression 'you have to spend money to make money' relates to which business decision?
Which of the following decisions relates to the current assets and current liabilities of the firm?
Question 767 idiom, corporate financial decision theory, no explanation
The sayings "Don't cry over spilt milk", "Don't regret the things that you can't change" and "What's done is done" are most closely related to which financial concept?
Question 768 accounting terminology, book and market values, no explanation
Accountants and finance professionals have lots of names for the same things which can be quite confusing.
Which of the following groups of items are NOT synonyms?
Question 729 book and market values, balance sheet, no explanation
If a firm makes a profit and pays no dividends, which of the following accounts will increase?
Question 737 financial statement, balance sheet, income statement
Where can a publicly listed firm's book value of equity be found? It can be sourced from the company's:
Question 738 financial statement, balance sheet, income statement
Where can a private firm's market value of equity be found? It can be sourced from the company's:
Question 531 bankruptcy or insolvency, capital structure, risk, limited liability
Who is most in danger of being personally bankrupt? Assume that all of their businesses' assets are highly liquid and can therefore be sold immediately.
Question 524 risk, expected and historical returns, bankruptcy or insolvency, capital structure, corporate financial decision theory, limited liability
Which of the following statements is NOT correct?
Which of the following statements about book and market equity is NOT correct?