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 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:
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 ##?
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.
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?
The following is the Dividend Discount Model (DDM) used to price stocks:
### P_0 = \frac{d_1}{rg} ###Assume that the assumptions of the DDM hold and that the time period is measured in years.
Which of the following is equal to the expected dividend in 3 years, ## d_3 ##?
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.
When using the dividend discount model to price a stock:
### p_{0} = \frac{d_1}{r  g} ###
The growth rate of dividends (g):
In the dividend discount model:
###P_0 = \dfrac{C_1}{rg}###
The return ##r## is supposed to be the:
The following equation is the Dividend Discount Model, also known as the 'Gordon Growth Model' or the 'Perpetuity with growth' equation.
###p_0=\frac{d_1}{r_\text{eff}g_\text{eff}}###
Which expression is NOT equal to the expected capital return?
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.
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?
When using the dividend discount model, care must be taken to avoid using a nominal dividend growth rate that exceeds the country's nominal GDP growth rate. Otherwise the firm is forecast to take over the country since it grows faster than the average business forever.
Suppose a firm's nominal dividend grows at 10% pa forever, and nominal GDP growth is 5% pa forever. The firm's total dividends are currently $1 billion (t=0). The country's GDP is currently $1,000 billion (t=0).
In approximately how many years will the company's total dividends be as large as the country's GDP?
Question 210 real estate, inflation, real and nominal returns and cash flows, income and capital returns
Assume that the Gordon Growth Model (same as the dividend discount model or perpetuity with growth formula) is an appropriate method to value real estate.
The rule of thumb in the real estate industry is that properties should yield a 5% pa rental return. Many investors also regard property to be as risky as the stock market, therefore property is thought to have a required total return of 9% pa which is the average total return on the stock market including dividends.
Assume that all returns are effective annual rates and they are nominal (not reduced by inflation). Inflation is expected to be 2% pa.
You're considering purchasing an investment property which has a rental yield of 5% pa and you expect it to have the same risk as the stock market. Select the most correct statement about this property.
Question 58 NPV, inflation, real and nominal returns and cash flows, Annuity
A project to build a toll bridge will take two years to complete, costing three payments of $100 million at the start of each year for the next three years, that is at t=0, 1 and 2.
After completion, the toll bridge will yield a constant $50 million at the end of each year for the next 10 years. So the first payment will be at t=3 and the last at t=12. After the last payment at t=12, the bridge will be given to the government.
The required return of the project is 21% pa given as an effective annual nominal rate.
All cash flows are real and the expected inflation rate is 10% pa given as an effective annual rate. Ignore taxes.
The Net Present Value is:
Question 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.
Jan asks you for a loan. He wants $100 now and offers to pay you back $120 in 1 year. You can borrow and lend from the bank at an interest rate of 10% pa, given as an effective annual rate.
Ignore credit risk. Remember:
### V_0 = \frac{V_t}{(1+r_\text{eff})^t} ###
Katya offers to pay you $10 at the end of every year for the next 5 years (t=1,2,3,4,5) if you pay her $50 now (t=0). You can borrow and lend from the bank at an interest rate of 10% pa, given as an effective annual rate.
Ignore credit risk.
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 $6, Carlos will sell you a share which will pay a dividend of $1 in one year and every year after that forever. The required return of the stock is 10% pa.
For a price of $102, Andrea will sell you a share which just paid a dividend of $10 yesterday, and is expected to pay dividends every year forever, growing at a rate of 5% pa.
So the next dividend will be ##10(1+0.05)^1=$10.50## in one year from now, and the year after it will be ##10(1+0.05)^2=11.025## and so on.
The required return of the stock is 15% pa.
For a price of $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.
For a price of $10.20 each, Renee will sell you 100 shares. Each share is expected to pay dividends in perpetuity, growing at a rate of 5% pa. The next dividend is one year away (t=1) and is expected to be $1 per share.
The required return of the stock is 15% pa.
For a price of $129, Joanne will sell you a share which is expected to pay a $30 dividend in one year, and a $10 dividend every year after that forever. So the stock's dividends will be $30 at t=1, $10 at t=2, $10 at t=3, and $10 forever onwards.
The required return of the stock is 10% pa.
For a price of $95, Sherylanne will sell you a share which is expected to pay its first dividend of $10 in 7 years (t=7), and will continue to pay the same $10 dividend every year after that forever.
The required return of the stock is 10% pa.
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.
A credit card offers an interest rate of 18% pa, compounding monthly.
Find the effective monthly rate, effective annual rate and the effective daily rate. Assume that there are 365 days in a year.
All answers are given in the same order:
### r_\text{eff monthly} , r_\text{eff yearly} , r_\text{eff daily} ###
A three year bond has a face value of $100, a yield of 10% and a fixed coupon rate of 5%, paid semiannually. What is its price?
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).
Your friend wants to borrow $1,000 and offers to pay you back $100 in 6 months, with more $100 payments at the end of every month for another 11 months. So there will be twelve $100 payments in total. She says that 12 payments of $100 equals $1,200 so she's being generous.
If interest rates are 12% pa, given as an APR compounding monthly, what is the Net Present Value (NPV) of your friend's deal?
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).
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 31 DDM, perpetuity with growth, effective rate conversion
What is the NPV of the following series of cash flows when the discount rate is 5% given as an effective annual rate?
The first payment of $10 is in 4 years, followed by payments every 6 months forever after that which shrink by 2% every 6 months. That is, the growth rate every 6 months is actually negative 2%, given as an effective 6 month rate. So the payment at ## t=4.5 ## years will be ## 10(10.02)^1=9.80 ##, and so on.
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?
Bonds A and B are issued by the same company. They have the same face value, maturity, seniority and coupon payment frequency. The only difference is that bond A has a 5% coupon rate, while bond B has a 10% coupon rate. The yield curve is flat, which means that yields are expected to stay the same.
Which bond would have the higher current price?
Question 35 bond pricing, zero coupon bond, term structure of interest rates, forward interest rate
A European company just issued two bonds, a
 1 year zero coupon bond at a yield of 8% pa, and a
 2 year zero coupon bond at a yield of 10% pa.
What is the company's forward rate over the second year (from t=1 to t=2)? Give your answer as an effective annual rate, which is how the above bond yields are quoted.
A 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?
If a project's net present value (NPV) is zero, then its internal rate of return (IRR) will be:
A two year Government bond has a face value of $100, a yield of 0.5% and a fixed coupon rate of 0.5%, paid semiannually. What is its price?
A stock is expected to pay the following dividends:
Cash Flows of a Stock  
Time (yrs)  0  1  2  3  4  ... 
Dividend ($)  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)?
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).
A project to build a toll road will take 3 years to complete, costing three payments of $50 million, paid at the start of each year (at times 0, 1, and 2).
After completion, the toll road will yield a constant $10 million at the end of each year forever with no costs. So the first payment will be at t=4.
The required return of the project is 10% pa given as an effective nominal rate. All cash flows are nominal.
What is the payback period?
The required return of a project is 10%, given as an effective annual rate. Assume that the cash flows shown in the table are paid all at once at the given point in time.
What is the Net Present Value (NPV) of the project?
Project Cash Flows  
Time (yrs)  Cash flow ($) 
0  100 
1  0 
2  121 
The phone company Telstra have 2 mobile service plans on offer which both have the same amount of phone call, text message and internet data credit. Both plans have a contract length of 24 months and the monthly cost is payable in advance. The only difference between the two plans is that one is a:
 'Bring Your Own' (BYO) mobile service plan, costing $50 per month. There is no phone included in this plan. The other plan is a:
 'Bundled' mobile service plan that comes with the latest smart phone, costing $71 per month. This plan includes the latest smart phone.
Neither plan has any additional payments at the start or end.
The only difference between the plans is the phone, so what is the implied cost of the phone as a present value?
Assume that the discount rate is 2% per month given as an effective monthly rate, the same high interest rate on credit cards.
Question 48 IRR, NPV, bond pricing, premium par and discount bonds, market efficiency
The theory of fixed interest bond pricing is an application of the theory of Net Present Value (NPV). Also, a 'fairly priced' asset is not over or underpriced. Buying or selling a fairly priced asset has an NPV of zero.
Considering this, which of the following statements is NOT correct?
Question 49 inflation, real and nominal returns and cash flows, APR, effective rate
In Australia, nominal yields on semiannual coupon paying Government Bonds with 2 years until maturity are currently 2.83% pa.
The inflation rate is currently 2.2% pa, given as an APR compounding per quarter. The inflation rate is not expected to change over the next 2 years.
What is the real yield on these bonds, given as an APR compounding every 6 months?
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?
A three year project's NPV is negative. The cash flows of the project include a negative cash flow at the very start and positive cash flows over its short life. The required return of the project is 10% pa. Select the most correct statement.
A two year Government bond has a face value of $100, a yield of 2.5% pa and a fixed coupon rate of 0.5% pa, paid semiannually. What is its price?
A stock is expected to pay the following dividends:
Cash Flows of a Stock  
Time (yrs)  0  1  2  3  4  ... 
Dividend ($)  0.00  1.15  1.10  1.05  1.00  ... 
After year 4, the annual dividend will grow in perpetuity at 5% pa. Note that this is a negative growth rate, so the dividend will actually shrink. So,
 the dividend at t=5 will be ##$1(10.05) = $0.95##,
 the dividend at t=6 will be ##$1(10.05)^2 = $0.9025##, and so on.
The required return on the stock is 10% pa. Both the growth rate and required return are given as effective annual rates.
What is the current price of the stock?
A stock is expected to pay the following dividends:
Cash Flows of a Stock  
Time (yrs)  0  1  2  3  4  ... 
Dividend ($)  0.00  1.15  1.10  1.05  1.00  ... 
After year 4, the annual dividend will grow in perpetuity at 5% pa. Note that this is a negative growth rate, so the dividend will actually shrink. So,
 the dividend at t=5 will be ##$1(10.05) = $0.95##,
 the dividend at t=6 will be ##$1(10.05)^2 = $0.9025##, 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 four and a half years (t = 4.5)?
Question 56 income and capital returns, bond pricing, premium par and discount bonds
Which of the following statements about risk free government bonds is NOT correct?
Hint: Total return can be broken into income and capital returns as follows:
###\begin{aligned} r_\text{total} &= \frac{c_1}{p_0} + \frac{p_1p_0}{p_0} \\ &= r_\text{income} + r_\text{capital} \end{aligned} ###
The capital return is the growth rate of the price.
The income return is the periodic cash flow. For a bond this is the coupon payment.
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 $3,300 in 25 years, how much will be owing on the mortgage?
The required return of a project is 10%, given as an effective annual rate. Assume that the cash flows shown in the table are paid all at once at the given point in time.
What is the Net Present Value (NPV) of the project?
Project Cash Flows  
Time (yrs)  Cash flow ($) 
0  100 
1  11 
2  121 
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 
In Australia, domestic university students are allowed to buy concession tickets for the bus, train and ferry which sell at a discount of 50% to fullprice tickets.
The Australian Government do not allow international university students to buy concession tickets, they have to pay the full price.
Some international students see this as unfair and they are willing to pay for fake university identification cards which have the concession sticker.
What is the most that an international student would be willing to pay for a fake identification card?
Assume that international students:
 consider buying their fake card on the morning of the first day of university from their neighbour, just before they leave to take the train into university.
 buy their weekly train tickets on the morning of the first day of each week.
 ride the train to university and back home again every day seven days per week until summer holidays 40 weeks from now. The concession card only lasts for those 40 weeks. Assume that there are 52 weeks in the year for the purpose of interest rate conversion.
 a single fullpriced oneway train ride costs $5.
 have a discount rate of 11% pa, given as an effective annual rate.
Approach this question from a purely financial view point, ignoring the illegality, embarrassment and the morality of committing fraud.
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?
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?
Question 65 annuity with growth, needs refinement
Which of the below formulas gives the present value of an annuity with growth?
Hint: The equation of a perpetuity without growth is: ###V_\text{0, perp without growth} = \frac{C_\text{1}}{r}###
The formula for the present value of an annuity without growth is derived from the formula for a perpetuity without growth.
The idea is than an annuity with T payments from t=1 to T inclusive is equivalent to a perpetuity starting at t=1 with fixed positive cash flows, plus a perpetuity starting T periods later (t=T+1) with fixed negative cash flows. The positive and negative cash flows after time period T cancel each other out, leaving the positive cash flows between t=1 to T, which is the annuity.
###\begin{aligned} V_\text{0, annuity} &= V_\text{0, perp without growth from t=1}  V_\text{0, perp without growth from t=T+1} \\ &= \dfrac{C_\text{1}}{r}  \dfrac{ \left( \dfrac{C_\text{T+1}}{r} \right) }{(1+r)^T} \\ &= \dfrac{C_\text{1}}{r}  \dfrac{ \left( \dfrac{C_\text{1}}{r} \right) }{(1+r)^T} \\ &= \dfrac{C_\text{1}}{r}\left(1  \dfrac{1}{(1+r)^T}\right) \\ \end{aligned}###
The equation of a perpetuity with growth is:
###V_\text{0, perp with growth} = \dfrac{C_\text{1}}{rg}###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?
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.
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.
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###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.
Question 353 income and capital returns, inflation, real and nominal returns and cash flows, real estate
A residential investment property has an expected nominal total return of 6% pa and nominal capital return of 3% pa.
Inflation is expected to be 2% pa. All rates are given as effective annual rates.
What are the property's expected real total, capital and income returns? The answer choices below are given in the same order.
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###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.
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?
An old 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 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?
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?
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?
In the dividend discount model:
### P_0= \frac{d_1}{rg} ###
The pronumeral ##g## is supposed to be the:
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?
Which of the below statements about effective rates and annualised percentage rates (APR's) is NOT correct?
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.
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?
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.
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?
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?
Diversification in a portfolio of two assets works best when the correlation between their returns is:
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 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?
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 share pays annual dividends. It just paid a dividend of $2. The growth rate in the dividend is 3% pa. You estimate that the stock's required return is 8% pa. Both the discount rate and growth rate are given as effective annual rates.
Using the dividend discount model, what is the share price?
A project has the following cash flows. Normally cash flows are assumed to happen at the given time. But here, assume that the cash flows are received smoothly over the year. So the $250 at time 2 is actually earned smoothly from t=1 to t=2:
Project Cash Flows  
Time (yrs)  Cash flow ($) 
0  400 
1  200 
2  250 
What is the payback period of the project in years?
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 share was bought for $10 (at t=0) and paid its annual dividend of $0.50 one year later (at t=1). Just after the dividend was paid, the share price was $11 (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{dividend}##.
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?
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?
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?
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?
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.
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?
Diversification is achieved by investing in a large amount of stocks. What type of risk is reduced by diversification?
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?
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.
A student just won the lottery. She won $1 million in cash after tax. She is trying to calculate how much she can spend per month for the rest of her life. She assumes that she will live for another 60 years. She wants to withdraw equal amounts at the beginning of every month, starting right now.
All of the cash is currently sitting in a bank account which pays interest at a rate of 6% pa, given as an APR compounding per month. On her last withdrawal, she intends to have nothing left in her bank account. How much can she withdraw at the beginning of each month?
Your poor friend asks to borrow some money from you. He would like $1,000 now (t=0) and every year for the next 5 years, so there will be 6 payments of $1,000 from t=0 to t=5 inclusive. In return he will pay you $10,000 in seven years from now (t=7).
What is the net present value (NPV) of lending to your friend?
Assume that your friend will definitely pay you back so the loan is riskfree, and that the yield on riskfree government debt is 10% pa, given as an effective annual rate.
Calculate the effective annual rates of the following three APR's:
 A credit card offering an interest rate of 18% pa, compounding monthly.
 A bond offering a yield of 6% pa, compounding 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}##
You're trying to save enough money to buy your first car which costs $2,500. You can save $100 at the end of each month starting from now. You currently have no money at all. You just opened a bank account with an interest rate of 6% pa payable monthly.
How many months will it take to save enough money to buy the car? Assume that the price of the car will stay the same over time.
A three year corporate bond yields 12% pa with a coupon rate of 10% pa, paid semiannually.
Find the effective six month yield, effective annual yield and the effective daily yield. Assume that each month has 30 days and that there are 360 days in a year.
All answers are given in the same order:
##r_\text{eff semiannual}##, ##r_\text{eff yearly}##, ##r_\text{eff daily}##.
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?
A 2 year government bond yields 5% pa with a coupon rate of 6% pa, paid semiannually.
Find the effective six month rate, effective annual rate and the effective daily rate. Assume that each month has 30 days and that there are 360 days in a year.
All answers are given in the same order:
##r_\text{eff semiannual}##, ##r_\text{eff yrly}##, ##r_\text{eff daily}##.
A 2 year corporate bond yields 3% pa with a coupon rate of 5% pa, paid semiannually.
Find the effective monthly rate, effective six month rate, and effective annual rate.
##r_\text{eff monthly}##, ##r_\text{eff 6 month}##, ##r_\text{eff annual}##.
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?
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?
Which of the following statements about effective rates and annualised percentage rates (APR's) is NOT correct?
Bonds X and Y are issued by the same US company. Both bonds yield 10% pa, and they have the same face value ($100), maturity, seniority, and payment frequency.
The only difference is that bond X and Y's coupon rates are 8 and 12% pa respectively. Which of the following statements is true?
Question 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 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.
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?
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.
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?
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 207 income and capital returns, bond pricing, coupon rate, no explanation
For a bond that pays fixed semiannual coupons, how is the annual coupon rate defined, and how is the bond's annual income yield from time 0 to 1 defined mathematically?
Let: ##P_0## be the bond price now,
##F_T## be the bond's face value,
##T## be the bond's maturity in years,
##r_\text{total}## be the bond's total yield,
##r_\text{income}## be the bond's income yield,
##r_\text{capital}## be the bond's capital yield, and
##C_t## be the bond's coupon at time t in years. So ##C_{0.5}## is the coupon in 6 months, ##C_1## is the coupon in 1 year, and so on.
Question 213 income and capital returns, bond pricing, premium par and discount bonds
The coupon rate of a fixed annualcoupon bond is constant (always the same).
What can you say about the income return (##r_\text{income}##) of a fixed annual coupon bond? Remember that:
###r_\text{total} = r_\text{income} + r_\text{capital}###
###r_\text{total, 0 to 1} = \frac{c_1}{p_0} + \frac{p_1p_0}{p_0}###
Assume that there is no change in the bond's total annual yield to maturity from when it is issued to when it matures.
Select the most correct statement.
From its date of issue until maturity, the income return of a fixed annual coupon:
Which one of the following bonds is trading at a premium?
An investor bought two fixedcoupon bonds issued by the same company, a zerocoupon bond and a 7% pa semiannual coupon bond. Both bonds have a face value of $1,000, mature in 10 years, and had a yield at the time of purchase of 8% pa.
A few years later, yields fell to 6% pa. Which of the following statements is correct? Note that a capital gain is an increase in price.
A firm wishes to raise $10 million now. They will issue 6% pa semiannual coupon bonds that will mature in 8 years and have a face value of $1,000 each. Bond yields are 10% pa, given as an APR compounding every 6 months, and the yield curve is flat.
How many bonds should the firm issue?
A four year bond has a face value of $100, a yield of 9% and a fixed coupon rate of 6%, paid semiannually. What is its price?
In these tough economic times, central banks around the world have cut interest rates so low that they are practically zero. In some countries, government bond yields are also very close to zero.
A three year government bond with a face value of $100 and a coupon rate of 2% pa paid semiannually was just issued at a yield of 0%. What is the price of the bond?
A 10 year bond has a face value of $100, a yield of 6% pa and a fixed coupon rate of 8% pa, paid semiannually. What is its price?
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?
Question 339 bond pricing, inflation, market efficiency, income and capital returns
Economic statistics released this morning were a surprise: they show a strong chance of consumer price inflation (CPI) reaching 5% pa over the next 2 years.
This is much higher than the previous forecast of 3% pa.
A vanilla fixedcoupon 2year riskfree government bond was issued at par this morning, just before the economic news was released.
What is the expected change in bond price after the economic news this morning, and in the next 2 years? Assume that:
 Inflation remains at 5% over the next 2 years.
 Investors demand a constant real bond yield.
 The bond price falls by the (aftertax) value of the coupon the night before the excoupon date, as in real life.
Why is Capital Expenditure (CapEx) subtracted in the Cash Flow From Assets (CFFA) formula?
###CFFA=NI+DeprCapEx  \Delta NWC+IntExp###
Interest expense (IntExp) is an important part of a company's income statement (or 'profit and loss' or 'statement of financial performance').
How does an accountant calculate the annual interest expense of a fixedcoupon bond that has a liquid secondary market? Select the most correct answer:
Annual interest expense is equal to:
Which one of the following will increase the Cash Flow From Assets in this year for a taxpaying firm, all else remaining constant?
A company increases the proportion of debt funding it uses to finance its assets by issuing bonds and using the cash to repurchase stock, leaving assets unchanged.
Ignoring the costs of financial distress, which of the following statements is NOT correct:
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###Stock A has a beta of 0.5 and stock B has a beta of 1. Which statement is NOT correct?
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?
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?
All things remaining equal, the variance of a portfolio of two positivelyweighted stocks rises as:
According to the theory of the Capital Asset Pricing Model (CAPM), total risk can be broken into two components, systematic risk and idiosyncratic risk. Which of the following events would be considered a systematic, undiversifiable event according to the theory of the CAPM?
A 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?
Stock A and B's returns have a correlation of 0.3. Which statement is NOT correct?
All things remaining equal, the higher the correlation of returns between two stocks:
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 __________.
Your credit card shows a $600 debt liability. The interest rate is 24% pa, payable monthly. You can't pay any of the debt off, except in 6 months when it's your birthday and you'll receive $50 which you'll use to pay off the credit card. If that is your only repayment, how much will the credit card debt liability be one year from now?
Two risky stocks A and B comprise an equalweighted portfolio. The correlation between the stocks' returns is 70%.
If the variance of stock A increases but the:
 Prices and expected returns of each stock stays the same,
 Variance of stock B's returns stays the same,
 Correlation of returns between the stocks stays the same.
Which of the following statements is NOT correct?
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 is 10% pa, given as an effective annual rate.
What is the price of the share now?
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. It just paid a dividend of $3. The growth rate in the dividend is 4% pa. You estimate that the stock's required return is 10% pa. Both the discount rate and growth rate are given as effective annual rates. Using the dividend discount model, what will be the share price?
A stock is expected to pay the following dividends:
Cash Flows of a Stock  
Time (yrs)  0  1  2  3  4  ... 
Dividend ($)  8  8  8  20  8  ... 
After year 4, the dividend will grow in perpetuity at 4% pa. 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 ($)  8  8  8  20  8  ... 
After year 4, the dividend will grow in perpetuity at 4% pa. 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 5 years (t = 5), just after the dividend at that time has been paid?
A stock pays annual dividends. It just paid a dividend of $5. The growth rate in the dividend is 1% pa. You estimate that the stock's required return is 8% pa. Both the discount rate and growth rate are given as effective annual rates.
Using the dividend discount model, what will be the share price?
A stock is expected to pay the following dividends:
Cash Flows of a Stock  
Time (yrs)  0  1  2  3  4  ... 
Dividend ($)  2  2  2  10  3  ... 
After year 4, the dividend will grow in perpetuity at 4% pa. 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 5 years (t = 5), just after the dividend at that time has been paid?
The following is the Dividend Discount Model used to price stocks:
### p_0=\frac{d_1}{rg} ###
All rates are effective annual rates and the cash flows (##d_1##) are received every year. Note that the r and g terms in the above DDM could also be labelled as below: ###r = r_{\text{total, 0}\rightarrow\text{1yr, eff 1yr}}### ###g = r_{\text{capital, 0}\rightarrow\text{1yr, eff 1yr}}### Which of the following statements is NOT correct?
A stock is expected to pay the following dividends:
Cash Flows of a Stock  
Time (yrs)  0  1  2  3  4  ... 
Dividend ($)  0  6  12  18  20  ... 
After year 4, the dividend will grow in perpetuity at 5% pa. The required return of 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 7 years (t = 7), just after the dividend at that time has been paid?
A share just paid its semiannual dividend of $5. The dividend is expected to grow at 1% every 6 months forever. This 1% growth rate is an effective 6 month rate.
Therefore the next dividend will be $5.05 in six months. The required return of the stock 8% pa, given as an effective annual rate.
What is the price of the share now?
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)?
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).
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).
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.
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:
Find Sidebar Corporation's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.
Sidebar Corp  
Income Statement for  
year ending 30th June 2013  
$m  
Sales  405  
COGS  100  
Depreciation  34  
Rent expense  22  
Interest expense  39  
Taxable Income  210  
Taxes at 30%  63  
Net income  147  
Sidebar Corp  
Balance Sheet  
as at 30th June  2013  2012 
$m  $m  
Inventory  70  50 
Trade debtors  11  16 
Rent paid in advance  4  3 
PPE  700  680 
Total assets  785  749 
Trade creditors  11  19 
Bond liabilities  400  390 
Contributed equity  220  220 
Retained profits  154  120 
Total L and OE  785  749 
Note: All figures are given in millions of dollars ($m).
The cash flow from assets was:
Over the next year, the management of an unlevered company plans to:
 Achieve firm free cash flow (FFCF or CFFA) of $1m.
 Pay dividends of $1.8m
 Complete a $1.3m share buyback.
 Spend $0.8m on new buildings without buying or selling any other fixed assets. This capital expenditure is included in the CFFA figure quoted above.
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 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?
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?
Your friend is trying to find the net present value of a project. The project is expected to last for just one year with:
 a negative cash flow of $1 million initially (t=0), and
 a positive cash flow of $1.1 million in one year (t=1).
The project has a total required return of 10% pa due to its moderate level of undiversifiable risk.
Your friend is aware of the importance of opportunity costs and the time value of money, but he is unsure of how to find the NPV of the project.
He knows that the opportunity cost of investing the $1m in the project is the expected gain from investing the money in shares instead. Like the project, shares also have an expected return of 10% since they have moderate undiversifiable risk. This opportunity cost is $0.1m ##(=1m \times 10\%)## which occurs in one year (t=1).
He knows that the time value of money should be accounted for, and this can be done by finding the present value of the cash flows in one year.
Your friend has listed a few different ways to find the NPV which are written down below.
(I) ##1m + \dfrac{1.1m}{(1+0.1)^1} ##
(II) ##1m + \dfrac{1.1m}{(1+0.1)^1}  \dfrac{1m}{(1+0.1)^1} \times 0.1 ##
(III) ##1m + \dfrac{1.1m}{(1+0.1)^1}  \dfrac{1.1m}{(1+0.1)^1} \times 0.1 ##
(IV) ##1m + 1.1m  \dfrac{1.1m}{(1+0.1)^1} \times 0.1 ##
(V) ##1m + 1.1m  1.1m \times 0.1 ##
Which of the above calculations give the correct NPV? Select the most correct answer.
There are many ways to calculate a firm's free cash flow (FFCF), also called cash flow from assets (CFFA). Some include the annual interest tax shield in the cash flow and some do not.
Which of the below FFCF formulas include the interest tax shield in the cash flow?
###(1) \quad FFCF=NI + Depr  CapEx ΔNWC + IntExp### ###(2) \quad FFCF=NI + Depr  CapEx ΔNWC + IntExp.(1t_c)### ###(3) \quad FFCF=EBIT.(1t_c )+ Depr CapEx ΔNWC+IntExp.t_c### ###(4) \quad FFCF=EBIT.(1t_c) + Depr CapEx ΔNWC### ###(5) \quad FFCF=EBITDA.(1t_c )+Depr.t_c CapEx ΔNWC+IntExp.t_c### ###(6) \quad FFCF=EBITDA.(1t_c )+Depr.t_c CapEx ΔNWC### ###(7) \quad FFCF=EBITTax + Depr  CapEx ΔNWC### ###(8) \quad FFCF=EBITTax + Depr  CapEx ΔNWCIntExp.t_c### ###(9) \quad FFCF=EBITDATax  CapEx ΔNWC### ###(10) \quad FFCF=EBITDATax  CapEx ΔNWCIntExp.t_c###The formulas for net income (NI also called earnings), EBIT and EBITDA are given below. Assume that depreciation and amortisation are both represented by 'Depr' and that 'FC' represents fixed costs such as rent.
###NI=(Rev  COGS  Depr  FC  IntExp).(1t_c )### ###EBIT=Rev  COGS  FCDepr### ###EBITDA=Rev  COGS  FC### ###Tax =(Rev  COGS  Depr  FC  IntExp).t_c= \dfrac{NI.t_c}{1t_c}###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} \\###
A manufacturing company is considering a new project in the more risky services industry. The cash flows from assets (CFFA) are estimated for the new project, with interest expense excluded from the calculations. To get the levered value of the project, what should these unlevered cash flows be discounted by?
Assume that the manufacturing firm has a target debttoassets ratio that it sticks to.
A retail furniture company buys furniture wholesale and distributes it through its retail stores. The owner believes that she has some good ideas for making stylish new furniture. She is considering a project to buy a factory and employ workers to manufacture the new furniture she's designed. Furniture manufacturing has more systematic risk than furniture retailing.
Her furniture retailing firm's aftertax WACC is 20%. Furniture manufacturing firms have an aftertax WACC of 30%. Both firms are optimally geared. Assume a classical tax system.
Which method(s) will give the correct valuation of the new furnituremaking project? Select the most correct answer.
The US firm Google operates in the online advertising business. In 2011 Google bought Motorola Mobility which manufactures mobile phones.
Assume the following:
 Google had a 10% aftertax weighted average cost of capital (WACC) before it bought Motorola.
 Motorola had a 20% aftertax WACC before it merged with Google.
 Google and Motorola have the same level of gearing.
 Both companies operate in a classical tax system.
You are a manager at Motorola. You must value a project for making mobile phones. Which method(s) will give the correct valuation of the mobile phone manufacturing project? Select the most correct answer.
The mobile phone manufacturing project's:
Value the following business project to manufacture a new product.
Project Data  
Project life  2 yrs  
Initial investment in equipment  $6m  
Depreciation of equipment per year  $3m  
Expected sale price of equipment at end of project  $0.6m  
Unit sales per year  4m  
Sale price per unit  $8  
Variable cost per unit  $5  
Fixed costs per year, paid at the end of each year  $1m  
Interest expense per year  0  
Tax rate  30%  
Weighted average cost of capital after tax per annum  10%  
Notes
 The firm's current assets and current liabilities are $3m and $2m respectively right now. This net working capital will not be used in this project, it will be used in other unrelated projects.
Due to the project, current assets (mostly inventory) will grow by $2m initially (at t = 0), and then by $0.2m at the end of the first year (t=1).
Current liabilities (mostly trade creditors) will increase by $0.1m at the end of the first year (t=1).
At the end of the project, the net working capital accumulated due to the project can be sold for the same price that it was bought.  The project cost $0.5m to research which was incurred one year ago.
Assumptions
 All cash flows occur at the start or end of the year as appropriate, not in the middle or throughout the year.
 All rates and cash flows are real. The inflation rate is 3% pa.
 All rates are given as effective annual rates.
 The business considering the project is run as a 'sole tradership' (run by an individual without a company) and is therefore eligible for a 50% capital gains tax discount when the equipment is sold, as permitted by the Australian Tax Office.
What is the expected net present value (NPV) of the project?
Question 69 interest tax shield, capital structure, leverage, WACC
Which statement about risk, required return and capital structure is the most correct?
A firm's weighted average cost of capital before tax (##r_\text{WACC before tax}##) would increase due to:
A company issues a large amount of bonds to raise money for new projects of similar risk to the company's existing projects. The net present value (NPV) of the new projects is positive but small. Assume a classical tax system. Which statement is NOT correct?
A firm 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.
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?
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##.
A firm changes its capital structure by issuing a large amount of debt and using the funds to repurchase shares. Its assets are unchanged. Ignore interest tax shields.
According to the Capital Asset Pricing Model (CAPM), which statement is correct?
Question 99 capital structure, interest tax shield, Miller and Modigliani, trade off theory of capital structure
A firm changes its capital structure by issuing a large amount of debt and using the funds to repurchase shares. Its assets are unchanged.
Assume that:
 The firm and individual investors can borrow at the same rate and have the same tax rates.
 The firm's debt and shares are fairly priced and the shares are repurchased at the market price, not at a premium.
 There are no market frictions relating to debt such as asymmetric information or transaction costs.
 Shareholders wealth is measured in terms of utiliity. Shareholders are wealthmaximising and riskaverse. They have a preferred level of overall leverage. Before the firm's capital restructure all shareholders were optimally levered.
According to Miller and Modigliani's theory, which statement is correct?
Question 104 CAPM, payout policy, capital structure, Miller and Modigliani, risk
Assume that there exists a perfect world with no transaction costs, no asymmetric information, no taxes, no agency costs, equal borrowing rates for corporations and individual investors, the ability to short the risk free asset, semistrong form efficient markets, the CAPM holds, investors are rational and riskaverse and there are no other market frictions.
For a firm operating in this perfect world, which statement(s) are correct?
(i) When a firm changes its capital structure and/or payout policy, share holders' wealth is unaffected.
(ii) When the idiosyncratic risk of a firm's assets increases, share holders do not expect higher returns.
(iii) When the systematic risk of a firm's assets increases, share holders do not expect higher returns.
Select the most correct response:
A 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?
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?
Your friend just bought a house for $1,000,000. He financed it using a $900,000 mortgage loan and a deposit of $100,000.
In the context of residential housing and mortgages, the 'equity' or 'net wealth' tied up in a house is the value of the house less the value of the mortgage loan. Assuming that your friend's only asset is his house, his net wealth is $100,000.
If house prices suddenly fall by 15%, what would be your friend's percentage change in net wealth?
Assume that:
 No income (rent) was received from the house during the short time over which house prices fell.
 Your friend will not declare bankruptcy, he will always pay off his debts.
Question 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?
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 stock's correlation with the market portfolio increases while its total risk is unchanged. What will happen to the stock's expected return and systematic risk?
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?
The total return of any asset can be broken down in different ways. One possible way is to use the dividend discount model (or Gordon growth model):
###p_0 = \frac{c_1}{r_\text{total}r_\text{capital}}###
Which, since ##c_1/p_0## is the income return (##r_\text{income}##), can be expressed as:
###r_\text{total}=r_\text{income}+r_\text{capital}###
So the total return of an asset is the income component plus the capital or price growth component.
Another way to break up total return is to use the Capital Asset Pricing Model:
###r_\text{total}=r_\text{f}+β(r_\text{m} r_\text{f})###
###r_\text{total}=r_\text{time value}+r_\text{risk premium}###
So the risk free rate is the time value of money and the term ##β(r_\text{m} r_\text{f})## is the compensation for taking on systematic risk.
Using the above theory and your general knowledge, which of the below equations, if any, are correct?
(I) ##r_\text{income}=r_\text{time value}##
(II) ##r_\text{income}=r_\text{risk premium}##
(III) ##r_\text{capital}=r_\text{time value}##
(IV) ##r_\text{capital}=r_\text{risk premium}##
(V) ##r_\text{income}+r_\text{capital}=r_\text{time value}+r_\text{risk premium}##
Which of the equations are correct?
Question 271 CAPM, option, risk, systematic risk, systematic and idiosyncratic risk
All things remaining equal, according to the capital asset pricing model, if the systematic variance of an asset increases, its required return will increase and its price will decrease.
If the idiosyncratic variance of an asset increases, its price will be unchanged.
What is the relationship between the price of a call or put option and the total, systematic and idiosyncratic variance of the underlying asset that the option is based on? Select the most correct answer.
Call and put option prices increase when the:
Question 338 market efficiency, CAPM, opportunity cost, technical analysis
A man inherits $500,000 worth of shares.
He believes that by learning the secrets of trading, keeping up with the financial news and doing complex trend analysis with charts that he can quit his job and become a selfemployed day trader in the equities markets.
What is the expected gain from doing this over the first year? Measure the net gain in wealth received at the end of this first year due to the decision to become a day trader. Assume the following:
 He earns $60,000 pa in his current job, paid in a lump sum at the end of each year.
 He enjoys examining share price graphs and day trading just as much as he enjoys his current job.
 Stock markets are weak form and semistrong form efficient.
 He has no inside information.
 He makes 1 trade every day and there are 250 trading days in the year. Trading costs are $20 per trade. His broker invoices him for the trading costs at the end of the year.
 The shares that he currently owns and the shares that he intends to trade have the same level of systematic risk as the market portfolio.
 The market portfolio's expected return is 10% pa.
Measure the net gain over the first year as an expected wealth increase at the end of the year.
Which of the following statements about the weighted average cost of capital (WACC) is NOT correct?
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.
A person is thinking about borrowing $100 from the bank at 7% pa and investing it in shares with an expected return of 10% pa. One year later the person will sell the shares and pay back the loan in full. Both the loan and the shares are fairly priced.
What is the Net Present Value (NPV) of this one year investment? Note that you are asked to find the present value (##V_0##), not the value in one year (##V_1##).
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?
A project has an internal rate of return (IRR) which is greater than its required return. Select the most correct statement.
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?
A project's net present value (NPV) is negative. Select the most correct statement.
A project's NPV is positive. Select the most correct statement:
A project's Profitability Index (PI) is less than 1. Select the most correct statement:
Question 218 NPV, IRR, profitability index, average accounting return
Which of the following statements is NOT correct?
Question 241 Miller and Modigliani, leverage, payout policy, diversification, NPV
One of Miller and Modigliani's (M&M's) important insights is that a firm's managers should not try to achieve a particular level of leverage or interest tax shields under certain assumptions. So the firm's capital structure is irrelevant. This is because investors can make their own personal leverage and interest tax shields, so there's no need for managers to try to make corporate leverage and interest tax shields. This is true under the assumptions of equal tax rates, interest rates and debt availability for the person and the corporation, no transaction costs and symmetric information.
This principal of 'homemade' or 'doityourself' leverage can also be applied to other topics. Read the following statements to decide which are true:
(I) Payout policy: a firm's managers should not try to achieve a particular pattern of equity payout.
(II) Agency costs: a firm's managers should not try to minimise agency costs.
(III) Diversification: a firm's managers should not try to diversify across industries.
(IV) Shareholder wealth: a firm's managers should not try to maximise shareholders' wealth.
Which of the above statement(s) are true?
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 $50,000 in the bank after that (t=2).
How much can you consume at each time?
Which statement(s) are correct?
(i) All stocks that plot on the Security Market Line (SML) are fairly priced.
(ii) All stocks that plot above the Security Market Line (SML) are overpriced.
(iii) All fairly priced stocks that plot on the Capital Market Line (CML) have zero idiosyncratic risk.
Select the most correct response:
Question 246 foreign exchange rate, forward foreign exchange rate, cross currency interest rate parity
Suppose the Australian cash rate is expected to be 8.15% pa and the US federal funds rate is expected to be 3.00% pa over the next 2 years, both given as nominal effective annual rates. The current exchange rate is at parity, so 1 USD = 1 AUD.
What is the implied 2 year forward foreign exchange rate?
In the 1997 Asian financial crisis many countries' exchange rates depreciated rapidly against the US dollar (USD). The Thai, Indonesian, Malaysian, Korean and Filipino currencies were severely affected. The below graph shows these Asian countries' currencies in USD per one unit of their currency, indexed to 100 in June 1997.
Of the statements below, which is NOT correct? The Asian countries':
What is the Internal Rate of Return (IRR) of the project detailed in the table below?
Assume that the cash flows shown in the table are paid all at once at the given point in time. All answers are given as effective annual rates.
Project Cash Flows  
Time (yrs)  Cash flow ($) 
0  100 
1  0 
2  121 
A project has the following cash flows:
Project Cash Flows  
Time (yrs)  Cash flow ($) 
0  400 
1  0 
2  500 
The required return on the project is 10%, given as an effective annual rate.
What is the Internal Rate of Return (IRR) of this project? The following choices are effective annual rates. Assume that the cash flows shown in the table are paid all at once at the given point in time.
Which of the following statements about shortselling is NOT true?
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?
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:
Question 100 market efficiency, technical analysis, joint hypothesis problem
A company selling charting and technical analysis software claims that independent academic studies have shown that its software makes significantly positive abnormal returns. Assuming the claim is true, which statement(s) are correct?
(I) Weak form market efficiency is broken.
(II) Semistrong form market efficiency is broken.
(III) Strong form market efficiency is broken.
(IV) The asset pricing model used to measure the abnormal returns (such as the CAPM) had misspecification error so the returns may not be abnormal but rather fair for the level of risk.
Select the most correct response:
Question 119 market efficiency, fundamental analysis, joint hypothesis problem
Your friend claims that by reading 'The Economist' magazine's economic news articles, she can identify shares that will have positive abnormal expected returns over the next 2 years. Assuming that her claim is true, which statement(s) are correct?
(i) Weak form market efficiency is broken.
(ii) Semistrong form market efficiency is broken.
(iii) Strong form market efficiency is broken.
(iv) The asset pricing model used to measure the abnormal returns (such as the CAPM) is either wrong (misspecification error) or is measured using the wrong inputs (data errors) so the returns may not be abnormal but rather fair for the level of risk.
Select the most correct response:
Select the most correct statement from the following.
'Chartists', also known as 'technical traders', believe that:
Fundamentalists who analyse company financial reports and news announcements (but who don't have inside information) will make positive abnormal returns if:
A very lowrisk stock just paid its semiannual dividend of $0.14, as it has for the last 5 years. You conservatively estimate that from now on the dividend will fall at a rate of 1% every 6 months.
If the stock currently sells for $3 per share, what must be its required total return as an effective annual rate?
If risk free government bonds are trading at a yield of 4% pa, given as an effective annual rate, would you consider buying or selling the stock?
The stock's required total return is:
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.
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 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##
A company has:
 50 million shares outstanding.
 The market price of one share is currently $6.
 The riskfree rate is 5% and the market return is 10%.
 Market analysts believe that the company's ordinary shares have a beta of 2.
 The company has 1 million preferred stock which have a face (or par) value of $100 and pay a constant dividend of 10% of par. They currently trade for $80 each.
 The company's debentures are publicly traded and their market price is equal to 90% of their face value.
 The debentures have a total face value of $60,000,000 and the current yield to maturity of corporate debentures is 10% per annum. The corporate tax rate is 30%.
What is the company's aftertax weighted average cost of capital (WACC)? Assume a classical tax system.
A 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.
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?
You're advising your superstar client 40cent who is weighing up buying a private jet or a luxury yacht. 40cent is just as happy with either, but he wants to go with the more costeffective option. These are the cash flows of the two options:
 The private jet can be bought for $6m now, which will cost $12,000 per month in fuel, piloting and airport costs, payable at the end of each month. The jet will last for 12 years.
 Or the luxury yacht can be bought for $4m now, which will cost $20,000 per month in fuel, crew and berthing costs, payable at the end of each month. The yacht will last for 20 years.
What's unusual about 40cent is that he is so famous that he will actually be able to sell his jet or yacht for the same price as it was bought since the next generation of superstar musicians will buy it from him as a status symbol.
Bank interest rates are 10% pa, given as an effective annual rate. You can assume that 40cent will live for another 60 years and that when the jet or yacht's life is at an end, he will buy a new one with the same details as above.
Would you advise 40cent to buy the or the ?
Note that the effective monthly rate is ##r_\text{eff monthly}=(1+0.1)^{1/12}1=0.00797414##
Which of the following investable assets are NOT suitable for valuation using PE multiples techniques?
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%?
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.
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?
Which firms tend to have high forwardlooking priceearnings (PE) ratios?
Below are 4 option graphs. Note that the yaxis is payoff at maturity (T). What options do they depict? List them in the order that they are numbered.
You have just sold an 'in the money' 6 month European put option on the mining company BHP at an exercise price of $40 for a premium of $3.
Which of the following statements best describes your situation?
Which one of the following is NOT usually considered an 'investable' asset for longterm wealth creation?
You believe that the price of a share will fall significantly very soon, but the rest of the market does not. The market thinks that the share price will remain the same. Assuming that your prediction will soon be true, which of the following trades is a bad idea? In other words, which trade will NOT make money or prevent losses?
Suppose that the US government recently announced that subsidies for fresh milk producers will be gradually phased out over the next year. Newspapers say that there are expectations of a 40% increase in the spot price of fresh milk over the next year.
Option prices on fresh milk trading on the Chicago Mercantile Exchange (CME) reflect expectations of this 40% increase in spot prices over the next year. Similarly to the rest of the market, you believe that prices will rise by 40% over the next year.
What option trades are likely to be profitable, or to be more specific, result in a positive Net Present Value (NPV)?
Assume that:
 Only the spot price is expected to increase and there is no change in expected volatility or other variables that affect option prices.
 No taxes, transaction costs, information asymmetry, bidask spreads or other market frictions.
Question 381 Merton model of corporate debt, option, real option
In the Merton model of corporate debt, buying a levered company's debt is equivalent to buying risk free government bonds and:
Question 382 Merton model of corporate debt, real option, option
In the Merton model of corporate debt, buying a levered company's shares is equivalent to:
Question 383 Merton model of corporate debt, real option, option
In the Merton model of corporate debt, buying a levered company's debt is equivalent to buying the company's assets and:
Which of the following is the least useful method or model to calculate the value of a real option in a project?
Question 385 Merton model of corporate debt, real option, option
A risky firm will last for one period only (t=0 to 1), then it will be liquidated. So it's assets will be sold and the debt holders and equity holders will be paid out in that order. The firm has the following quantities:
##V## = Market value of assets.
##E## = Market value of (levered) equity.
##D## = Market value of zero coupon bonds.
##F_1## = Total face value of zero coupon bonds which is promised to be paid in one year.
The levered equity graph above contains bold labels a to e. Which of the following statements about those labels is NOT correct?
Question 386 Merton model of corporate debt, real option, option
A risky firm will last for one period only (t=0 to 1), then it will be liquidated. So it's assets will be sold and the debt holders and equity holders will be paid out in that order. The firm has the following quantities:
##V## = Market value of assets.
##E## = Market value of (levered) equity.
##D## = Market value of zero coupon bonds.
##F_1## = Total face value of zero coupon bonds which is promised to be paid in one year.
The risky corporate debt graph above contains bold labels a to e. Which of the following statements about those labels is NOT correct?
One of the reasons why firms may not begin projects with relatively small positive net present values (NPV's) is because they wish to maximise the value of their:
A moped is a bicycle with pedals and a little motor that can be switched on to assist the rider. Mopeds offer the rider:
You're thinking of starting a new cafe business, but you're not sure if it will be profitable.
You have to decide what type of cups, mugs and glasses you wish to buy. You can pay to have your cafe's name printed on them, or just buy the plain unmarked ones. For marketing reasons it's better to have the cafe name printed. But the plain unmarked cups, mugs and glasses maximise your:
Some financially minded people insist on a prenuptial agreement before committing to marry their partner. This agreement states how the couple's assets should be divided in case they divorce. Prenuptial agreements are designed to give the richer partner more of the couples' assets if they divorce, thus maximising the richer partner's:
The cheapest mobile phones available tend to be those that are 'locked' into a cell phone operator's network. Locked phones can not be used with other cell phone operators' networks.
Locked mobile phones are cheaper than unlocked phones because the lockedin network operator helps create a monopoly by:
Your firm's research scientists can begin an exciting new project at a cost of $10m now, after which there’s a:
 70% chance that cash flows will be $1m per year forever, starting in 5 years (t=5). This is the A state of the world.
 20% chance that cash flows will be $3m per year forever, starting in 5 years (t=5). This is the B state of the world.
 10% chance of a major break through in which case the cash flows will be $20m per year forever starting in 5 years (t=5), or the project can be expanded by investing another $10m (at t=5) which is expected to give cash flows of $60m per year forever, starting at year 9 (t=9). This is the C state of the world.
The firm's cost of capital is 10% pa.
What's the present value (at t=0) of the option to expand in year 5?
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.
Acquirer firm plans to launch a takeover of Target firm. The deal is expected to create a present value of synergies totaling $105 million. A cash offer will be made that pays the fair price for the target's shares plus 75% of the total synergy value. The cash will be paid out of the firm's cash holdings, no new debt or equity will be raised.
Firms Involved in the Takeover  
Acquirer  Target  
Assets ($m)  6,000  700 
Debt ($m)  4,800  400 
Share price ($)  40  20 
Number of shares (m)  30  15 
Ignore transaction costs and fees. Assume that the firms' debt and equity are fairly priced, and that each firms' debts' risk, yield and values remain constant. The acquisition is planned to occur immediately, so ignore the time value of money.
Calculate the merged firm's share price and total number of shares after the takeover has been completed.
Acquirer firm plans to launch a takeover of Target firm. The deal is expected to create a present value of synergies totaling $105 million. A scrip offer will be made that pays the fair price for the target's shares plus 75% of the total synergy value.
Firms Involved in the Takeover  
Acquirer  Target  
Assets ($m)  6,000  700 
Debt ($m)  4,800  400 
Share price ($)  40  20 
Number of shares (m)  30  15 
Ignore transaction costs and fees. Assume that the firms' debt and equity are fairly priced, and that each firms' debts' risk, yield and values remain constant. The acquisition is planned to occur immediately, so ignore the time value of money.
Calculate the merged firm's share price and total number of shares after the takeover has been completed.
Acquirer firm plans to launch a takeover of Target firm. The firms operate in different industries and the CEO's rationale for the merger is to increase diversification and thereby decrease risk. The deal is not expected to create any synergies. An 80% scrip and 20% cash offer will be made that pays the fair price for the target's shares. The cash will be paid out of the firms' cash holdings, no new debt or equity will be raised.
Firms Involved in the Takeover  
Acquirer  Target  
Assets ($m)  6,000  700 
Debt ($m)  4,800  400 
Share price ($)  40  20 
Number of shares (m)  30  15 
Ignore transaction costs and fees. Assume that the firms' debt and equity are fairly priced, and that each firms' debts' risk, yield and values remain constant. The acquisition is planned to occur immediately, so ignore the time value of money.
Calculate the merged firm's share price and total number of shares after the takeover has been completed.
Acquirer firm plans to launch a takeover of Target firm. The deal is expected to create a present value of synergies totaling $105 million. A 40% scrip and 60% cash offer will be made that pays the fair price for the target's shares plus 75% of the total synergy value. The cash will be paid out of the firm's cash holdings, no new debt or equity will be raised.
Firms Involved in the Takeover  
Acquirer  Target  
Assets ($m)  6,000  700 
Debt ($m)  4,800  400 
Share price ($)  40  20 
Number of shares (m)  30  15 
Ignore transaction costs and fees. Assume that the firms' debt and equity are fairly priced, and that each firms' debts' risk, yield and values remain constant. The acquisition is planned to occur immediately, so ignore the time value of money.
Calculate the merged firm's share price and total number of shares after the takeover has been completed.