Solutions to Chapter 10

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Solutions to Chapter 10

    Solutions to Chapter 11

    Risk, Return, and Capital Budgeting

    1. a. False. Investors require higher expected rates of return on investments with

    high market risk, not high total risk. Variability of returns is a measure of total

    risk. Stocks with high total risk (highly variable returns) can have low market

    risk. That is, their returns have low correlation with the market.

     b. False. If beta = 0, the asset’s expected return should equal the risk-free rate,

    not zero.

     c. False. The portfolio is one-third invested in Treasury bills and two-thirds in the

    market. Its beta will be

     1/3 0 + 2/3 1.0 = 2/3.

     d. True. High exposure to macroeconomic changes cannot be diversified away in

    a portfolio. Thus stocks with higher sensitivity to macroeconomic risks have

    higher market risk and higher expected returns when compared to stocks with

    lower sensitivity to macroeconomic changes.

     e. True. For similar reasons as in (d). Sensitivity to fluctuations in the stock

    market cannot be diversified away. Such stocks have higher systematic risk and

    higher expected rates of return.

    2. The risks of deaths of individual policyholders are largely independent, and therefore

    are diversifiable. Therefore, the insurance company is satisfied to charge a premium

    that reflects actuarial probabilities of death, without an additional risk premium. In

    contrast, flood damage is not independent across policyholders. If my coastal home

    floods in a storm, there is a greater chance that my neighbor's will too. Because

    flood risk is not diversifiable, the insurance company may not be satisfied to charge a

    premium that reflects only the expected value of payouts.

    3. The actual returns on the Snake Oil fund exhibit considerable variation around the

    regression line. This indicates that the fund is subject to diversifiable risk: it is not

    well diversified. The variation in the fund's returns is influenced by more than just

    market-wide events.

    4. Investors would buy shares of firms with high degrees of diversifiable risk, and earn

    high risk premiums. But by holding these shares in diversified portfolios, they would

    not necessarily bear a high degree of portfolio risk. This would represent a profit

    opportunity, however. As investors seek these shares, we would expect their prices


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    to rise, and the expected rate of return to investors buying at these higher prices to

    fall. This process would continue until the reward for bearing diversifiable risk


5. a. Required return = r + (r r) = 4% + .6 (11% 4%) = 8.2% fmf

     With an IRR of 14%, the project is attractive.

     b. If beta = 1.6, required return increases to:

     4% + 1.6 (11% 4%) = 15.2%

     which is greater than the project IRR. You should now reject the project.

     c. Given its IRR, the project is attractive when its risk and therefore its required

    return are low. At a higher risk level, the IRR is no longer higher than the

    expected return on comparable risk assets available elsewhere in the capital


    6. a. The expected cash flows from the firm are in the form of a perpetuity. The

    discount rate is:

     r + (r r) = 5% + .4×7% = 7.8%. fmf

     Therefore, the value of the firm would be:

    Cash flow$10,000 P = = = $128,205 0r.078

     b. If the true beta is actually .6, the discount rate should be:

     r + (r r) = 5% + .6×7% = 9.2% fmf

     Therefore, the value of the firm is:

    Cash flow$10,000 P = = = $108,696 0r.092

     By underestimating beta, you would overvalue the firm by

     $128,205 108,696 =$19,509


    Copyright ? 2006 McGraw-Hill Ryerson Limited

7. Required return = r + (r r) = 4% + 1.25(11% 4%) = 12.75% fmf

     Expected return = 11%

     The stock’s expected return is less than the required return given its risk. Thus the

    stock is overpriced. Why? Given the stock’s future cash flows and its current price,

    investors can expect to earn only 11%. Comparable risk investments earn 12.75%.

    At the current price, investors are better off investing in these other investments.

    This lack of demand will cause the stock price to fall until its expected return

    increases to the required return of 12.75%.

8. Required return = riskfree rate + beta × [expected return on market riskfree rate]

     = r + (r r) fmf

    For the stock, we know that 12% = r + .8 ( 14% - r ) ff

    Using the CAPM, solve for the riskfree rate of interest:

     r r) = (12% - .8 × 14%) / (1 - .8) = 4% f = (Required return - m) / ( 1 -

    We assume that the riskfree rate is not changed. Therefore, if the market return turns

    out to be 10%, we expect that the stock’s return will be 4% + .8(10% - 4%) = 8.8%.

    9. a. A diversified investor will find the highest-beta stock most risky. This is

    Microsoft, which has a beta of 1.53.

     b. Ford has the highest total volatility; the standard deviation of its returns is


     c. = (1.34 + .97 + 1.53)/3 = 1.28

     d. The portfolio will have the same beta as Microsoft, 1.53. The total risk of the

    portfolio will be 1.53 times the total risk of the market portfolio because the

    effect of firm-specific risk will be diversified away. The standard deviation of

    the portfolio is therefore 1.53 20% = 30.6%.

     e. Using the CAPM, we compute the expected rate of return on each stock from

    the equation r = r + (r r). In this case, r = 4% and (r r) = 7%. fm ffm f

     Ford: r = 4% + 1.34(7%) = 13.38%

     General Electric: r = 4% + .97(7%) = 10.79%

     Microsoft: r = 4% + 1.53(7%) = 14.71%


    Copyright ? 2006 McGraw-Hill Ryerson Limited

10. The following table shows the average return on Tumblehome for various values of

    the market return. It is clear from the table that, when the market return increases by

    1%, Tumblehome’s return increases on average by 1.5%. Therefore, = 1.5. If you

    prepare a plot of the return on Tumblehome as a function of the market return, you

    will find that the slope of the line through the points is 1.5.

     Market return(%) Average return on Tumblehome(%)

     ;2 ;3.0

     ;1 ;1.5

     0 0.0

     1 1.5

     2 3.0

     Note: If your calculator supports statistics then you can estimate this. Enter points

    as X,Y values. In stats linear mode you see that b = 1.5 which is the slope of the line.

    Using the SLOPE function in Excel will also calculate the slope of 1.5.

    11. a. Beta is the responsiveness of each stock's return to changes in the market return.


    rA38 (;10)48 = = = = 1.2 A40r32 (;8)m

    rD24 (;6)30 = = = = .75 D40r32 (;8)m

     D is considered to be a more defensive stock than A because its return is less

    sensitive to the return of the overall market. In a recession, D will usually

    outperform both stock A and the market portfolio.

     b. We take an average of returns in each scenario to obtain the expected return.

     r = (32% 8%)/2 = 12% m

     r = (38% 10%)/2 = 14% A

     r = (24% 6%)/2 = 9% D


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     c. According to the CAPM, the expected returns that investors will demand of

    each stock, given the stock betas and given the expected return on the market,


     r = r + (r r) fm f

     r = 4% + 1.2(12% 4%) = 13.6% A

     r = 4% + .75(12% 4%) = 10.0% D

     d. The return you actually expect for stock A, 14%, is above the fair return,

    13.6%. The return you expect for stock D, 9%, is below the fair return, 10%.

    Therefore stock A is the better buy.

12. Figure follows below.

    Cost of capital = risk-free rate + beta × market risk premium

    Since the risk-free rate is 4% and the market risk premium is 7%, we can write the

    cost of capital as:

    Cost of capital = 4% + beta × 7%

     Cost of capital (from CAPM)

     Beta = 10% + beta × 8%

     .75 4% + .75 7% = 9.25%

     1.75 4% + 1.75 7% = 16.25%



    11% 7% = market risk




    0 1.0


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     The cost of capital of each project is calculated using the above CAPM formula.

    Thus, for Project P, its cost of capital is: 4% + 1.0 × 7% = 11%.

    If the cost of capital is greater than IRR, then the NPV is negative. If the cost of

    capital equals the IRR, then the NPV is zero. Otherwise, if the cost of capital is less

    than the IRR, the NPV is positive.

    Project Beta Cost of capital IRR NPV

    P 1.0 11.0% 11% 0

    Q 0.0 4.0 6 +

    R 2.0 18.0 17 ;

    S 0.4 6.8 7 +

    T 1.6 15.2 16 +

13. The appropriate discount rate for the project is:

     r = r+ (r r) = 4% + 1.4(11% 4%) = 13.8% f m f


     NPV = 100 + 15 annuity factor(13.8%, 10 years) = 100 + 78.8563 = -$21.14

     You should reject the project.

14. We need to find the discount rate for which:

     15 annuity factor(r, 10 years) = 100.

     Solving this equation on the calculator, we find that the project IRR is 8.14%. The

    IRR is less than the opportunity cost of capital, 13.8%. Therefore you should reject

    the project, just as you found from the NPV rule.

15. From the CAPM, the appropriate discount rate is:

     r = r+ (r r) = 4% +.75(7%) = 9.25% f m f

    2 + (P 50)DIV + capital gain1 r = .0925 = = price50

     P= $52.625 1


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    16. If investors believe the year-end stock price will be $54, then the expected return on

    the stock is:

    2 + (54 50) = .12 = 12%, 50

     which is greater than the opportunity cost of capital. Alternatively, the “fair” price of

    the stock (that is, the present value of the investor's expected cash flows) is

     (2 + 54)/1.0925 = $51.26, which is greater than the current price. Investors will

    want to buy the stock, in the process bidding up its price until it reaches $51.26. At

    that point, the expected return is a “fair” 9.25%:

    2 + (54 51.26) = .0925 = 9.25%. 51.26

    17. a. The expected return of the portfolio is the weighted average of the returns on

    the TSX and T-bills. Similarly, the beta of the portfolio is a weighted average

    of the beta of the TSX (which is 1.0) and the beta of T-bills (which is zero).

     (i) E(r) = 0 13% + 1.0 5% = 5% = 0 1 + 1 0 = 0

     (ii) E(r) = .25 13% + .75 5% = 7% = .25 1 + .75 0 = .25

     (iii) E(r) = .50 13% + .50 5% = 9% = .50 1 + .50 0 = .50

     (iv) E(r) = .75 13% + .25 5% = 11% = .75 1 + .25 0 = .75

     (v) E(r) = 1.00 13% + 0 5% = 13% = 1.0 1 + 0 0 = 1.0

     b. For every increase of .25 in the of the portfolio, the expected return increases

    by 2%. The slope of the relationship (additional return per unit of additional

    risk) is therefore 2%/.25 = 8%.

     c. The slope of the return per unit of risk relationship is the market risk premium:

     r = 13% 5% = 8%, which is exactly what the SML predicts. The SML rMf

    says that the risk premium equals beta times the market risk premium.

18. a. Call the weight in the TSX w and the weight in T-bills (1 w). Then w must

    satisfy the equation:

     w 10% + (1 w) 5% = 8%

     which implies that w = .6. The portfolio would be 60% in the TSX and 40% in

    T-bills. The beta of the portfolio would be the weighted average of the betas

    of the TSX and T-Bills. Since T-Bills are risk-free, their beta is zero. The beta

    of the portfolio is: .6×1 + .4×0 = .6


    Copyright ? 2006 McGraw-Hill Ryerson Limited

     b. To form a portfolio with a beta of .4, use a weight of .40 in the TSX and a

    weight of .60 in T-bills. Then, the portfolio beta would be:

     = .40 1 + .60 0 = .40

    The expected return on this portfolio is .4 × 10% + .6 × 5% = 7%

     c. Both portfolios have the same ratio of risk premium to beta:

    8% - 5%7% - 5% = = 5%. .6.4

     Notice that the ratio of risk premium to risk (i.e., beta) equals the market risk

    premium (5%) for both stocks.

    19. If the systematic risk were comparable to that of the market, the discount rate would

    be 12.0%. The property would be worth $50,000/.120 = $416,667.

20. The CAPM states that r = r+ (r r). If < 0, then r < r. Investors would f m ff

    invest in a security with an expected return below the risk-free rate because of the

    hedging value such a security provides for the rest of the portfolio. Investors get

    their “reward” in terms of risk reduction rather than in the form of high expected


    21. The historical risk premium on the market portfolio has been about 7%. Therefore,

    using this value and the assumed risk-free rate of 3%, we can use the CAPM to

    derive the cost of capital for these firms as 3% + 7%.

     Beta Return

    CHC Helicopter 1.34 12.38%

    Open Text 1.52 13.64%

    Loblaw Companies 0.71 7.97%

    Tim Hortons 0.9 9.30%


    CHC Helicopter : (TSX: FLY-A.TO) CHC is a world leader in search and rescue (SAR), helicopter training, and repair and overhaul (R&O), operating the world's only facility for the repair and overhaul of Super Pumas the No. 1 aircraft for the offshore industry

     in Stavanger, Norway. Approximately 69 per cent of CHC's total revenue involves providing helicopter support to the oil and gas industry, primarily providing service to offshore platforms operated by the world's major oil and gas companies. The stock beta


    Copyright ? 2006 McGraw-Hill Ryerson Limited

is 1.34, indicating that returns on CHC’s stock are quite sensitive to changes in the

    market. In a booming economy, the demand for helicopter services in the oil and gas industry will be quite high but in a recession, the demand will be low. It is not surprise that the stock beta is well above 1.

    Open Text: (Nasdaq: OTEX) (TSX: OTC) is the market leader in providing Collaboration, Enterprise Content Management software solutions. The stock beta is 1.52, indicating an even higher sensitivity to variations in the market than CHC Helicopters. Like CHC, the customers of Open Text are other businesses. The demand for Open Text’s solutions will be higher when the economy is growing and businesses are investing in new technologies. Likewise, the demand will be low when the economy is down. It makes sense that a high tech company such as Open Text will have a stock beta of 1.52.

    Loblaw Companies: (TSX:L-PA.TO) is Canada’s largest food distributor, with grocery

    stores across the country. Since food is an essential for survival, it is expected that a grocery chain’s earnings won’t vary much with the business cycle. It is not surprising

    the beta of the Loblaw is the lowest of these four and is less than 1. The sensitivity of the return on Loblaw stock to changes in market is low. We say that the market risk of a grocery chain is low.

    Tim Hortons: (TSX:THI.TO) Offers coffee and doughnuts in locations across Canada and the United States. The beta of Tim Hortons is a bit less than 1, indicating that the sensitivity of the return on Tim Hortons stock to changes in the market is less than average. This makes sense. The demand for coffee and doughnuts is not hugely variable with market conditions.

23. r = r+ (r r) f m f

     5 = r+ .5(r r) (stock A) f m f

     13 = r+ 1.5(r r) (stock B) f m f

     Solve these simultaneous equations to find that r= 1% and r= 9%. Thus the f m

    market risk premium is 9% - 1%, or 8%.

24. r = r+ (r r) f m f


    13.6 = 3 + ×7


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     = (13.6 3)/7 = 1.51


    5.5 = 3 + ×7

     = (5.5 3)/7 = 0.36

    25. 3 month Treasury Bills yield 2.22% as of Oct 2008. 7% market premium.

    TD Bank:

    Beta = 1.13, r = 2.22%+1.13×7% = 10.13%

    The Toronto-Dominion Bank and its subsidiaries provides financial services in North

    America. It operates through four segments: Canadian Personal and Commercial

    Banking, Wealth Management, U.S. Personal and Commercial Banking, and

    Wholesale Banking. The Canadian Personal and Commercial Banking segment

    provides personal and business banking services. It offers various financial products

    and services to approximately 11 million personal and small business customers. This

    segment also provides financing, investment, cash management, international trade,

    and day-today banking services; and insurance products, including home and

    automobile coverage, life and health insurance, and credit protection coverage. As of

    October 31, 2007, it offered banking solutions through telephone and Internet

    banking, approximately 2,500 automated banking machines, and a network of 1,070

    branches. The Wealth Management segment provides various investment products

    and services, including advisory, distribution, and asset management; trader program

    and long-term investor solutions; and discount brokerage, financial planning, and

    private client services to retail and institutional customers. The U.S. Personal and

    Commercial Banking segment provides personal and commercial banking products

    and services, insurance agency, wealth management, mortgage banking, and other

    financial services to approximately 1.5 million households. As of the above date, it

    offered products and services through a network of 617 branches and 761

    automated banking machines. The Wholesale Banking segment provides various

    capital markets and investment banking products and services, which include

    underwriting and distribution of new debt and equity issues, providing advice on

    strategic acquisitions and divestitures, and executing daily trading and investment

    needs primarily to corporate, government, and institutional customers. The company

    was founded in 1855 and is headquartered in Toronto, Canada.

     Find 4 other Canadian firms the same way as it is done to TD.


    MX.TO) large-format film company. IMAX: (TSX: I


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