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ADMS 3530 (82)
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Review Questions 10F11 (1).pdf

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Department
Administrative Studies
Course
ADMS 3530
Professor
Lois King
Semester
Summer

Description
Review Questions 10 Textbook Page Questions 358 2, 3, 4, 5 361 12, 14, 16, 17, 20 362 21. 28, 29, 30 363 31, 32, 33, 34, 35 Solutions 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. However, 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 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 dissipated. 5. a. Required return = r f (r m – rf) = 4% + .6 (11% – 4%) = 8.2% 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 market. 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% r SML 11% 7% = market risk premium 4% beta 0 1.0 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 IRR NPV Cost of capital 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 + - 2 - 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. 16. If investors believe the year-end stock price will be $54, then the expected return on the stock is: 2 + (54 – 50) 50 = .12 = 12%, 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: rM– r f 13% – 5% = 8%, which is exactly what the SML predicts. The SML says that the risk premium equals beta times the market risk premium. - 3 - 20. The CAPM states that r = r + f(r m – rf). If  < 0, then r f r . Investors would 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 return. 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% 28. a. False. The stock’s risk premium, not its expected rate of return, is twice as high as the market’s. b. True. The stock’s unique risk does not affect its contribution to portfolio risk but its market risk does. c. False. A stock plotting below the SML offers too low an expected return relative to the expected return indicated by th
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