E8-1. Total annual return Answer: ($0 $12,000 $10,000) $10,000 $2,000 $10,000 20%

Logistics, Inc. doubled the annual rate of return predicted by the analyst. The negative net income is irrelevant to the problem. E8-2. Expected return Answer: Analyst 1 2 3 4 Total Probability 0.35 0.05 0.20 0.40 1.00 Return 5% 5% 10% 3% Expected return Weighted Value 1.75% 0.25% 2.0% 1.2% 4.70%

E8-3. Comparing the risk of two investments Answer: CV1 0.10 0.15 0.6667 CV2 0.05

0.12

0.4167

Based solely on standard deviations, Investment 2 has lower risk than Investment 1. Based on coefficients of variation, Investment 2 is still less risky than Investment 1. Since the two investments have different expected returns, using the coefficient of variation to assess risk is better than simply comparing standard deviations because the coefficient of variation considers the relative size of the expected returns of each investment. E8-4. Computing the expected return of a portfolio Answer: rp (0.45 0.038) (0.4 0.123) (0.15 0.174) (0.0171) (0.0492) (0.0261 0.0924 9.24% The portfolio is expected to have a return of approximately 9.2%. E8-5. Calculating a portfolio beta Answer: Beta (0.20 1.15) (0.10 0.85) (0.15 1.60) (0.20 1.35) (0.35 1.85) 0.2300 0.0850 0.2400 0.2700 0.6475 1.4725 E8-6. Calculating the required rate of return Answer: a. Required return 0.05 1.8 (0.10 0.05) 0.05 0.09 0.14 b. Required return 0.05 1.8 (0.13 0.05) 0.05 0.144 0.194 c. Although the risk-free rate does not change, as the market return increases, the required return on the asset rises by 180% of the change in the market’s return.

P8-1.

Solutions to Problems

Rate of return: rt = LG 1; Basic a. Investment X: Return Investment Y: Return ($21,000 $20,000 $1,500) 12.50% $20,000 ($55,000 $55,000 $6,800) 12.36% $55,000

(Pt Pt 1 Ct ) Pt 1

b. Investment X should be selected because it has a higher rate of return for the same level of risk. P8-2. Return calculations: rt = LG 1; Basic Investment A B C D E P8-3. ($1,100 ($118,000 ($48,000 ($500 ($12,400 $800 Calculation $100) $800 $15,000) $7,000) $600 $1,500) $12,500 $120,000 $45,000 $120,000 $45,000 $80) $12,500 rt(%) 25.00 10.83 22.22 3.33 11.20

(Pt Pt 1 Ct ) Pt 1

$600

Risk preferences LG 1; Intermediate a. The risk-neutral manager would accept Investments X and Y because these have higher returns than the 12% required return and the risk doesn’t matter. b. The risk-averse manager would accept Investment X because it provides the highest return and has the lowest amount of risk. Investment X offers an increase in return for taking on more risk than what the firm currently earns. c. The risk-seeking manager would accept Investments Y and Z because he or she is willing to take greater risk without an increase in return. d. Traditionally, financial managers are risk averse and would choose Investment X, since it provides the required increase in return for an increase in risk.

P8-4.

Risk analysis LG 2; Intermediate a. Expansion A B 24% 30% Range 16% 10% 8% 20%

b. Project A is less risky, since the range of outcomes for A is smaller than the range for Project B. c. Since the most likely return for both projects is 20% and the initial investments are equal, the answer depends on your risk preference. d. The answer is no longer clear, since it now involves a risk-return tradeoff. Project B has a slightly higher return but more risk, while A has both lower return and lower risk. P8-5. Risk and probability LG 2; Intermediate a. Camera R S b. Possible Outcomes Camera R Pessimistic Most likely Optimistic Probability Pri 0.25 0.50 0.25 1.00 0.20 0.55 0.25 1.00 c. Expected Return ri 20 25 30 Expected return 15 25 35 Expected return Weighted Value (%)(ri Pri) 5.00% 12.50% 7.50% 25.00% 3.00% 13.75% 8.75% 25.50% 30% 35% Range 20% 15% 10% 20%

Camera S

Pessimistic Most likely Optimistic

Camera S is considered more risky than Camera R because it has a much broader...