Question

Problem 20-12 Portfolio consideration and risk aversion [LO20-4] General Meters is considering two mergers. The first is with Firm A in its own volatile industry, the auto speedometer industry, while the second is a merger with Firm B in an industry that moves in the opposite direction (and will tend to level out performance due to negative correlation). General Meters Merger with Firm A General Meters Merger with Firm B Possible Earnings ($ in millions) Probability Possible Earnings ($ in millions) Probability $ 10 .20 $ 10 .15 20 .20 20 .30 30 .60 30 .55 a. Compute the mean, standard deviation, and coefficient of variation for both investments. (Do not round intermediate calculations. Enter your answers in millions. Round "Coefficient of variation" to 3 decimal places and "Standard deviation" to 2 decimal places.) b. Assuming investors are risk-averse, which alternative can be expected to bring the higher valuation? Merger A Merger B

Answer 1

Answer a.

Firm A:

Expected Return = 0.20 * 10 + 0.20 * 20 + 0.60 * 30
Expected Return = 24

Variance = 0.20 * (10 - 24)^2 + 0.20 * (20 - 24)^2 + 0.60 * (30 - 24)^2
Variance = 64

Standard Deviation = (64)^(1/2)
Standard Deviation = 8

Coefficient of Variation = Standard Deviation / Expected Return
Coefficient of Variation = 8 / 24
Coefficient of Variation = 0.333

Firm B:

Expected Return = 0.15 * 10 + 0.30 * 20 + 0.55 * 30
Expected Return = 24

Variance = 0.15 * (10 - 24)^2 + 0.30 * (20 - 24)^2 + 0.55 * (30 - 24)^2
Variance = 54

Standard Deviation = (54)^(1/2)
Standard Deviation = 7.35

Coefficient of Variation = Standard Deviation / Expected Return
Coefficient of Variation = 7.35 / 24
Coefficient of Variation = 0.306

Answer b.

Firm B has low risk than Firm A as coefficient of variation is lower. So, if investors are risk-averse then Merger B will bring the higher valuation.