Question

Kyle's Shoe Stores Inc. is considering opening an additional suburban outlet. An aftertax expected cash flow of $100 per week is anticipated from two stores that are being evaluated. Both stores have positive net present values. Site A Probability 0.2 0.4 Cash Flows 50 100 Site B Probability Cash Flows 0.1 20 0.2 50 100 0.2 150 180 2.2 110 150 a. Compute the coefficient of variation for each site. (Do not round intermediate calculations. Round your answers to 3 decimal places.) Coefficient of Variation Site A Site B b. Which store site would you select based on the distribution of these cash flows? Use the coefficient of variation as your measure of risk. Site A Site B

Answer 1

Answer a.

Site A:

Expected Cash Flow = 0.20 * 50 + 0.40 * 100 + 0.20 * 110 + 0.10 * 150
Expected Cash Flow = 87

Variance = 0.20 * (50 - 87)^2 + 0.40 * (100 - 87)^2 + 0.20 * (110 - 87)^2 + 0.10 * (150 - 87)^2
Variance = 844.10

Standard Deviation = (844.10)^(1/2)
Standard Deviation = 29.0534

Coefficient of Variation = Standard Deviation / Expected Cash Flow
Coefficient of Variation = 29.0534 / 87
Coefficient of Variation = 0.334

Site B:

Expected Cash Flow = 0.10 * 20 + 0.20 * 50 + 0.40 * 100 + 0.20 * 150 + 0.10 * 180
Expected Cash Flow = 100

Variance = 0.10 * (20 - 100)^2 + 0.20 * (50 - 100)^2 + 0.40 * (100 - 100)^2 + 0.20 * (150 - 100)^2 + 0.10 * (180 - 100)^2
Variance = 2,280

Standard Deviation = (2,280)^(1/2)
Standard Deviation = 47.7493

Coefficient of Variation = Standard Deviation / Expected Cash Flow
Coefficient of Variation = 47.7493 / 100
Coefficient of Variation = 0.477

Answer b.

Coefficient of Variation of Site B is higher than that of Site A, therefore you should select Store Site A.