Question

Kyle’s Shoe Stores Inc. is considering opening an additional suburban outlet. An aftertax expected cash flow of $120 per week is anticipated from two stores that are being evaluated. Both stores have positive net present values.
  

Site A								Site B
Probability				Cash Flows				Probability				Cash Flows
	.2				70				.1				40
	.3				120				.2				70
	.3				130				.2				120
	.2				155				.4				150
									.1				180

a. Compute the coefficient of variation for each site. (Do not round intermediate calculations. Round your answers to 3 decimal places.)
  

  
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 Flows = 0.20 * 70 + 0.30 * 120 + 0.30 * 130 + 0.20 * 155
Expected Cash Flows = 120

Variance of Cash Flows = 0.20 * (70 - 120)^2 + 0.30 * (120 - 120)^2 + 0.30 * (130 - 120)^2 + 0.20 * (155 - 120)^2
Variance of Cash Flows = 775

Standard Deviation of Cash Flows = (775)^(1/2)
Standard Deviation of Cash Flows = 27.84

Coefficient of Variation = Standard Deviation of Cash Flows / Expected Cash Flows
Coefficient of Variation = 27.84 / 120
Coefficient of Variation = 0.232

Site B:

Expected Cash Flows = 0.10 * 40 + 0.20 * 70 + 0.20 * 120 + 0.40 * 150 + 0.10 * 180
Expected Cash Flows = 120

Variance of Cash Flows = 0.10 * (40 - 120)^2 + 0.20 * (70 - 120)^2 + 0.20 * (120 - 120)^2 + 0.40 * (150 - 120)^2 + 0.10 * (180 - 120)^2
Variance of Cash Flows = 1,860

Standard Deviation of Cash Flows = (1,860)^(1/2)
Standard Deviation of Cash Flows = 43.13

Coefficient of Variation = Standard Deviation of Cash Flows / Expected Cash Flows
Coefficient of Variation = 43.13 / 120
Coefficient of Variation = 0.359

Answer b.

Coefficient of variation of Site B is higher than that of Site A. So, Site B has more risk. Therefore, you should select Site A.