Question

Problem 13-18 Coefficient of variation and investment decision [LO13-1] Mr. Sam Golff desires to invest a portion of his assets in rental property. He has narrowed his choices down to two apartment complexes, Palmer Heights and Crenshaw Village. After conferring with the present owners, Mr. Golff has developed the following estimates of the cash flows for these properties. Palmer Heights Yearly Aftertax Cash Inflow (in thousands) Probability $ 60 .2 65 .2 80 .2 95 .2 100 .2 Crenshaw Village Yearly Aftertax Cash Inflow (in thousands) Probability $ 65 .4 70 .2 80 .1 90 .3 a. Find the expected cash flow from each apartment complex. (Enter your answers in thousands (e.g, $10,000 should be enter as "10").) b. What is the coefficient of variation for each apartment complex? (Do not round intermediate calculations. Round your answers to 3 decimal places.) c. Which apartment complex has more risk? Palmer Heights Crenshaw Village

Answer 1

Answer a.

Palmer Heights:

Expected Cash Flow = 0.20 * 60 + 0.20 * 65 + 0.20 * 80 + 0.20 * 95 + 0.20 * 100
Expected Cash Flow = 80

Crenshaw Village:

Expected Cash Flow = 0.40 * 65 + 0.20 * 70 + 0.10 * 80 + 0.30 * 90
Expected Cash Flow = 75

Answer b.

Palmer Heights:

Variance = 0.20 * (60 - 80)^2 + 0.20 * (65 - 80)^2 + 0.20 * (80 - 80)^2 + 0.20 * (95 - 80)^2 + 0.20 * (100 - 80)^2
Variance = 250

Standard Deviation = (250)^(1/2)
Standard Deviation = 15.81

Coefficient of Variation = Standard Deviation / Expected Cash Flow
Coefficient of Variation = 15.81 / 80
Coefficient of Variation = 0.198

Crenshaw Village:

Variance = 0.40 * (65 - 75)^2 + 0.20 * (70 - 75)^2 + 0.10 * (80 - 75)^2 + 0.30 * (90 - 75)^2
Variance = 115

Standard Deviation = (115)^(1/2)
Standard Deviation = 10.72

Coefficient of Variation = Standard Deviation / Expected Cash Flow
Coefficient of Variation = 10.72 / 75
Coefficient of Variation = 0.143

Answer c.

Coefficient of variation of Palmer Heights is higher than that of Crenshaw Village. So, Palmer Heights has more risk than Crenshaw Village.