Question

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
$	120				.2
	125				.2
	140				.2
	155				.2
	160				.2

  

Crenshaw Village
Yearly Aftertax Cash Inflow (in thousands)				Probability
$	125				.2
	130				.3
	140				.4
	150				.1

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

a). Expected Cash Flows = [Probability_i * Cash Flows_i]

Palmer Heights' Expected Cash Flows = [0.20 * 120] + [0.20 * 125] + [0.20 * 140] + [0.20 * 155] + [0.20 * 160]

= 24 + 25 + 28 + 31 + 32 = $140

Crenshaw Village's Expected Cash Flows = [0.20 * 125] + [0.30 * 130] + [0.40 * 140] + [0.10 * 150]

= 25 + 39 + 56 + 15 = $135

b). Standard Deviation = [{Probability_i * (Expected Cash Flow - Cash Flows_i)²}]^1/2

Palmer Heights' Standard Deviation = [{0.2 * (140 - 120)²} + {0.2 * (140 - 125)²} + {0.2 * (140 - 140)²} + {0.2 * (140 - 155)²} + {0.2 * (140 - 160)²}]^1/2

= [80 + 45 + 0 + 45 + 80]^1/2 = [250]^1/2 = $15.81

Crenshaw Village's Standard Deviation = [{0.2 * (135 - 125)²} + {0.3 * (135 - 130)²} + {0.4 * (135 - 140)²} + {0.1 * (135 - 150)²}]^1/2

= [20 + 7.5 + 10 + 22.5]^1/2 = [60]^1/2 = $7.75

Coefficient of Variation(CV) = Standard deviation / Expected Return

Palmer Heights' CV = 15.81 / 140 = 0.1129, or 11.29%

Crenshaw Village's CV = 7.75 / 135 = 0.0574, or 5.74%

c). Palmer Heights has more risk.