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

\( 70 ........................ 0.2

75 ........................ 0.2

90 ........................ 0.2

105 ........................ 0.2

110 ........................ 0.2

Crenshaw Village

Yearly Aftertax Cash Inflow (in thousands) Probability

\) 75 ........................ 0.2

80 ........................ 0.3

90 ........................ 0.4

100 ........................ 0.1

a. Find the expected cash flow from each apartment complex.

b. What is the coefficient of variation for each apartment complex?

c. Which apartment complex has more risk?

Step by step solution

01

Computation of the expected value of the cash flow

Palmer Heights

Probability (a)	Cash flow (in thousands) (b)	Expected Cash flow (in thousands) (a*b)
0.2	$70	14
0.2	$75	15
0.2	$90	18
0.2	$105	21
0.2	$110	22
		90

Crenshaw Village

Probability (a)	Cash flow (in thousands) (b)	Expected Cash flow (in thousands) (a*b)
0.2	$75	15
0.3	$80	24
0.4	$90	36
0.1	$100	10
		85

02

Computation of total probability

Palmer Heights

Probability (a)	Cash flow (in thousands) (b)	Probability*(sales-Expected sales)2	Total
0.2	$70	0.20*(70-90)2	80
0.2	$75	0.20*(75-90)2	45
0.2	$90	0.20*(90-90)2	0
0.2	$105	0.20*(105-90)2	45
0.2	$110	0.20*(100-90)2	20
			190

Crenshaw Village

Probability (a)	Cash flow (in thousands) (b)	Probability*(sales-Expected sales)2	Total
0.2	$75	0.20*(75-85)2	20
0.3	$80	0.30*(80-85)2	7.5
0.4	$90	0.40*(90-85)2	10
0.1	$100	0.10*(100-85)2	22.5
			60

03

Computation of Palmer Height’s Standard deviation ( approx )

$\begin{array}{c}\mathbf{Standard}\mathbf{}\mathbf{deviation}\mathbf{=}\sqrt{\begin{array}{l}\mathbf{Probability}\mathbf{\times }{(\mathbf{sales}\mathbf{-}\mathbf{Expected}\mathbf{}\mathbf{sales})}^2\end{array}}\\ \mathbf{=}\sqrt{190}\\ \mathbf{=}\mathbf{13}\mathbf{.}\mathbf{7840}\mathbf{units}\end{array}$

04

Computation of Crenshaw Village’s Standard deviation ( approx )

$\begin{array}{c}\mathbf{Standard}\mathbf{}\mathbf{deviation}\mathbf{=}\sqrt{\begin{array}{l}\mathbf{Probability}\mathbf{\times }{(\mathbf{sales}\mathbf{-}\mathbf{Expected}\mathbf{}\mathbf{sales})}^2\end{array}}\\ \mathbf{=}\sqrt{60}\\ \mathbf{=}\mathbf{7}\mathbf{.}\mathbf{7460}\mathbf{units}\end{array}$

05

Computation of Palmer Height’s coefficient of variation 

$\begin{array}{c}\mathbf{Coefficient}\mathbf{}\mathbf{of}\mathbf{}\mathbf{variation}\mathbf{=}\frac{\mathrm{Standard}\mathrm{deviation}}{\mathrm{Expected}\mathrm{sales}}\\ \mathbf{=}\frac{\mathbf{13}\mathbf{.}\mathbf{7840}}{90}\\ \mathbf{=}\mathbf{0}\mathbf{.}\mathbf{1532}\end{array}$

06

Computation of Crenshaw Village’s coefficient of variation

$\begin{array}{c}\mathbf{Coefficient}\mathbf{}\mathbf{of}\mathbf{}\mathbf{variation}\mathbf{=}\frac{\mathrm{Standard}\mathrm{deviation}}{\mathrm{Expected}\mathrm{sales}}\\ \mathbf{=}\frac{\mathbf{7}\mathbf{.}\mathbf{7460}}{85}\\ \mathbf{=}\mathbf{0}\mathbf{.}\mathbf{0911}\end{array}$

07

Analysis

The coefficient of variation allows investors to identify the level of risk. The coefficient of variation of Palmer height is higher in comparison to Crenshaw village i.e., 0.1532 that indicates higher risk as well.

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