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
$10 0.1
15 0.2
30 0.4
45 0.2
50 0.1

Crenshaw Village

Yearly Aftertax Cash Inflow (in thousands) Probability
$15 0.2
20 0.3
30 0.4
40 0.1

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?

Answer 1

(a) The expected cash flow from Palmer Heights is $30,000 and from Crenshaw Village is $25,000.

(b) The coefficient of variation for Palmer Heights is 43.47% and for Crenshaw Village is 31%.

Explanation:

The formula to compute the expected value of a discrete probability distribution is:

`E(X)=\sum x.P(X=x)`

The formula to compute the variance of a discrete probability distribution is:

`SD(X)=\sqrt{E(X^(2))-(E(X))^(2)}`

The formula to compute the coefficient of variation is:

`CV=(SD(X))/(E(X))* 100`

Denote:

X = Palmer Heights

Y = Crenshaw Village

(a)

Compute the expected cash flow from Palmer Heights as follows:

`E(X)=\sum x.P(X=x)\\=[(10*0.1)+(15*0.2)+(30*0.4)+(45*0.2)+(50*0.1)]\\=30`

Compute the expected cash flow from Crenshaw Village as follows:

`E(Y)=\sum y.P(Y=y)\\=[(15*0.2)+(20*0.3)+(30*0.4)+(40*0.1)]\\=25`

Thus, the expected cash flow from Palmer Heights is $30,000 and from Crenshaw Village is $25,000.

(b)

Compute the standard deviation of cash flow from each apartment as follows:

`SD(X)=\sqrt{E(X^(2))-(E(X))^(2)} \\=\sqrt{\sum x^(2)P(X=x)-(30)^(2)}\\=√(1070-900)\\=√(170)\\=13.04`

`SD(Y)=\sqrt{E(Y^(2))-(E(Y))^(2)} \\=\sqrt{\sum y^(2)P(Y=y)-(25)^(2)}\\=√(685-625)\\=√(60)\\=7.75`

Compute the coefficient of variation for Palmer Heights as follows:

`CV=(SD(X))/(E(X))* 100=(13.04)/(30)*100=43.46667\approx43.47\%`

Compute the coefficient of variation for Crenshaw Village as follows:

`CV=(SD(Y))/(E(Y))* 100=(7.75)/(25)*100=31\%`

Thus, the coefficient of variation for Palmer Heights is 43.47% and for Crenshaw Village is 31%.