Chapter 4: Q12BP (page 441)

Kyle’s Shoe Stores Inc. is considering opening an additional suburban outlet. An aftertax expected cash flow of $130 per week is anticipated from two stores that are being evaluated. Both stores have positive net present values.
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
Probability Cash Flows Probability Cash Flows
0.3 $ 80 0.2 $ 50
0.3 130 0.2 80
0.1 160 0.3 130
0.3 170 0.1 180
0.2 235

Short Answer

Expert verified

The coefficient of variation of the companies-

Site A	0.0421
Site B	0.0499

The Site A shall be selected as the coefficient of variation is lower in comparison to Site B i.e., 0.0421 that means the risk is low in choosing Site A.

Step by step solution

Computation of the expected value of the cash flow-

Site A

Probability (a)	Cash flow (in thousands) (b)	Expected Cash flow (in thousands) (a*b)
0.3	$80	24
0.3	$130	39
0.1	$160	16
0.3	$170	51
		130

Site B

Probability (a)	Cash flow (in thousands) (b)	Expected Cash flow (in thousands) (a*b)
0.2	$50	10
0.2	$80	16
0.3	$130	39
0.1	$180	18
0.2	$235	47
		130

Computation of total probability-

Site A

Probability (a)	Cash flow (in thousands) (b)	Probability*(sales-Expected sales)²	Total
0.3	$80	0.30*(80-130)²	15
0.3	$130	0.30*(130-130)²	0
0.1	$160	0.10*(160-130)²	3
0.3	$170	0.30*(170-130)²	12
			30

Site B

Probability (a)	Cash flow (in thousands) (b)	Probability*(sales-Expected sales)²	Total
0.2	$50	0.20*(50-130)²	16
0.2	$80	0.20*(80-130)²	10
0.3	$130	0.30*(130-130)²	0
0.1	$180	0.10*(180-130)²	5
0.2	$235	0.20*(235-130)²	11
			42

Computation of Site A Standard deviation ( approx )-

$\begin{matrix} Standard deviation = \sqrt{\begin{array}{l} Probability \times {(sales - Expected sales)}^{2} \end{array}} \\ = \sqrt{30} \\ = 5.4772 units \end{matrix}$

Computation of Site B Standard deviation ( approx )-

$\begin{matrix} Standard deviation = \sqrt{\begin{array}{l} Probability \times {(sales - Expected sales)}^{2} \end{array}} \\ = \sqrt{42} \\ = 6.4807 units \end{matrix}$

Computation of Site A coefficient of variation-

$\begin{matrix} Coefficient of variation = \frac{Standard deviation}{Expected sales} \\ = \frac{5.4772}{130} \\ = 0.0421 \end{matrix}$

Computation of Site B coefficient of variation-

$\begin{matrix} Coefficient of variation = \frac{Standard deviation}{Expected sales} \\ = \frac{6.4807}{130} \\ = 0.0499 \end{matrix}$

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Short Answer

Step by step solution

Computation of the expected value of the cash flow-

Computation of total probability-

Computation of Site A Standard deviation ( approx )-

Computation of Site B Standard deviation ( approx )-

Computation of Site A coefficient of variation-

Computation of Site B coefficient of variation-

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