Debby’s Dance Studios is considering the purchase of new sound equipment that will enhance the popularity of its aerobics dancing. The equipment will cost \(27,900. Debby is not sure how many members the new equipment will attract, but she estimates that her increased annual cash flows for each of the next five years will have the following probability distribution. Debby’s cost of capital is 15 percent.

Cash Flow Probability

\)4,570 ........................ 0.1

5,550 ........................ 0.3

7,400 ........................ 0.4

9,930 ........................ 0.2

a. What is the expected value of the cash flow? The value you compute will apply to each of the five years.

b. What is the expected net present value?

c. Should Debby buy the new equipment?

Step by step solution

01

Computation of the expected value of the cash flow

Probability (a)	Cash Flow (b)	Expected Cash flow (a*b)
0.1	$4,570	457
0.3	$5,550	1665
0.4	$7,400	2960
0.2	$9,930	1986
		7,068

02

Computation of the expected net present value

$\begin{array}{c}\mathrm{Expected}\mathrm{net}\mathrm{present}\mathrm{value}=\mathrm{Present}\mathrm{value}\mathrm{of}\mathrm{expected}\mathrm{cash}\mathrm{flow}-\mathrm{Investment}\\ \mathbf{=}(\mathbf{7}\mathbf{,}\mathbf{068}\mathbf{\times }\mathbf{Presentvaluefactorforannuity}\mathbf{@}\mathbf{15}\mathbf{\%}\mathbf{,}\mathbf{3}\mathbf{years})\mathbf{-}\mathbf{20}\mathbf{,}\mathbf{900}\\ \mathbf{=}(\mathbf{7068}\mathbf{\times }\mathbf{2}\mathbf{.}\mathbf{283})\mathbf{-}\mathbf{20}\mathbf{,}\mathbf{900}\\ =(4,764)\end{array}$

03

Analysis

The Net present value of the company is ($4,764) i.e., negative net present value. A negative Net present value represents that an investment is unprofitable. Thus, the company shall not opt for the purchase of new equipment.

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