Question

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 $24,400. 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 14 percent.

Cash Flow -- Probability

$ 4,360 -- 0.3

$5,770 -- .03

$8,230 -- 0.1

$10,710 -- 0.3

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?
**(Negative amount should be indicated by a minus sign. Do
not round intermediate calculations and round your answer to 2
decimal places.)**

**c.** Should Debby buy the new equipment? Yes OR
No

Answer #1

a.expected value of cash flow:

cash flow | P | Cash flow *probability |

$4,360 | 0.30 | $1,308 |

5,770 | 0.30 | 1,731 |

8,230 | 0.10 | 823 |

10,710 | 0.30 | 3,213 |

expected value of cash flow | $7,075 |

b.Net present value:

present value of cash inflows - present value of cash outflows.

here,

present value of cash inflows = $7075 * Present value of annuity factor....(since the cash flows are in form of a constant annuity).

present value of annuity factor = [1 - (1+r)^(-n)] /r

here.

r = 14% =>0.14

n=5 years.

so

present value of cash inflows = 7075 * [1-(1.14)^(-5)]/0.14

=>7075 * [3.4330807]

=>$24,289.046

now,

net present value =$26,289.046 - 24,400

=>-$110.95

C.No.

since NPV is negative, the new equipment should not be bought.

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