Cleaners, Inc.is considering purchasing equipment costing $30,000 with a 6-year useful life.The equipment will provide cost savings of $7,300 and will be depreciated straight-line over its useful life with no salvage value.Cleaners, Inc.requires a 10% rate of return.What is the approximate net present value of this investment? $\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\text { Present Value of an Annuity of } 1$
$\begin{array}{llcc}
\underline{\text { Period }} &\underline{8 \%}&\underline{9 \%} & \underline{10 \%}&\underline{11 \%} &\underline{12 \%}& \underline{15 \%}\
6&4.623&4.486&4.355&4.231&4.111&3.784
\end{array}$

Question

Quizplus · Accepted Answer

1. Calculate the present value of cost savings using the formula PV = CF / (1 + r)^n, where CF = $7,300, r = 10%, and n = 1 to 6 (since the savings occur at the end of each year).

PV = $7,300 / (1 + 0.10)^1 + $7,300 / (1 + 0.10)^2 + ... + $7,300 / (1 + 0.10)^6 
PV = $7,300 / 1.10 + $6,636.36 / 1.10^2 + ... + $3,336.54 / 1.10^6 
PV = $31,511.52

2. Calculate the present value of the equipment purchase using the formula PV = -C / (1 + r)^n, where C = $30,000, r = 10%, and n = 1 to 6 (since the purchase occurs at the beginning of year 1).

PV = -$30,000 / 1.10 + -$30,000 / 1.10^2 + ... + -$30,000 / 1.10^6 
PV = -$30,000 / 1.10 + -$27,272.73 / 1.10^2 + ... + -$13,637.84 / 1.10^6 
PV = -$99,781.05

3. Calculate the net present value (NPV) by subtracting the present value of the equipment purchase from the present value of the cost savings.

NPV = $31,511.52 - $99,781.05 
NPV = -$68,269.53

Since the NPV is negative, the investment is not expected to generate a 10% rate of return and is therefore not a good investment. Choice B is the correct answer, representing the approximate NPV of the investment.

Cleaners, Inc \quad \quad \quad \quad \quad

Cleaners, Inc $\quad$ $\quad$ $\quad$ $\quad$ $\quad$