Sansariff Company invests in a new piece of equipment costing $40,000. The equipment is expected to yield the following amounts per year for the equipment's four-year useful life: $\begin{array}{lc}
\text { Cash revenues } & \$ 60,000 \
\text { Cash expenses } & (32,000) \
\text { Depreciation expenses (straight-line) } & (10,000) \
\text { Income provided from equipment } & \$ 18,000\
\text { Cost of capital }&14\%
\end{array}$ What is the net present value of this investment in equipment, assuming no taxes are paid?

Question

Quizplus · Accepted Answer

The net present value (NPV) of an investment is calculated by discounting the net cash flows from the investment at the cost of capital and then subtracting the initial investment. Given the information, the net cash flow each year is the cash revenues minus the cash expenses, which is $60,000 - $32,000 = $28,000. Depreciation is not a cash flow, so it is not subtracted in the NPV calculation. The cost of capital is 14%, which is used as the discount rate.The NPV formula is: $$NPV = \sum \frac{C_t}{(1+r)^t} - C_0$$Where:- $C_t$ is the net cash inflow during the period t,- $r$ is the discount rate (cost of capital),- $t$ is the number of time periods,- $C_0$ is the initial investment.For this investment:- $C_t = \$28,000$ for each of the four years,- $r = 14\% = 0.14$,- $C_0 = \$40,000$.Calculating the NPV:$$NPV = \frac{\$28,000}{(1+0.14)^1} + \frac{\$28,000}{(1+0.14)^2} + \frac{\$28,000}{(1+0.14)^3} + \frac{\$28,000}{(1+0.14)^4} - \$40,000$$$$NPV = \$24,561.40 + \$21,535.79 + \$18,891.57 + \$16,603.31 - \$40,000$$$$NPV = \$41,591.07$$Rounding to the nearest dollar gives an NPV of approximately \$41,592, which matches choice C.

Sansariff Company Invests in a New Piece of Equipment Costing