Palmetto Products is considering the purchase of a new industrial machine.The estimated cost of the machine is $50 000.The machine is expected to generate annual cash inflows for the next four years as follows:
$\begin{array}{cc}
\text { Year } & \text { Annual cash flow } \
\hline 1 & \$ 25000 \
2 & \$ 20000 \
3 & \$ 20000 \
4 & \$ 15000
\end{array}$

The machine is not expected to have a residual value at the end of its useful life.If Palmetto uses a discount rate of 16 per cent,what is the expected net present value of the machine? (ignore taxes)

Question

Palmetto Products is considering the purchase of a new industrial machine.The estimated cost of the machine is $50 000.The machine is expected to generate annual cash inflows for the next four years as follows:
$\begin{array}{cc}
\text { Year } & \text { Annual cash flow } \
\hline 1 & \$ 25000 \
2 & \$ 20000 \
3 & \$ 20000 \
4 & \$ 15000
\end{array}$

The machine is not expected to have a residual value at the end of its useful life.If Palmetto uses a discount rate of 16 per cent,what is the expected net present value of the machine? (ignore taxes)

Quizplus · Accepted Answer

To calculate the net present value (NPV), we discount each of the annual cash flows back to their present value using the given discount rate of 16% and then subtract the initial investment. The formula for the present value of a future cash flow is $PV = \frac{CF}{(1 + r)^n}$, where $PV$ is the present value, $CF$ is the cash flow, $r$ is the discount rate, and $n$ is the number of periods.Year 1: $PV = \frac{25000}{(1 + 0.16)^1} = \frac{25000}{1.16} = 21551.72$Year 2: $PV = \frac{20000}{(1 + 0.16)^2} = \frac{20000}{1.3456} = 14878.09$Year 3: $PV = \frac{20000}{(1 + 0.16)^3} = \frac{20000}{1.5589} = 12828.39$Year 4: $PV = \frac{15000}{(1 + 0.16)^4} = \frac{15000}{1.8061} = 8306.80$Adding these present values together gives the total present value of the cash inflows: $21551.72 + 14878.09 + 12828.39 + 8306.80 = 57565$Subtracting the initial investment of $50,000 gives the NPV: $57565 - 50000 = 7565$The closest answer provided is $7515, so the correct choice is D.