Pristine Products is considering the purchase of a new machine.The estimated cost of the machine is $25 000.The machine is expected to generate annual cash inflows for the next four years as follows:
$\begin{array}{cc}
\text { Year } & \text { Annual cash flow } \
\hline 1 & \$ 15000 \
2 & \$ 10000 \
3 & \$ 5000 \
4 & \$ 5000
\end{array}$

The machine is not expected to have a residual value at the end of its useful life.If the company uses a discount rate of 12 per cent,what is the expected net present value of the machine? (ignore taxes)

Question

Pristine Products is considering the purchase of a new machine.The estimated cost of the machine is $25 000.The machine is expected to generate annual cash inflows for the next four years as follows:
$\begin{array}{cc}
\text { Year } & \text { Annual cash flow } \
\hline 1 & \$ 15000 \
2 & \$ 10000 \
3 & \$ 5000 \
4 & \$ 5000
\end{array}$

The machine is not expected to have a residual value at the end of its useful life.If the company uses a discount rate of 12 per cent,what is the expected net present value of the machine? (ignore taxes)

Quizplus · Accepted Answer

The net present value (NPV) is calculated by discounting the future cash flows back to their present value and then subtracting the initial investment. The formula for NPV is: $$NPV = \sum \frac{CF_t}{(1+r)^t} - Initial\ Investment$$ where $CF_t$ is the cash flow in year $t$, $r$ is the discount rate, and $t$ is the year. For this problem: $$NPV = \frac{15000}{(1+0.12)^1} + \frac{10000}{(1+0.12)^2} + \frac{5000}{(1+0.12)^3} + \frac{5000}{(1+0.12)^4} - 25000$$ Calculating each term: $$\frac{15000}{1.12} \approx 13392.86$$ $$\frac{10000}{1.12^2} \approx 7971.93$$ $$\frac{5000}{1.12^3} \approx 3552.62$$ $$\frac{5000}{1.12^4} \approx 3171.49$$ Summing these and subtracting the initial investment: $$13392.86 + 7971.93 + 3552.62 + 3171.49 - 25000 \approx 3102$$ Therefore, the expected net present value of the machine is approximately $3102.