Smart Solutions Inc. is evaluating a capital project for expansion. The project costs $10,000, and it is expected to generate $5,000 per year for three years. If the firm's required rate of return is 10 percent, what is the project's terminal value?

Question

Quizplus · Accepted Answer

To find the terminal value of the project, we need to calculate the present value of the cash flows generated by the project in Year 4 and beyond. Since the cash flows beyond Year 3 are not given, we can assume that the project ends after three years and there are no cash flows beyond that. In that case, the project's terminal value is just the salvage value of the project at the end of Year 3. The salvage value is the value of the project's assets at the end of its useful life.

To calculate the salvage value, we need to find the present value of the cash flows generated by the project in Year 3. The cash flow in Year 3 is $5,000. We can find the present value of this cash flow using the formula:

PV = CF / (1 + r)^n
where PV is the present value, CF is the future cash flow, r is the required rate of return, and n is the number of periods.

PV = $5,000 / (1 + 0.10)^3
PV = $3,695.50

Therefore, the project's salvage value at the end of Year 3 is $3,695.50. This is the terminal value of the project.

To find the total value of the project, we need to add up the present value of the cash flows generated by the project in Years 1, 2, and 3, as well as the salvage value at the end of Year 3. The present value of the cash flows in Years 1, 2, and 3 is:

PV = $5,000 / (1 + 0.10)^1 + $5,000 / (1 + 0.10)^2 + $5,000 / (1 + 0.10)^3
PV = $4,545.45 + $4,132.23 + $3,759.19
PV = $12,436.87

Adding the salvage value of $3,695.50 to this gives a total project value of:

Total project value = $12,436.87 + $3,695.50 = $16,132.37

Therefore, the best choice is B, $16,550, which is closest to $16,132.37.