This is the present value of the expected annual cash inflows. The NPV of a project is the present value of the expected cash inflows minus the present value of the expected cash outflows. If the initial investment were $29,160, the present value of the project would be zero. But the present value of the project is $3,000.
The NPV of a project is the present value of the expected cash inflows minus the present value of the expected cash outflows. We know the NPV ($3,000) and we can calculate the present value of the future expected cash inflows of $9,000 per year. Once we have that, we can easily calculate the amount of the initial investment, since the only cash outflow is the initial investment. The present value of the expected annual cash inflows of $9,000 per year for 4 years, discounted at 9% is: $9,000 × 3.24 = $29,160 Since the only cash outflow is the initial investment, that is the amount we need to find. We do not need to discount it to find its present value. We already have its present value, since it occurs at Year 0. Since a project's NPV is the present value of its future expected cash inflows minus the initial cash outflow, letting X stand for the initial investment, our formula is: $29,160 ? X = $3,000 X = $26,160 If the initial investment is $(26,160) and the present value of the future cash inflows is $29,160, that results in an NPV of $3,000 ($29,160 ? $26,160).
This answer results from two errors. (1) The present value of the future expected cash inflows of $9,000 is discounted as one cash inflow occurring at Year 1. This is incorrect because the future cash inflows of $9,000 are expected for four years. (2) A project's NPV is the present value of its future expected cash inflows minus the initial cash outflow. Therefore, the initial investment will be the present value of the future expected cash inflows minus the NPV. This answer is calculated by adding the NPV to the present value of the future expected cash inflows instead of subtracting it.
This answer results from four errors. (1) The NPV of $3,000 is used as the amount of the annual cash inflow instead of $9,000. (2) The $3,000 being used incorrectly as the present value of the future expected cash inflows is discounted as one cash inflow occurring at Year 4. This is incorrect because the future cash inflows (which should be $9,000 instead of $3,000) are an annuity that is expected for four years. (3) The annual cash inflow of $9,000 is used as the amount of the NPV instead of $3,000. (4) A project's NPV is the present value of its future expected cash inflows minus the initial cash outflow. Therefore, the initial investment will be the present value of the future expected cash inflows minus the NPV. This answer is calculated by adding the NPV (the incorrect NPV of $9,000 instead of the correct NPV of $3,000) to the present value of the future expected cash inflows instead of subtracting it.
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