A project costs $50,000 and returns $15,000 a year for 5 years at a 10% discount rate. Find the NPV.

Answer

The NPV is about $6,862, so the project is worth taking at a 10% required return.

Explanation

Step 1 — Lay the cash flows on a timeline

period	cash flow
0	−50,000
1–5	+15,000 each year

The inflows are equal and evenly spaced, which makes them an ordinary annuity — that is what lets you discount all five at once instead of one at a time.

Step 2 — State the formula

NPV = CF × [(1 − (1 + r)⁻ⁿ) / r] − initial outlay

with CF = 15,000, r = 0.10 and n = 5.

Step 3 — Work out the annuity factor

1.10⁵ = 1.61051, so 1.10⁻⁵ = 0.62092 (1 − 0.62092) / 0.10 = 3.79079

Step 4 — Substitute

present value of the inflows = 15,000 × 3.79079 = 56,861.80 NPV = 56,861.80 − 50,000 = $6,861.80

Check

Discounting each year separately gives 13,636 + 12,397 + 11,270 + 10,245 + 9,314 = 56,862, which matches the annuity result to the nearest dollar. A positive NPV means the project earns more than the 10% required return.