Calculating NPV Over a 5-Year Horizon
A 5-year timeline is one of the most common capital budgeting horizons used in corporate finance, pension bridge calculations, and equipment leasing decisions.
The 5-Year NPV Equation
NPV = −C0 + [ C1 / (1 + r)1 ] + [ C2 / (1 + r)2 ] + [ C3 / (1 + r)3 ] + [ C4 / (1 + r)4 ] + [ C5 / (1 + r)5 ]
Step-by-Step 5-Year Example
Imagine an upfront investment of $50,000 with projected annual cash inflows of $15,000 each year for 5 years at an 8% discount rate (r = 0.08):
| Year (t) | Nominal Cash Flow | Discount Factor (1 / 1.08t) | Present Value (PV) |
|---|---|---|---|
| Year 1 | $15,000 | 0.9259 | $13,889 |
| Year 2 | $15,000 | 0.8573 | $12,860 |
| Year 3 | $15,000 | 0.7938 | $11,907 |
| Year 4 | $15,000 | 0.7350 | $11,025 |
| Year 5 | $15,000 | 0.6806 | $10,209 |
| Gross Present Value of 5-Year Inflows | $59,890 | ||
| Less Initial Investment (C0) | −$50,000 | ||
| 5-Year Net Present Value (NPV) | +$9,890 | ||
Shortcut: The 5-Year Constant Annuity Formula
When the cash flow received each year is identical (as in a fixed annuity or bridge pension), you do not need to discount each year manually. Instead, apply the 5-year annuity present value factor:
Plugging in r = 0.08: PV = $15,000 × [ (1 - 1.08^-5) / 0.08 ] = $15,000 × 3.9927 = $59,890. Subtracting the $50,000 initial cost gives the exact same +$9,890 NPV.