Discounted Payback Period Calculator
Calculate the time required to recover an investment while accounting for the time value of money.
Understanding the Discounted Payback Period
The Discounted Payback Period (DPP) is a capital budgeting metric used to determine the amount of time it takes for an investment to reach its break-even point based on the Net Present Value (NPV) of its cash flows. Unlike the standard payback period, which ignores the time value of money, the DPP accounts for the fact that a dollar today is worth more than a dollar tomorrow.
Why the Discount Rate Matters
In finance, the discount rate (often the Weighted Average Cost of Capital, or WACC) represents the opportunity cost of capital. By applying this rate to future cash flows, we "shrink" their value back to present-day terms. This provides a more realistic view of how long it actually takes to recoup the initial outlay in terms of today's purchasing power.
The Formula and Calculation Logic
The calculation involves a step-by-step process:
- Calculate the Present Value (PV) of each year's cash flow:
PV = Cash Flow / (1 + r)^n - Subtract each year's PV from the initial investment cost.
- The moment the cumulative PV equals the initial cost is the Discounted Payback Period.
Practical Example
Imagine you invest $10,000 in a solar panel project that generates $3,000 per year. If your discount rate is 10%:
- Year 1: $3,000 / (1.10)^1 = $2,727.27
- Year 2: $3,000 / (1.10)^2 = $2,479.34 (Cumulative: $5,206.61)
- Year 3: $3,000 / (1.10)^3 = $2,253.94 (Cumulative: $7,460.55)
- Year 4: $3,000 / (1.10)^4 = $2,049.04 (Cumulative: $9,509.59)
- Year 5: $3,000 / (1.10)^5 = $1,862.76 (Cumulative: $11,372.35)
The payback occurs between year 4 and year 5. Using interpolation, the exact period is approximately 4.26 years. Without discounting, the payback would have been a simpler 3.33 years, which underestimates the true economic time required to break even.