Discounted Payback Period
Time required to recover the initial investment from cumulative discounted cash flows. The same logic as Payback Period but each cash flow is first discounted at the required rate before being summed.
When to use: Use as a liquidity screen that respects the time value of money. Always longer than the simple payback period (since discounted cash flows are smaller). Useful as a quick yes/no test alongside NPV.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| DiscountedPayback | Discounted Payback Period | Time required to recover the initial investment from discounted cumulative cash flows | years |
| CashFlows | Cash Flows | Sequence of cash flows starting at period 0 (negative for outflows, positive for inflows) | $ |
| k | Discount Rate | Cost of capital or required rate of return as a decimal (e.g. 0.10 for 10%) | % |
Real-Life Examples
Example 1: 4-Year Project at 10%
Invest $1,000, receive $400/year for 4 years. Discount rate 10%.
Given
Step-by-Step
Discounted payback ≈ 3.02 years vs simple payback of 2.5 — the gap widens with higher discount rates and longer projects.
Frequently Asked Questions
Yes (assuming positive discount rate and conventional cash flows). Discounting shrinks future cash flows, so the cumulative sum reaches zero later. The gap grows with higher discount rates.
No — same weakness as simple payback. It only addresses the time-value-of-money flaw. A project with 4-year discounted payback but 30 years of subsequent cash flows still gets the same payback number as one that ends at year 4.
If discounted cash flows in later years are too small to ever cover the initial outlay (which is exactly the case when NPV < 0). A project with a negative NPV by definition never has a discounted payback period.