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.

Calculator

Formula

\text{DiscountedPayback} = t^* + \frac{|\text{CumDiscCF}_{t^*}|}{CF_{t^*+1}/(1+k)^{t^*+1}}

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

CashFlows = [-1000, 400, 400, 400, 400]k = 10.0000%

Step-by-Step

1.Discounted CFs: -1000, 363.64, 330.58, 300.53, 273.21

2.Cumulative: -1000, -636.36, -305.78, -5.25, +267.95

3.Crosses zero between year 3 and 4: 3 + 5.25/273.21 ≈ 3.02 years

Result:3.02 years

Discounted payback ≈ 3.02 years vs simple payback of 2.5 — the gap widens with higher discount rates and longer projects.

Frequently Asked Questions

Only for conventional cash flows after the initial outlay. Later negative cash flows can undo an earlier recovery. At zero discount rate, −100, +200, −200 has interpolated payback at 0.5 years but final NPV of −100.

The calculator prorates the discounted cash flow within the recovery year, assuming it accrues evenly. If cash arrives only at year-end, recovery occurs at that year-end instead.

No. It measures first recovery and ignores later cash flows. Use NPV for the full discounted cash-flow value.

Related Formulas

Payback Period