RatedrillDiscounted payback period
The discounted payback period is the time until the cumulative present value of the cash inflows equals the initial investment. Discount each inflow at the required rate, accumulate, and interpolate in the year recovery happens. It is always longer than the simple payback, and a project that never reaches discounted payback has a negative NPV.
Syntax
discounted payback = years before PV recovery + (unrecovered PV) / (PV of the next year's cash flow)| Part | What it is |
|---|---|
investment | Initial outlay at time 0 |
CF_t | Cash inflow in year t |
r | Discount rate |
Examples
Invest 1,000; inflows 500, 500, 500; r = 10%
PVs: 454.55, 413.22, 375.66
After year 2: 867.77 recovered, 132.23 left
2 + 132.23 / 375.66Result: Discounted payback = 2.35 years (simple payback: 2.0)
Invest 10,000; inflows 3,000, 4,000, 5,000; r = 8%
PVs: 2,777.78, 3,429.36, 3,969.16
After year 2: 6,207.13 recovered, 3,792.87 left
2 + 3,792.87 / 3,969.16Result: Discounted payback = 2.96 years (simple payback: 2.6)
Common mistakes
- Discounting the cumulative total instead of each year's cash flow separately.
- Using the wrong exponent: year 2's inflow is divided by (1 + r)^2, not (1 + r).
- Expecting a result when the project never recovers its cost in present value terms; in that case the NPV is negative and the discounted payback is undefined.
Practice Discounted payback period
These drills check your answer on live data, free, no account needed.
- Discounted payback periodA project costs $20,000 and returns $13,000, $11,500, $10,500 and $11,000 in years 1 to 4, earned evenly through each year. At a discount rate of 7.25%, what is its discounted payback period, to 2 decimals? Discount each year's cash flow as a year-end amount.
- Payback periodA machine costs $110,000 and is expected to save $34,000, $30,500, $51,000, $42,500 and $32,000 in years 1 to 5, earned evenly through each year. What is its payback period in years, to 2 decimals?
Questions
What is the difference between payback and discounted payback?
Simple payback adds up raw cash flows; discounted payback adds up their present values. Discounting makes later inflows worth less, so the discounted payback is longer.
How do I compute discounted payback in Excel?
Put years in column A and cash flows in B. In C compute =B2/(1+r)^A2, in D a running sum of C, then find the first year D turns positive and interpolate.
Related
- Payback periodPayback period is the time it takes cumulative cash inflows to equal the initial investment. Formula for even and uneven cash flows, examples, interpolation.
- NPV (net present value)Net present value is the sum of discounted cash flows minus the initial investment. Examples at 10% and 8%, the accept rule, Excel NPV and the sign mistake.
- Present valueHow to calculate present value with PV = FV / (1 + r)^n, what discounting means, examples with yearly and quarterly rates, the Excel PV function and mistakes.
- IRR (internal rate of return)The IRR is the discount rate that makes NPV zero. How to find it by trial, what Excel IRR returns, worked examples, the accept rule and where IRR fails.