Discounted Payback Period
The discounted payback period is the time it takes to recover a project's cost using discounted cash flows instead of raw ones. It fixes the biggest flaw of simple payback by accounting for the time value of money, so it always takes at least as long as ordinary payback.
Discounted payback explained simply
Discounted payback is the time it takes to recover a project's cost using discounted cash flows. It always takes at least as long as simple payback. In the example, at 10%, it's about 3.15 years, against 2.6 years for simple payback.
Correction: at 3:27 in the video, the Year 4 cash flow should be $35, not $24.
What this discounted payback lesson covers
- How discounted payback differs from simple payback
- How to discount each year's cash flow to today
- How to build a discounted cumulative cash flow table
- How to calculate the fraction of the final year
- What the result tells you, and what it still ignores
Discounted payback formula, explained
- CFₜ
- cash flow in year t
- r
- discount rate
- Y
- last full year before the discounted cumulative total turns positive
How to calculate discounted payback step by step (worked example)
A project costs $10,000 and returns $3,000, $4,000, $5,000 and $2,000 in years 1 to 4. The discount rate is 10%. Find the discounted payback period.
- Discount each cash flow: 2,727.27; 3,305.79; 3,756.57; 1,366.03
- Discounted cumulative: −7,272.73 after year 1, −3,966.94 after year 2
- After year 3: −3,966.94 + 3,756.57 = −210.37, still not recovered
- Fraction of year 4: 210.37 ÷ 1,366.03 = 0.154
- Discounted payback = 3 + 0.154 ≈ 3.15 years
Answer: Discounted payback ≈ 3.15 years (rounded to two decimals), compared with 2.6 years for simple payback on the same cash flows.
Simple payback vs discounted payback
| Simple payback | Discounted payback | |
|---|---|---|
| Cash flows used | Raw | Discounted at the required return |
| In the example | About 2.6 years | About 3.15 years |
| Ignores cash after the cut-off | Yes | Yes |
| If it pays back, NPV is | Not necessarily positive | Positive (or zero) |
Harder discounted payback questions
What is the project's NPV at 10%?
The four discounted cash flows add up to about $11,155.66, so NPV ≈ $1,155.66. If a project reaches discounted payback within its life, its NPV can't be negative.
What happens at a 15% discount rate?
NPV falls to about $64.36, so the project barely pays back by the end of Year 4. Higher rates push discounted payback later.
Common discounted payback questions
What is the discounted payback period formula?
Discount each cash flow with CFₜ ÷ (1 + r)ᵗ, then add them cumulatively. Discounted payback equals the last full year before the total turns positive, plus the unrecovered discounted amount divided by the next year's discounted cash flow.
What is the difference between payback and discounted payback?
Simple payback uses raw cash flows and ignores the time value of money. Discounted payback first converts each cash flow into today's money at the discount rate. Because discounted amounts are smaller, discounted payback is always the same or longer.
What does it mean if a project never reaches discounted payback?
It means the discounted cash flows never cover the initial cost, so the project's NPV is negative at that discount rate. In other words, the project does not earn its required return and should normally be rejected.
Is discounted payback better than NPV?
No. Discounted payback is a useful risk and liquidity check, but it still ignores cash flows after the payback point. NPV counts every cash flow, so it remains the main decision rule for accepting projects.