Discounted Payback Period

What it is

The discounted payback period (DPBP) is the time required for the present value of a project’s discounted cash inflows to equal its initial investment. Unlike the simple payback period, DPBP accounts for the time value of money by discounting future cash flows.

Why it matters

DPBP is used in capital budgeting to assess how quickly a project recovers its initial cost in present-value terms. It helps managers compare projects when timing of cash flows matters and when a break-even deadline exists.

How it works (step-by-step)

1. Estimate the project’s periodic cash inflows.
2. Choose an appropriate discount rate (reflecting required return, opportunity cost, or cost of capital).
3. Discount each future cash inflow to its present value: PV = CFt / (1 + r)^t.
4. Cumulate discounted inflows and compare them to the initial outlay.
5. The DPBP is the point in time when cumulative discounted inflows first equal or exceed the initial investment. If recovery occurs within a year, interpolate to estimate the fractional year.

Formula and interpolation

• Discounted cash flow for period t: PVt = CFt / (1 + r)^t
• DPBP occurs when ΣPVt ≥ Initial Investment
• To get a fractional year:
  DPBP = N + (Unrecovered amount at end of year N) / (Discounted inflow in year N+1)
  where N is the last full year before full recovery.

Example

Initial investment: $3,000
Annual cash inflow: $1,000 for 5 years
Discount rate: 4%

Discounted inflows:
– Year 1: 1,000 / 1.04 = 961.54
– Year 2: 1,000 / 1.04^2 = 924.56
– Year 3: 1,000 / 1.04^3 = 889.00
Cumulative after 3 years = 2,775.09
Unrecovered = 3,000 − 2,775.09 = 224.91
Year 4 discounted inflow = 854.80

Fractional year = 224.91 / 854.80 ≈ 0.26

Discounted payback period ≈ 3.26 years

Payback Period vs Discounted Payback Period

• Payback period uses nominal cash flows and ignores time value of money.
• Discounted payback period discounts future cash flows and therefore usually yields a longer recovery time.
• DPBP gives a better timing-based risk assessment but can differ significantly from simple payback when cash flows are back-loaded.

Decision rule

• A project may be acceptable if its DPBP is shorter than a target break-even threshold (for example, the asset’s useful life or a management-specified cutoff).
• When comparing projects, a shorter DPBP is preferred if speed of recovery is a key objective.

Limitations

• Ignores cash flows after the payback point (so it does not measure total profitability).
• Results depend on the chosen discount rate.
• Does not account for project scale; a project with a short DPBP may still have low overall return compared with others.
• Not a substitute for NPV or IRR when evaluating long-term value.

Bottom line

The discounted payback period is a useful, time-sensitive screening tool that shows how quickly an investment recovers its initial cost in present-value terms. Use it to assess short-term recovery risk and to compare projects by payback speed, but complement it with NPV, IRR, or other profitability measures for full project evaluation.