Actuarial Mathematics for Modelling · Project appraisal

Payback Period and Discounted Payback Period Explained

Updated 11 October 2026 · Fact-checked

The payback period is the time a project takes to recover its initial outlay from its net cash inflows. The discounted payback period does the same using the present values of those cash flows. Add up cumulative (discounted) cash flows until they reach zero, then interpolate within the final year.

Understand Payback Period and Discounted Payback Period

A project costs money now and returns money later. The payback period answers a simple question: how long until I get my money back? You add the net cash flows year by year until the running total reaches the initial outlay.

The simple payback ignores the time value of money. ₹1,00,000 received in year 4 counts the same as ₹1,00,000 received in year 1. The discounted payback period fixes this. You first discount each cash flow at the stated interest rate, then find when the cumulative present value reaches the outlay. Because discounting shrinks later cash flows, the discounted payback is never shorter than the simple payback when the rate is positive and cash flows are positive.

Both measures are usually found by linear interpolation within the year in which the cumulative total crosses zero. This assumes cash flows arrive evenly through that year. State this assumption in your answer. If cash flows are received at year-end only, a strict reading says the project pays back at the end of that year. Follow the wording of the question.

The limitations matter as much as the calculation. Payback ignores all cash flows after the payback date, so it can favour a project that returns quickly but earns little overall. Simple payback ignores timing and the cost of capital. Discounted payback allows for interest but still ignores later cash flows. Neither gives the profit from the project. That is why NPV and IRR are the main appraisal tools, with payback used as a secondary check on liquidity and risk.

Key rules to remember

Payback period (cumulative method): Find the smallest n such that Σ(t=1 to n) Ct ≥ C0; C0 is the initial outlay and Ct the net cash inflow at time t. Interpolate within year n.
Interpolated payback: Payback = (n − 1) + (C0 − cumulative inflow to time n−1) ÷ Cn; Assumes Cn is received evenly through year n. Use the cash flow of that year only in the denominator.
Discounted payback period: Find the smallest n such that Σ(t=1 to n) Ct × vᵗ ≥ C0, where v = 1 ÷ (1 + i); Discount each cash flow first, then accumulate. Interpolate using the discounted cash flow of year n.
Discounted payback with varying rates: PV of Ct = Ct × v(t), using the discount factor for time t; Use the given spot rates or force of interest if the question does not give a single rate.
Link to NPV: NPV at discounted payback date = 0 on cash flows up to that date; Discounted payback is the time at which the NPV of the project, counting only flows to that date, reaches zero.

How to solve Payback Period and Discounted Payback Period questions

Use this method for any payback question. Set it out in a table so the marker can follow your working.

1Write down the initial outlay C0 and the net cash flow in each period. Net means inflows minus any running costs.
2Check whether the question wants simple or discounted payback, and note the interest rate.
3For discounted payback, compute the discount factor vᵗ for each period and multiply it by the cash flow.
4Build a cumulative column of cash flows (or discounted cash flows) and compare it with C0.
5Identify the year in which the cumulative total first reaches or passes C0.
6Interpolate: take the unrecovered amount at the start of that year and divide by that year's cash flow (or discounted cash flow).
7Add the whole years completed to the fraction and state the answer in years, with the even-flow assumption.
8If asked, comment on limitations or compare with NPV and IRR.

Quickest way: Cumulative table with running balance

When to use it: Use for most MCQs and short written parts where cash flows are given year by year.

Start with the balance −C0.
Add each year's (discounted) cash flow to the balance.
Stop when the balance turns from negative to positive.
Fraction of final year = negative balance just before ÷ that year's (discounted) flow.
For discounted payback, compute discount factors once with a calculator memory: multiply by v repeatedly.
Sense-check: discounted payback must be at least the simple payback.

Common mistakes in Payback Period and Discounted Payback Period

Discounting the cumulative total instead of each cash flow
Students accumulate first because simple payback works that way.
Fix: Discount every cash flow to time 0 individually, then accumulate the present values.
Using the cumulative flow in the interpolation denominator
The cumulative column is in front of you and looks like the right figure.
Fix: Divide the unrecovered balance by the cash flow of the crossing year only.
Reporting the year in which payback occurs instead of the fraction
Students stop once the balance turns positive.
Fix: Interpolate unless the question says cash flows arrive only at year-end.
Saying payback measures profitability
A short payback feels like a good project.
Fix: Say it measures speed of recovery and liquidity only. It ignores flows after payback.
Claiming discounted payback removes all limitations
It includes interest, so it seems complete.
Fix: State that it still ignores cash flows after the payback date and depends on the chosen rate.
Forgetting that a project may never pay back on a discounted basis
Students assume the total of undiscounted inflows decides the answer.
Fix: Check the total present value of inflows against C0. If it is less, there is no discounted payback.

Worked examples

Example 1

A project costs ₹10,00,000 now and returns net cash flows of ₹3,00,000, ₹4,00,000, ₹5,00,000 and ₹2,00,000 at the end of years 1 to 4. Find the simple payback period, assuming flows arrive evenly through each year.

Show the solution

Cumulative inflows: year 1 = 3,00,000; year 2 = 7,00,000; year 3 = 12,00,000.
The total passes ₹10,00,000 during year 3.
Unrecovered at start of year 3 = 10,00,000 − 7,00,000 = 3,00,000.
Fraction of year 3 = 3,00,000 ÷ 5,00,000 = 0.6.
Payback = 2 + 0.6 = 2.6 years.

Answer: Simple payback period = 2.6 years.

Example 2

Using the same project, find the discounted payback period at 10% per annum effective.

Show the solution

Discount factors: v = 0.909091, v² = 0.826446, v³ = 0.751315, v⁴ = 0.683013.
Present values: year 1 = 3,00,000 × 0.909091 = 2,72,727; year 2 = 4,00,000 × 0.826446 = 3,30,579; year 3 = 5,00,000 × 0.751315 = 3,75,657; year 4 = 2,00,000 × 0.683013 = 1,36,603.
Cumulative PV: year 1 = 2,72,727; year 2 = 6,03,306; year 3 = 9,78,963; year 4 = 11,15,566.
The total passes ₹10,00,000 during year 4.
Unrecovered at start of year 4 = 10,00,000 − 9,78,963 = 21,037.
Fraction of year 4 = 21,037 ÷ 1,36,603 = 0.154.
Discounted payback = 3 + 0.154 = 3.15 years (to 2 decimal places).

Answer: Discounted payback period ≈ 3.15 years, longer than the simple payback of 2.6 years.

Exam tips

Show a table with columns for time, cash flow, discount factor, present value and cumulative total. It earns method marks even if arithmetic slips.
State the assumption that cash flows arise evenly within the year when you interpolate.
When asked to compare or comment, mention both ignoring later cash flows and ignoring (or only partly allowing for) the time value of money.
In MCQs, check the rate and the timing of the first cash flow before calculating. Small changes shift the answer to a different year.
Link to NPV: if the discounted payback is within the project term, the NPV at that rate is positive.

Practice questions from Project appraisal

Payback Period and Discounted Payback Period in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Payback Period and Discounted Payback Period: frequently asked questions

What is the difference between payback period and discounted payback period?

Payback adds up raw cash flows until the outlay is recovered. Discounted payback first converts each cash flow to present value at the given interest rate. Discounted payback is longer for positive rates and positive cash flows.

How do I calculate discounted payback period?

Discount each cash flow using vᵗ, build a cumulative present value total, and find the year it reaches the initial outlay. Then interpolate in that year using the unrecovered amount divided by that year's present value.

What are the disadvantages of the payback period?

It ignores cash flows after the payback date and, in its simple form, the time value of money. It also gives no measure of total profit and depends on a cut-off the investor chooses.

Can a project have no discounted payback period?

Yes. If the total present value of all inflows is less than the initial outlay, the cumulative discounted total never reaches zero. The project also has a negative NPV at that rate.