Management Accounting · Asset budgeting and investment appraisal

Discounted Payback and Comparing Investment Appraisal Methods

Updated 11 October 2026 · Fact-checked

Discounted payback is the time a project takes to recover its initial investment from discounted cash flows. Discount each year's cash flow at the cost of capital, build a cumulative total, then interpolate within the recovery year. To compare methods, remember NPV is the best guide to wealth, while payback and ARR are simpler but weaker.

Understand Discounted Payback and Appraisal Method Comparison

Payback tells you how long a project takes to get its money back. Its big flaw is that it treats $1 received in year 3 the same as $1 received today. Discounted payback fixes this. You first convert each cash flow to present value using the cost of capital, then find when the cumulative present values reach the initial investment.

Because discounted cash flows are smaller than undiscounted ones, discounted payback is always longer than ordinary payback (for a positive cost of capital). If a project never recovers its cost on a discounted basis, its NPV over that period is negative. A project with a discounted payback inside its life has a positive NPV over its whole life, provided later cash flows are not negative.

Discounted payback still has weaknesses. It ignores cash flows after the payback point, so it can reject a project with large later inflows. It also needs a target period, which is a management choice. It does consider risk and liquidity better than NPV does in one sense: it favours early cash.

The exam also asks you to compare all the methods. Think of two groups. Cash flow and time value methods are NPV, IRR and discounted payback. Simple methods are payback and ARR. ARR uses accounting profit, not cash, and ignores timing. NPV gives an absolute dollar gain in wealth and is the theoretically best method. IRR gives a percentage return that managers find easy to understand, but it can mislead when projects are mutually exclusive or cash flows change sign more than once.

Key formulas to remember

Present value of a cash flow: PV = cash flow × 1 ÷ (1 + r)^n; r is the cost of capital as a decimal and n is the year. In the exam you normally use the discount factor from the tables given.
Discounted payback period: DPP = last full year before recovery + (unrecovered investment ÷ PV of cash flow in the recovery year); Use cumulative present values. This assumes cash arrives evenly through the recovery year.
Net present value: NPV = Σ PV of cash inflows − initial investment; Accept if NPV is greater than zero. Among mutually exclusive projects, choose the highest positive NPV.
Internal rate of return (interpolation): IRR = a + [NPV at a ÷ (NPV at a − NPV at b)] × (b − a); a is the lower rate and b the higher rate. Accept if IRR is greater than the cost of capital.
Payback period: Payback = last full year before recovery + (unrecovered investment ÷ cash flow in the recovery year); Undiscounted. With equal annual inflows, payback = investment ÷ annual inflow.
Accounting rate of return: ARR = average annual accounting profit ÷ average investment × 100%; Average investment is (initial investment + residual value) ÷ 2. Some questions use initial investment instead, so follow the question wording.

How to solve Discounted Payback and Appraisal Method Comparison questions

Use this method for any discounted payback or method-comparison question.

1Read the question and note the cost of capital, the cash flows, the timing and the exact measure asked for.
2Check that the cash flows are relevant cash flows only. Exclude depreciation and sunk costs, and include working capital and scrap value where given.
3Multiply each year's cash flow by its discount factor to get present values. Keep the initial outlay at year 0 with a factor of 1.
4Add the present values into a running cumulative total and find the year in which the total first covers the investment.
5Interpolate: unrecovered amount at the start of that year ÷ that year's present value. Add this fraction to the previous whole years.
6If the question compares methods, state each decision rule and say which methods give the same advice and which conflict.
7For recommendations, give NPV priority for wealth maximisation, and mention limits such as risk, liquidity and non-financial factors.

Quickest way: Cumulative PV table in one pass

When to use it: Use this for number-entry or multiple-choice questions on discounted payback where time is short.

Write the years across and the discount factors below them from the tables.
Multiply and round each present value to the nearest dollar, then calculate the cumulative total in one line.
Stop as soon as the cumulative total passes the investment. Do not calculate later years.
Compute the fraction once and add it to the whole years. Check that the answer is longer than ordinary payback.
For a theory question, eliminate any option that says payback or ARR uses discounted cash flows, or that IRR gives a dollar gain.

Common mistakes in Discounted Payback and Appraisal Method Comparison

Interpolating with the undiscounted cash flow in the recovery year
Students discount the earlier years correctly but then divide by the original cash flow out of habit.
Fix: Divide the unrecovered amount by the present value of the recovery year's cash flow, never the raw cash flow.
Using the cumulative present value total as the unrecovered amount
Students confuse the running total with what is still outstanding.
Fix: Subtract the cumulative present value at the end of the previous year from the investment to get the amount still to recover.
Including depreciation in the cash flows
Profit figures are given alongside cash flows and depreciation looks like a cost.
Fix: Depreciation is not a cash flow. Use it only for ARR, where accounting profit is needed.
Choosing the project with the highest IRR when projects are mutually exclusive
A higher percentage feels better.
Fix: For mutually exclusive projects, choose the highest positive NPV. IRR ignores the scale of the investment.
Saying payback or ARR considers the time value of money
Students mix up payback with discounted payback.
Fix: Ordinary payback and ARR ignore the time value of money. Only NPV, IRR and discounted payback use discounting.
Giving a decision from discounted payback alone
Students treat the target period as the full answer.
Fix: Note that it ignores cash flows after the payback point, and support the decision with NPV.

Worked examples

Example 1

A project costs $90,000 now and gives cash inflows of $40,000 a year for four years. The cost of capital is 10%. Discount factors are year 1: 0.909, year 2: 0.826, year 3: 0.751, year 4: 0.683. Calculate the discounted payback period and the NPV.

Show the solution

Present values: year 1 = 40,000 × 0.909 = 36,360. Year 2 = 40,000 × 0.826 = 33,040. Year 3 = 40,000 × 0.751 = 30,040. Year 4 = 40,000 × 0.683 = 27,320.
Cumulative present values: year 1 = 36,360. Year 2 = 69,400. Year 3 = 99,440.
The investment of 90,000 is recovered during year 3. Unrecovered after year 2 = 90,000 − 69,400 = 20,600.
Fraction of year 3 = 20,600 ÷ 30,040 = 0.686.
Discounted payback = 2 + 0.686 = 2.69 years, about 2 years and 8 months.
Total present value of inflows = 36,360 + 33,040 + 30,040 + 27,320 = 126,760.
NPV = 126,760 − 90,000 = 36,760.

Answer: Discounted payback is about 2.69 years and NPV is $36,760. Ordinary payback would be 90,000 ÷ 40,000 = 2.25 years, which is shorter.

Example 2

Two mutually exclusive projects are evaluated at a cost of capital of 10%. Project A has NPV of $50,000, IRR of 14% and payback of 4 years. Project B has NPV of $40,000, IRR of 18% and payback of 2 years. Which should the company choose, and why might the methods disagree?

Show the solution

Both projects have a positive NPV and an IRR above 10%, so both are acceptable on their own.
The projects are mutually exclusive, so only one can be chosen.
NPV measures the absolute increase in shareholder wealth in dollars. A adds $50,000 and B adds $40,000.
IRR is a percentage and ignores the size of the investment. B has the higher IRR, but a higher percentage does not mean a larger dollar gain.
Payback favours B because it returns cash sooner. This matters for liquidity and risk, but payback ignores cash after the payback point and the time value of money.
The methods disagree because they measure different things: dollar wealth, percentage return and speed of recovery.

Answer: Choose Project A, because it has the higher NPV and so adds more to shareholder wealth. Mention that B is better for liquidity and quick recovery, which management may weigh as a non-financial or risk factor.

Exam tips

For discounted payback, show the cumulative present value line. Even in a computer-based test, writing it on your scratch paper makes the answer easy to check.
Always check that the discounted payback is longer than ordinary payback. If it is shorter, you have made an error.
In multiple-response theory questions, test each statement against one fact: does the method use cash flows, does it discount, and does it give a dollar or percentage answer?
If a question says projects are mutually exclusive or capital is not rationed, choose the highest NPV. Do not use IRR to rank them.
Round discount factors and present values as the question instructs, and pick the closest answer if your figure differs slightly from the options.

Practice questions from Asset budgeting and investment appraisal

Discounted Payback and Appraisal Method Comparison in other exams

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

Discounted Payback and Appraisal Method Comparison: frequently asked questions

How do you calculate discounted payback period?

Discount each year's cash flow at the cost of capital and add them up year by year. Find the year in which the cumulative total passes the initial investment. Then divide the amount still unrecovered by that year's present value and add it to the previous whole years.

Is discounted payback better than ordinary payback?

Yes, because it takes account of the time value of money. It still ignores cash flows after the payback point, so it does not measure total profitability. NPV is a better measure of overall value.

Which investment appraisal method is best?

NPV is generally considered the best because it uses all cash flows, allows for the time value of money and shows the dollar gain in shareholder wealth. Other methods can add useful information, such as IRR for a percentage return and payback for liquidity and risk.

What are the main disadvantages of ARR and payback?

Both ignore the time value of money. Payback also ignores cash flows after the payback point. ARR uses accounting profit rather than cash flow and can be affected by the depreciation method used.