Investment Appraisal: Payback, ARR, NPV and IRR Explained
How businesses decide whether a project is worth the money, with two worked examples.
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The example projects
The cost of capital (discount rate) is 10%. Cash flows are assumed to arrive at the end of each year.
| Year 0 (cost) | Year 1 | Year 2 | Year 3 | Year 4 | |
|---|---|---|---|---|---|
| Project A | (50,000) | 20,000 | 20,000 | 20,000 | – |
| Project B | (40,000) | 15,000 | 18,000 | 20,000 | 12,000 |
1. Payback period
Payback is the time needed for cash inflows to recover the initial investment.
- Project A: after 2 years, 40,000 is recovered. The last 10,000 takes 10,000 ÷ 20,000 = 0.5 of year 3. Payback = 2.5 years.
- Project B: after 2 years, 33,000 is recovered. The last 7,000 takes 7,000 ÷ 20,000 = 0.35 of year 3. Payback = 2.35 years.
Weaknesses: it ignores cash flows after the payback date and ignores the time value of money.
2. Accounting rate of return (ARR)
Project B (no residual value): total inflows are 65,000, so total profit over 4 years = 65,000 − 40,000 = 25,000. Average annual profit = 25,000 ÷ 4 = 6,250. Average investment = 40,000 ÷ 2 = 20,000. ARR = 6,250 ÷ 20,000 × 100 = 31.25%. (Using the initial investment instead gives 6,250 ÷ 40,000 = 15.6%. State which basis you use.)
3. Net present value (NPV)
Money received later is worth less than money today. NPV discounts each cash flow at the cost of capital and adds them up.
| Year | Discount factor at 10% | Project A cash flow | A present value | Project B cash flow | B present value |
|---|---|---|---|---|---|
| 0 | 1.0000 | (50,000) | (50,000) | (40,000) | (40,000) |
| 1 | 0.9091 | 20,000 | 18,182 | 15,000 | 13,637 |
| 2 | 0.8264 | 20,000 | 16,528 | 18,000 | 14,875 |
| 3 | 0.7513 | 20,000 | 15,026 | 20,000 | 15,026 |
| 4 | 0.6830 | – | – | 12,000 | 8,196 |
| Net present value | (264) | 11,734 | |||
Decision rule: accept projects with a positive NPV. Project B (+11,734) should be accepted. Project A (−264) is marginally below the required 10% return, even though its payback of 2.5 years looks reasonable. That is the weakness of payback: it ignores the time value of money.
4. Internal rate of return (IRR)
The IRR is the discount rate that makes NPV equal zero. Accept a project if its IRR is above the cost of capital. For Project A, the NPV at 9% is about +626 and at 10% is −264, so the IRR lies between them, at about 9.7%. That is below the 10% cost of capital, which agrees with the negative NPV.
Comparing the methods
| Method | Strength | Weakness |
|---|---|---|
| Payback | Simple; shows liquidity and risk | Ignores later cash flows and the time value of money |
| ARR | Easy; uses accounting profit | Ignores timing; depends on accounting policies |
| NPV | Uses all cash flows and time value; shows value added | Needs a discount rate; absolute amount |
| IRR | A percentage that is easy to compare with the cost of capital | Can mislead for unusual cash flows or when comparing projects of different size |
Common mistakes
- Forgetting the initial outlay at year 0, which is not discounted.
- Including depreciation or sunk costs in NPV cash flows. Use only future cash flows.
- Using the wrong discount factor. Match the year and the rate.
- Relying on payback alone. A quick payback does not mean a project adds value.
Quick check
1. A project costs 30,000 and returns 12,000 a year for 4 years. What is the payback period?
After 2 years, 24,000 is recovered. The last 6,000 takes 6,000 ÷ 12,000 = 0.5 years. Payback = 2.5 years.
2. A project has an NPV of +5,000 at the company’s cost of capital. Should it be accepted?
Yes. A positive NPV means the project earns more than the required return and adds value.
Practise with Problem 8 (payback and NPV).
Frequently asked questions
What is net present value?
The sum of all future cash flows from a project discounted to today’s value, minus the initial investment. A positive NPV means the project adds value.
Why is NPV considered better than payback?
NPV uses all the cash flows and accounts for the time value of money. Payback ignores cash flows after the payback date and treats a pound today as equal to a pound later.
What is the internal rate of return?
The discount rate at which a project’s NPV is zero. A project is acceptable if its IRR exceeds the cost of capital.
Keep learning
This lesson is for general learning. Terminology and layouts vary by syllabus and country. Discount factors are rounded to four decimal places.
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