How to Calculate Payback Period, ARR and NPV
Learn how to calculate payback period, average rate of return and NPV for A Level Business, with formulas, a worked example and a key exam mistake to avoid.
Payback period tells you how long it takes to recover the initial investment. Average rate of return (ARR) measures average annual profit as a percentage of the initial investment. Net present value (NPV) measures the value of future net cash flows after discounting them and subtracting the initial investment.
How to calculate each measure
- Payback period: Add the annual net cash inflows until they equal the initial investment. If payback occurs partway through a year, divide the amount still needed by that year's net cash inflow. This gives a fraction of a year, assuming cash arrives evenly throughout the year.
- ARR: Find average annual profit, then calculate ARR=average annual profitinitial investment×100%\text{ARR}=\frac{\text{average annual profit}}{\text{initial investment}}\times 100\%ARR=initial investmentaverage annual profit×100%.
- NPV: Multiply each year's net cash flow by its discount factor, add the resulting present values, then subtract the initial investment. A discount factor adjusts a future amount to reflect that money received later is worth less than money received now.
Worked example
Suppose a project costs £10,000\pounds 10{,}000£10,000 and generates a net cash inflow of £4,000\pounds 4{,}000£4,000 in each of four years. For payback, assume inflows arrive evenly during each year; for NPV, treat them as arriving at year-end. Assume no residual value, other costs or accounting adjustments, and a discount rate of 10%10\%10%.
After two years, the business has recovered £8,000\pounds 8{,}000£8,000. It needs another £2,000\pounds 2{,}000£2,000, which is half of the third year's inflow. Payback is 2.52.52.5 years.
Total net cash inflows are £16,000\pounds 16{,}000£16,000, so average annual profit is (£16,000−£10,000)/4=£1,500(\pounds 16{,}000-\pounds 10{,}000)/4=\pounds 1{,}500(£16,000−£10,000)/4=£1,500. ARR is (£1,500/£10,000)×100%=15%(\pounds 1{,}500/\pounds 10{,}000)\times 100\%=15\%(£1,500/£10,000)×100%=15%.
For NPV, discount each year's inflow separately:
NPV=∑t=14£4,000(1.10)t−£10,000≈£2,679.46 \text{NPV}=\sum_{t=1}^{4}\frac{\pounds 4{,}000}{(1.10)^t}-\pounds 10{,}000\approx\pounds 2{,}679.46 NPV=t=1∑4(1.10)t£4,000−£10,000≈£2,679.46The key exam mistake is treating ARR and NPV as though they use the same figures: ARR uses average annual profit; NPV uses discounted net cash flows. Payback ignores inflows after recovery, while ARR does not reflect when cash arrives. A positive NPV means discounted inflows exceed the initial investment.
