Investment appraisal calculator
One project at 10%
NPV: £15,750
A positive NPV: at 10%, the project earns more than it costs in today's money.
- Payback
- 2 years 6 months
- ARR
- 12.5%
- NPV
- £15,750
| Year | Net cash flow | Cumulative | Discount factor | Present value |
|---|---|---|---|---|
| 0 | −£80,000 | −£80,000 | 1.000 | −£80,000 |
| 1 | £30,000 | −£50,000 | 0.909 | £27,270 |
| 2 | £30,000 | −£20,000 | 0.826 | £24,780 |
| 3 | £40,000 | £20,000 | 0.751 | £30,040 |
| 4 | £20,000 | £40,000 | 0.683 | £13,660 |
Payback: 2 years 6 months
- After 2 years the running total is £60,000.
- Still to recover: £80,000 − £60,000 = £20,000.
- Year 3 brings £40,000, so £20,000 ÷ £40,000 = 0.5 of that year, if its cash arrives evenly.
- Payback = 2 + 0.5 = 2.5 years (2 years 6 months).
ARR: 12.5%
- Total net inflows = £120,000.
- Total profit = £120,000 − £80,000 = £40,000.
- Average annual profit = £40,000 ÷ 4 = £10,000.
- ARR = £10,000 ÷ £80,000 × 100 = 12.5%.
NPV: £15,750
- Year 1: £30,000 × 0.909 = £27,270.
- Year 2: £30,000 × 0.826 = £24,780.
- Year 3: £40,000 × 0.751 = £30,040.
- Year 4: £20,000 × 0.683 = £13,660.
- Total present value = £95,750.
- NPV = £95,750 − £80,000 = £15,750.
Questions people ask
How do you calculate payback with a part year?
Add the inflows until you pass the cost. If a £80,000 machine brings in £30,000, £30,000 and then £40,000, after two years £60,000 is back and £20,000 is still to recover. £20,000 ÷ £40,000 = 0.5, so payback is 2.5 years, or 2 years 6 months.
What is the ARR formula for Edexcel A-level Business?
ARR = average annual profit ÷ initial investment × 100. Take the cost off the total net inflows once, divide by the number of years, then divide by the initial cost. £120,000 of inflows over 4 years on an £80,000 machine gives £40,000 profit, £10,000 a year, and an ARR of 12.5%.
How do you work out NPV?
Multiply each year's net cash flow by its discount factor, add up the present values and subtract the initial cost. A positive NPV means the project earns more than the discount rate; a negative NPV means it earns less.
Why do payback, ARR and NPV sometimes disagree?
They measure different things. Payback measures speed and ignores cash after payback; ARR averages profit and ignores timing; NPV measures total value in today's money. A firm short of cash may prefer the faster payback, while a firm focused on long-term value will lean on NPV.
Should I include the initial cost when I discount the cash flows?
No. The cost is paid now, in year 0, so its discount factor is 1. Discount the future inflows and take the cost off once at the end.
How we work this out
What it does
Payback, average rate of return and net present value for one project or two, with every line of working.
The three investment appraisal methods in Edexcel A-level Business (9BS0) 3.3.2: payback, average rate of return (ARR) and net present value (NPV), for up to eight years of net cash flows.
Method
- Payback adds the net cash inflows year by year until the running total reaches the initial cost. The part year is the amount still to recover divided by that year's inflow, which assumes the cash arrives evenly through the year.
- ARR takes the initial cost off the total net inflows once to give total profit, divides by the number of years for the average annual profit, then divides by the initial investment and multiplies by 100.
- NPV multiplies each year's net cash flow by its discount factor, adds the present values, and takes off the initial cost, which is paid now and is not discounted.
- For a discount rate of r%, the factor for year t is 1 ÷ (1 + r/100)^t, rounded to three decimal places, as exam tables print them.
- With two projects, the calculator says which one each method prefers and whether the methods agree.