Investment project appraisal: How we calculate
Assess net present value (NPV) and payback from three annual cash flows.
How we calculate
Three annual cash flows are discounted to project start. Net present value (NPV) = present value − initial investment. Internal rate of return (IRR) is shown only for conventional nonnegative later cash flows; this is not dated XIRR. Cash flows occur at each year-end. Simple payback uses undiscounted cash flows and assumes a uniform cash flow within the year when payback is reached. IRR is the discount rate at which these cash flows have zero NPV. It is neither a simple average nor a guaranteed return; NPV accounts for the time value of money and is not accounting profit.
What the figures mean
- Cash flows valued today, less initial outlay (NPV)
Future receipts and payments are valued today using the chosen required return, then the initial investment is subtracted. This is not the undiscounted profit.
Simple example: Invest €100 today and receive €120 after one year at a required 10%: 120 / 1.10 − 100 ≈ €9.09.
- Calculated annual investment return (IRR)
The annual rate at which future cash flows valued today equal the initial outlay. It is a scenario calculation, not a guaranteed rate; some cash-flow patterns have no unique result.
Simple example: Invest €100 now and receive €120 one year later: the calculated return is 20%.
- Valuing future money today
A future amount is reduced using the chosen required return to compare it with money today. This is discounting, not a shop discount or solely an inflation adjustment.
Simple example: €110 in one year at a 10% rate corresponds to €100 today.
- Receipts per euro invested
Future net cash flows valued today divided by the initial outlay. This profitability index depends on the chosen discount rate.
Simple example: €100 invested and €110 present value of future cash flows give an index of 1.10.
Worked example
These illustrative inputs let you check the method. They are not figures for a real company or automatically current tax rates.
Inputs
- Initial investment
- 100,000
- Discount rate (%)
- 10
- Year 1 cash flow
- 30,000
- Year 2 cash flow
- 40,000
- Year 3 cash flow
- 50,000
Results
- Net present value (NPV)
- -2,103.6814
- Present value of flows
- 97,896.3186
- Profitability index
- 0.979
- Internal rate of return (IRR)
- 8.8963
- Payback · years
- 2.6
Change assumptions in the calculator and compare outcomes. Money follows your input unit; figures from different periods need adjustment before comparison.