How do I calculate NPV when the cash flows are different every year?
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The question
My corporate finance assignment gives a project costing £100,000 with cash inflows of £30,000, £40,000, £50,000 and £20,000 over four years. The required return is 10%.
Every example in my notes uses an annuity with the same cash flow each year, so I do not know how to handle it when they change. Do I still use one formula?
Short answer
Discount each year's cash flow separately using 1 / (1 + r)^t, add the present values together, then subtract the initial investment. For this project the NPV is about £11,557, so it should be accepted at a 10% required return.
Full expert answer
Corporate finance tutor
MSc Accounting and Finance, ACCA
The annuity formula is a shortcut that only works when every cash flow is identical. When they differ, you go back to first principles and discount each year on its own. It is more arithmetic, not a different idea.
Step 1: find the discount factor for each year
The discount factor for year t is 1 / (1 + r)^t. At 10% that gives 0.9091 for year 1, 0.8264 for year 2, 0.7513 for year 3 and 0.6830 for year 4.
Step 2: discount each cash flow
- Year 1: £30,000 × 0.9091 = £27,273
- Year 2: £40,000 × 0.8264 = £33,058
- Year 3: £50,000 × 0.7513 = £37,566
- Year 4: £20,000 × 0.6830 = £13,660
Step 3: add them up and subtract the investment
The present values total £111,557. Subtract the £100,000 paid today, which is not discounted because it happens at time zero, and the NPV is roughly £11,557.
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