Profitability index and internal rate of return

Profitability index (PI)

PI = present value of future net cash inflows / initial investment

• PI above 1 means a positive NPV: accept.
• It shows the return per £1 invested, so it ranks projects when capital is limited (capital rationing): choose the projects with the highest PI first.

Some texts use NPV / initial investment instead (above 0 is acceptable); the June 2025 examiners accepted both methods, so state the formula you use.

Internal rate of return (IRR)

The IRR is the discount rate that makes NPV = 0: the project's own rate of return.

1. Calculate NPV at a lower rate (giving a positive NPV) and at a higher rate (giving a negative NPV).

2. Interpolate:

IRR = L + [NPV at L / (NPV at L - NPV at H)] x (H - L)

where L and H are the lower and higher rates. (This is the formula in the WAC12 mark schemes.)

Decision: accept if IRR is above the cost of capital (WACC).

Worked IRR

Cost £120,000; net inflows £40,000 a year for 4 years.

Comparing the methods

• IRR gives a percentage that managers find easy to compare with the cost of borrowing.
• But interpolation gives an approximation (the NPV curve is not a straight line), and IRR ignores the size of the project: a small project can have a high IRR but a small NPV. If NPV and IRR disagree when choosing between projects, NPV is preferred because it measures the increase in wealth.
• PI is useful when funds are limited but, like IRR, does not show the absolute gain.

Worked example

Using the table, calculate the IRR and the profitability index at 10%.

1. IRR = 10 + [6,760 / (6,760 - (-3,480))] x 4
2. = 10 + 0.6602 x 4 = 12.64%
3. PI = 126,760 / 120,000 = 1.06

Answer: IRR = 12.64%; PI = 1.06

Check yourself

1. The present value of a project's future net cash inflows is £345,000 and its initial cost is £300,000. Calculate the profitability index.
   Show answer

   1.15. 345,000 / 300,000 = 1.15.

2. A project has an NPV of £18,000 at 8% and -£6,000 at 14%. Estimate the IRR to 1 decimal place.
   Show answer

   12.5 %. 8 + 18,000 / 24,000 x 6 = 12.5%.

3. NPV at 10% is £4,250 and NPV at 15% is -£2,750. Estimate the IRR to 2 decimal places.
   Show answer

   13.04 %. 10 + 4,250 / 7,000 x 5 = 13.04%.

4. A project costs £500,000 and has an NPV of £60,000. Calculate the PI using PV of inflows / initial cost.
   Show answer

   1.12. PV of inflows = 560,000; PI = 560,000 / 500,000 = 1.12.

5. A company has £1,000,000 to invest and several projects with positive NPVs costing more than that in total. Which measure helps rank them?
   • Payback period alone
   • Gross profit margin
   • Dividend cover
   • Profitability index
   Show answer

   Profitability index. PI shows the NPV generated per £1 invested.

6. A project's IRR is 13.5% and the company's WACC is 11%. What does this suggest?
   • Reject: IRR should be below WACC
   • Accept: the project's return exceeds the cost of capital
   • The NPV at 11% is negative
   • The payback period is 13.5 years
   Show answer

   Accept: the project's return exceeds the cost of capital. IRR above the cost of capital means NPV at that cost is positive.

7. Project A has the higher NPV but project B has the higher IRR. They are mutually exclusive. Which should usually be chosen?
   • B, because a percentage is always better
   • Neither
   • Whichever has the shorter life
   • A, because NPV measures the increase in shareholders' wealth
   Show answer

   A, because NPV measures the increase in shareholders' wealth. NPV is the preferred method when rankings conflict.

Practise with instant feedback Print this lesson

Sources

• Pearson Edexcel International Advanced Subsidiary/Advanced Level in Accounting specification (XAC11/YAC11), Issue 2
• Pearson Edexcel IAL Accounting WAC12 Unit 2 mark scheme, June 2022
• Pearson Edexcel IAL Accounting WAC12 Unit 2 mark scheme, October 2024
• Pearson Edexcel IAL Accounting WAC12 examiners' report, June 2025

Last updated 8 November 2026. Spotted a mistake? Tell us.