Strategic Management and Corporate Finance · Project Evaluation

Discounted Techniques: NPV, PI and IRR in Project Evaluation

Updated 11 October 2026 · Fact-checked

NPV, PI and IRR are discounted cash flow techniques that value a project's cash flows at today's money. NPV is the present value of inflows minus the outlay. PI is that present value divided by the outlay. IRR is the rate at which NPV is zero. Accept a project if NPV > 0, PI > 1, or IRR > cost of capital.

Understand Discounted Techniques: NPV, PI and IRR

Money received later is worth less than money received today, because you could invest today's money and earn a return. Discounted techniques respect this. They convert every future cash flow into its present value using a discount rate, which is usually the project's cost of capital.

Net Present Value (NPV) adds the present values of all cash inflows and subtracts the initial outlay. A positive NPV means the project earns more than the required return, so it adds to shareholder wealth. NPV gives an absolute rupee figure.

Profitability Index (PI) is a ratio: present value of inflows divided by present value of outflows. It tells you the value created per rupee invested. It is useful when you compare projects of different sizes.

Internal Rate of Return (IRR) is the discount rate that makes NPV exactly zero. It is the project's own rate of return. You compare it with the cost of capital. Because IRR cannot be solved directly for uneven cash flows, you find it by trial and then interpolation.

For a normal project (one outflow at the start, then inflows), the three methods give the same accept or reject answer for a single project. They can disagree when you rank mutually exclusive projects. That is covered in the NPV vs IRR conflicts topic.

Key rules to remember

Net Present Value: NPV = Σ [Ct ÷ (1 + k)^t] − C0; Ct is the cash inflow in year t, k is the discount rate, C0 is the initial outlay. Accept if NPV > 0.
Profitability Index: PI = PV of cash inflows ÷ PV of cash outflows (initial outlay); Also PI = 1 + NPV ÷ outlay when the outlay is all at time zero. Accept if PI > 1.
Net PI: Net PI = PI − 1 = NPV ÷ outlay; Accept if Net PI > 0.
IRR definition: Σ [Ct ÷ (1 + r)^t] − C0 = 0; r is the IRR. Accept if IRR > cost of capital (required rate).
Interpolated IRR: IRR = L + [NPV at L ÷ (NPV at L − NPV at H)] × (H − L); L is the lower trial rate with positive NPV, H is the higher rate with negative NPV. The result is an approximation.
Annuity shortcut for IRR: Annuity factor = Initial outlay ÷ Annual inflow; For equal annual inflows, find the rate whose annuity factor for the project life equals this value.
Modified IRR (MIRR): MIRR = (Terminal value of inflows ÷ PV of outflows)^(1/n) − 1; Terminal value compounds inflows to year n at the reinvestment rate. Outflows are discounted at the financing rate. It removes the assumption that inflows are reinvested at the IRR.

How to solve Discounted Techniques: NPV, PI and IRR questions

Use this sequence for any NPV, PI or IRR question. Work in a neat table so the examiner can follow each mark.

1List the cash flows year by year. Use after-tax operating cash flows and include working capital, salvage value and any other terminal flows.
2Note the discount rate given (cost of capital or required return). Pick the present value factors from the table in the question.
3Multiply each year's cash flow by its discount factor. For equal annual inflows, use the annuity factor once.
4Add the present values of inflows. Subtract the outlay to get NPV. Divide inflows by outlay to get PI.
5For IRR, if inflows are equal, find the annuity factor (outlay ÷ inflow) and read the rate from the table. If uneven, compute the average inflow, estimate a rate, and test.
6Adjust the trial rate until you have one rate with positive NPV and one with negative NPV. Then interpolate.
7State the decision rule for each measure: NPV > 0, PI > 1, IRR > cost of capital.
8Conclude clearly: accept or reject, and for competing projects, say which method you rely on and why.

Quickest way: Annuity factor shortcut and bracketing

When to use it: Use when inflows are equal each year, or when you must estimate a starting rate for uneven inflows under time pressure.

For equal inflows, divide outlay by annual inflow to get the target annuity factor.
Run along the row for the project life in the table. Find the two rates whose factors are just above and below the target.
Interpolate between those two rates.
For uneven inflows, find the average inflow, divide the outlay by it, and use that factor to pick a first trial rate. Test it, then move up if NPV is positive and down if negative.
Check the sign: NPV at the lower rate must be positive and at the higher rate negative, before you interpolate.

Common mistakes in Discounted Techniques: NPV, PI and IRR

Forgetting to subtract the initial outlay and reporting the present value of inflows as NPV.
Students stop once the discounted inflows are added.
Fix: Write NPV = PV of inflows − outlay as the last line of every table.
Using PI = NPV ÷ outlay and calling it PI.
The formulas look similar, and Net PI is easy to confuse with PI.
Fix: PI is inflows ÷ outlay. NPV ÷ outlay is Net PI, which is PI − 1.
Interpolating with two rates that both give positive NPV.
Students rush and do not check signs.
Fix: Bracket the IRR. One trial must give a positive NPV and the other a negative NPV.
Using the wrong sign or order in the interpolation formula, so the IRR falls outside the two trial rates.
The formula is memorised without the logic.
Fix: Remember that IRR lies between L and H. Add to L the fraction NPV at L ÷ (total gap between the two NPVs) times the rate gap.
Treating IRR as the exact answer and the reinvestment assumption as irrelevant.
Interpolation gives a clean figure, and students forget it is an approximation.
Fix: Say that interpolation gives an approximate IRR. Mention that IRR assumes inflows are reinvested at the IRR, and that MIRR corrects this.
Including depreciation as a cash flow or ignoring salvage value and working capital recovery.
The cash flow estimation step is rushed.
Fix: Use cash flows only. Add back non-cash charges after tax and include terminal flows in the final year.

Worked examples

Example 1

A company is considering a project that needs an outlay of ₹10,00,000. Cash inflows are ₹3,00,000, ₹4,00,000, ₹4,00,000 and ₹3,00,000 in years 1 to 4. The cost of capital is 10%. PV factors at 10%: 0.9091, 0.8264, 0.7513, 0.6830. Compute NPV and PI and advise.

Show the solution

Year 1: 3,00,000 × 0.9091 = ₹2,72,730.
Year 2: 4,00,000 × 0.8264 = ₹3,30,560.
Year 3: 4,00,000 × 0.7513 = ₹3,00,520.
Year 4: 3,00,000 × 0.6830 = ₹2,04,900.
Total PV of inflows = 2,72,730 + 3,30,560 + 3,00,520 + 2,04,900 = ₹11,08,710.
NPV = 11,08,710 − 10,00,000 = ₹1,08,710.
PI = 11,08,710 ÷ 10,00,000 = 1.109 (about 1.11).

Answer: NPV is ₹1,08,710 (positive) and PI is about 1.11 (greater than 1). Accept the project, as it earns more than the 10% required return.

Example 2

A project costs ₹2,00,000 and gives equal annual inflows of ₹1,00,000 for 3 years. Find the IRR by interpolation. Cumulative PV annuity factors for 3 years: 20% = 2.1064; 25% = 1.9520.

Show the solution

Target annuity factor = 2,00,000 ÷ 1,00,000 = 2.00.
This lies between the factors at 20% (2.1064) and 25% (1.9520), so IRR is between 20% and 25%.
NPV at 20% = 1,00,000 × 2.1064 − 2,00,000 = +₹10,640.
NPV at 25% = 1,00,000 × 1.9520 − 2,00,000 = −₹4,800.
IRR = 20% + [10,640 ÷ (10,640 + 4,800)] × (25% − 20%).
10,640 ÷ 15,440 = 0.6891.
IRR = 20% + 0.6891 × 5% = 20% + 3.45% = 23.45%.

Answer: IRR is approximately 23.45%. If the cost of capital is below this figure, for example 15%, accept the project. The result is an interpolated approximation.

Exam tips

Draw a table with columns for year, cash flow, discount factor and present value. Marks are given for method even if the arithmetic slips.
Always state the decision rule and give a one-line conclusion. Case-style questions reward the recommendation, not just the number.
Use the discount factors given in the question exactly as printed, and mention that the IRR from interpolation is approximate.
If the question gives the MIRR data, compound the inflows to the end of the project at the reinvestment rate first, then solve for the rate.
Be ready to explain the difference between NPV and IRR in words: NPV gives a rupee value at the cost of capital, IRR gives a percentage return and assumes reinvestment at the IRR.

Practice questions from Project Evaluation

Discounted Techniques: NPV, PI and IRR in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Discounted Techniques: NPV, PI and IRR: frequently asked questions

What is the difference between NPV and IRR?

NPV is the rupee value created after discounting at the cost of capital. IRR is the discount rate at which NPV equals zero. NPV assumes reinvestment at the cost of capital, while IRR assumes reinvestment at the IRR itself.

How do I calculate IRR by interpolation?

Find one rate that gives a positive NPV and another that gives a negative NPV. Then apply: IRR = L + NPV at L ÷ (NPV at L − NPV at H) × (H − L). Check that the answer lies between the two rates.

What is the decision rule for the profitability index?

Accept a project if PI is greater than 1, which means NPV is positive. Reject it if PI is less than 1. If PI equals 1, the project only earns the required return.

What is the MIRR formula?

MIRR = (Terminal value of inflows ÷ PV of outflows)^(1/n) − 1. Compound inflows to year n at the reinvestment rate and discount outflows at the financing rate. It avoids the IRR assumption of reinvestment at the IRR.