Business Finance · Key principles of finance

Investment Appraisal: NPV and IRR Explained

Updated 11 October 2026 · Fact-checked

Investment appraisal tests whether a project is worth doing. NPV discounts all future cash flows at the cost of capital and subtracts the initial outlay; accept if NPV is positive. IRR is the discount rate that gives NPV of zero; accept if it exceeds the required return. Payback measures how fast the outlay is recovered.

Understand Investment Appraisal: NPV and IRR

A company has limited money and many possible projects. Investment appraisal gives a rule to decide which projects add value for shareholders. The core idea is that a rupee today is worth more than a rupee later, so future cash flows must be discounted before you compare them with the cost.

Net present value (NPV) is the present value of all project cash inflows minus the present value of all outflows. It is measured in rupees. A positive NPV means the project earns more than the required return, so it adds that amount of value. NPV is the method that matches the aim of maximising shareholder wealth.

Internal rate of return (IRR) is the discount rate at which NPV equals zero. It is the project's own break-even return. You accept the project if the IRR is higher than the cost of capital (the hurdle rate). IRR is quoted as a percentage, which many managers find easy to read.

Payback period is the time taken for cumulative cash inflows to repay the initial outlay. It is simple and focuses on liquidity and risk, but it ignores the time value of money (in its simple form) and ignores cash flows after the payback date. A discounted version fixes the first problem but not the second.

For a single conventional project (one outflow at the start, then inflows), NPV and IRR give the same accept or reject answer. They can disagree when you rank mutually exclusive projects, when projects differ in scale or timing, or when cash flows change sign more than once. In those cases NPV is the more reliable guide, because it measures absolute value added and implicitly assumes reinvestment at the cost of capital.

Key rules to remember

Net present value: NPV = Σ [CFt ÷ (1 + r)^t], summed from t = 0 to n; CF0 is normally negative (the outlay). r is the cost of capital. Accept if NPV > 0.
Annuity present value: PV = C × [1 − (1 + r)^−n] ÷ r; Use for level cash flows at the end of each year for n years.
Perpetuity present value: PV = C ÷ r; Level cash flow C at the end of each year forever.
IRR condition: Σ [CFt ÷ (1 + IRR)^t] = 0; Accept if IRR > required return, for a conventional project.
IRR by linear interpolation: IRR ≈ r1 + [NPV1 ÷ (NPV1 − NPV2)] × (r2 − r1); NPV1 and NPV2 are computed at two trial rates r1 and r2, ideally one giving a positive and one a negative NPV, close together. The result is an estimate.
Simple payback: Payback = full years before recovery + (unrecovered amount ÷ cash flow in recovery year); Assumes cash flows arise evenly through the year. Use cumulative cash flows.

How to solve Investment Appraisal: NPV and IRR questions

Use this method for any NPV, IRR or payback question.

1Identify the relevant cash flows only: incremental, after-tax if tax is given, and in cash terms. Ignore sunk costs and non-cash items such as depreciation.
2Include working capital and its release at the end, and any scrap value.
3Lay out cash flows by year, starting with t = 0 for the outlay.
4Choose the discount rate: the required return or cost of capital given in the question.
5Discount each flow, or use annuity factors for level flows, and sum to get NPV.
6For IRR, compute NPV at two rates either side of zero and interpolate. State that the answer is an estimate.
7Apply the decision rule: accept if NPV > 0 or IRR > hurdle rate. For payback, compare with the target period.
8For comparisons, rank mutually exclusive projects by NPV, and comment on the limits of each method.

Quickest way: Annuity shortcut and two-rate IRR

When to use it: When cash inflows are level or almost level and you have little time.

Write the outlay and the level inflow C.
Compute NPV = C × annuity factor − outlay in one line.
If asked for IRR, find the annuity factor needed: outlay ÷ C. Then find which rate gives that factor for n years.
For uneven flows, pick two trial rates about 5 percentage points apart, compute both NPVs and interpolate.
Check the sign: a positive NPV at a rate means IRR is higher than that rate.

Common mistakes in Investment Appraisal: NPV and IRR

Including depreciation or sunk costs in the cash flows.
Students copy figures from the profit statement rather than build cash flows.
Fix: Use only future incremental cash flows. Add back depreciation if you started from profit, and ignore costs already incurred.
Forgetting working capital and its recovery at the end.
It is mentioned in a note and not in the main table.
Fix: Put the increase in working capital as an outflow when it arises and the release as an inflow in the final year.
Choosing between mutually exclusive projects by highest IRR.
IRR looks like a single clean number.
Fix: Rank by NPV at the cost of capital. A smaller project can have a higher IRR but a lower NPV.
Treating interpolated IRR as exact.
The calculation gives a precise-looking figure.
Fix: Say it is an approximation, since NPV is not a straight line in the rate. Use trial rates close to each other.
Saying payback accounts for the time value of money.
Mixing up simple payback with discounted payback.
Fix: Simple payback does not discount. Discounted payback does, but both ignore flows after the cut-off.
Applying the IRR rule to cash flows with several sign changes.
Students assume one IRR always exists.
Fix: With multiple sign changes there can be several IRRs or none that make sense. Use NPV.

Worked examples

Example 1

A project costs ₹10,00,000 now and gives net cash inflows of ₹3,00,000 at the end of each year for 5 years. The cost of capital is 10% a year. Calculate the NPV, state the decision, and find the payback period.

Show the solution

Annuity factor for 5 years at 10% = [1 − 1.1^−5] ÷ 0.1.
1.1^5 = 1.61051, so 1.1^−5 = 0.620921.
Annuity factor = (1 − 0.620921) ÷ 0.1 = 3.79079.
PV of inflows = 3,00,000 × 3.79079 = ₹11,37,237.
NPV = 11,37,237 − 10,00,000 = ₹1,37,237.
NPV is positive, so accept.
Payback: after 3 years cumulative inflow = ₹9,00,000. Unrecovered = ₹1,00,000.
Year 4 inflow is ₹3,00,000, so fraction = 1,00,000 ÷ 3,00,000 = 0.333 years.
Payback = 3.33 years.

Answer: NPV ≈ ₹1,37,237 (accept). Simple payback ≈ 3.33 years.

Example 2

A project needs an outlay of ₹1,00,000 now and returns ₹60,000 at the end of year 1 and ₹60,000 at the end of year 2. The required return is 8%. Find the NPV at 8%, and decide using IRR by testing 10% and 20%.

Show the solution

Discount factors at 8%: year 1 = 1 ÷ 1.08 = 0.925926; year 2 = 1 ÷ 1.1664 = 0.857339.
Sum = 1.783265.
PV of inflows = 60,000 × 1.783265 = ₹1,06,996.
NPV at 8% = 1,06,996 − 1,00,000 = ₹6,996. Positive.
At 10%: factors 0.909091 and 0.826446, sum 1.735537. PV = 60,000 × 1.735537 = ₹1,04,132. NPV = ₹4,132.
At 20%: factors 0.833333 and 0.694444, sum 1.527778. PV = 60,000 × 1.527778 = ₹91,667. NPV = −₹8,333.
Interpolate: IRR ≈ 10% + [4,132 ÷ (4,132 + 8,333)] × 10% = 10% + 0.3315 × 10% = 13.3%.
The IRR estimate of about 13.3% is above 8%, so accept. This agrees with the positive NPV.

Answer: NPV at 8% ≈ ₹6,996 (accept). IRR ≈ 13.3% by interpolation (the exact IRR is slightly lower, about 13.1%), which exceeds 8%, so accept.

Exam tips

Show a cash flow table with years across the top. Marks go for correct timing and for each included item.
State your assumptions: cash flows at year end, discount rate used, tax and working capital treatment.
In discussion parts, link each method to shareholder wealth. Say NPV measures value added; IRR is a percentage and can mislead on ranking.
For payback questions, give both an advantage (simple, shows liquidity risk) and a disadvantage (ignores time value and later cash flows).
MCQs often test the decision rule or what to include. Check whether a cost is sunk or non-cash before you calculate.

Practice questions from Key principles of finance

Investment Appraisal: NPV 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.

Investment Appraisal: NPV and IRR: frequently asked questions

What is the difference between NPV and IRR?

NPV gives the rupee value a project adds, using the cost of capital as the discount rate. IRR gives the rate at which NPV is zero. They agree on accept or reject for a normal single project but can conflict when ranking mutually exclusive projects.

Which is better, NPV or IRR?

NPV is generally preferred because it measures absolute value added and is consistent with maximising shareholder wealth. IRR is useful as a percentage margin over the hurdle rate. Use NPV when the two disagree.

What are the advantages and disadvantages of payback?

Payback is simple, easy to explain and highlights how quickly money is recovered, which suits risky or liquidity-tight settings. Simple payback ignores the time value of money and any cash flows after the cut-off. It also has no link to shareholder wealth.

How do I find IRR in an exam without a calculator function?

Compute NPV at two trial rates, ideally one positive and one negative, then use linear interpolation. State that the answer is an estimate. Choose rates close together for a better result.