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Financial Management and Strategic Management · Investment Decisions

Net Present Value (NPV) and Profitability Index Explained

Updated 4 October 2026 · Fact-checked

NPV is the present value of a project's cash inflows minus the present value of its cash outflows, discounted at the cost of capital. Accept if NPV is positive. Profitability Index is PV of inflows ÷ PV of outflows; accept if it is above 1. Discount each year's cash flow, add, then apply the rule.

Understand Net Present Value (NPV) and Profitability Index

Money received today is worth more than the same money received later, because you can invest it and earn a return. Discounted cash flow (DCF) techniques respect this. They convert all future cash flows into their value today.

Net Present Value (NPV) adds up the present value of all cash inflows and subtracts the present value of all cash outflows. The discount rate is normally the firm's cost of capital, or the required rate of return given in the question. A positive NPV means the project earns more than the required return and adds to shareholder wealth. A negative NPV means it earns less.

Profitability Index (PI), also called the benefit-cost ratio, expresses the same information as a ratio. It tells you the present value you get for every rupee invested. PI above 1 means NPV is positive. PI below 1 means NPV is negative. PI equal to 1 means NPV is zero.

For a single independent project, NPV and PI always give the same accept or reject answer. They can disagree when you rank several projects, especially when projects differ in size. NPV gives the absolute rupee gain. PI gives the gain per rupee invested. When funds are limited, PI helps rank projects. When funds are not limited and projects are mutually exclusive, NPV is generally preferred because it measures the total addition to wealth.

Key rules to remember

Present value of a single cash flow
PV = Cash flow in year n ÷ (1 + r)^n
r is the discount rate. In exams you usually multiply by the PV factor given in the question instead.
Net Present Value
NPV = Σ [Ct ÷ (1 + r)^t] − C0
Ct is the net cash inflow in year t. C0 is the initial outflow. Include working capital and salvage value in the right years.
NPV with annuity
NPV = (Annual cash inflow × Annuity PV factor) − Initial outflow
Use only when inflows are equal each year.
Profitability Index
PI = PV of cash inflows ÷ PV of cash outflows
If outflows occur only at time 0, the denominator is the initial investment.
Relationship between NPV and PI
PI = 1 + (NPV ÷ PV of outflows)
Holds when outflows are all at time 0. NPV > 0 means PI > 1.
Decision rule for a single project
Accept if NPV > 0 (PI > 1); reject if NPV < 0 (PI < 1)
At NPV = 0 (PI = 1) the project earns exactly the required rate, so you are indifferent.
Decision rule for mutually exclusive projects
Choose the project with the highest positive NPV
Compare projects on the same discount rate and the same time basis.

How to solve Net Present Value (NPV) and Profitability Index questions

Use this method for any NPV or PI question. Lay out a clean table so you earn step marks even if one figure is wrong.

  1. 1Note the discount rate and the PV factors given. If a factor is missing, compute it as 1 ÷ (1 + r)^n.
  2. 2Find the initial outflow at year 0: cost of asset, installation, and any working capital you must put in.
  3. 3Work out the net cash inflow for each year. Start from profit before depreciation, deduct tax, or use profit after tax plus depreciation. Ignore sunk costs and financing costs such as interest.
  4. 4Add year-end items: salvage value of the asset and recovery of working capital in the final year.
  5. 5Multiply each year's cash flow by its PV factor and write the present values in a table.
  6. 6Total the present values of inflows. Subtract the initial outflow to get NPV.
  7. 7Calculate PI as PV of inflows ÷ initial outflow, if asked.
  8. 8State the decision in one line using the rule, and compare projects if there are two or more.

Quickest way: Table-first method for NPV under time pressure

When to use it: Use it for every numerical. It works for equal and unequal cash flows and for MCQs.

  1. Draw columns: Year, Cash flow, PV factor, Present value.
  2. If cash flows are equal, use the annuity factor once instead of one line per year.
  3. For MCQs, estimate first. If total undiscounted inflows are less than the outflow, NPV must be negative, so cut those options.
  4. For PI MCQs, compute PV of inflows once, then divide. Do not recompute NPV separately.
  5. Check the sign: PI above 1 must match positive NPV. If they disagree, you made an error.
  6. In written answers, write the formula, the table and a one-line conclusion. These three earn separate marks.

Common mistakes in Net Present Value (NPV) and Profitability Index

  • Including interest on borrowed funds in the cash flows

    Students treat interest as a normal cash cost of the project.

    Fix: Leave financing costs out. The discount rate already reflects the cost of funds.

  • Forgetting to add back depreciation

    Students start from profit after tax and treat it as cash flow.

    Fix: Depreciation is non-cash. Cash flow after tax = PAT + depreciation, but still deduct the tax effect correctly.

  • Ignoring working capital and salvage value

    These items are given in the question as notes and are easy to miss.

    Fix: Put working capital in year 0 and release it in the final year. Add salvage value in the final year.

  • Discounting the initial outflow

    Students apply a factor to every row of the table by habit.

    Fix: Year 0 outflow has a PV factor of 1. Do not discount it.

  • Using PI alone to choose between mutually exclusive projects

    A higher ratio looks better.

    Fix: PI ignores project size. Check NPV too, and explain which rule suits the situation, such as capital rationing.

  • Treating sunk costs as outflows

    Money already spent, such as a feasibility study paid earlier, appears in the question.

    Fix: Include only future incremental cash flows. Sunk costs are irrelevant.

Worked examples

Example 1

A project needs an initial investment of ₹5,00,000. It gives net cash inflows after tax of ₹2,00,000 each year for 4 years. The cost of capital is 10%. The PV annuity factor for 4 years at 10% is 3.170. Calculate NPV and Profitability Index and state whether to accept the project.

Show the solution
  1. Present value of inflows = ₹2,00,000 × 3.170 = ₹6,34,000.
  2. NPV = ₹6,34,000 − ₹5,00,000 = ₹1,34,000.
  3. PI = ₹6,34,000 ÷ ₹5,00,000 = 1.268.
  4. NPV is positive and PI is above 1, so the project earns more than 10%.

Answer: NPV = ₹1,34,000 and PI = 1.268 (about 1.27). Accept the project.

Example 2

Two mutually exclusive projects have a cost of capital of 10%. PV factors at 10%: year 1 = 0.909, year 2 = 0.826, year 3 = 0.751. Project X: outlay ₹1,00,000; inflows ₹50,000, ₹50,000, ₹50,000 in years 1 to 3. Project Y: outlay ₹60,000; inflows ₹30,000, ₹30,000, ₹40,000 in years 1 to 3. Calculate NPV and PI of each and advise which to choose.

Show the solution
  1. Project X: sum of PV factors = 0.909 + 0.826 + 0.751 = 2.486. PV of inflows = ₹50,000 × 2.486 = ₹1,24,300.
  2. NPV of X = ₹1,24,300 − ₹1,00,000 = ₹24,300. PI of X = 1,24,300 ÷ 1,00,000 = 1.243.
  3. Project Y: PV of year 1 = 30,000 × 0.909 = ₹27,270. Year 2 = 30,000 × 0.826 = ₹24,780. Year 3 = 40,000 × 0.751 = ₹30,040.
  4. PV of inflows of Y = 27,270 + 24,780 + 30,040 = ₹82,090.
  5. NPV of Y = ₹82,090 − ₹60,000 = ₹22,090. PI of Y = 82,090 ÷ 60,000 = 1.368.
  6. Both are acceptable. X has the higher NPV. Y has the higher PI because it uses less capital.
  7. The projects are mutually exclusive and no capital constraint is stated, so choose on NPV, which measures total wealth added.

Answer: X: NPV ₹24,300, PI 1.243. Y: NPV ₹22,090, PI 1.368. Choose Project X because it has the higher NPV. Y ranks higher on PI only because it needs a smaller investment.

Exam tips

  • Always show the PV table. ICAI awards marks for each step of working, not just the final NPV.
  • Read the notes carefully for working capital, salvage value, tax rate and depreciation method. Most lost marks come from missed notes.
  • When NPV and PI conflict, write one sentence explaining why: PI ignores project size. Then give your recommendation.
  • In MCQs, check the sign of NPV by comparing total inflows with the outflow before doing full calculations. No negative marking, so always attempt.
  • Use the PV factors given in the question exactly. Do not recompute them unless they are missing.

Practice questions from Investment Decisions

Net Present Value (NPV) and Profitability Index in other exams

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

Net Present Value (NPV) and Profitability Index: frequently asked questions

What is the decision rule for NPV?

Accept the project if NPV is positive and reject it if negative. If NPV is zero, the project earns exactly the required return. For mutually exclusive projects, choose the one with the highest positive NPV.

What is the difference between NPV and Profitability Index?

NPV gives the absolute rupee value added by the project. PI gives the present value earned per rupee invested, as a ratio. Both give the same accept or reject answer for one project, but they can rank projects differently.

Which discount rate do I use for NPV?

Use the cost of capital or required rate of return given in the question. It is the minimum return the project must earn. If the question gives a WACC, use that.

Should I include depreciation in NPV calculations?

Do not treat depreciation as a cash outflow. Use it only to work out tax savings, then add it back to profit after tax. Cash flow is what actually moves in and out of the business.