Skip to content

Financial Management and Business Data Analytics · Capital Budgeting

Net Present Value (NPV) and Profitability Index: Formula and Decision Rule

Updated 10 October 2026 · Fact-checked

Net Present Value is the present value of all cash inflows of a project minus the initial outlay, discounted at the cost of capital. Accept the project if NPV is positive. The Profitability Index is PV of inflows ÷ initial outlay; accept if it is greater than 1. Discount, add, subtract, then decide.

Understand Net Present Value (NPV) and Profitability Index

A rupee received today is worth more than a rupee received later. So you cannot add up cash flows of different years directly. Net Present Value (NPV) fixes this by bringing every cash flow to today's value using a discount rate.

The discount rate is the minimum return the firm must earn, usually the cost of capital or the required rate of return. Cash inflows are discounted to present value. The initial investment, which happens today (year 0), is not discounted. The difference is NPV.

A positive NPV means the project earns more than the required return and adds to shareholders' wealth. A negative NPV means it earns less. A zero NPV means it just meets the required return.

The Profitability Index (PI), also called the benefit-cost ratio, expresses the same information as a ratio: present value of inflows for each rupee invested. It is useful when funds are limited and you need to compare projects of different sizes, because NPV is an absolute amount and favours big projects.

NPV and PI always agree on accept or reject for a single project. NPV > 0 exactly when PI > 1. They can disagree only when ranking mutually exclusive or capital-rationed projects.

Key rules to remember

Net Present Value
NPV = Σ [Ct ÷ (1 + k)^t] − C0, for t = 1 to n
Ct is the net cash inflow in year t, k is the discount rate, C0 is the initial outlay at time 0. Add the PV of salvage value and released working capital in the final year.
NPV with scrap and working capital
NPV = PV of operating inflows + PV of salvage value + PV of working capital recovered − (initial outlay + working capital invested)
Working capital is invested at the start and recovered at the end of the project life.
Profitability Index
PI = PV of cash inflows ÷ PV of cash outflows (initial outlay)
Also called benefit-cost ratio or desirability factor.
Net Profitability Index
Net PI = NPV ÷ Initial outlay = PI − 1
Use this if the question asks for net PI.
Decision rules
Accept if NPV > 0 (PI > 1); reject if NPV < 0 (PI < 1)
For mutually exclusive projects, choose the highest NPV. Under capital rationing, rank by PI, subject to the budget and indivisibility.

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

Use this method for any NPV or PI question. Lay it out in a table so each step earns marks.

  1. 1Find the annual net cash inflows after tax. Add back depreciation if you started from profit, and do not include interest on funds.
  2. 2Identify the initial outlay at year 0, including working capital and installation cost, less the sale proceeds of any old asset if the question gives them.
  3. 3Note the year-end items: salvage value and recovery of working capital.
  4. 4Pick the discount rate given in the question and write the PV factor for each year.
  5. 5Multiply each cash flow by its PV factor. Use the annuity factor only if the inflows are equal each year.
  6. 6Total the PV of inflows, then subtract the PV of outflows to get NPV.
  7. 7Compute PI = PV of inflows ÷ initial outlay if asked.
  8. 8State the decision in one line, with the reason.

Quickest way: Annuity factor shortcut

When to use it: When annual cash inflows are equal, or can be split into an equal part plus a few one-off amounts.

  1. Add the PV factors for years 1 to n, or use the cumulative factor given in the question.
  2. Multiply by the annual inflow in one step.
  3. Add separately the PV of one-off items such as salvage value.
  4. Subtract the outlay, then divide the PV of inflows by the outlay for PI.
  5. If PI is asked, check: NPV > 0 must match PI > 1.

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

  • Discounting the initial outlay

    Students apply a PV factor to every number in the table.

    Fix: The outlay at time 0 has a factor of 1. Never discount it.

  • Forgetting working capital recovery

    Students treat working capital as a cost only.

    Fix: Show it as an outflow at year 0 and an inflow in the last year, and discount the inflow.

  • Deducting depreciation or interest from cash flow

    Students use accounting profit as the cash flow.

    Fix: Use profit after tax plus depreciation. Depreciation is non-cash. Interest is covered by the discount rate, so exclude it.

  • Computing PI as NPV ÷ outlay

    It looks similar to the formula.

    Fix: PI = PV of inflows ÷ outlay. NPV ÷ outlay is net PI, which is PI − 1.

  • Using the wrong PV factor year

    Inflows are placed in the wrong row, especially with a gestation period.

    Fix: Write the year against each cash flow before multiplying.

  • Ranking mutually exclusive projects by PI

    Students assume the higher ratio is always better.

    Fix: Pick the higher NPV when funds are not limited. Use PI only for rationing.

Worked examples

Example 1

Sunrise Textiles Ltd is considering a machine costing ₹5,00,000. It will give net cash inflows after tax of ₹1,80,000 each year for 4 years. The salvage value at the end of year 4 is ₹50,000. The cost of capital is 10%. PV factors at 10%: year 1 = 0.909, year 2 = 0.826, year 3 = 0.751, year 4 = 0.683. Calculate NPV and PI and advise.

Show the solution
  1. Sum of PV factors for years 1 to 4 = 0.909 + 0.826 + 0.751 + 0.683 = 3.169.
  2. PV of annual inflows = 1,80,000 × 3.169 = ₹5,70,420.
  3. PV of salvage value = 50,000 × 0.683 = ₹34,150.
  4. Total PV of inflows = 5,70,420 + 34,150 = ₹6,04,570.
  5. NPV = 6,04,570 − 5,00,000 = ₹1,04,570.
  6. PI = 6,04,570 ÷ 5,00,000 = 1.209.

Answer: NPV = ₹1,04,570 (positive) and PI = 1.209 (above 1). Accept the machine.

Example 2

Kaveri Foods Ltd has two projects, each with a life of 3 years and a discount rate of 12%. PV factors at 12%: year 1 = 0.893, year 2 = 0.797, year 3 = 0.712. Project A: outlay ₹2,00,000; inflows ₹90,000, ₹1,00,000, ₹80,000. Project B: outlay ₹1,00,000; inflows ₹50,000, ₹50,000, ₹60,000. Compute NPV and PI of each. Which is better if the projects are independent and funds are limited to ₹1,00,000?

Show the solution
  1. Project A: 90,000 × 0.893 = 80,370; 1,00,000 × 0.797 = 79,700; 80,000 × 0.712 = 56,960.
  2. PV of inflows of A = 80,370 + 79,700 + 56,960 = ₹2,17,030.
  3. NPV of A = 2,17,030 − 2,00,000 = ₹17,030. PI of A = 2,17,030 ÷ 2,00,000 = 1.085.
  4. Project B: 50,000 × 0.893 = 44,650; 50,000 × 0.797 = 39,850; 60,000 × 0.712 = 42,720.
  5. PV of inflows of B = 44,650 + 39,850 + 42,720 = ₹1,27,220.
  6. NPV of B = 1,27,220 − 1,00,000 = ₹27,220. PI of B = 1,27,220 ÷ 1,00,000 = 1.272.
  7. With only ₹1,00,000 available, A cannot be funded. B fits the budget and also has the higher NPV and PI.

Answer: A: NPV ₹17,030, PI 1.085. B: NPV ₹27,220, PI 1.272. Both are acceptable, but with a ₹1,00,000 limit choose Project B.

Exam tips

  • Draw a table with columns Year, Cash flow, PV factor and PV. Step marks are given for each row.
  • Read whether the cash flows are given before or after tax and whether depreciation is already added back.
  • Write the decision rule and your conclusion in a sentence. Many questions carry a mark for interpretation.
  • In MCQs, test quickly: if PV of inflows exceeds the outlay, NPV is positive and PI is above 1. You may not need to calculate both.
  • Use the PV factors given in the question exactly, even if they differ slightly from your tables.

Practice questions from Capital Budgeting

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 a project if its NPV is positive and reject it if negative. If projects are mutually exclusive, choose the one with the highest positive NPV.

What are the advantages of NPV?

It considers the time value of money and all cash flows of the project. It measures the addition to shareholders' wealth directly. It also allows NPVs of different projects to be added.

What are the limitations of NPV?

It needs a correct discount rate, which is hard to estimate. It gives an absolute amount, so it favours larger projects and is not good for comparing projects of different sizes. Projects with unequal lives need extra adjustment.

How is the profitability index different from NPV?

NPV is a rupee amount, while PI is a ratio of PV of inflows to the outlay. Both give the same accept or reject answer for one project. PI is more useful for ranking when capital is limited.

Can PI be negative?

Not normally, because PV of inflows is usually positive. PI below 1 shows a negative NPV, so the project should be rejected.