Profitability analysis: payback, ROI, NPV and IRR

Payback period, return on investment, net present value and internal rate of return: how each is calculated, what each ignores, and how to use them to accept or rank projects.

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Why it matters

A company always has more project ideas than money, so each one must be ranked by how well it uses capital. Payback period, return on investment, net present value and internal rate of return are the four measures used in practice; the first two are quick screens, the last two account for the time value of money and drive the final decision. Knowing what each one ignores matters as much as knowing how to compute it.

Key ideas

Minimum acceptable rate of return (MARR). A company sets a minimum return, based on its cost of capital plus an allowance for risk, below which it will not invest. Every measure below is compared, directly or indirectly, with it.

Methods that ignore the time value of money.

  • Rate of return on investment (ROI) — average annual net profit (after tax) divided by total capital investment, as a percentage. Simple and widely quoted, but it treats a rupee in year 10 the same as one in year 1. Some texts use profit before tax or fixed capital only; read the definition the question uses.
  • Payback period — the time to recover the depreciable fixed capital from the annual cash flow (net profit + depreciation). Some texts measure from the start of construction, or use total investment. Payback measures liquidity and risk, not profitability: it ignores everything after the payback point.

Methods that use the time value of money (discounted cash flow).

  • Net present value (NPV) — the sum of all cash flows, each discounted to time zero at the MARR. NPV > 0 means the project earns more than the MARR and adds that much value in today's rupees. For mutually exclusive projects of equal life, choose the higher NPV.
  • Internal rate of return (IRR), also called the discounted-cash-flow rate of return — the interest rate at which NPV = 0. Accept the project if IRR > MARR. IRR must be found by trial and interpolation (or a calculator). For projects with more than one sign change in their cash flows there may be several IRRs, and ranking mutually exclusive projects by IRR can disagree with NPV; then NPV (or incremental IRR) governs.
  • Discounted payback — the time for cumulative discounted cash flow to reach zero; always longer than the simple payback.
  • Profitability index — present worth of future cash flows divided by the initial investment; > 1 is acceptable.

Conventions. Cash flows occur at year ends; investment at time zero unless construction years are given; working capital, land and salvage are recovered in the last year. Use after-tax cash flows from the taxes topic.

Choosing a method. Use ROI and payback for early screening and to communicate quickly; use NPV and IRR for the final decision. NPV is the most reliable single criterion.

Formulas

ROI = (average annual net profit / total capital investment) × 100% Payback period = depreciable fixed capital / (average annual net profit + annual depreciation) NPV = Σ CF_k / (1 + i)^k, k = 0 to n IRR: Σ CF_k / (1 + IRR)^k = 0 Linear interpolation for IRR between rates i₁ (NPV₁ > 0) and i₂ (NPV₂ < 0): IRR ≈ i₁ + (i₂ − i₁)·NPV₁ / (NPV₁ − NPV₂) Uniform cash flow A for n years after investment C₀: NPV = −C₀ + A·[(1 + i)ⁿ − 1] / [i·(1 + i)ⁿ] Profitability index = (Σ_{k≥1} CF_k/(1 + i)^k) / C₀

Symbols: CF_k net cash flow in year k (₹, negative for outlays), i discount rate (MARR, decimal), n project life (years), C₀ initial investment (₹), A uniform annual cash flow (₹/yr).

Worked examples

Example 1 (standard). FCI = ₹40 crore (all depreciable), working capital ₹5 crore. Average annual net profit after tax ₹6 crore; depreciation ₹4 crore/yr. Find ROI and payback period.

  1. ROI = 6/(40 + 5) × 100 = 13.3%.
  2. Annual cash flow = 6 + 4 = ₹10 crore/yr.
  3. Payback = 40/10 = 4.0 years.
  4. ROI = 13.3% per year; payback = 4 years.

Example 2 (GATE level). A project needs ₹50 crore at time zero (₹45 crore fixed capital, ₹5 crore working capital). After-tax cash flows in years 1–5 are ₹12, 14, 16, 16 and 16 crore, and the working capital is recovered at the end of year 5. MARR = 12%. Find NPV and IRR.

  1. Year-5 cash flow including recovery = 16 + 5 = ₹21 crore.
  2. Discount factors at 12%: 0.8929, 0.7972, 0.7118, 0.6355, 0.5674.
  3. Present values: 10.714 + 11.161 + 11.388 + 10.168 + 11.916 = ₹55.35 crore.
  4. NPV(12%) = 55.35 − 50 = +₹5.35 crore.
  5. Try 15%: NPV = +1.13; try 18%: NPV = −2.61.
  6. IRR ≈ 15 + 3 × 1.13/(1.13 + 2.61) = 15 + 0.91 = 15.9%.
  7. NPV = ₹5.35 crore at 12%; IRR ≈ 15.9% > MARR, so the project is acceptable. (Simple payback: cumulative cash goes from −8 at year 3 to +8 at year 4, so about 3.5 years.)

Common mistakes

  • Dividing total profit over the life by investment and calling it ROI (ROI is an annual rate).
  • Using net profit instead of cash flow (profit + depreciation) in payback.
  • Discounting the year-0 investment, or forgetting to recover working capital and salvage.
  • Ranking mutually exclusive projects of different size by IRR alone.
  • Interpolating IRR between rates far apart: the NPV curve is not linear, so bracket closely.
  • Taking a positive NPV at one rate as proof that IRR is above any other rate.

For GATE CH

Typical questions: payback or ROI from given profit, depreciation and investment; NPV of uniform or uneven cash flows at a given rate; IRR of a uniform series, often by checking which option makes NPV zero; and conceptual questions on which methods ignore the time value of money. Practise the annuity factor and quick interpolation.

Quick check

  1. Investment ₹10 crore; uniform cash flow ₹2.5 crore/yr. Payback?
  2. Net profit ₹3 crore/yr on TCI ₹20 crore. ROI?
  3. What does NPV = 0 at 14% tell you?
  4. Which two methods ignore the time value of money?

Answers: 1. 4 years. 2. 15%. 3. The IRR is 14%. 4. Simple payback period and ROI.

Interview questions

All Plant Design and Economics interview questions

Try answering each one aloud before you open it.

  1. 1.What is the payback period in the context of plant design and economics?Concept

    Payback period is the time needed to recover the depreciable fixed capital from the project's annual cash flow, i.e. net profit after tax plus depreciation; some definitions count from the start of construction or use total investment. A shorter payback means faster recovery and lower exposure to risk. Its weaknesses are that it ignores the time value of money and everything that happens after the payback point, so it is a screening and liquidity measure, not a profitability criterion.

  2. 2.Explain the concept of return on investment (ROI) and its importance in profitability analysis.Concept

    ROI is the average annual net profit (usually after tax) expressed as a percentage of the total capital investment (fixed plus working capital). It is quick to compute from a cost sheet and easy to compare with a company's minimum acceptable return, which makes it popular for early screening. Its weakness is that it uses average profits and ignores their timing, so two projects with the same ROI can have very different present worths; final decisions use NPV or IRR.

  3. 3.Define Net Present Value (NPV) and explain its significance in investment decisions.Concept

    Net Present Value (NPV) is the difference between the present value of cash inflows and the present value of cash outflows over a period of time. It is used to assess the profitability of an investment. A positive NPV indicates that the projected earnings exceed the anticipated costs, making the investment potentially profitable. NPV is significant because it accounts for the time value of money, providing a more accurate assessment of an investment's value.

  4. 4.What is the Internal Rate of Return (IRR) and how is it used in evaluating projects?Concept

    The Internal Rate of Return (IRR) is the discount rate that makes the Net Present Value (NPV) of all cash flows from a particular project equal to zero. It is used to evaluate the attractiveness of a project or investment. A project is generally considered acceptable if its IRR is greater than the required rate of return. IRR helps in comparing the profitability of different projects.

  5. 5.Why is NPV preferred over payback period in evaluating long-term projects?Application

    NPV is preferred over the payback period for long-term projects because it considers the time value of money, providing a more comprehensive assessment of an investment's profitability. While the payback period only measures how quickly an investment can be recovered, NPV evaluates the total value added by the project over its entire lifespan, making it a more accurate measure for long-term investments.

  6. 6.What happens if the IRR of a project is lower than the cost of capital?Application

    If the IRR of a project is lower than the cost of capital, it means that the project is not expected to generate enough returns to cover the cost of the investment. This would result in a negative NPV, indicating that the project is not financially viable. In such cases, the project should typically be rejected unless there are other strategic reasons to proceed.

  7. 7.How does inflation affect the calculation of NPV?Application

    Inflation raises future prices and costs, and market interest rates already include an allowance for expected inflation. The rule is consistency: discount cash flows forecast in inflated (money-of-the-day) rupees at the market rate, or cash flows in constant (today's) rupees at the real rate, where (1 + market) = (1 + real)(1 + inflation). Discounting constant-rupee cash flows at the market rate understates NPV; discounting inflated cash flows at the real rate overstates it. Depreciation, fixed in rupees at purchase, does not inflate, so high inflation reduces the real value of its tax shield.

  8. 8.Calculate the payback period for a project with a depreciable investment of ₹1 crore and a uniform annual cash flow (net profit + depreciation) of ₹25 lakh.Numerical

    Payback = depreciable investment / annual cash flow = 100 lakh / 25 lakh per year = 4 years. Note that the cash flow, not the net profit alone, is used, and that payback says nothing about the cash flows after year 4 or about the time value of money.

  9. 9.A project costs ₹2,00,000 now and returns ₹50,000 at the end of each year for 6 years. Find the NPV at 10%.Numerical

    Present worth of the annuity = 50,000 × (1.1⁶ − 1)/(0.1 × 1.1⁶) = 50,000 × 4.3553 = ₹2,17,763. NPV = 2,17,763 − 2,00,000 = +₹17,763. Since NPV is positive, the project earns more than 10% (its IRR is about 13%).

  10. 10.Explain why IRR might not be reliable for projects with non-conventional cash flows.Application

    IRR might not be reliable for projects with non-conventional cash flows because such projects can have multiple IRRs or no IRR at all. Non-conventional cash flows involve changes in the direction of cash flow (e.g., from positive to negative and back to positive), which can lead to multiple solutions for IRR. This makes it difficult to determine the true rate of return, and alternative methods like NPV are preferred in such cases.

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