Strategic Financial Management · Investment Decisions, Project Planning and Control

Traditional and DCF Appraisal Techniques for Capital Budgeting

Updated 11 October 2026 · Fact-checked

Appraisal techniques test whether a project is worth its cost. Traditional methods (payback, ARR) ignore the time value of money. DCF methods (NPV, IRR, MIRR, profitability index, discounted payback) discount cash flows. To solve a question, list the cash flows, discount at the required rate, compute the measure, and compare it with the decision rule.

Understand Traditional and DCF Appraisal Techniques

A capital project costs money today and returns cash over several years. Appraisal techniques give you a rule to accept or reject it, or to rank it against other projects.

Traditional techniques do not discount. Payback is the time taken to recover the initial outlay from cash inflows. Accounting rate of return (ARR) uses accounting profit, not cash flow, divided by investment. They are simple, but payback ignores cash flows after the cut-off and ARR ignores timing completely.

DCF techniques convert every cash flow to its present value at the cost of capital. NPV is the sum of present values of inflows less the outlay. Accept if NPV is above zero. IRR is the discount rate at which NPV is zero. Accept if IRR is above the cost of capital. Profitability index (PI) is the present value of inflows divided by the outlay. Accept if PI is above 1. Discounted payback is payback computed on discounted cash flows.

MIRR fixes a weakness of IRR. IRR assumes interim cash flows are reinvested at the IRR itself. MIRR compounds inflows forward to the end of the project at a stated reinvestment rate and then finds the single rate that links that terminal value to the present value of outflows.

For a single conventional project, NPV, IRR and PI give the same accept or reject answer. They can disagree when you rank mutually exclusive projects. The usual causes are different project size, different timing of cash flows, and different project lives. In such a conflict, NPV is preferred because it measures the actual rupee addition to shareholder wealth and assumes reinvestment at the cost of capital, which is more realistic.

Key rules to remember

Payback period: Payback = Years before full recovery + (Unrecovered cost at start of the year ÷ Cash inflow of that year); For even inflows: Initial outlay ÷ Annual cash inflow. Undiscounted cash flows.
Discounted payback: Same as payback, but use present values: PV of inflow = Cash inflow ÷ (1 + r)^t; Always at least as long as simple payback for a positive discount rate. Needs a cost of capital.
ARR: ARR = Average annual accounting profit after depreciation (and tax) ÷ Investment × 100; Investment may be the initial or the average investment. Use whichever the question states. Average investment = (Initial cost + Salvage value) ÷ 2.
Net present value: NPV = Σ [CFt ÷ (1 + r)^t] − Initial outlay; Accept if NPV > 0. For mutually exclusive projects choose the highest NPV.
Internal rate of return: IRR: the r at which Σ [CFt ÷ (1 + r)^t] = Initial outlay. Interpolation: IRR = Lower rate + [NPV at lower rate ÷ (NPV at lower rate − NPV at higher rate)] × (Higher rate − Lower rate); Accept if IRR > cost of capital. For even inflows, outlay ÷ inflow gives the annuity factor to look up in the table.
Profitability index: PI = PV of cash inflows ÷ PV of cash outflows = 1 + (NPV ÷ Initial outlay); Accept if PI > 1. Useful for ranking under a budget limit.
MIRR: MIRR = (Terminal value of inflows ÷ PV of outflows)^(1 ÷ n) − 1, where Terminal value = Σ CFt × (1 + reinvestment rate)^(n − t); PV of outflows is at the finance rate (usually the cost of capital). n is the project life in years.
Crossover (Fisher's) rate: Rate at which NPV of two projects is equal; solve using the incremental cash flows (A − B) and find the IRR of the difference; Below this rate, NPV and IRR rankings can conflict. Above it, they agree.

How to solve Traditional and DCF Appraisal Techniques questions

Use this order for any question on appraisal techniques. It works whether you are asked for one measure or a full comparison.

1Read what is asked: one measure, a ranking, or a recommendation. Note the required rate, reinvestment rate and whether projects are independent or mutually exclusive.
2Write the cash flow line by year, with the outlay at year 0. If profit data is given, convert to cash flow by adding back depreciation after tax. Do not discount the sunk costs.
3Compute the traditional measures first if asked: payback with a cumulative cash flow column, and ARR from accounting profit.
4Prepare a present value column using the discount factors. Reuse these to get NPV, PI and discounted payback together.
5For IRR, try two rates that give NPVs of opposite sign, then interpolate. For even inflows, use the annuity factor method.
6For MIRR, compound each inflow to the end of the last year, add them, divide by the PV of outflows, take the nth root and subtract 1.
7Apply the decision rule for each measure and compare. If the rankings conflict, name the cause (scale, timing or life) and rely on NPV.
8Write a one-line recommendation with the reason. Examiners award marks for the conclusion.

Quickest way: One discounting table for every measure

When to use it: Use when a question asks for several measures on the same cash flows, which is common in the 14-mark questions.

Build one table with columns: Year, Cash flow, Cumulative cash flow, PV factor, PV, Cumulative PV.
Read simple payback from the cumulative cash flow column and discounted payback from the cumulative PV column.
Total the PV column. Subtract the outlay for NPV and divide by the outlay for PI.
For IRR, estimate from the PI. If PI is close to 1, IRR is slightly above the cost of capital, so try a rate 2 to 3 points higher.
For MIRR, only the inflows need compounding. Do not recompute the whole table.
For MCQs, check the decision rule first. If NPV > 0, then IRR > cost of capital and PI > 1. Eliminate options that contradict this.

Common mistakes in Traditional and DCF Appraisal Techniques

Treating payback or ARR as a time-value-adjusted measure, or ignoring cash flows after the payback period
Payback gives a quick answer, so students forget it is a liquidity measure, not a profitability measure.
Fix: State its limits in the answer: no time value, ignores later flows. Use it only as a secondary screen.
Calculating ARR on cash flow instead of accounting profit
Students carry over the cash flow line from the NPV workings.
Fix: For ARR, deduct depreciation from the cash flow, then tax if stated, to get accounting profit. Check whether investment is initial or average.
Using IRR to choose between mutually exclusive projects when it conflicts with NPV
A higher percentage looks better.
Fix: Choose the higher NPV at the cost of capital. If asked, compute the crossover rate or incremental IRR to explain the conflict.
Computing PI as NPV ÷ outlay
Students confuse PI with the net version of the index.
Fix: PI = PV of inflows ÷ outlay. NPV ÷ outlay is PI − 1. Check the question for which one it means.
Compounding the outflow, or using the wrong number of years in MIRR
Students mix up the terminal value approach with the NPV approach.
Fix: Compound inflows only, to the end of the project. Discount any later outflows to year 0. Use n = project life as the root.
Stating that IRR is unique for every project
Students assume one sign change in every cash flow pattern.
Fix: Cash flows that change sign more than once can give multiple IRRs. In such cases, use NPV or MIRR.

Worked examples

Example 1

Pragati Foods Ltd is considering a machine costing ₹5,00,000. Expected net cash inflows are ₹2,00,000 in each of years 1 to 3 and ₹1,50,000 in year 4. The cost of capital is 10%. PV factors at 10%: year 1 0.9091, year 2 0.8264, year 3 0.7513, year 4 0.6830. Calculate payback, discounted payback, NPV and profitability index, and advise.

Show the solution

Payback: cumulative inflows are ₹2,00,000, ₹4,00,000 and ₹6,00,000 at the end of years 1, 2 and 3. Recovery occurs in year 3. Payback = 2 + (1,00,000 ÷ 2,00,000) = 2.5 years.
Present values: Year 1 = 2,00,000 × 0.9091 = ₹1,81,820. Year 2 = 2,00,000 × 0.8264 = ₹1,65,280. Year 3 = 2,00,000 × 0.7513 = ₹1,50,260. Year 4 = 1,50,000 × 0.6830 = ₹1,02,450.
Cumulative PV: ₹1,81,820; ₹3,47,100; ₹4,97,360; ₹5,99,810.
Discounted payback: ₹4,97,360 is recovered by the end of year 3. Balance = 5,00,000 − 4,97,360 = ₹2,640. Fraction = 2,640 ÷ 1,02,450 = 0.026. Discounted payback = about 3.03 years.
NPV = 5,99,810 − 5,00,000 = ₹99,810.
PI = 5,99,810 ÷ 5,00,000 = 1.20 (rounded).
Decision: NPV is positive and PI is above 1, so the project earns more than 10%. Discounted payback is within the 4-year life.

Answer: Payback 2.5 years; discounted payback about 3.03 years; NPV ₹99,810; PI about 1.20. Accept the project.

Example 2

A project needs an outlay of ₹10,00,000 and gives cash inflows of ₹3,00,000, ₹4,00,000, ₹5,00,000 and ₹3,00,000 at the end of years 1 to 4. The cost of capital and the reinvestment rate are both 10%. Calculate the IRR (approximately) and the MIRR, and explain why they differ.

Show the solution

IRR at 18%: factors 0.8475, 0.7182, 0.6086, 0.5158. PVs = 2,54,250 + 2,87,280 + 3,04,300 + 1,54,740 = ₹10,00,570. NPV = +₹570.
IRR at 20%: factors 0.8333, 0.6944, 0.5787, 0.4823. PVs = 2,50,000 + 2,77,760 + 2,89,350 + 1,44,690 = ₹9,61,800. NPV = −₹38,200.
Interpolation: IRR = 18 + [570 ÷ (570 + 38,200)] × 2 = 18 + 0.03 = about 18.03%.
MIRR terminal value at the end of year 4 at 10%: 3,00,000 × 1.10³ = 3,99,300. 4,00,000 × 1.10² = 4,84,000. 5,00,000 × 1.10 = 5,50,000. Year 4 inflow = 3,00,000. Total = ₹17,33,300.
PV of outflows = ₹10,00,000 (all at year 0).
MIRR = (17,33,300 ÷ 10,00,000)^(1/4) − 1 = (1.7333)^0.25 − 1. Square root of 1.7333 is about 1.3166, and the square root of that is about 1.1474. MIRR = about 14.74%.
Reason for the difference: IRR assumes inflows are reinvested at about 18%. MIRR assumes reinvestment at 10%, which is the realistic rate, so MIRR is lower.
Decision: both exceed 10%, so accept the project.

Answer: IRR is about 18.03% and MIRR is about 14.74%. MIRR is lower because it reinvests at 10%, not at the IRR. The project is acceptable.

Exam tips

In ranking questions, always give the NPV ranking as the final recommendation and explain the cause of any conflict in one or two lines. This is a regular 14-mark theory portion.
Show the PV table clearly. Even if the final figure is off, method marks are awarded for the discount factors and the structure.
In MCQs, test the decision rule first. If a project's NPV is positive, an option saying its IRR is below the cost of capital is wrong.
Read the question for the reinvestment rate. If MIRR is asked and no rate is given, state the assumption you use, usually the cost of capital.
When the question asks for discounted payback, give the answer in years and months or in decimals, and say what the unrecovered balance was.

Practice questions from Investment Decisions, Project Planning and Control

Traditional and DCF Appraisal Techniques: frequently asked questions

What is the difference between NPV and IRR, and why do they conflict?

NPV gives the absolute rupee gain at the cost of capital. IRR gives the percentage return that makes NPV zero. They can conflict for mutually exclusive projects because of differences in size, cash flow timing or life. NPV is preferred because it assumes reinvestment at the cost of capital and maximises wealth.

How do I calculate MIRR?

Compound all inflows to the end of the project at the reinvestment rate and add them to get the terminal value. Discount any outflows to year 0. Then MIRR = (Terminal value ÷ PV of outflows)^(1 ÷ n) − 1.

Why is discounted payback longer than simple payback?

Discounting reduces each future inflow. With a positive rate, it takes longer to recover the same outlay. It still ignores cash flows after the recovery point, so it is not a full measure of value.

When should I use the profitability index?

Use it to rank independent projects when funds are limited, since it shows value created per rupee invested. For a single project, PI above 1 gives the same decision as a positive NPV. For mutually exclusive projects, NPV is still the primary guide.

Which technique is best for capital budgeting?

NPV is generally regarded as the most reliable because it uses all cash flows, considers time value and measures the addition to wealth. The other techniques are useful as supporting information, such as liquidity from payback or rate of return from IRR.