Advanced Financial Management · Advanced Capital Budgeting Decisions

Capital Budgeting Basics and Appraisal Techniques for CA Final AFM

Updated 5 October 2026 · Fact-checked

Capital budgeting is the process of evaluating long-term investments by comparing the cash they cost with the cash they return. Discount the cash flows at the cost of capital to get NPV, find the rate where NPV is zero for IRR, and use MIRR, PI and payback as supporting checks. Accept if NPV is positive.

Understand Capital Budgeting Basics and Appraisal Techniques

A capital investment decision commits a large sum today for benefits that come over several years. It is hard to reverse, so you appraise it with care. The question is simple: does the project return more than the money invested, after allowing for the time value of money and the risk?

All discounted methods start from the same idea. A rupee received later is worth less than a rupee today. So you bring every future cash flow to present value at the cost of capital (the required return for the project's risk). The Net Present Value (NPV) is the present value of inflows minus the initial outlay. A positive NPV means the project adds value to shareholders. NPV is the primary rule because its result is in rupees of value created.

The Internal Rate of Return (IRR) is the discount rate at which NPV equals zero. You accept if IRR exceeds the cost of capital. The Profitability Index (PI) is present value of inflows divided by the outlay. It is a relative measure, useful when funds are limited. Payback is the time taken to recover the outlay. It ignores cash flows after the payback point, and the simple version ignores the time value of money. Discounted payback fixes the second problem only.

IRR assumes that intermediate cash inflows are reinvested at the IRR itself. This is often unrealistic. MIRR fixes this. You compound all inflows to the end of the project at a stated reinvestment rate, discount the outlays to today at a finance rate, and find the rate that equates the two. MIRR gives one answer, even where the cash flows change sign more than once.

For a single project with conventional cash flows (outflow first, then inflows), NPV, IRR and PI give the same accept or reject answer. For mutually exclusive projects, they can rank differently. This happens when projects differ in size or in the timing of cash flows. The crossover rate (the rate at which the two projects have equal NPV) explains it. Below it one project has the higher NPV, above it the other. In such a conflict, follow NPV, as it assumes reinvestment at the cost of capital and measures value added. Non-conventional cash flows can also give multiple IRRs, or none.

Key rules to remember

Net Present Value: NPV = Σ [CFt ÷ (1 + k)^t] − Initial outlay; k is the cost of capital. Accept if NPV > 0. Rank mutually exclusive projects by higher NPV.
Internal Rate of Return (interpolation): IRR = L + [NPV at L ÷ (NPV at L − NPV at H)] × (H − L); L is the lower trial rate (NPV positive), H the higher trial rate (NPV negative). Accept if IRR > cost of capital. The result is an approximation.
Profitability Index: PI = PV of cash inflows ÷ PV of cash outflows; PI > 1 is the same as NPV > 0. Equivalent to 1 + (NPV ÷ outlay) when there is a single initial outlay.
Modified IRR: MIRR = (Terminal value of inflows ÷ PV of outflows)^(1 ÷ n) − 1; Terminal value = Σ CFt × (1 + r)^(n − t), with r the reinvestment rate. Outflows are discounted at the finance rate. n is the project life.
Payback period: Payback = Years before full recovery + (Unrecovered outlay ÷ Cash flow of the recovery year); Uses cumulative cash flows. Assumes cash flows are spread evenly within the year. For discounted payback, use cumulative present values.
Accounting-based check: Average rate of return: ARR = Average annual accounting profit ÷ Average (or initial) investment; Use the base the question states. Uses profit, not cash, and ignores time value.

How to solve Capital Budgeting Basics and Appraisal Techniques questions

Use this order for any appraisal question. It keeps the working clean and shows the examiner each mark-earning step.

1Read what is asked: the method, the cost of capital, whether projects are independent or mutually exclusive, and the life of each project.
2List the cash flows year by year, with year 0 first. Use cash flows, not accounting profit, and keep the outlay as a negative.
3Pick the discount factors for the cost of capital. Use the table values given in the question and keep the same number of decimals throughout.
4Compute the present value of each inflow, total them, and subtract the outlay to get NPV. Compute PI from the same totals.
5For IRR, try two rates around the answer so NPV is positive at one and negative at the other. Then interpolate. For MIRR, compound the inflows to the end year and use the MIRR formula.
6For payback, build the cumulative cash flow column and locate the recovery year. For discounted payback, use cumulative present values.
7Compare each result with its decision rule. If rankings conflict for mutually exclusive projects, state the reason (scale or timing) and recommend the project with the higher NPV.
8Write a one-line conclusion naming the project to accept and the reason.

Quickest way: NPV first, then PI and payback from the same table

When to use it: Use when time is short and the question asks for several measures on the same cash flows.

Build one table: year, cash flow, discount factor, present value, cumulative cash flow, cumulative present value.
Total the present values for NPV and PI. Read payback and discounted payback from the cumulative columns, with no extra calculation.
For IRR, guess the rate from the ratio of outlay to annual inflow, using the annuity factor table, then verify with one more rate.
For MIRR, find the terminal value in one line using compounding factors and take the nth root with the factor tables or a calculator.
If the question only needs a ranking decision, compute NPV for each project and stop.

Common mistakes in Capital Budgeting Basics and Appraisal Techniques

Choosing the project with the higher IRR when the projects are mutually exclusive and NPV ranks them the other way.
IRR is a percentage and looks like an easy comparison, so students forget it ignores scale and assumes reinvestment at the IRR.
Fix: Follow NPV for mutually exclusive projects. State the cause of the conflict (scale or timing) and the crossover rate if given.
Using the wrong discount rate, such as the IRR or the coupon rate, instead of the cost of capital.
Several rates appear in the question and students pick the first one.
Fix: Use the rate the question labels as the cost of capital or required return. Underline it before you start.
Taking the PI as NPV ÷ outlay and then comparing it with 1.
Students mix the net and gross forms of the index.
Fix: PI = PV of inflows ÷ outlay, so the cut-off is 1. If you use NPV ÷ outlay (net PI), the cut-off is 0.
Computing payback from the wrong point or applying a fraction to the wrong year.
Students divide by the first year's cash flow instead of the cash flow in the year of recovery.
Fix: Use cumulative cash flows. The fraction is unrecovered balance at the start of the recovery year ÷ that year's cash flow.
In MIRR, compounding the inflows to the wrong year or discounting the initial outlay again.
The outlay is at time 0 already, and students apply a factor to it by habit.
Fix: Compound each inflow to year n. Take the year 0 outlay as it stands, and discount only later outflows at the finance rate.
Including sunk costs, depreciation or interest in the cash flows.
Students copy figures from the profit statement.
Fix: Use only incremental after-tax cash flows. Depreciation matters only through its tax shield, and financing cost is already in the discount rate.

Worked examples

Example 1

A company is evaluating a machine costing ₹10,00,000 with a life of 4 years. Expected net cash inflows are ₹3,00,000, ₹4,00,000, ₹4,00,000 and ₹3,00,000 in years 1 to 4. The cost of capital is 10%. Present value factors at 10% are 0.9091, 0.8264, 0.7513 and 0.6830. Compute the NPV, profitability index, payback and discounted payback, and advise whether to accept.

Show the solution

PV of year 1: 3,00,000 × 0.9091 = ₹2,72,730.
PV of year 2: 4,00,000 × 0.8264 = ₹3,30,560.
PV of year 3: 4,00,000 × 0.7513 = ₹3,00,520.
PV of year 4: 3,00,000 × 0.6830 = ₹2,04,900.
Total PV of inflows = 2,72,730 + 3,30,560 + 3,00,520 + 2,04,900 = ₹11,08,710.
NPV = 11,08,710 − 10,00,000 = ₹1,08,710.
PI = 11,08,710 ÷ 10,00,000 = 1.11 (approx.).
Payback: cumulative inflows are ₹3,00,000 after year 1 and ₹7,00,000 after year 2. The balance of ₹3,00,000 is recovered in year 3, whose inflow is ₹4,00,000. Payback = 2 + 3,00,000 ÷ 4,00,000 = 2.75 years.
Discounted payback: cumulative PV is ₹2,72,730, ₹6,03,290 and ₹9,03,810 after years 1, 2 and 3. Balance = 10,00,000 − 9,03,810 = ₹96,190. Year 4 PV is ₹2,04,900. Discounted payback = 3 + 96,190 ÷ 2,04,900 = 3.47 years (approx.).

Answer: NPV = ₹1,08,710 (positive) and PI = 1.11 (above 1), so accept the machine. Payback is 2.75 years and discounted payback is about 3.47 years, both within the 4-year life.

Example 2

A project needs an outlay of ₹5,00,000 now and gives cash inflows of ₹2,00,000, ₹2,50,000 and ₹3,00,000 at the end of years 1, 2 and 3. Both the finance rate and the reinvestment rate are 10%, which is also the cost of capital. Compute the MIRR and state whether the project should be accepted.

Show the solution

There are no outflows after year 0, so the PV of outflows is ₹5,00,000.
Compound each inflow to the end of year 3 at 10%.
Year 1 inflow: 2,00,000 × (1.10)² = 2,00,000 × 1.21 = ₹2,42,000.
Year 2 inflow: 2,50,000 × 1.10 = ₹2,75,000.
Year 3 inflow: ₹3,00,000 (already at year 3).
Terminal value = 2,42,000 + 2,75,000 + 3,00,000 = ₹8,17,000.
MIRR = (8,17,000 ÷ 5,00,000)^(1/3) − 1 = (1.634)^(1/3) − 1.
Since 1.178³ is about 1.635, the cube root of 1.634 is about 1.178, so MIRR is about 17.8%.
Cross-check with NPV: 8,17,000 ÷ (1.10)³ = 8,17,000 ÷ 1.331 = ₹6,13,824 (approx.). NPV = 6,13,824 − 5,00,000 = ₹1,13,824, which is positive and agrees with MIRR above 10%.

Answer: MIRR is about 17.8%, which is higher than the 10% cost of capital. The NPV cross-check is about ₹1,13,824 (positive). Accept the project.

Exam tips

In written answers, show the table of cash flows and discount factors first. Marks are given for each step even if the final figure is off.
When the question gives a single IRR trial rate or a table, use only those values. Do not switch to your own calculator figures midway.
If two mutually exclusive projects are given, calculate NPV and IRR for both and comment on the conflict. The comment on cause and the final NPV-based recommendation usually carry marks.
For MCQ case scenarios, check the decision rule first. For example, if NPV is positive then PI is above 1 and IRR is above the cost of capital for conventional flows. This can remove options without calculation.
State assumptions where the question is silent, such as year-end cash flows and the reinvestment rate used for MIRR.

Practice questions from Advanced Capital Budgeting Decisions

Capital Budgeting Basics and Appraisal Techniques in other exams

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

Capital Budgeting Basics and Appraisal Techniques: frequently asked questions

Why do NPV and IRR give different rankings?

They can differ for mutually exclusive projects when the projects have different sizes or different timing of cash flows. IRR assumes reinvestment at the IRR, while NPV assumes reinvestment at the cost of capital. Prefer NPV in that case.

How is MIRR different from IRR?

IRR assumes inflows are reinvested at the IRR itself. MIRR compounds inflows at a stated reinvestment rate and discounts outlays at a finance rate, so it gives a more realistic single rate. It also avoids the multiple-IRR problem.

When can a project have more than one IRR?

This can happen when cash flows change sign more than once, such as an outflow, then inflows, then another outflow. The NPV equation then has more than one root. Use NPV or MIRR in such cases.

Is payback a good method to use?

It is simple and shows how quickly money is recovered, which helps when liquidity or risk is a concern. But it ignores cash flows after the payback point, and simple payback ignores time value. Use it only as a supporting measure alongside NPV.

What does a profitability index of 1 mean?

It means the present value of inflows equals the outlay, so NPV is zero and the project earns exactly the cost of capital. You would be indifferent on value grounds. Normally accept only if PI is above 1.