CAIIB ABFM NPV & IRR — Capital Budgeting Complete Guide with Worked Examples
Quick Answer: NPV and IRR are CAIIB ABFM’s highest-yield calculation topics — together worth 12–18 marks in Module B (Capital Budgeting & Project Appraisal). NPV discounts all project cash flows at the cost of capital and accepts the project if the result is positive. IRR finds the discount rate at which NPV equals zero, using the interpolation method when cash flows don’t divide evenly. This guide covers both with complete worked examples, plus Payback Period, Profitability Index, and the NPV-vs-IRR decision rules IIBF tests.
CAIIB ABFM NPV & IRR — Capital Budgeting Complete Guide with Worked Examples
Capital budgeting is how a bank — or any borrower — decides whether a project is worth funding. ABFM Module B tests this through NPV and IRR more than any other sub-topic, and the two are almost always tested together in the same question: calculate NPV, then estimate IRR using interpolation, then state which to prefer if they conflict.
If you’ve appraised term loans using DSCR, you already understand the underlying logic — money today is worth more than the same money in three years. This guide formalises that intuition into the exact calculation sequence IIBF expects.
Capital Budgeting — Topic Map & Priority
| Topic | Est. Marks | Priority |
|---|---|---|
| Net Present Value (NPV) | 6–8 | HIGHEST |
| Internal Rate of Return (IRR) | 6–8 | HIGHEST |
| Payback Period (Simple & Discounted) | 3–4 | MEDIUM |
| Profitability Index (PI) | 2–3 | MEDIUM |
| Accounting Rate of Return (ARR) | 2–3 | MEDIUM |
| NPV vs IRR Conflict & Capital Rationing | 2–3 | MEDIUM |
Net Present Value (NPV)
NPV discounts every future cash flow back to today’s value using the cost of capital, then subtracts the initial investment. A positive NPV means the project creates value above the required return; a negative NPV means it destroys value.
Formula
Where: CFₜ = cash flow in year t, r = discount rate (cost of capital), t = year
Worked Example — Uneven Cash Flows
Q: A project requires an initial investment of ₹5,00,000. Expected cash flows: Year 1 = ₹1,50,000, Year 2 = ₹2,00,000, Year 3 = ₹2,50,000, Year 4 = ₹1,00,000. Cost of capital = 10%. Calculate NPV and recommend whether to accept.
| Year | Cash Flow | PV Factor @10% | Present Value |
|---|---|---|---|
| 1 | 1,50,000 | 0.9091 | 1,36,364 |
| 2 | 2,00,000 | 0.8264 | 1,65,289 |
| 3 | 2,50,000 | 0.7513 | 1,87,829 |
| 4 | 1,00,000 | 0.6830 | 68,301 |
| Total PV of Inflows | 5,57,783 | ||
Decision: Accept the project — NPV is positive, meaning it generates value above the 10% required return.
Internal Rate of Return (IRR)
IRR is the discount rate at which NPV becomes exactly zero. Since this usually can’t be solved directly with uneven cash flows, IIBF tests the interpolation method: calculate NPV at two different discount rates (one giving a positive NPV, one giving a negative NPV), then interpolate between them.
Interpolation Formula
Where: LR = Lower discount rate (positive NPV)
HR = Higher discount rate (negative NPV)
NPV(LR), NPV(HR) = NPV calculated at each rate
Worked Example — Same Project as Above
Q: Using the same project (Initial Investment ₹5,00,000; CFs: 1,50,000 / 2,00,000 / 2,50,000 / 1,00,000), find the IRR. NPV at 10% = ₹57,783 (positive, calculated above).
| Year | Cash Flow | PV Factor @16% | Present Value |
|---|---|---|---|
| 1 | 1,50,000 | 0.8621 | 1,29,310 |
| 2 | 2,00,000 | 0.7432 | 1,48,631 |
| 3 | 2,50,000 | 0.6407 | 1,60,164 |
| 4 | 1,00,000 | 0.5523 | 55,229 |
| Total PV of Inflows | 4,93,334 | ||
Step 2 — Apply interpolation:
LR = 10%, NPV(LR) = +57,783
HR = 16%, NPV(HR) = −6,666
IRR = 10 + [57,783 / (57,783 − (−6,666))] × (16 − 10)
= 10 + [57,783 / 64,449] × 6
= 10 + 0.8966 × 6
= 10 + 5.38
= 15.38%
IRR ≈ 15.38%. Since IRR (15.38%) > Cost of Capital (10%), the project is acceptable — consistent with the positive NPV result.
Choosing your two trial rates: Pick a lower rate close to where you expect NPV to be small and positive, and a higher rate where it turns negative. If your first guess gives two positive (or two negative) results, widen the gap and try again. A 4–6 percentage point gap between LR and HR usually gives accurate interpolation results.
Payback Period — Simple & Discounted
Simple Payback (even cash flows)
Payback = Initial Investment / Annual CF
Payback (uneven cash flows)
Full years + (Unrecovered amount / Next year’s CF)
Worked Example — Same Project
Cumulative CF: Y1 = 1,50,000 → Y2 = 3,50,000 → Y3 = 6,00,000 (exceeds 5,00,000 here)
Payback = 2 years + (5,00,000 − 3,50,000) / 2,50,000 = 2 + 0.6 = 2.6 years
Discounted Payback (using PV of cash flows @10% from NPV table):
Cumulative PV: Y1 = 1,36,364 → Y2 = 3,01,653 → Y3 = 4,89,482 → Y4 = 5,57,783 (exceeds here)
Discounted Payback = 3 years + (5,00,000 − 4,89,482) / 68,301 = 3 + 0.154 = 3.15 years
Profitability Index (PI) & ARR
Profitability Index
PI = PV of Cash Inflows / Initial Investment
PI > 1 → Accept · PI < 1 → Reject
Accounting Rate of Return
ARR = Avg Annual Profit / Avg Investment × 100
Avg Investment = (Initial + Salvage) / 2
Worked Example — Profitability Index (same project)
PI > 1 → Accept. Confirms the same decision as NPV and IRR.
NPV vs IRR — When They Conflict
For a single, independent project, NPV and IRR almost always agree on accept/reject. But when comparing two mutually exclusive projects (you can only choose one), NPV and IRR can rank them differently — usually because of differences in project scale or the timing of cash flows.
| Aspect | NPV | IRR |
|---|---|---|
| Result format | Absolute ₹ value | Percentage rate |
| Reinvestment assumption | Reinvested at cost of capital | Reinvested at IRR itself (less realistic) |
| Scale sensitivity | Reflects absolute value created | Ignores project size |
| When they conflict, prefer | NPV — it directly measures wealth created in rupee terms | |
IIBF’s standard conflict question: Project A has lower IRR but higher NPV than Project B (because A is a larger project). The exam asks which to choose. Answer: choose Project A based on NPV, because NPV measures the actual rupee value created — which is what matters to shareholders/the bank, not the percentage return alone.
Capital Budgeting — Formula Quick Reference
| Method | Formula | Decision Rule |
|---|---|---|
| NPV | Σ[CFₜ/(1+r)ᵗ] − Investment | Accept if NPV > 0 |
| IRR (interpolation) | LR + [NPV(LR)/(NPV(LR)−NPV(HR))]×(HR−LR) | Accept if IRR > Cost of Capital |
| Simple Payback | Investment / Annual CF | Accept if < target payback period |
| Discounted Payback | Yrs + (Unrecovered PV / Next yr PV) | Always longer than simple payback |
| Profitability Index | PV of Inflows / Investment | Accept if PI > 1 |
| ARR | Avg Profit / Avg Investment × 100 | Accept if > target ARR |
Frequently Asked Questions — ABFM NPV & IRR
Do I need to memorise present value factor tables for the exam?
No — use the on-screen calculator to compute (1+r)⁻ᵗ directly. IIBF sometimes provides a PV factor table in the question itself for convenience, but you can always calculate factors manually using the calculator. What matters is knowing which factor applies to which year and discount rate.
How do I pick the two trial rates for IRR interpolation if the question doesn’t specify them?
Start with the cost of capital or a round number near it (e.g., 10%), calculate NPV. If positive, try a rate 5–8 percentage points higher. If that NPV is negative, you have your bracket — interpolate between them. If still positive, go higher again. The wider the bracket, the less accurate the interpolation (it assumes a straight line between two points on a curve), so don’t go more than 8–10 points apart.
Is the interpolated IRR exact or approximate?
Approximate. Linear interpolation assumes NPV changes in a straight line between your two trial rates, but the actual NPV-vs-rate relationship is curved. For IIBF’s purposes this approximation is accepted as the standard method and the expected answer. Don’t worry about small decimal differences — the methodology is what’s being tested.
What’s the difference between NPV and Profitability Index — don’t they give the same accept/reject answer?
For a single project evaluated independently, yes — both give the same accept/reject decision (NPV > 0 is equivalent to PI > 1). They diverge in capital rationing situations, where you have limited funds and must choose among several positive-NPV projects. PI ranks projects by “bang for the buck” (value created per rupee invested), which is more useful than NPV alone when you can’t fund every positive-NPV project.
How much of ABFM Module B is NPV/IRR versus other capital budgeting methods?
NPV and IRR together account for roughly half of Module B’s numerical questions. The remaining marks come from Payback Period, Profitability Index, ARR, and conceptual questions about capital rationing and project ranking. Master NPV and IRR first — they unlock the underlying logic that makes the other methods easy to learn quickly afterward.