Capital budgeting: NPV, profitability index and IRR
Financial Management · Unit IV · Topic 14 of 16 · 4 min read
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Cases checked to exist. Read the judgment before quoting a holding.
Every case cited here has been checked to exist — the citation resolves and names the right parties. The propositions attributed to each case have not been verified line by line against the judgment. Case names link through to the full judgment: read it before quoting a holding in an examination answer, and never carry a proposition from notes into court on trust.
1. Net present value
NPV = Σ CFATt ÷ (1 + k)t − outlay, where k is the cost of capital. It recognises the time value of money, uses all cash flows, and measures the increase in shareholders’ wealth directly, which is why it is the preferred method. Its limits: k must be known, and it favours large projects in absolute terms.
C and S company (January 2026). CFAT from the previous note; cost of capital 15%.
| Year | CFAT | PV at 15% | PV Rs. |
|---|---|---|---|
| 1 | 1,00,000 | 0.870 | 87,000 |
| 2 | 1,00,000 | 0.756 | 75,600 |
| 3 | 88,000 | 0.658 | 57,904 |
| 4 | 88,000 | 0.572 | 50,336 |
| 5 | 70,000 | 0.497 | 34,790 |
| Total PV | 3,05,630 | ||
| Less outlay | 2,00,000 | ||
| NPV | 1,05,630 | ||
NPV positive: accept. (PI = 3,05,630 ÷ 2,00,000 = 1.53.)
2. Profitability index
PI (benefit–cost ratio) = PV of inflows ÷ PV of outlay. Accept if above 1. It ranks projects of different sizes and is the method for capital rationing.
ABC Ltd (February 2025). CFAT 17,000; 17,600; 19,100; 23,960; 24,200 (previous note); factors at 10%.
| Year | CFAT | PV at 10% | PV Rs. |
|---|---|---|---|
| 1 | 17,000 | 0.909 | 15,453 |
| 2 | 17,600 | 0.826 | 14,538 |
| 3 | 19,100 | 0.751 | 14,344 |
| 4 | 23,960 | 0.683 | 16,365 |
| 5 | 24,200 | 0.621 | 15,028 |
| Total PV | 75,728 | ||
NPV = 75,728 − 1,00,000 = −Rs. 24,272; PI = 75,728 ÷ 1,00,000 = 0.76. Reject: the project does not recover its cost in present-value terms.
3. Mutually exclusive machines (February 2025)
Each costs Rs. 2,50,000; straight-line depreciation over 5 years = Rs. 50,000; CFAT given; discount rate 10%.
| Year | PV 10% | A CFAT | A PV | B CFAT | B PV |
|---|---|---|---|---|---|
| 1 | 0.909 | 3,00,000 | 2,72,700 | 50,000 | 45,450 |
| 2 | 0.826 | 4,00,000 | 3,30,400 | 1,50,000 | 1,23,900 |
| 3 | 0.751 | 5,00,000 | 3,75,500 | 2,00,000 | 1,50,200 |
| 4 | 0.683 | 3,00,000 | 2,04,900 | 3,00,000 | 2,04,900 |
| 5 | 0.621 | 2,00,000 | 1,24,200 | 2,00,000 | 1,24,200 |
| Total | 17,00,000 | 13,07,700 | 9,00,000 | 6,48,650 | |
| Method | Machine A | Machine B |
|---|---|---|
| NPV (PV − 2,50,000) | 10,57,700 | 3,98,650 |
| PI (PV ÷ 2,50,000) | 5.23 | 2.59 |
| Average CFAT | 3,40,000 | 1,80,000 |
| Average profit (− dep. 50,000) | 2,90,000 | 1,30,000 |
| ARR on average investment 1,25,000 | 232% | 104% |
Machine A is more profitable on all three methods. (ARR on original investment: 116% and 52%.)
4. August 2024: NPV, payback and PI
Outlay Rs. 1,00,000; life 5 years; scrap Rs. 10,000; profit after tax before depreciation (= CFAT) 6,000; 14,000; 24,000; 16,000; nil; factors at 10%.
PV of CFAT = 5,454 + 11,564 + 18,024 + 10,928 + 0 = 45,970; PV of scrap 10,000 × 0.621 = 6,210; total 52,180. NPV = 52,180 − 1,00,000 = −Rs. 47,820; PI = 0.52. Cumulative CFAT is only Rs. 60,000 by year 4 and Rs. 70,000 with scrap in year 5: the outlay is never recovered, so there is no payback within the life. Reject on every method. (Write this conclusion plainly; examiners set such figures to test whether you can say “no payback”.)
5. Internal rate of return
IRR is the discount rate r at which PV of inflows equals the outlay (NPV = 0). Accept if r exceeds the cost of capital. Find it by trial: choose a rate, compute NPV; if positive, try a higher rate; interpolate between a positive and a negative NPV:
IRR = L + [NPVL ÷ (NPVL − NPVH)] × (H − L)
August 2024. Cost Rs. 22,000; inflows 12,000; 4,000; 2,000; 10,000.
| Year | Inflow | PV 10% | PV Rs. | PV 12% | PV Rs. |
|---|---|---|---|---|---|
| 1 | 12,000 | 0.909 | 10,908 | 0.893 | 10,716 |
| 2 | 4,000 | 0.826 | 3,304 | 0.797 | 3,188 |
| 3 | 2,000 | 0.751 | 1,502 | 0.712 | 1,424 |
| 4 | 10,000 | 0.683 | 6,830 | 0.636 | 6,360 |
| Total PV | 22,544 | 21,688 | |||
| NPV (− 22,000) | +544 | −312 | |||
IRR = 10 + [544 ÷ (544 + 312)] × 2 = 10 + 1.27 = 11.27%. (Exact computation gives 11.25%.)
6. NPV against IRR
- For a single conventional project both give the same accept–reject decision.
- For mutually exclusive projects they can conflict, when the projects differ in size or in the timing of flows. NPV assumes reinvestment at the cost of capital, IRR at the IRR itself; the NPV assumption is more realistic, so NPV is preferred.
- Unconventional flows (negative flows later in life) can give more than one IRR, or none.
- IRR is popular with managers because a percentage is easy to compare with the cost of capital.
How this is examined
Every paper has one of these problems for 10 marks in Unit IV. Write the formula, the CFAT table, the PV table, and a one-line decision for each method asked. In an IRR question, show both trial rates and the interpolation. If the question gives “income after depreciation before tax” (January 2026), tax it and add depreciation back; if it gives “profit after tax before depreciation” (August 2024), that figure is already the CFAT.
Now try the real questions: Financial Management past question papers.