Question 2 OR
Two mutually exclusive projects: payback, NPV, PI and IRR
15 marks
- Time to write
- About 30 minutes
From an older CBCS paper
Question
Question 2 OR · 15 marksA firm with a cost of capital of 10% is considering two mutually exclusive projects, A and B, whose details are below:
| Items | Year | Project A | Project B |
|---|---|---|---|
| Cost | 0 | ₹ 60,000 | ₹ 60,000 |
| Cash Inflows | 1 | ₹ 6,000 | ₹ 30,000 |
| 2 | ₹ 12,000 | ₹ 24,000 | |
| 3 | ₹ 18,000 | ₹ 12,000 | |
| 4 | ₹ 27,000 | ₹ 6,000 | |
| 5 | ₹ 36,000 | ₹ 6,000 |
For both projects, compute the Pay Back Period, the Net Present Value at 10%, the Profitability Index, and the Internal Rate of Return. Which of the two project you would recommend, and why?
Reworded from the university paper: names and figures differ, the task is the same. The original paper belongs to the University of Delhi. See DU's question bank.
Before you write
Read off the question and its marks
Read from the question
- and whyEach answer needs its reason, not just the answer.
- Pay Back PeriodCash flows year by year in one table, then discount, then a one-line decision.
Write it in this order
- Read the data; note exactly what is asked 2 min
- 1 Payback periods 3 marks 5 min
- 2 NPVs 4 marks 7 min
- 3 Profitability indexes 2 marks 4 min
- 4 IRRs 4 marks 7 min
- 5 Recommendation with reasons 2 marks 3 min
- Check: arithmetic, units (₹, %), final answer underlined 2 min
Short on time? End with step 5's one-line decision, whatever happens: never leave the figures without it.
Try it first. About 30 minutes for 15 marks. Write it out, then open the solution.
Solution
Hover or tap a marked figure, like 72,000, to see how it is made and where else it appears.
Payback period (cumulative cash inflows)
1Rekha puts her savings into a juice cart—the jar on the counter starts empty.
Payback periodThe number of years a project takes to recover its initial investment from its cash inflows.
2Orange by orange, the jar fills back towards what the cart cost her.
Why it is a measure of liquidityHow quickly the funds locked in a project come back and can be put to other uses.
3The jar full, the counting stops—the measure never looks at all the selling still to come.
Why it is not a measure of profitabilityIt ignores the cash inflows after the payback period, however large.
| Year | Project A | Cumulative A | Project B | Cumulative B |
|---|---|---|---|---|
| 1 | 6,000 | 6,000 | 30,000 | 30,000 |
| 2 | 12,000 | 18,000 | 24,000 | 54,000 |
| 3 | 18,000 | 36,000 | 12,000 | 66,000 |
| 4 | 27,000 | 63,000 | 6,000 | 72,000 |
| 5 | 36,000 | 99,000 | 6,000 | 78,000 |
- A: 3 + (60,000 − 36,000) ÷ 27,000 = 3.89 years.
- B: 2 + (60,000 − 54,000) ÷ 12,000 = 2.50 years.
NPV at 10% and profitability index
| Year | PVF @ 10% | PV (A) | PV (B) |
|---|---|---|---|
| 1 | 0.909 | 5,454 | 27,270 |
| 2 | 0.826 | 9,912 | 19,824 |
| 3 | 0.751 | 13,518 | 9,012 |
| 4 | 0.683 | 18,441 | 4,098 |
| 5 | 0.621 | 22,356 | 3,726 |
| Total PV | 69,681 | 63,930 |
| Particulars | Project A | Project B |
|---|---|---|
| Less: cost (₹) | 60,000 | 60,000 |
| NPV (₹) | 9,681 | 3,930 |
| PI (PV ÷ cost) | 1.1614 | 1.0655 |
IRR (trial and interpolation, 3-decimal factors)
- A: NPV +₹1,308 at 14%, −₹528 at 15%: IRR = 14% + 1,308 ÷ 1,836 × 1% = 14.71%.
- B: NPV +₹594 at 13%, −₹468 at 14%: IRR = 13% + 594 ÷ 1,062 × 1% = 13.56%.
| Measure | A | B | Better |
|---|---|---|---|
| Payback (years) | 3.89 | 2.50 | B |
| NPV (₹) | 9,681 | 3,930 | A |
| PI | 1.1614 | 1.0655 | A |
| IRR (%) | 14.71 | 13.56 | A |
Recommend Project A. It has the higher NPV, PI and IRR. B recovers its cost sooner, but payback ignores the time value of money and the large inflows A earns in years 4 and 5, after its payback period. Since the outlays are equal, the discounted measures agree, and NPV, the measure of the addition to shareholders' wealth, decides the choice.
Where the 15 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Payback periods | 3 |
| 2 | NPVs | 4 |
| 3 | Profitability indexes | 2 |
| 4 | IRRs | 4 |
| 5 | Recommendation with reasons | 2 |
| Total | 15 |
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