Question 2 (b)
NPV and profitability index of two projects of different size
8 marks
- Time to write
- About 16 minutes
From an older CBCS paper
Question
Question 2 (b) · 8 marksA company's management is considering two alternative proposals. Project A needs a capital outlay of Rs 14,40,000, and project B Rs 21,60,000. Each is estimated to generate cash flows over five years: Project A Rs. 4,80,000 per year, and Project B Rs. 6,96,000 per year. With a cost of capital of 10%, determine, on the basis of the methods below, which of the two projects should be selected:
the net present value method, and
the profitability index method.
If they conflict, which criteria should be followed, and why? 8
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.
- net present valueCash flows year by year in one table, then discount, then a one-line decision.
What the paper leaves open
The projects differ in size, so NPV and PI can rank them differently; the answer states which to follow when they conflict.
Write it in this order
- Read the data; note exactly what is asked 1 min
- 1 PV of cash flows and NPV 3 marks 5 min
- 2 Profitability index 2 marks 4 min
- 3 Conflict and the criterion to follow 3 marks 5 min
- Check: arithmetic, units (₹, %), final answer underlined 1 min
Try it first. About 16 minutes for 8 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.
Annuity factor, 5 years at 10% = 3.791.
| Particulars (₹) | Project A | Project B |
|---|---|---|
| Annual cash flow | 4,80,000 | 6,96,000 |
| PV of cash flows (× 3.791) | 18,19,680 | 26,38,536 |
| Less: capital outlay | 14,40,000 | 21,60,000 |
| (i) NPV | 3,79,680 | 4,78,536 |
| (ii) PI (PV ÷ outlay) | 1.2637 | 1.2215 |
Results. By NPV, Project B is better (₹4,78,536 against ₹3,79,680); a project is accepted if its NPV is positive. By PI, Project A is better (1.2637 against 1.2215); PI is the ratio of the present value of the inflows to the outlay, accepted if above 1.
Which to follow? The conflict arises because the projects differ in size: PI is a relative measure (value per rupee), NPV an absolute one (value added). When funds are not limited and the projects are mutually exclusive, follow NPV: it measures the absolute increase in the shareholders' wealth, which is the objective, and B adds ₹98,856 more. PI cannot aggregate several small projects to compare with a large one and is useful mainly under capital rationing. Select Project B.
Where the 8 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | PV of cash flows and NPV | 3 |
| 2 | Profitability index | 2 |
| 3 | Conflict and the criterion to follow | 3 |
| Total | 8 |
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