Question 2 OR (b)
NPV and profitability index of two projects
12 marks
- Time to write
- About 24 minutes
Question
Question 2 OR (b) · 12 marksA company's management is considering two alternative proposals. Project A needs a capital outlay of Rs. 14,40,000, while Project B needs a capital outlay of Rs. 21,60,000. Each is estimated to generate cash flows for five years: Rs. 4,80,000 per annum for Project A and Rs. 6,96,000 for Project B. The cost of capital is 10%. Of the two projects, determine which is to be selected on the basis of:
- the Net Present Value method; and
- the Profitability Index method. If the two conflict, which criteria should be followed 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.
- Net Present ValueCash flows year by year in one table, then discount, then a one-line decision.
What the paper leaves open
"Criteria" is printed for "criterion" and is kept.
Write it in this order
- Read the data; note exactly what is asked 2 min
- 1 Present values of inflows 2 marks 3 min
- 2 (i) NPV and selection 3 marks 5 min
- 3 (ii) PI and selection 3 marks 5 min
- 4 Conflict explained and criterion chosen 4 marks 7 min
- Check: arithmetic, units (₹, %), final answer underlined 2 min
Try it first. About 24 minutes for 12 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.
The 5-year annuity factor at 10% is the sum of the yearly factors 0.909 + 0.826 + 0.751 + 0.683 + 0.621 = 3.790.
| ₹ | Project A | Project B |
|---|---|---|
| Annual cash inflow | 4,80,000 | 6,96,000 |
| PV of inflows (× 3.790) | 18,19,200 | 26,37,840 |
| Less: capital outlay | 14,40,000 | 21,60,000 |
| (i) NPV | 3,79,200 | 4,77,840 |
| (ii) Profitability index (PV of inflows ÷ outlay) | 1.2633 | 1.2212 |
- (i) NPV = PV of inflows − outlay: Project B is better (₹4,77,840 against ₹3,79,200).
- (ii) PI = PV of inflows ÷ PV of outflows: Project A is better (1.26 against 1.22). Both exceed 1, so both are acceptable on their own.
The conflict and which criterion to follow. The rankings conflict because the projects differ in size: B needs ₹7,20,000 more. PI is a relative measure (return per rupee), NPV an absolute one. NPV should be followed when the projects are mutually exclusive and funds are not limited: B adds ₹98,640 more to shareholders' wealth, and a project with a larger outlay can add more in absolute terms even if its rate of return is lower. The incremental investment in B (₹7,20,000 for an extra ₹2,16,000 a year) itself has a positive NPV of ₹98,640. PI would be preferred only under capital rationing, where the aim is the most NPV from a limited budget.
Where the 12 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Present values of inflows | 2 |
| 2 | (i) NPV and selection | 3 |
| 3 | (ii) PI and selection | 3 |
| 4 | Conflict explained and criterion chosen | 4 |
| Total | 12 |
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