Question 2
Payback, NPV and IRR of a project that never recovers its cost
18.75 marks
- Time to write
- About 38 minutes
From an older CBCS paper
Question
Question 2 · 18.75 marksA project needs an initial investment of Rs.6, 00,000. Its estimated life is 6 years, and its estimated net cash flows are as follows:
| Year | Net Cash Flow (Rs.) |
|---|---|
| 1 | 55,000 |
| 2 | 75,000 |
| 3 | 95,000 |
| 4 | 1,05,000 |
| 5 | 1,15,000 |
| 6 | 85,000 |
The hurdle rate is 10%. Calculate-
The Payback period
The Net Present Value
The project's IRR.
Assume a standard payback period of 4 years. As per each of these measures, should the project be accepted? If the decisions conflict, which method should be preferred 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
- Should…?Which…?Two asks in one question: answer both. Where it asks why, give reasons, not a description.
- Assume a standard payback period of…The paper fixes this: use it as given, and say so in your answer.
- Payback periodCash flows year by year in one table, then discount, then a one-line decision.
What the paper leaves open
No mark is printed for the question; the paper asks for any four of six, equal marks. The cash inflows total less than the outlay, so the project does not pay back within its life and its IRR is negative; the answer says so rather than forcing a positive figure.
Write it in this order
- Read the data; note exactly what is asked 2 min
- 1 Payback period 4 marks 7 min
- 2 NPV 5 marks 9 min
- 3 IRR 5 marks 9 min
- 4 Decisions and which method to prefer 4.8 marks 9 min
- Check: arithmetic, units (₹, %), final answer underlined 2 min
Try it first. About 38 minutes for 18.75 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.
a. Payback period. Cumulating the cash flows:
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 | Net cash flow (₹) | Cumulative (₹) |
|---|---|---|
| 1 | 55,000 | 55,000 |
| 2 | 75,000 | 1,30,000 |
| 3 | 95,000 | 2,25,000 |
| 4 | 1,05,000 | 3,30,000 |
| 5 | 1,15,000 | 4,45,000 |
| 6 | 85,000 | 5,30,000 |
The inflows over the whole life total ₹5,30,000, less than the ₹6,00,000 invested (paper note). The project never pays back: there is no payback period within its six-year life, against the standard of 4 years.
| Year | Cash flow (₹) | PVF @ 10% | PV (₹) |
|---|---|---|---|
| 1 | 55,000 | 0.909 | 49,995 |
| 2 | 75,000 | 0.826 | 61,950 |
| 3 | 95,000 | 0.751 | 71,345 |
| 4 | 1,05,000 | 0.683 | 71,715 |
| 5 | 1,15,000 | 0.621 | 71,415 |
| 6 | 85,000 | 0.564 | 47,940 |
| Total PV | 3,74,360 |
NPV = 3,74,360 − 6,00,000 = −₹2,25,640.
c. Internal rate of return. Since the undiscounted inflows (₹5,30,000) are below the outlay, the NPV is negative even at a 0% discount rate; the IRR is therefore negative. Solving NPV = 0 gives an IRR of about −3.21%, far below the 10% hurdle rate.
| Measure | Result | Standard | Decision |
|---|---|---|---|
| Payback | Not recovered in 6 years | 4 years | Reject |
| NPV | −₹2,25,640 | NPV ≥ 0 | Reject |
| IRR | −3.21% | 10% | Reject |
There is no conflict: every measure rejects the project. Had the methods conflicted, NPV (supported by IRR) should be preferred over payback: payback ignores the time value of money and the cash flows after the payback period, while NPV measures the project's addition to shareholders' wealth.
Where the 18.75 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Payback period | 4 |
| 2 | NPV | 5 |
| 3 | IRR | 5 |
| 4 | Decisions and which method to prefer | 4.75 |
| Total | 18.75 |
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