Question 2 OR (b)
Payback period and NPV
12 marks
- Time to write
- About 24 minutes
Question
Question 2 OR (b) · 12 marksA company needs an initial investment of ₹48,000. Its estimated net cash flows (in ₹) over the next 10 years are given below:
| Year | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| Cash flow (net) | 8,400 | 8,400 | 8,400 | 8,400 | 8,400 | 9,600 | 12,000 | 18,000 | 12,000 | 4,800 |
Calculate the following, using a discount rate of 10% per annum:
Payback Period
Net Present Value (NPV)
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
- Payback 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 (i) Cumulative cash flows and payback period 4 marks 7 min
- 2 (ii) Present values 6 marks 10 min
- 3 NPV and comment 2 marks 3 min
- Check: arithmetic, units (₹, %), final answer underlined 2 min
Short on time? Step 2 carries 6 of the 12 marks: guard its minutes.
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.
(i) Payback period. The payback period is the time needed to recover the initial outlay. Cash flows are taken to arise evenly within each year.
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 | Cash flow (₹) | Cumulative (₹) |
|---|---|---|
| 1 | 8,400 | 8,400 |
| 2 | 8,400 | 16,800 |
| 3 | 8,400 | 25,200 |
| 4 | 8,400 | 33,600 |
| 5 | 8,400 | 42,000 |
| 6 | 9,600 | 51,600 |
By the end of year 5, ₹42,000 is recovered; the remaining ₹6,000 comes from year 6's ₹9,600. Payback period = 5 + 6,000 ÷ 9,600 = 5.625 years (about 5 years 7½ months).
| Year | Cash flow (₹) | PV factor @ 10% | Present value (₹) |
|---|---|---|---|
| 1 | 8,400 | 0.909 | 7,635.60 |
| 2 | 8,400 | 0.826 | 6,938.40 |
| 3 | 8,400 | 0.751 | 6,308.40 |
| 4 | 8,400 | 0.683 | 5,737.20 |
| 5 | 8,400 | 0.621 | 5,216.40 |
| 6 | 9,600 | 0.564 | 5,414.40 |
| 7 | 12,000 | 0.513 | 6,156.00 |
| 8 | 18,000 | 0.467 | 8,406.00 |
| 9 | 12,000 | 0.424 | 5,088.00 |
| 10 | 4,800 | 0.386 | 1,852.80 |
| Total PV | 58,753.20 |
NPV = 58,753.20 − 48,000 = ₹10,753.20. The NPV is positive, so the project is acceptable at 10%.
Where the 12 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | (i) Cumulative cash flows and payback period | 4 |
| 2 | (ii) Present values | 6 |
| 3 | NPV and comment | 2 |
| Total | 12 |
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