Question 2 OR (a)
Payback period and profitability index
8 marks
- Time to write
- About 16 minutes
From an older CBCS paper
Question
Question 2 OR (a) · 8 marksS Limited is considering to instal a new project, costing Rs. 9,00,000, which will have a life of 6 years and no salvage value at its end. The company pays tax at the rate of 40%, and follows the straight line method of depreciation. Its profits before depreciation and tax (PBDT) are estimated as:
| Year | Rs. |
|---|---|
| 1 | 1,80,000 |
| 2 | 2,40,000 |
| 3 | 2,70,000 |
| 4 | 3,00,000 |
| 5 | 3,60,000 |
| 6 | 4,80,000 |
Compute:
The Payback period
The Profitability index at a 12% discount rate. 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
- 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 1 min
- 1 Cash flows after tax 3 marks 5 min
- 2 Payback period 2 marks 4 min
- 3 Present values and PI 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.
Cash flows after tax. Depreciation = 9,00,000 ÷ 6 = ₹1,50,000 a year; cash flow = profit after tax + depreciation.
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 | PBDT | Depreciation | PBT | Tax @ 40% | PAT | Add: depreciation | Cash flow |
|---|---|---|---|---|---|---|---|
| 1 | 1,80,000 | 1,50,000 | 30,000 | 12,000 | 18,000 | 1,50,000 | 1,68,000 |
| 2 | 2,40,000 | 1,50,000 | 90,000 | 36,000 | 54,000 | 1,50,000 | 2,04,000 |
| 3 | 2,70,000 | 1,50,000 | 1,20,000 | 48,000 | 72,000 | 1,50,000 | 2,22,000 |
| 4 | 3,00,000 | 1,50,000 | 1,50,000 | 60,000 | 90,000 | 1,50,000 | 2,40,000 |
| 5 | 3,60,000 | 1,50,000 | 2,10,000 | 84,000 | 1,26,000 | 1,50,000 | 2,76,000 |
| 6 | 4,80,000 | 1,50,000 | 3,30,000 | 1,32,000 | 1,98,000 | 1,50,000 | 3,48,000 |
(i) Payback period. Cumulative cash flows: 1,68,000; 3,72,000; 5,94,000; 8,34,000 by year 4, leaving 66,000 to recover from year 5's 2,76,000. With unequal inflows, payback is found by cumulating them:
Payback = 4 + 66,000 ÷ 2,76,000 = 4.24 years.
(ii) Profitability index at 12%
| Year | Cash flow | PVF @ 12% | PV |
|---|---|---|---|
| 1 | 1,68,000 | 0.893 | 1,50,024 |
| 2 | 2,04,000 | 0.797 | 1,62,588 |
| 3 | 2,22,000 | 0.712 | 1,58,064 |
| 4 | 2,40,000 | 0.636 | 1,52,640 |
| 5 | 2,76,000 | 0.567 | 1,56,492 |
| 6 | 3,48,000 | 0.507 | 1,76,436 |
| Total PV | 9,56,244 |
PI = PV of inflows ÷ outlay = 9,56,244 ÷ 9,00,000 = 1.0625. Since PI > 1 (NPV ₹56,244), the project is acceptable at 12%.
Where the 8 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Cash flows after tax | 3 |
| 2 | Payback period | 2 |
| 3 | Present values and PI | 3 |
| Total | 8 |
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