Question 2 (a)
Discounted payback period and profitability index
8 marks
- Time to write
- About 16 minutes
From an older CBCS paper
Question
Question 2 (a) · 8 marks- Zenith Industries has under consideration an investment proposal: a project costing ₹6,00,000, which will have a life of 5 years and no salvage value at its end. The company pays tax at the rate of 40% and charges depreciation on the Straight line method; its cost of capital is 12%. Estimates of the profits before depreciation and tax (PBDT) are as follows:
| Year | PBDT |
|---|---|
| 1 | ₹ 1,62,000 |
| 2 | ₹ 1,74,000 |
| 3 | ₹ 1,80,000 |
| 4 | ₹ 2,22,000 |
| 5 | ₹ 2,64,000 |
Compute:
The Discounted Payback Period
The Profitability Index
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 Discounted cash flows and discounted payback 3 marks 5 min
- 3 Profitability index and conclusion 2 marks 4 min
- Check: arithmetic, units (₹, %), final answer underlined 1 min
Short on time? End with step 3's one-line conclusion, whatever happens: never leave the figures without it.
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 = 6,00,000 ÷ 5 = ₹1,20,000; 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 | CFAT |
|---|---|---|---|---|---|---|---|
| 1 | 1,62,000 | 1,20,000 | 42,000 | 16,800 | 25,200 | 1,20,000 | 1,45,200 |
| 2 | 1,74,000 | 1,20,000 | 54,000 | 21,600 | 32,400 | 1,20,000 | 1,52,400 |
| 3 | 1,80,000 | 1,20,000 | 60,000 | 24,000 | 36,000 | 1,20,000 | 1,56,000 |
| 4 | 2,22,000 | 1,20,000 | 1,02,000 | 40,800 | 61,200 | 1,20,000 | 1,81,200 |
| 5 | 2,64,000 | 1,20,000 | 1,44,000 | 57,600 | 86,400 | 1,20,000 | 2,06,400 |
| Year | CFAT | PVF @ 12% | PV | Cumulative PV |
|---|---|---|---|---|
| 1 | 1,45,200 | 0.893 | 1,29,663.60 | 1,29,663.60 |
| 2 | 1,52,400 | 0.797 | 1,21,462.80 | 2,51,126.40 |
| 3 | 1,56,000 | 0.712 | 1,11,072 | 3,62,198.40 |
| 4 | 1,81,200 | 0.636 | 1,15,243.20 | 4,77,441.60 |
| 5 | 2,06,400 | 0.567 | 1,17,028.80 | 5,94,470.40 |
(i) Discounted payback period. The simple payback ignores the time value of money; to correct this, the cash inflows are discounted at the required rate of return and the payback is read from their cumulative present values. Here the cumulative PV at the end of year 5 is ₹5,94,470.40, still ₹5,529.60 short of the ₹6,00,000 cost: the project does not pay back on a discounted basis within its 5-year life.
(ii) Profitability index = PV of inflows ÷ outlay = 5,94,470.40 ÷ 6,00,000 = 0.9908.
Conclusion. PI is below 1 (NPV −₹5,529.60), consistent with the missing discounted payback: at a 12% cost of capital the project should be rejected.
Where the 8 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Cash flows after tax | 3 |
| 2 | Discounted cash flows and discounted payback | 3 |
| 3 | Profitability index and conclusion | 2 |
| Total | 8 |
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