Question 2 OR (b)
Drying equipment: payback, NPV and IRR
7 marks
- Time to write
- About 14 minutes
From an older CBCS paper
Question
Question 2 OR (b) · 7 marksA company is considering a proposal to install a drying equipment, involving a cash outlay of Rs. 7,20,000/- and net working capital of Rs. 96,000/-. The project's expected life is 5 years, with no salvage value. The working capital is to be realized in the last year. Assume that the company may charge depreciation on a straight-line basis for income tax purpose. The estimated cash inflows before tax and depreciation are:
| Year | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Inflows of cash | Rs.2,88,000 | Rs.3,30,000 | Rs.2,52,000 | Rs.2,16,000 | Rs.1,92,000 |
The income-tax rate applicable to the Company is 35%. With an opportunity cost of capital of 12%, calculate, for the equipment, the Payback Period, Net Present Value and. Also advice the Company on installing the Equipment. (7)
Present Values factors at 12%, 14% and 15%:
| Year | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| 12% (PV factor) | 0.8929 | 0.7972 | 0.7118 | 0.6355 | 0.5674 |
| 14% (PV factor) | 0.8772 | 0.7695 | 0.6950 | 0.5921 | 0.5194 |
| 15% (PV factor) | 0.8696 | 0.7561 | 0.6575 | 0.5718 | 0.4972 |
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
- Assume that the company may charge…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
"Net Present Value and." is printed with a word missing; the 14% and 15% factors suggest the IRR, so the answer also computes the IRR and states this. The paper prints the 14% factor for year 3 as 0.6950; the correct factor is 0.6750, and the answer uses the correct factor and says so. "Advice" is kept as printed.
Write it in this order
- Read the data; note exactly what is asked 1 min
- 1 Cash flows after tax 2 marks 3 min
- 2 Payback period 1½ marks 3 min
- 3 NPV 2 marks 3 min
- 4 IRR, with the misprint noted 1 mark 2 min
- 5 Advice ½ mark 1 min
- Check: arithmetic, units (₹, %), final answer underlined 1 min
Short on time? End with step 5's one-line decision, whatever happens: never leave the figures without it.
Try it first. About 14 minutes for 7 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 (straight line, no salvage) = 7,20,000 ÷ 5 = ₹1,44,000 a year; CFAT = profit after tax + depreciation. Total outlay = equipment 7,20,000 + working capital 96,000 = ₹8,16,000; the working capital is released in year 5.
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 | CFBT | Less: depreciation | PBT | Tax @ 35% | PAT | Add: depreciation | CFAT |
|---|---|---|---|---|---|---|---|
| 1 | 2,88,000 | 1,44,000 | 1,44,000 | 50,400 | 93,600 | 1,44,000 | 2,37,600 |
| 2 | 3,30,000 | 1,44,000 | 1,86,000 | 65,100 | 1,20,900 | 1,44,000 | 2,64,900 |
| 3 | 2,52,000 | 1,44,000 | 1,08,000 | 37,800 | 70,200 | 1,44,000 | 2,14,200 |
| 4 | 2,16,000 | 1,44,000 | 72,000 | 25,200 | 46,800 | 1,44,000 | 1,90,800 |
| 5 | 1,92,000 | 1,44,000 | 48,000 | 16,800 | 31,200 | 1,44,000 | 1,75,200 |
Payback period (total outlay ₹8,16,000, operating cash flows cumulated): 2,37,600; 5,02,500; 7,16,700 by year 3; the remaining 99,300 comes from year 4's 1,90,800. Payback = 3 + 99,300 ÷ 1,90,800 = 3.52 years.
NPV at 12% (year 5 includes the ₹96,000 working capital released: 2,71,200)
| Year | Net cash flow | PVF @ 12% | PV |
|---|---|---|---|
| 1 | 2,37,600 | 0.8929 | 2,12,153.04 |
| 2 | 2,64,900 | 0.7972 | 2,11,178.28 |
| 3 | 2,14,200 | 0.7118 | 1,52,467.56 |
| 4 | 1,90,800 | 0.6355 | 1,21,253.40 |
| 5 | 2,71,200 | 0.5674 | 1,53,878.88 |
| Total PV | 8,50,931.16 |
NPV = 8,50,931.16 − 8,16,000 = ₹34,931.16.
IRR (paper note: the requirement after "Net Present Value and" is missing; the 14% and 15% factors point to the IRR, so it is computed). The paper's 14% factor for year 3 (0.6950) is a misprint for 0.6750, which is used. At 14% the NPV is −₹5,317.77 and at 15% −₹24,315.57: the IRR lies below 14%. Interpolating between 12% and 14%:
IRR = 12% + 34,931.16 ÷ (34,931.16 + 5,317.77) × 2% = 13.74%.
Advice. NPV is positive and the IRR (13.74%) exceeds the 12% cost of capital, and the outlay is recovered in 3.52 of the 5 years: the company should install the equipment.
Where the 7 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Cash flows after tax | 2 |
| 2 | Payback period | 1.5 |
| 3 | NPV | 2 |
| 4 | IRR, with the misprint noted | 1 |
| 5 | Advice | 0.5 |
| Total | 7 |
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