Question 2 OR
Mechanisation project: payback period and NPV
15 marks
- Time to write
- About 30 minutes
From an older CBCS paper
Question
Question 2 OR · 15 marksRST Limited is evaluating a project for installing a machine system. It estimates the annual savings from mechanization to include a cut of 5 clerical employees, each with an annual salary of Rs. 36000, Rs. 19200 in material losses in production, and Rs. 8400 in other operating costs. The system's purchase price is Rs. 2.4 lakh, and its installation costs are Rs. 60000. Its useful life is estimated to be 5 years. These outlays will be written down, on a straight-line basis, to a book salvage value of Rs. 24,000. Though its market value after 5 years will be zero. Running the new system needs two trained operators, at an annual salary of Rs. 50400 per person. Annual maintenance and operating cash expenses of Rs. 9600 are also estimated to be required. The tax rate of the company is 40%, and the ROR (cost of capital) it requires on this project is 12%. Calculate the payback period and NPV of the project, and advise the company whether it should purchase the system?
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.
What the paper leaves open
(1) The machine is depreciated to the book salvage value, but sells for nothing at the end of year 5; the answer treats the unrecovered book value as a loss at year 5, with its tax effect, and states this.
Write it in this order
- Read the data; note exactly what is asked 2 min
- 1 Net annual saving 3 marks 5 min
- 2 Depreciation and annual cash inflow after tax 3 marks 5 min
- 3 Year-5 loss on the book salvage and its tax saving 2 marks 4 min
- 4 Payback period 2 marks 4 min
- 5 NPV at 12% 4 marks 7 min
- 6 Advice 1 mark 1 min
- Check: arithmetic, units (₹, %), final answer underlined 2 min
Short on time? End with step 6's one-line decision, whatever happens: never leave the figures without it.
Try it first. About 30 minutes for 15 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.
Annual saving before depreciation and tax (₹)
| Particulars | ₹ |
|---|---|
| Salaries of 5 clerical employees (5 × 36,000) | 1,80,000 |
| Material losses avoided | 19,200 |
| Other operating costs saved | 8,400 |
| Gross annual savings | 2,07,600 |
| Salaries of 2 operators (2 × 50,400) | 1,00,800 |
| Maintenance and operating cash expenses | 9,600 |
| Extra annual costs | 1,10,400 |
| Net annual saving (2,07,600 − 1,10,400) | 97,200 |
Depreciation (straight line to the book salvage) = (2,40,000 + 60,000 − 24,000) ÷ 5 = ₹55,200. Depreciation is a non-cash item: it lowers the tax, and its tax saving is a cash inflow.
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.
Annual cash inflow after tax: EBT = 97,200 − 55,200 = 42,000; tax @ 40% = 16,800; EAT = 25,200.
| Particulars | ₹ |
|---|---|
| Earnings after tax | 25,200 |
| Add: depreciation | 55,200 |
| Cash inflow after tax (each year) | 80,400 |
Year 5. The system is written down to ₹24,000 but sells for nothing, so the ₹24,000 book value is a loss at the end of year 5, saving tax of ₹9,600 (paper note 1). Year-5 inflow = 80,400 + 9,600 = ₹90,000.
(a) Payback period. Outlay = 2,40,000 + 60,000 = ₹3,00,000. After 3 years ₹2,41,200 is recovered; ₹58,800 remains, against ₹80,400 in year 4: payback = 3 + 58,800 ÷ 80,400 = 3.73 years. The payback is accepted only against a cut-off period set by management; none is given.
| Year | Cash inflow | PV factor @ 12% | Present value |
|---|---|---|---|
| 1 | 80,400 | 0.893 | 71,797.20 |
| 2 | 80,400 | 0.797 | 64,078.80 |
| 3 | 80,400 | 0.712 | 57,244.80 |
| 4 | 80,400 | 0.636 | 51,134.40 |
| 5 (80,400 + tax saving on the loss 9,600) | 90,000 | 0.567 | 51,030 |
| Total present value | 2,95,285.20 | ||
| Less: outlay | 3,00,000 | ||
| NPV | −4,714.80 |
Advice. A project is accepted only if its NPV is positive and rejected if it is negative. The NPV is negative (−₹4,714.80), so although the system pays back in 3.73 years of a 5-year life, RST Limited should not purchase it: it does not earn the 12% required. (Ignoring the tax saving on the year-5 loss would make the NPV more negative, −₹10,158.)
Where the 15 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Net annual saving | 3 |
| 2 | Depreciation and annual cash inflow after tax | 3 |
| 3 | Year-5 loss on the book salvage and its tax saving | 2 |
| 4 | Payback period | 2 |
| 5 | NPV at 12% | 4 |
| 6 | Advice | 1 |
| Total | 15 |
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