Question 4 (b)
Is a photocopying machine worth buying? Present value of net annual earnings
6 marks
- Time to write
- About 12 minutes
Question
Question 4 (b) · 6 marksA person is considering installing a photocopying machine at a cost of ₹12,00,000. Its productive life span is 5 years, during which the supplier will maintain the machine free of cost. On average he can photocopy 2,500 pages per day and charge the customers 60 paise for each page. The toner cartridge must be replaced after every 4,000 pages, at a cost of ₹600. A loan can be obtained to buy the machine at 10% p.a. effective. Find out whether the purchase is worthwhile or not, assuming that the machine is used for 300 days in a year.
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
- assuming that the machine is used…The paper fixes this: use it as given, and say so in your answer.
- Find outFormula first, then the working, then the answer with its unit (₹, %, units).
What the paper leaves open
Part of "Attempt any three"; 6 marks, from the marker printed after part (d).
Write it in this order
- Read the data; note exactly what is asked 1 min
- 1 Net annual earnings 2 marks 3 min
- 2 Present value of the earnings 2 marks 3 min
- 3 Comparison and decision 2 marks 3 min
- Check: arithmetic, units (₹, %), final answer underlined 2 min
Short on time? End with step 3's one-line decision, whatever happens: never leave the figures without it.
Try it first. About 12 minutes for 6 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.
The purchase is worthwhile if the present value of the net annual earnings over the machine's life, discounted at the 10% effective loan rate, exceeds its cost (a capital expenditure decision by present values).
Net annual earnings (300 working days a year; maintenance is free)
| Item | Working | ₹ a year |
|---|---|---|
| Pages copied | 2,500 × 300 = 7,50,000 pages | |
| Receipts | 7,50,000 × ₹0.60 | 4,50,000 |
| Toner cartridges | (7,50,000/4,000) = 187.5 cartridges × ₹600 | 1,12,500 |
| Net earnings | 3,37,500 |
Present value of 5 annual net earnings at 10% (taken at the end of each year, an ordinary annuity):
P(5, 0.10) = [1 − (1.10)⁻⁵]/0.10 = 3.790787.
PV = 3,37,500 × 3.790787 = ₹12,79,390.53.
| ₹ | |
|---|---|
| Cost of the machine | 12,00,000.00 |
| Excess of present value over cost | 79,390.53 |
| Present value of net earnings | 12,79,390.53 |
The present value of the net earnings (₹12,79,390.53) exceeds the cost (₹12,00,000) by ₹79,390.53, so the purchase is worthwhile. Equivalently, the equal annual instalment needed to repay a ₹12,00,000 loan over 5 years at 10%, 12,00,000/3.790787 = ₹3,16,556.98, is less than the net annual earnings of ₹3,37,500.
Where the 6 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Net annual earnings | 2 |
| 2 | Present value of the earnings | 2 |
| 3 | Comparison and decision | 2 |
| Total | 6 |
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