Question 4 (b)
Machine A or Machine B: present value of labour savings at 12%
6 marks
- Time to write
- About 12 minutes
Question
Question 4 (b) · 6 marksMachine A costs ₹9,000, with a useful life of 8 years; Machine B costs ₹7,000, with a useful life of 6 years. Suppose Machine A generates an annual labour savings of ₹2,200 while Machine B generates an annual labour savings of ₹1,900. Assuming that the time value of money of the corporation is 12% per annum, which machine is preferable?
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 time value of…The paper fixes this: use it as given, and say so in your answer.
- which machine is preferableEnd with a one-line decision that follows from your figures.
What the paper leaves open
The paper sets this part under the instruction to answer any three questions, and gives it 6 marks.
Write it in this order
- Read the data; note exactly what is asked 1 min
- 1 Present value of savings, A and B 3 marks 5 min
- 2 Comparison allowing for different lives 2 marks 4 min
- 3 Decision 1 mark 1 min
- Check: arithmetic, units (₹, %), final answer underlined 1 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.
Each machine is judged by the present value of its labour savings over its life, at the corporation's 12% time value of money, against its cost (a capital expenditure decision by present values). Savings are taken at the end of each year, an ordinary annuity with P(n, i) = [1 − (1 + i)⁻ⁿ]/i.
P(8, 0.12) = 4.967640; P(6, 0.12) = 4.111407.
| Machine A | Machine B | |
|---|---|---|
| Annual labour saving (₹) | 2,200 | 1,900 |
| Life (years) | 8 | 6 |
| Annuity factor at 12% | 4.967640 | 4.111407 |
| Cost (₹) | 9,000.00 | 7,000.00 |
| Net present value (₹) | 1,928.81 | 811.67 |
| Present value of savings (₹) | 10,928.81 | 7,811.67 |
Both machines are worth buying (each NPV is positive), and Machine A gives the larger net present value (₹1,928.81 against ₹811.67).
Allowing for the different lives. Spreading each NPV over its own life as an equal annual amount: A: 1,928.81/4.967640 = ₹388.27 a year; B: 811.67/4.111407 = ₹197.42 a year. Machine A is still better. (Equivalently, the annual cost of capital is 9,000/4.967640 = ₹1,811.73 for A against a saving of ₹2,200, and 7,000/4.111407 = ₹1,702.58 for B against ₹1,900.)
Where the 6 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Present value of savings, A and B | 3 |
| 2 | Comparison allowing for different lives | 2 |
| 3 | Decision | 1 |
| Total | 6 |
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