Question 1 (b)
Perpetuity offer: accept or reject at 12% and 11%
7 marks
- Time to write
- About 14 minutes
From an older CBCS paper
Question
Question 1 (b) · 7 marksA finance company has made an offer to deposit a sum of Rs. 42,000 and then receive Rs. 4,752 p.a. as a return, perpetually. If the rate of return is 12% p.a., should the offer be accepted? If the rate of return is 11% p.a., will the decision change? 7
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
- should theEnd with a one-line decision that follows from your figures.
Write it in this order
- Read the data; note exactly what is asked 1 min
- 1 Perpetuity formula 2 marks 4 min
- 2 PV and decision at 12% 2½ marks 4 min
- 3 PV and decision at 11% 2½ marks 4 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 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.
Approach. A perpetuity is an annuity that continues for ever; its present value is the annual amount divided by the rate of return: PV = A ÷ r. The same perpetuity calculation gives the cost of irredeemable preference shares, the dividend divided by the price. The offer is worth accepting if the PV of the receipts exceeds the ₹42,000 deposited.
| Rate of return | PV of ₹4,752 a year for ever | Compared with ₹42,000 | Decision |
|---|---|---|---|
| 12% | 4,752 ÷ 0.12 = 39,600 | ₹2,400 less | Reject |
| 11% | 4,752 ÷ 0.11 = 43,200 | ₹1,200 more | Accept |
Equivalently, the offer yields 4,752 ÷ 42,000 = 11.31% a year: below a required 12% but above 11%.
Yes, the decision changes: at 12% the offer should be rejected, at 11% it should be accepted.
Where the 7 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Perpetuity formula | 2 |
| 2 | PV and decision at 12% | 2.5 |
| 3 | PV and decision at 11% | 2.5 |
| Total | 7 |
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