Question 1 OR (c)
Fund for a growing perpetual scholarship
3 marks
- Time to write
- About 6 minutes
- Topic
- Time value of money
Question
Question 1 OR (c) · 3 marksThe Honorable Vice-Chancellor of University of Delhi wishes to start a scholarship paying ₹30, 000 p.a. to the student with an outstanding performance at the Center of IKS Studies. The scholarship amount is expected to increase at 5% p.a to commensurate with the inflation. He would like to know how much he can invest at 12.5% p.a. so as to pay the scholarship till perpetuity?
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
- how muchFormula first, then the working, then the answer with its unit (₹, %, units).
What the paper leaves open
The amount is printed with a space ("₹30, 000") and is read as ₹30,000. The scholarship is read as a growing perpetuity whose first payment falls one year from now.
Write it in this order
- 1 Growing perpetuity formula 1 mark 2 min
- 2 Amount to invest 2 marks 4 min
Try it first. About 6 minutes for 3 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.
Reading (paper note). ₹30,000 is paid one year from now and grows at 5% a year for ever: a growing perpetuity.
The present value of a stream that starts at C₁ and grows at a constant rate g for ever, discounted at r (r > g), is PV = C₁ ÷ (r − g). This is the same constant-growth formula used to value a share whose dividend grows at a constant rate, P = D₁ ÷ (ke − g).
PV = 30,000 ÷ (0.125 − 0.05) = 30,000 ÷ 0.075 = ₹4,00,000.
The Vice-Chancellor must invest ₹4,00,000 now at 12.5%. Each year the fund earns 12.5% and pays out the scholarship, which is 7.5% of the fund at the start of that year; the remaining 5% stays in the fund, so the fund and the scholarship both grow at 5% a year for ever.
Where the 3 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Growing perpetuity formula | 1 |
| 2 | Amount to invest | 2 |
| Total | 3 |
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