Question 3 OR (c)
Expected return on a Sovereign Gold Bond
6 marks
- Time to write
- About 12 minutes
- Topic
- Risk and return
Question
Question 3 OR (c) · 6 marksYou are thinking of buying a Sovereign Gold Bond (SGB), whose current price is the market rate of ₹9,720 per gram of gold. The bond has a lock-in period of 8 years, at the end of which it will be redeemed at the market price of gold then prevailing. According to your analysis, gold has historically given an average annual return of 8%, and you expect this to continue in future. Besides potential capital gains, the bond pays coupon interest of 2.5% per annum on its current value. What rate of return can you expect on this bond?
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
Write it in this order
- Read the data; note exactly what is asked 1 min
- 1 Cash flows: coupon and redemption value 2 marks 3 min
- 2 Return as the rate equating PV with the price 2 marks 3 min
- 3 Rate of return computed 2 marks 3 min
- Check: arithmetic, units (₹, %), final answer underlined 2 min
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.
Cash flows of one bond (per gram).
- Outlay today: ₹9,720.
- Coupon: 2.5% a year on its current value, ₹9,720 × 2.5% = ₹243 a year for 8 years.
- Redemption after 8 years at the gold price then: 9,720 × 1.08⁸ = ₹17,991.04, if gold keeps rising at 8% a year.
Expected rate of return. The return is the discount rate at which the present value of the coupons and the redemption value equals the price paid, i.e. the internal rate of return of the bond's cash flows:
9,720 = 243 × PVIFA(r, 8) + 17,991.04 × PVIF(r, 8).
| Rate | PV of coupons (₹) | PV of redemption (₹) | Total PV (₹) |
|---|---|---|---|
| 9% | 1,344.96 | 9,029.10 | 10,374.06 |
| 10% | 1,296.39 | 8,392.95 | 9,689.34 |
The rate lies just below 10%. Solved exactly, the expected rate of return is about 9.95% a year, made up of the 8% expected rise in the price of gold and the coupon, which is worth a little under 2% a year because it is fixed at 2.5% of today's price while the bond's value rises.
Where the 6 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Cash flows: coupon and redemption value | 2 |
| 2 | Return as the rate equating PV with the price | 2 |
| 3 | Rate of return computed | 2 |
| Total | 6 |
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