Question 1 (b)
Maximum price of a bond at the required return
8 marks
- Time to write
- About 16 minutes
From an older CBCS paper
Question
Question 1 (b) · 8 marksAn investor is thinking of buying a bond with the following characteristics: the bond pays 9% per year on its ₹3000 principal, or face value. The bond will mature in 8 years. At maturity, the bondholder will receive interest for year 8 plus ₹3000 face value. What maximum purchase price should be paid for this bond if the investor requires a 14% rate of return?
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 Valuation approach: present value of interest and maturity value at the required return 2 marks 4 min
- 2 Cash flows: annual interest for 8 years and at maturity 2 marks 3 min
- 3 Discount factors and present values 3 marks 5 min
- 4 Maximum price and conclusion 1 mark 2 min
- Check: arithmetic, units (₹, %), final answer underlined 1 min
Short on time? End with step 4's one-line conclusion, whatever happens: never leave the figures without it.
Try it first. About 16 minutes for 8 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. The most the investor should pay is the bond's value to him: the present value of the cash flows the bond will pay, discounted at the minimum return he expects. Interest is worked out on the face value at the coupon rate, so the value is annual interest × PVIFA plus the maturity value × PVIF, both at the required rate.
- Annual interest = 9% × ₹3,000 = ₹270, received at the end of each of years 1 to 8 (year 8's interest is the last instalment of this annuity).
- Maturity value = face value ₹3,000, received at the end of year 8.
- Discount factors at 14%: the question prints none, so present-value table factors to 3 decimals are used: annuity factor for 8 years 4.639 and single-sum factor for year 8 0.351.
Value of the bond at a 14% required return
| Cash flow | Timing | Amount (₹) | PV factor @ 14% | Present value (₹) |
|---|---|---|---|---|
| Interest | End of years 1 to 8 | 270 | 4.639 | 1,252.53 |
| Face value repaid | End of year 8 | 3,000 | 0.351 | 1,053 |
| Value of the bond | 2,305.53 |
Conclusion. The maximum price the investor should pay is ₹2,305.53. The bond is worth less than its ₹3,000 face value because the return the investor requires (14%) is higher than the 9% coupon the bond pays; when the market yield is above the coupon rate, the bond has to be sold at a discount. (With exact factors, 1 ÷ 1.14 raised to the power of each year, the value is ₹2,304.17; the ₹1.36 gap is only the rounding of the table factors.)
Where the 8 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Valuation approach: present value of interest and maturity value at the required return | 2 |
| 2 | Cash flows: annual interest ₹270 for 8 years and ₹3,000 at maturity | 2 |
| 3 | Discount factors and present values | 3 |
| 4 | Maximum price and conclusion | 1 |
| Total | 8 |
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