On January 1, 2022, you bought a three-year, annual-pay coupon bond with a 6% coupon rate, $1000 face value, and yield to maturity of 6%. On January 1, 2023, you received the first coupon of the bond, and on January 1, 2024, you receive the second coupon. Immediately after receiving the second coupon, you sell the bond. Assume that yields on bonds of all maturities are equal to 4.5% on January 1, 2024. What is the selling price of the bond on January 1, 2024?

Question

BlackTom AI · Accepted Answer

Bond price equals the present value of remaining cash flows discounted at the prevailing market yield. Here, after receiving the Jan 1, 2024 coupon, the only remaining cash flow is the final coupon plus principal one year later: 60 + 1000 = 1060.

1. Relevant concepts
- Coupon bond price = PV of remaining coupons and principal using current market yield.
- Ex-dividend (immediately after coupon payment) price excludes the coupon just received.
- If market yields fall below the coupon rate, bond prices rise above par.

2. Step-by-step reasoning
- Original coupon payments were $60 annually on $1,000 face.
- On Jan 1, 2024 you have just received the 2nd $60 coupon; one payment remains at Jan 1, 2025: $1,060.
- Market yield for all maturities on Jan 1, 2024 is 4.5%, so discount the single remaining cash flow one year at 4.5%.

3. Calculations (all intermediate steps)
- One-year discount factor = 1 + y = 1 + 0.045 = 1.045.
- Present value = 1060 / 1.045.
- Compute numerator/denominator: 1,060,000 / 1,045 = 1,014.354… (long division: 1045 × 1014 = 1,059,630; remainder 370 → decimal 0.354…).
- Round to cents: $1,014.35.

4. Why this answer is correct
- It correctly values only the remaining cash flow and uses the market yield (4.5%) that determines price at that date. The lower yield relative to coupon (6%) produces a price above par; discounting 1060 one year at 4.5% yields $1,014.35.

5. Why other plausible answers would be incorrect
- $1,060 would ignore discounting and treat the future payment as already at present value. 
- $1,000 (par) would be the price if yield equaled the coupon yield (6%), but market yield fell to 4.5% so price > par.
- Discounting at 6% (1060/1.06 = 1000) is wrong because yields changed to 4.5%.

6. Conclusion
The correct selling price on Jan 1, 2024 is $1,014.35, matching the provided answer.

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