Question10 A coupon bond that pays interest semi-annually is selling at par value of $1,000, matures in 7 years, and has a coupon rate of 8.6%. The yield to maturity on this bond is: Select one alternative: A. 9.0% B. 8.6% C. 8.0% D. 10.0% E. None of these is correct. ResetMaximum marks: 2 Flag question undefined单项选择题
A
A. 9.0%
B
B. 8.6%
C
C. 8.0%
D
D. 10.0%
E
E. None of these is correct.

Question

Question10 A coupon bond that pays interest semi-annually is selling at par value of $1,000, matures in 7 years, and has a coupon rate of 8.6%. The yield to maturity on this bond is: Select one alternative: A. 9.0% B. 8.6% C. 8.0% D. 10.0% E. None of these is correct. ResetMaximum marks: 2 Flag question undefined单项选择题

A

A. 9.0%

B

B. 8.6%

C

C. 8.0%

D

D. 10.0%

E

E. None of these is correct.

BlackTom AI · Accepted Answer

A bond selling at par has its yield to maturity equal to its coupon rate, so the YTM here will equal 8.6%.

1) Relevant concepts
- Coupon rate = annual coupon payment divided by face value.
- Yield to maturity (YTM) is the discount rate that makes the present value of the bond’s cash flows equal to its price.
- For a bond priced at par (price = face value), the coupon rate equals the YTM (this holds regardless of payment frequency).

2) Step-by-step reasoning
- Face value (FV) = $1,000; coupon rate = 8.6% → annual coupon = 0.086 × 1000 = $86.
- Semiannual payments → each period coupon = $86/2 = $43; number of periods = 7 years × 2 = 14.
- Let y be the annual YTM (nominal, compounded semiannually). The semiannual yield = y/2.
- Bond price formula: Price = 43 × [1 − (1 + y/2)^(−14)]/(y/2) + 1000 × (1 + y/2)^(−14).
- If the bond sells at par (Price = 1000) and the coupon equals 86, the solution for y is y = 8.6% (the general identity: coupon rate = YTM when price = par).

3) Calculation check (plugging y = 8.6%)
- Semiannual yield = 8.6%/2 = 4.3% = 0.043.
- (1 + 0.043)^14 ≈ 1.043^14 ≈ 1.803 → (1 + 0.043)^−14 ≈ 0.5548.
- PV of coupons = 43 × [1 − 0.5548]/0.043 = 43 × 0.4452/0.043 ≈ 43 × 10.350 ≈ 444.99.
- PV of principal = 1000 × 0.5548 ≈ 554.80.
- Total PV ≈ 444.99 + 554.80 ≈ 999.79 ≈ 1000 (rounding), confirming y = 8.6%.

4) Why the correct answer is correct
Because the bond is priced at par and its coupon payments equal the market-required return, the YTM must equal the coupon rate. The numerical check above shows the present value of cash flows at 8.6% equals the $1,000 price.

5) Why the other choices are incorrect
- A (9.0%): higher than coupon → bond would trade below par, not at par.
- C (8.0%): lower than coupon → bond would trade above par.
- D (10.0%): much higher, would imply deep discount.
- E: incorrect because one of the listed options (B) is correct.

6) Conclusion
The yield to maturity is 8.6%, matching option B. This confirms the provided answer: B. 8.6%.

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