Werden Drilling offers 5.5 percent coupon bonds with semiannual payments and a yield to maturity of 7 percent. The bonds mature in 10 years. What is the market price per bond if the face value is $1,000?

Question

BlackTom AI · Accepted Answer

A bond's price equals the present value of its future coupon payments (an annuity) plus the present value of its face (par) value at maturity.

1) Relevant concepts
- Coupon payment per period = (annual coupon rate × face value) / number of periods per year.
- Periodic yield = annual YTM / number of periods per year.
- Number of periods = years to maturity × periods per year.
- Price = C × [1 − (1 + r)^−N]/r + F × (1 + r)^−N, where C = coupon per period, r = periodic yield, N = total periods, F = face value.

2) Given values and conversion to semiannual terms
- Face value F = $1,000.
- Annual coupon rate = 5.5% → semiannual coupon payment C = 0.055 × 1000 / 2 = $27.50.
- Annual YTM = 7.0% → semiannual yield r = 0.07 / 2 = 0.035 (3.5%).
- Maturity = 10 years → total periods N = 10 × 2 = 20.

3) Step-by-step calculation (showing intermediate steps)
- Compute (1 + r)^N = (1.035)^20 ≈ 1.98948.
- Discount factor for principal: (1 + r)^−N = 1 / 1.98948 ≈ 0.50264.
- Annuity present-value factor: [1 − (1 + r)^−N] / r = (1 − 0.50264) / 0.035 = 0.49736 / 0.035 ≈ 14.2103.
- PV of coupons = C × annuity factor = 27.50 × 14.2103 ≈ 390.783.
- PV of face value = F × (1 + r)^−N = 1000 × 0.50264 = 502.64.
- Total price = 390.783 + 502.64 = 893.423 ≈ $893.41.

4) Why this answer is correct
Because the coupon rate (5.5%) is lower than the YTM (7%), investors demand a discount; the present-value calculation above yields approximately $893.41, matching the computed price.

5) Why the other options are incorrect
- $894.65: very close but slightly off due to rounding; precise calculation gives $893.41.
- $937.63: would imply a lower yield or higher coupon; not consistent with given 7% YTM.
- $671.36: far too low, corresponding to a much higher yield than 7%.
- $1,114.20: above par — would occur only if coupon > YTM, which is not the case here.

Final confirmation: the correct market price per bond is $893.41, which matches the provided answer.

Werden Drilling offers 5.5 percent coupon bonds with semiannual payments and a yield to maturity of 7 percent. The bonds mature in 10 years. What is the market price per bond if the face value is $1,000?单项选择题

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