An 8% coupon-paying bond has a yield to maturity of 10% p.a. The bond has a face value of $100 and 19 months to maturity. Coupons are paid semi-annually. What is the bond’s clean price? Choose the closest answer. A. $98.89 B. $96.84 C. $97.12 D. $100
Question
An 8% coupon-paying bond has a yield to maturity of 10% p.a. The bond has a face value of $100 and 19 months to maturity. Coupons are paid semi-annually. What is the bond’s clean price? Choose the closest answer.
A. $98.89
B. $96.84
C. $97.12
D. $100
Solution
The clean price of a bond is the price without considering the accrued interest.
To calculate the clean price of a bond, we need to calculate the present value of its future cash flows, which include the semi-annual coupon payments and the face value at maturity, discounted at the yield to maturity.
The bond pays an 8% coupon semi-annually, which is 100 * 8% / 2).
The bond has 19 months to maturity, which is approximately 3 semi-annual periods (19/6 ≈ 3).
The yield to maturity is 10% per annum, which is 5% per semi-annual period (10% / 2).
The present value of the coupon payments is:
PV(coupons) = 4 / (1 + 5%)^2 + 11.14
The present value of the face value is:
PV(face value) = 86.38
So, the clean price of the bond is the sum of these two present values:
Clean price = PV(coupons) + PV(face value) ≈ 86.38 ≈ $97.52
The closest answer is C. $97.12.
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