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.$100B.$96.84C.$97.12D.$98.89
Question
An 8% coupon-paying bond has a yield to maturity of 10% p.a. The bond has a face value of 100B.97.12D.$98.89
Solution
To find the bond's clean price, we need to calculate the present value of its future cash flows, which are the coupon payments and the face value at maturity.
Step 1: Calculate the semi-annual coupon payment The bond pays coupons semi-annually, so the coupon payment is 8%/2 = 4% of the face value. Therefore, the semi-annual coupon payment is 4.
Step 2: Calculate the semi-annual yield to maturity The YTM is also given on an annual basis, so we need to divide it by 2 to get the semi-annual YTM. Therefore, the semi-annual YTM is 10%/2 = 5%.
Step 3: Calculate the number of periods to maturity The bond has 19 months to maturity. Since coupons are paid semi-annually, we need to convert this to semi-annual periods. Therefore, the number of periods to maturity is 19/6 ≈ 3.17. Since we cannot have a fraction of a period, we round this up to 4 periods.
Step 4: Calculate the bond's price The price of a bond is the present value of its future cash flows, which are the coupon payments and the face value at maturity. The formula to calculate the price of a bond is:
P = C * (1 - (1 + r)^-n) / r + FV / (1 + r)^n
where: P = price of the bond C = semi-annual coupon payment r = semi-annual YTM n = number of periods to maturity FV = face value of the bond
Substituting the values into the formula, we get:
P = 100 / (1 + 5%)^4 = $96.84
So, the closest answer is B. $96.84.
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