What would be the initial offering price for the following ( assume semiannual compounding), a 15-year zero coupon bond with a YTM of 12 percent
To calculate the initial offering price of a 15-year zero coupon bond with a YTM (Yield to Maturity) of 12 percent with semiannual compounding, we need to follow these steps:
Step 1: Convert the annual YTM to a semiannual yield by dividing the annual YTM by 2. In this case, the semiannual yield would be 12% / 2 = 6%.
Step 2: Calculate the total number of compounding periods for the bond. Since the bond has a maturity of 15 years and semiannual compounding, the total number of periods would be 15 years * 2 = 30 periods.
Step 3: Use the semiannual yield and the number of compounding periods to calculate the discount factor.
Discount Factor = 1 / (1 + semiannual yield)^number of compounding periods
Discount Factor = 1 / (1 + 6%)^30
Step 4: Calculate the initial offering price by dividing the face value of the bond by the discount factor.
Initial Offering Price = Face Value / Discount Factor
Note: Since it is a zero coupon bond, the face value will be the future value of the bond at maturity.
Based on the information provided, the initial offering price can be calculated using these steps.