Final answer:
The current bond price is determined by the present value of the semiannual interest payments based on a 7.8% coupon rate and the face value payment, discounted at the semiannual YTM of 5.35%. Since the YTM is higher than the coupon rate, the bond price will be below the face value.
Step-by-step explanation:
The student is asking how to calculate the current bond price of a 10-year bond with a face value of $1,000, a coupon rate of 7.8%, and a yield to maturity (YTM) of 10.7%, given the bonds make semiannual payments. The bond price can be calculated using the present value of its future cash flows, which include the semiannual interest payments and the principal amount paid at maturity.
To find the bond's price, you need to discount each of its future cash flows back to the present value using the YTM as the discount rate. The cash flows consist of semiannual interest payments of 7.8% of $1,000 (which is $39 every six months) for the remaining 9.5 years (since one semiannual period has passed), and the face value of $1,000 that will be paid at the end of the 10-year period.
Considering that bond prices fall when interest rates rise, as the YTM of 10.7% is higher than the coupon rate of 7.8%, we can anticipate that the current price of the bond will be less than its face value. To perform this calculation, one must use a financial calculator or present value formula, inputting the cash flows, the number of periods remaining (which is 19 for a 10-year bond with semiannual payments, after one year has passed), and the semiannual YTM (which is 5.35%, half of the annual YTM), to find the bond's current price.