Final answer:
The annual coupon interest rate of Peng Corporation's bonds is 8%, calculated using the present value of an annuity formula based on the current market price, required rate of return, and bond's maturity value.
Step-by-step explanation:
The Peng Corporation has 100 bonds with a current market value of $768 each, a 10% required rate of return, a $1,000 maturity value, and semiannual interest payments. To find the annual coupon interest rate, we can use the bond pricing formula which incorporates the present value of annuity for the coupon payments and the present value of a lump sum for the face value of the bond. Since the coupon payments are semiannual, they occur twice per year, and therefore the required rate of return per period is 5% (10% annual rate divided by two).
By using the present value of an annuity formula, we want to find the coupon payment that would make the sum of the present values of the coupon payments and the maturity value equal the current market price of $768. Through this calculation, we can determine that the coupon payments equal $40 per period, resulting in an annual coupon interest rate of 8% ($40 coupon per period x 2 semiannual periods per year).
Therefore, the correct answer is:
a. 8%
When interest rates rise, existing bonds with lower coupon rates sell for less, as newer bonds would come with higher interest rates. Conversely, if interest rates fall, bonds with higher interest rates increase in value as they become more desirable compared to new bonds with lower rates.