Final answer:
The required return on a bond can be viewed as its yield to maturity (YTM), which includes both periodic coupon payments and the capital gain on the bond. This takes into account the bond's semiannual coupon rate, current price, and maturity value. The YTM calculation involves equating the present value of the bond's future cash flows to its current price, but a detailed calculation would require a financial calculator or software.
Step-by-step explanation:
To calculate the required return on a bond with a semiannual coupon rate, we need to consider the current price of the bond, the coupon payments it generates, and the value of the bond at maturity. In this case, the bond has a semiannual coupon rate of 9%, a purchase price of $936.50, and a maturity value of $1,000 in 10 years. Since coupons are paid semiannually, the annual coupon payment is 9% of the $1,000 face value, which equals $90 per year, or $45 every six months.
The bond's yield or return can be calculated using the bond's price, coupon payments, and maturity value. Considering both the periodic interest payments (coupons) and the capital gain (the difference between the purchase price and the maturity value), one can use the formula for yield to maturity (YTM). This involves solving for the discount rate that equates the present value of the bond's future cash flows to its current price. While the exact YTM calculation requires financial calculators or software, the concept of yield reflects the total return considering interest payments and capital gains.
Therefore, the required return can be viewed as the YTM that a bond investor is targeting given the bond's current price, coupon rate, and time to maturity.