Final answer:
To determine the value of the stock, subtract the face value of the bond ($1,000) from the total value of the stock and bond ($1,222.10), resulting in a stock value of $222.10. Since we do not have enough information to calculate the exact present value of the bond because the current market price of the bond is not provided, we base our assumption on the face value of the bond. Thus, the correct choice is option a, $222.10.
Step-by-step explanation:
The question asks us to determine the value of a stock when we know the total value of a stock and a bond combined, and have details about the bond's yield to maturity (YTM), coupon rate, and face value.
Since the bond has a YTM of 12.71%, a semi-annual coupon rate of 8.54%, and a face value of $1,000.00, we must find its present value to understand how much the stock is worth. The bond's coupon payment can be calculated as 8.54% of $1,000 face value, which is $85.40 per year or $42.70 per semi-annual period. To find the present value of the bond, we would discount these coupon payments plus the face value at the YTM rate. However, since we are not explicitly asked to calculate the bond's value and don't have the bond's current market price, we can't calculate it directly. Instead, we are given the combined price of the bond and the stock, which is $1,222.10.
Assuming that the bond's value is close to its face value and based on the YTM being higher than the coupon rate, the bond might sell for less than face value. However, without specific bond valuation, we can solve for the stock's value by subtracting the bond's face value from the total value of the securities. Thus, the value of the stock would be $1,222.10 (total value) - $1,000.00 (bond's face value) = $222.10.
Therefore, the stock is valued at $222.10, which corresponds to option a.