Final answer:
To raise $41 million, a company would issue 41,000 semiannual coupon bonds with a face value of $1,000 at a coupon rate of 6.1%. For zero coupon bonds, the quantity required would be higher since they sell for less than the par value.
Step-by-step explanation:
To calculate the number of semiannual coupon bonds, you need to know the face value of the bonds, the total amount to be raised, and the coupon rate. Since each bond has a face value of $1,000, a coupon rate equal to the required return rate, and the interest is paid semiannually, then each bond will pay a semiannual interest of ($1,000 * 6.1%) / 2 = $30.5. The total proceeds from each bond would be its face value because the coupon rate equals the market rate, so to raise $41 million, you need to issue $41,000,000 / $1,000 = 41,000 bonds.
For zero coupon bonds, they would each be sold at a discount to compensate the investor for the lack of periodic interest payments. To calculate the number of zero coupon bonds to be issued, you would need to determine the present value of each $1,000 bond at the required return rate (discount rate) compounded semiannually over the 20-year period. For this example, we would need additional information to calculate the specific price at which each zero coupon bond would be sold. However, usually it is less than the par value due to the discount for lack of coupon payments. Therefore, to raise $41 million, the number of zero coupon bonds would be higher than 41,000 since each bond sells for less than $1,000.