The current price of a bond is calculated by taking the present value of the future cash flows discounted at the current yield to maturity (YTM). For the Weismann Co.'s bonds, which make semiannual payments with a par value of $1,000 and a coupon rate of 11%, the bond price can be found by discounting these future cash flows at the YTM of 12%, resulting in a price lower than the face value.
The student is asking how to calculate the current price of Weismann Co.'s bonds, which were issued at an 11% coupon rate but the yield to maturity (YTM) is now 12%. Given that the bonds make semiannual payments and have a par value of $1,000, and understanding that the bond has 13 years remaining after being issued a year ago, we need to calculate the present value of the future cash flows discounted at the current YTM. The bond's coupon payment for one period will be $1,000 x 5.5% (half of the 11% annual coupon rate), which is $55.
To find the bond price, we calculate the present value of all future coupon payments, plus the present value of the $1,000 par value to be received at the end of 13 years. The formula for the present value of an annuity (the semiannual coupon payments) is used alongside the present value of a lump sum (the par value repayment) at the YTM of 12% (semiannual rate of 6%). We use these calculations to determine the bond's current market price.
Calculating the exact price would require a financial calculator or spreadsheet software. For our example, to demonstrate understanding, if we ignore the semiannual nature of the payments for simplicity and assume annual payments: PV = $55 / (1 + 0.12) + $55 / (1 + 0.12)^2 + ... + $55 / (1 + 0.12)^13 + $1,000 / (1 + 0.12)^13. The calculated sum of these discounted cash flows would give us the bond's current price, which will be lower than the face value because the YTM is higher than the coupon rate.