Midland Oil has $1,000 par value bonds outstanding at 8 percent interest. The bonds will mature in 25 years. Compute the current price of the bonds if the present yield to maturity is:
A. 7 percent.
B. 10 percent.
C. 13 percent.
To compute the current price of the bonds, we need to calculate the present value of the bond's future cash flows, which are the interest payments and the par value payment at maturity.
Let's break down the calculation step by step for each yield to maturity scenario:
A. 7 percent yield to maturity:
Step 1: Calculate the annual interest payment.
The annual interest payment is equal to the par value of the bond multiplied by the interest rate. In this case, it is $1,000 x 8% = $80.
Step 2: Calculate the present value of the interest payments.
Since the bond matures in 25 years, we have 25 interest payments. To calculate the present value, we discount each interest payment using the current yield to maturity rate. Using a financial calculator or a spreadsheet, calculate the present value of the 25 interest payments of $80 each discounted at 7% yield to maturity.
Once you have the present value of the interest payments, add them together.
Step 3: Calculate the present value of the par value payment at maturity.
The par value payment is $1,000, and it will be received in 25 years. Calculate the present value of this payment using the yield to maturity rate. Add it to the present value of the interest payments calculated in step 2.
The sum of the present value of the interest payments and the present value of the par value payment is the current price of the bonds.
Repeat the above steps for the other yield to maturity scenarios:
B. 10 percent yield to maturity:
Follow the same steps as before but use the 10% yield to maturity rate to calculate the present value of the interest payments and the par value payment.
C. 13 percent yield to maturity:
Again, repeat the calculation steps using the 13% yield to maturity rate to calculate the present value of the interest payments and the par value payment.