Problem

A 7.25 percent coupon bond with 25 years left to maturity can be called in five years. The call premium is one year of coupon payments. It is offered for sale at \$1,066.24. What is the yield to call of the bond? (Assume that interest payments are paid semiannually and par value is $\$ 1,000$.)

Answer

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Answer

Solve for the yield to call \( r \): Find the value of \( r \) that makes the present value of the bond's cash flows equal to \$1,066.24

Steps

Step 1 :Calculate the semiannual coupon payment: \( \text{Coupon payment} = \frac{7.25\% \times \$1,000}{2} = \$72.50 \)

Step 2 :Calculate the total number of semiannual periods until the call date: \( 5 \times 2 = 10 \)

Step 3 :Calculate the call premium: \( \text{Call premium} = \$72.50 \times 2 = \$145 \)

Step 4 :Calculate the future value at the call date: \( \text{Future value} = \$1,000 + \$145 = \$1,145 \)

Step 5 :Calculate the present value of the bond's cash flows: \( PV = \sum_{n=1}^{10} \frac{\text{Coupon payment}}{(1 + r)^n} + \frac{\text{Future value at call date}}{(1 + r)^{10}} \)

Step 6 :Solve for the yield to call \( r \): Find the value of \( r \) that makes the present value of the bond's cash flows equal to \$1,066.24

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