To calculate the yield to call of a bond, we need to compare the present value of all remaining cash flows from the bond to the call price. If the present value of the remaining coupons and the call price are equal, then the yield to call is the interest rate that makes this equation true. To calculate the yield to call, we use the present value formula, adjusting for the number of periods and the call price.
To calculate the yield to call of a bond, we need to compare the present value of all remaining cash flows from the bond to the call price. If the present value of the remaining coupons and the call price are equal, then the yield to call is the interest rate that makes this equation true.
a. To calculate the yield to call in this case, we need to use the present value formula. The present value of a regular bond payment is given by: PV = C / (1 + r) + C / (1 + r)^2 + ... + C / (1 + r)^n + F / (1 + r)^n, where PV is the present value, C is the periodic coupon payment, r is the interest rate, and F is the face value of the bond. For this bond, C = 9% / 12 * $1,000 = $7.50, F = $1,000.
Using the present value formula, we can calculate the present value of the bond if it is called in 6 years at a call price of $1,075:
PV = $7.50 / (1 + r) + $7.50 / (1 + r)^2 + ... + $7.50 / (1 + r)^60 + $1,000 / (1 + r)^60 = $1,075
Solving this equation for r will give us the yield to call.
b. To calculate the yield to call if the bond is called back in 4 years instead of 6 years at a call price of $1,125, we use the same present value formula. However, we need to adjust the number of periods and the call price:
PV = $7.50 / (1 + r) + $7.50 / (1 + r)^2 + ... + $7.50 / (1 + r)^48 + $1,125 / (1 + r)^48 = $1,125
Solving this equation for r will give us the yield to call in this case.