A corporate bond with an 11 percent semiannual coupon has a yield to maturity of 9 percent. The bond matures in 20 years but is callable in ten years. The maturity value is $1,000. The call price is $1,055. What is the bond's yield to call?

Question

Quizplus · Accepted Answer

To calculate the yield to call, we need to find the rate at which the present value of the remaining cash flows (coupon payments and call price) equals the current price of the bond. Here's the calculation:

Step 1: Find the present value of the remaining cash flows if the bond is held to maturity in 20 years:

PMT = 55 (11% of $1,000 / 2 semiannual payments per year)
N = 20 * 2 = 40 (total number of semiannual periods)
I/Y = 4.5% (half of the annual yield of 9%)
FV = 1,000 (maturity value)
CPT PV = $887.89

Step 2: Find the present value of the remaining cash flows if the bond is called in 10 years:

PMT = 55 (11% of $1,000 / 2 semiannual payments per year)
N = 10 * 2 = 20 (remaining number of semiannual periods until call date)
I/Y = ? (what we're solving for)
FV = 1,055 (call price)
CPT PV = -$1,000 (the cash flows are negative because we're assuming the bond will be called and the investor will receive the call price, which is higher than the face value)

Using trial and error or a financial calculator, we can find that the yield to call is 8.58%. This is the rate at which the present value of the remaining cash flows equals the current price of the bond, which is the call price of $1,055.

A Corporate Bond with an 11 Percent Semiannual Coupon Has