A company issues a 10-year, callable bond at par with 8% annual coupon payments. The bond can be called at par in one year after issue or any time after that on a coupon payment date. The call price is $105 per $100 of face value. What is the yield to call if this bond is called in one year?

Question

Quizplus · Accepted Answer

To calculate yield to call, we need to find the rate at which the present value of the bond's cash flows (coupon payments and call price) equals the current market price ($100).

At issuance, the bond is sold at par ($100) and pays an annual coupon of 8%, which means $8 coupon payment each year.

If the bond is called in one year, the investor will receive $105 per $100 face value, representing a capital gain of $5. However, the investor will miss out on 9 more years of $8 coupon payments.

Therefore, we can calculate the present value of cash flows as follows:

PV = ($8 / 1.08) + ($8 / (1.08)^2) + ... + ($8 / (1.08)^9) + ($105 / (1.08)^1)

PV = $8 x [1 - (1 / (1.08)^10)] / 0.08 + $105 / (1.08)^1

PV = $93.93

To solve for yield to call, we need to find the interest rate (i) that makes the present value of cash flows equal to the bond's current market price ($100):

$100 = $8 x [1 - (1 / (1+i)^10)] / i + $105 / (1+i)^1

Solving for i using trial and error or a financial calculator, we find that yield to call equals approximately 13%. Therefore, the best choice is A.

A Company Issues a 10-Year, Callable Bond at Par with 8