Question

A firm made a coupon payment yesterday on its $1000 par value, 8.4%, semi-annual-coupon bonds, which mature in 19 years and have a yield to maturity of 7%. If the firm can call these bonds for a call price of $1084 four years from now, what is the yield to call on these bonds? (percent with 4 decimals.)

Answer 1

Bond Par Value = $ 1000, Bond Tenure = 19 years or (19 x 2) = 38 half-years, Coupon Rate = 8.4 % per annum payable semi-annually, Yield to Maturity = 7% per annum pr (7/2) = 3.5 % per half-year

Semi-Annual Coupon = 0.084 x 0.5 x 1000 = $ 42

Bond Price = 42 x (1/0.035) x [1-{1/(1.035)^(38)}] + 1000 / (1.035)^(38) = $ 1145.8876 ~ $ 1145.89

Call Price = $ 1084 and Time to Call = 4 years or (4 x 2) = 8 half-years

Let the yield to call be 2y

Therefore, 1145.89 = 42 x (1/y) x [1-{1/(1+y)^(8)}] + 1084 / (1+y)^(8)

Using EXCEL's Goal Seek Function to solve the above equation, we get:

y = 0.030592 or 3.0592 % ~ 3.06 %

Yield to Call = 2 x y = 2 x 3.06 = 6.1183 %