Question

A 10-year maturity, 7.5% coupon bond paying coupons semiannually is callable in five years at a call price of $1,200. The bond currently sells at a yield to maturity of 5% (2.5% per half-year).

a. What is the yield to call annually? (Do not round intermediate calculations. Round your answer to 3 decimal places.)

b. What is the yield to call annually if the call price is only $1,150? (Do not round intermediate calculations. Round your answer to 3 decimal places.)

c. What is the yield to call annually if the call price is $1,200, but the bond can be called in two years instead of five years? (Do not round intermediate calculations. Round your answer to 3 decimal places.)

Answer 1

(a) Bond Par Value = $ 1000, Yield to Maturity (YTM) = 5 % per annum or 2.5 % per half-year, Coupon Rate = 7.5 % per annum payable semi-annually, Tenure = 10 years or (10 x 2) = 20 half-years

Semi-Annual Coupon = 0.075 x 0.5 x 1000 = $ 37.5

Bond Price = Sum of Present Values of Semi-Annual Coupons + PV of Redeemed Par Value at Maturity = 37.5 x (1/0.025) x [1-{1/(1.025)^(20)}] + 1000 / (1.025)^(20) = $ 1194.86

Call Price = $ 1200 and Time to Call = 5 years or 10 half-years

Let the yield to call be 2Rc

Therefore, 1194.86 = 37.5 x (1/Rc) x [1-{1/(1+Rc)^(10)}] + 1200 / (1+Rc)^(10)

Using EXCEL's Goal Seek Function / hit and trial method/ a financial calculator to solve the above equation, we get:

Rc = 0.03176 or 3.176 %

Therefore, Yield to Call = 2 x Rc = 2 x 3.176 = 6.352 %

(b) New Call Price = $ 1150 and Time to Call = 5 years or 10 half-years

Let the yield to call be 2Rc

Therefore, 1194.86 = 37.5 x (1/Rc) x [1-{1/(1+Rc)^(10)}] + 1150 / (1+Rc)^(10)

Using EXCEL's Goal Seek Function / hit and trial method/ a financial calculator to solve the above equation, we get:

Rc = 0.02808 or 2.808 %

Therefore, Yield to Call = 2 x Rc = 2 x 2.808 = 5.616 %

(c) Call price = $ 1200 and New tenure = 2 years or (2 x 2) = 4 half-years

Let the yield to call be 2Rc

Therefore, 1194.86 = 37.5 x (1/Rc) x [1-{1/(1+Rc)^(4)}] + 1200 / (1+Rc)^(4)

Using EXCEL's Goal Seek Function / hit and trial method/ a financial calculator to solve the above equation, we get:

Rc = 0.03241 or 3.241 %

Therefore, Yield to Call = 2 x Rc = 2 x 3.241 = 6.482 %