Question

1. A 30-year maturity, 12% coupon bond paying coupons semiannually is callable in ten years at a call price of $1,100. The bond currently sells at a yield to maturity of 8%.
2. What is the yield to call?
3. What is the yield to call if the call price is only $1,050?
4. What is the yield to call if the call price is $1,100 but the bond can be called in five years instead of ten years?

Answer 1

(a) Coupon Payment = C = 12% of $1000 = $120
Face Value of bond = FP = $1000
Call Price = CP = $1100
Number of Years to call = n = 10

Yield to Call = YTC = [ C + (FP - CP)/n ] / [ (FP + CP) / 2 ] = [ 120 + (1000 - 1100)/10 ] / [ (1000 + 1100) / 2 ] = 0.1048 or 10.48%

(b) If Call Price = CP = $1050

=> Yield to Call = YTC = [ C + (FP - CP)/n ] / [ (FP + CP) / 2 ] = [ 120 + (1000 - 1050)/10 ] / [ (1000 + 1050) / 2 ] = 0.1122 or 11.22%

(c) If Call Price = CP = $1100
Number of Years to call = n = 5

=> Yield to Call = YTC = [ C + (FP - CP)/n ] / [ (FP + CP) / 2 ] = [ 120 + (1000 - 1100)/5 ] / [ (1000 + 1100) / 2 ] = 0.0953 or 9.53%