McCue Inc.\'s bonds currently sell for $950. They pay a $90 annual coupon, have
ID: 2745545 • Letter: M
Question
McCue Inc.'s bonds currently sell for $950. They pay a $90 annual coupon, have a 25-year maturity, and a $1,000 par value, but they can be called in 5 years at $1,050. Assume that no costs other than the call premium would be incurred to call and refund the bonds, and also assume that the yield curve is horizontal, with rates expected to remain at current levels on into the future. What is the difference between this bond's YTM and its YTC? (Subtract the YTC from the YTM; it is possible to get a negative answer.)
Explanation / Answer
YTC = { Int + [call value-B0 of callable bond]/call years } / [ call value + B0 of callable bond]/2
YTC = { 90 + [1050-950]/5 } / [1050+950]/2
YTC = 0.11
YTC = 11%
YTM = { Int + [Maturity value-B0 of bond]/ life } / [ Maturity Value + B0 of bond]/2
YTM = { 90 + [1000-950]/25 } / [1000+950]/2
YTM = 0.1179
YTM = 11.79%
Difference = YTM - YTC
= 11.79% - 11.00%
= 0.79%