Consider the case of BTR Co.: BTR Co. has 9% annual coupon bonds that are callable and have 18 years left until maturity. The bonds have a par value of $1,000, and their current market price is $1,130.35. However, BTR Co. may call the bonds in eight years at a call price of $1,060. What are the YTM and the yield to call (YTC) on BTR Co.'s bonds?

YTM is 7.77 % and YTC is 7.41 %

Explanation:

YTM stands for Yield to Maturity. It is refer to internal rate of return that bond holder will earn if he purchases the bond and keep it till its maturity period.

YTM = [Interest payment + (Future Value - Present Value) / no. of years] / [ (Future value of bond + Present value of bond) / 2]

Annual interest Payment = $ 90 i. e 9 % annual coupon

No. of Years = 18

Future value of bond = $ 1000

Present value of bond = $ 1130.35

YTM = [ $ 90 + ($1000-1130.35) / 18] / [ ($ 1000 + $ 1130.35) / 2]

YTM = 7.77 % = Yield to Maturity

Yield to Call : These are callable bond which the issuer can redeem at any time before maturity of the bond. It is denoted by YTC.

Future value of bond when called = $ 1060

The issuer may call it at 8 year.

YTC = [Interest payment + (Future Value - Present Value) / no. of years] / [ (Future value of bond + Present value of bond) / 2]

YTC = [ $ 90 + ($1060 - $ 1130.35) / 8] / [ ($ 1060 + $ 1130.35) / 2]

YTC = 7.41 % = Yield to Call.