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 $1,160.35. 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?

Answer: the yield to maturity and yield to call on BTR Co.'s bonds are:

YTM = 0.07507 (7.507%)

YTC = 0.06977 (6.977%)

Explanation:

Using yield to maturity formula below;

YTM = C + (fv - pv) / n : (fv+pv) / 2

C = coupon rate; 9% of par value

9% of $1000

= 9/100 * 1000 = $90

fv = face value/par value = $1,000

pv = price value/market price = $1,160.35

n = number of years to maturity = 18

YTM = 90 + (1000 - 1160.35) / 18 : (1000+1160.35) / 2

YTM = 90 + (-160.35) / 18 : (2160.35) / 2

YTM = 90 + (-8.90833333)

: 1080.175

YTM = 81.0916667 : 1080.175

YTM = 0.07507

= 7.507% (converted to percentage)

To calculate the yield to call, let s make use of the yield to call (YTC) formula below;

YTC = C + (cp - mp) / n : (cp + mp) / 2

C = coupon rate = $90

cp = call price = $1,060

mp = market price/price value = $1,160.35

n = number of years to call = 8

YTC = 90 + (1060-1160.35) / 8 : (1060+1160.35) / 2

YTC = 90 + (-100.35) / 8 : (2220.35) / 2

YTC = 90 - 12.54375 : 1110.175

YTC = 77.45625 : 1110.175

YTC = 0.06977

= 6.977% in percentage