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
