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(Bond valuation) Hamilton, Inc
(Bond valuation) Hamilton, Inc. bonds have a coupon rate of 16 percent. The interest is paid semiannually, and the bonds mature in 9 years. Their par value is $1,000. If your required rate of return is 15 percent, what is the value of the bond? What is the value if the interest is paid annually? a. If the interest is paid semiannually, the value of the bond is $ (Round to the nearest cent.)
Expert Solution
a) If the Interest is paid Semiannually
Semiannual Coupon Amount = $1000*16%/2 = $80
No of Coupons = 9*2 = 18
Semiannual YTM = 15%/2 = 0.075 (assuming YTM is semiannually Compounded)
So, Price of the bond
P = $80/1.075 + $80/1.075^2+.....+$80/1.075^18+ $1000/1.075^18
= 80/0.075*(1-1/1.075^18)+1000/1.075^18
=$1048.53
(PS if YTM is annually Compounded rate , then Price will be $1075.35)
If the Interest is paid annually
annual Coupon Amount = $1000*16% = $160
No of Coupons = 9
YTM = 15% 0.15 (assuming YTM is annually Compounded)
So, Price of the bond
P = $160/1.15 + $160/1.15^2+.....+$160/1.15^9+ $1000/1.15^9
= 160/0.15*(1-1/1.15^9)+1000/1.15^9
=$1047.72
(PS if YTM is semiannually Compounded rate , then Price will be $1020.46)
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