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1
1. Answer the following questions regarding bond valuation and bond yields (Underline your final answer, e.g., Ans.: XXXX): a. A coupon bond that pays interest semi-annually has a par value of $1,000, matures in ten years, and has a yield to maturity of 12%. If the coupon rate is 10%, what is the intrinsic value of the bond today? (5%) b. A coupon bond that pays interest of $100 semi-annually has a par value of $1,000, matures in ten years, and is selling today at a $72 discount from par value. What is the yield to maturity on this bond? (10%) c. A 10% coupon bond with semi-annual payments is callable in ten years. The call price is $1,150. If the bond is selling today for $1,110, what is the yield to call? (10%)
Expert Solution
a). Bond's Market Value = PV of Coupon Payment + PV of Maturity Value
= [Periodic Coupon Payment * {(1 - (1 + r)^-n) / r}] + [Face Value / (1 + r)^n]
= [{(10%/2)*$1,000} * {(1 - (1 + 0.12/2)^-(10*2)) / (0.12/2)}] + [$1,000 / {1 + (0.12/2)}^(10*2)]
= [$50 * {0.6882 / 0.06}] + [$1,000 / 3.2071]
= [$50 * 11.4699] + $311.80
= $573.50 + $311.80 = $885.30
b). To find the YTM, we need to put the following values in the financial calculator:
N = 10*2 = 20;
PV = -(1000-72) = -928;
PMT = 100;
FV = 1000;
Press CPT, then I/Y, which gives us 10.89
Periodic Rate = 10.89%
So, YTM = Periodic Rate * No. of compounding periods in a year
= 10.89%*2 = 21.80%
c). To find the YTC, we need to put the following values in the financial calculator:
N = 10*2 = 20;
PV = -1110;
PMT = (10%/2)*1000 = 50;
FV = 1150;
Press CPT, then I/Y, which gives us 4.62
Periodic Rate = 4.62%
So, YTC = Periodic Rate * No. of compounding periods in a year
= 4.62%*2 = 9.24%
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