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1) Hamilton, Inc
1) Hamilton, Inc. bonds have an 8% coupon rate. The interest is paid semiannually, and the bonds mature in 5 years. Their par value is $1,000.
a) If your required rate of return is 10% what is the value of the bond?
b) If your required rate of return is 10% and interest is paid annually, what is the value of the bond?
2) ABC bonds have an annual coupon rate of 8% and a par value of $800 and will mature in 20 years. If you require a return of 7.5%, what price would you be willing to pay for the bond? What happens if you pay more for the bond? What happens if you pay less for the bond?
7) You own a bond that pays $60 in annual interest, with a $1,000 par value. It matures in 17 years and your required rate of return is 7%. What is the value of the bond?
8) XYZ Corp plans on issuing bonds that pay no interest but can be converted into $2,200 (you receive when bond matures), 12 years from their purchase. It is determined that they should yield 6.5%, compounded annually. What price should XYZ Corp sell the bonds?
Expert Solution
5-a) Computation of the value of bond:-
Value of bond = (C*((1-1/(1+rate)^n)/rate)) + (FV/(1+rate)^n)
Here,
Rate = 10%/2 = 5% (semiannual)
Coupon payment = $1,000*8%/2 = $40
n = 5*2 = 10 periods (semiannual)
Value of bond = ($40*((1-1/(1+5%)^10)/5%)) + ($1,000/(1+5%)^10)
= ($40*7.72173) + ($1,000/1.62889)
= $308.87 + $613.91
= $922.78
5-b) Computation of the value of bond:-
Value of bond = (C*((1-1/(1+rate)^n)/rate)) + (FV/(1+rate)^n)
Here, Coupon payment = $1,000*8% = $80
Value of bond = ($80*((1-1/(1+10%)^5)/10%)) + ($1,000/(1+10%)^5)
= ($80*3.79079) + ($1,000/1.61051)
= $303.26 + $620.92
= $924.18
6) Computation of the price of the bond:-
Price of bond = (C*((1-1/(1+rate)^n)/rate)) + (FV/(1+rate)^n)
Here,
Coupon payment = $800*8% = $64
Price of bond = ($64*((1-1/(1+7.5%)^20)/7.5%)) + ($800/(1+7.5%)^20)
= ($64*10.19449) + ($800/4.24785)
= $652.45 + $188.33
= $840.78
If I pay more for the bond, I will earn a return less than the required return of 7.5%
If I pay less for the bond, I will earn a return more than the required return of 7.5%
7) Computation of the value of the bond:-
Value of bond = (C*((1-1/(1+rate)^n)/rate)) + (FV/(1+rate)^n)
= ($60*((1-1/(1+7%)^17)/7%)) + ($1,000/(1+7%)^15)
= ($60*9.76322) + ($1,000/3.15882)
= $585.79 + $316.57
= $902.37
8) Computation of the price of bond:-
Price of bond = Maturity value / (1+rate)^n
= $2,200/(1+6.5%)^12
= $2,200/2.12910
= $1,033.30
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