Answer:
The value of a bond can be calculated by the formula;
[tex]= Coupon * \frac{1 - (1 + r) ^{-n} }{r} + \frac{P}{(1 + r)^{n} }[/tex]
r is the required return
n is the number of periods
P is the par value
Coupon = 10% * 1,000 = $100
1. Required return is 8%.
[tex]= Coupon * \frac{1 - (1 + r) ^{-n} }{r} + \frac{P}{(1 + r)^{n} }[/tex]
[tex]= 100 * \frac{1 - (1 + 0.08) ^{-10} }{0.08} + \frac{1,000}{(1 + 0.08)^{10} }\\\\= 1,134.20[/tex]
= $1,134.20
2. Required return is 10%
[tex]= 100 * \frac{1 - (1 + 0.1) ^{-10} }{0.1} + \frac{1,000}{(1 + 0.1)^{10} }\\\\= 1,000[/tex]
= $1,000
3. Require return is 12%;
[tex]= 100 * \frac{1 - (1 + 0.12) ^{-10} }{0.12} + \frac{1,000}{(1 + 0.12)^{10} }\\\\= 887.00[/tex]
= $887.00
The Market Value of the bond at 8% required rate of return is $1134.
The Interest on the bond will be:
= 1000 * 10% = 100
The Market Value of the bond at 8% required rate of return
= $100(PVIFA i,n) + $1000(PVIFi,n) = $100(6.710) + $1000(0.463)
= $671 +$463
= $1134
The Market Value of the bond at 12% required rate of return will be:
= $100(PVIFAi,n)+$1000(PVIFi,n) = $100(5.650)+$1000(.322)
= $565 + $322
= $887
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