Answer:
d. Bond Y sells for more than bond X
Here is the question in proper order:
Bond X and bond Y both are issued by the same company. Each of the bonds has a maturity value of $100,000 and each matures in 10 years. Bond X pays 8% interest while bond Y pays 9% interest. The current market rate of interest is 8%. Which of the following is correct?
a. Bond X sells for more than bond Y.
b. Both bonds sell at a discount.
c. Both bonds sell for the same amount.
d. Bond Y sells for more than bond X
Explanation:
Bond price is calculated using the relation
[tex]Bond Price = C * \frac{[1 - \frac{1}{(1 + r)^{2} } ]}{[r + \frac{M}{(1+r)^{2} } ]}[/tex]
where
C = coupon amount
r = current market rate of interest
n = no of years
M = face value (amount)
Now for bond X
C = $100,000 x 8% = $8,000
r = 8% or 0.08
n = 10 years
M = face value
substituting in the equation
[tex]Bond price = 8000 * \frac{[1 - \frac{1}{(1+0.08)^{10} } ]}{[0.08 + \frac{100000}{(1+0.08)^{10} } ]}[/tex]
=8,000 x [1-{1/(1.08)10/0.08 +100,000/(1.08)10
=8,000 x [1-{1/2.158925]0.08 +100,000/2.158925
=8,000 x [1-0.463193]0.08 + 46,319.35
=8,000 x [0.5368065]0.08 +46,319.35
=8,000 x 6.7100814 +46,319.35
= 53,680.65 +46,319.35
=$100,000
Bond price = $100,000
For bond Y
only C is different and C = $9000
[tex]Bond price = 9000 * \frac{[1 - \frac{1}{(1+0.08)^{10} } ]}{[0.08 + \frac{100000}{(1+0.08)^{10} } ]}[/tex]
= 9,000 x [1-{1/(1+0.08)10}]/0.08 + 100,000/(1+0.08)10
=9,000 x [1-{1/(1.08)10/0.08 +100,000/(1.08)10
=9,000 x [1-{1/2.158925]0.08 +100,000/2.158925
=9,000 x [1-0.463193]0.08 + 46,319.35
=9,000 x [0.5368065]0.08 +46,319.35
=9,000 x 6.7100814 +46,319.35
= 60,390.73 +46,319.35
=$ 106,710.08
