Question

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? Bond X sells for more than bond Y. Both bonds sell at a discount. Both bonds sell for the same amount. Bond Y sells for more than bond X.

Answer 1

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

$Bond Price = C * \frac{[1 - \frac{1}{(1 + r)^{2} } ]}{[r + \frac{M}{(1+r)^{2} } ]}$

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

$Bond price = 8000 * \frac{[1 - \frac{1}{(1+0.08)^{10} } ]}{[0.08 + \frac{100000}{(1+0.08)^{10} } ]}$

=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

$Bond price = 9000 * \frac{[1 - \frac{1}{(1+0.08)^{10} } ]}{[0.08 + \frac{100000}{(1+0.08)^{10} } ]}$

= 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