Question

3. To expand its business, the Kingston Outlet factory would like to issue a bond with par value of $1,000, coupon rate of 10 percent, and maturity of 10 years from now. What is the value of the bond if the required rate of return is 1) 8 percent, 2) 10 percent, and 3) 12 percent?

Answer 1

Answer:

The value of a bond can be calculated by the formula;

$= Coupon * \frac{1 - (1 + r) ^{-n} }{r} + \frac{P}{(1 + r)^{n} }$

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%.

$= Coupon * \frac{1 - (1 + r) ^{-n} }{r} + \frac{P}{(1 + r)^{n} }$

$= 100 * \frac{1 - (1 + 0.08) ^{-10} }{0.08} + \frac{1,000}{(1 + 0.08)^{10} }\\\\= 1,134.20$

= $1,134.20

2. Required return is 10%

$= 100 * \frac{1 - (1 + 0.1) ^{-10} }{0.1} + \frac{1,000}{(1 + 0.1)^{10} }\\\\= 1,000$

= $1,000

3. Require return is 12%;

$= 100 * \frac{1 - (1 + 0.12) ^{-10} }{0.12} + \frac{1,000}{(1 + 0.12)^{10} }\\\\= 887.00$

= $887.00