Question

= (Bond valuation) Enterprise, Inc. bonds have an annual coupon rate of 13 percent. The interest is paid semiannually and the bonds mature in 10 years. Their par value is $1,000. If the market's required yield to maturity on a comparable-risk bond is 9 percent, what is the value of the bond? What is its value if the interest is paid annually? a. The value of the Enterprise bonds if the interest is paid semiannually is $. (Round to the nearest cent.) Clear all Check answer​

Answer 1

$1,144.36.

Explanation:

The value of the Enterprise bonds if the interest is paid semiannually is $1,144.36.

Here's the calculation:

• Annual coupon rate = 13%

• Semiannual coupon rate = 13% / 2 = 6.5%

• Number of periods = 10 years * 2 = 20

• Market's required yield to maturity = 9% / 2 = 4.5%

• Par value = $1,000

Present value of the coupons = (Semiannual coupon rate * Par value) * [1 - (1 + 0.045)^(-20)] / 0.045

= (0.065 * 1,000) * [1 - (1.045)^(-20)] / 0.045

= $793.19

Present value of the par value = Par value * [1 - (1 + 0.045)^(-20)] / 0.045

= 1,000 * [1 - (1.045)^(-20)] / 0.045

= $351.17

Value of the bond = Present value of the coupons + Present value of the par value

= $793.19 + $351.17

= $1,144.36

The value of the bond would be slightly lower if the interest were paid annually. This is because the bondholder would receive the coupons less frequently, so the present value of the coupons would be lower. The exact value of the bond if the interest were paid annually would depend on the number of days in the coupon period.