Bond valuation Hamilton Inc bonds have a coupon rate of 9 pe

(Bond valuation) Hamilton, Inc. bonds have a coupon rate of 9 percent. The interest is paid semiannually, and the bonds mature in 8 years. Their par value is $1,000. If your required rate of return is 13 percent, what is the value of the bond? What is the value if the interest is paid annually? a. If the interest is paid semiannually, the value of the bond is S. (Round to the nearest cent.) b. If the interest is paid annually, the value of the bond is S Round to the nearest cent.)

Solution

Answer a.

Face Value = $1,000

Annual Coupon Rate = 9%
Semiannual Coupon Rate = 4.5%
Semiannual Coupon = 4.5% * $1,000
Semiannual Coupon = $45

Annual Interest Rate = 13%
Semiannual Interest Rate = 6.5%

Time to Maturity = 8
Semiannual Period to Maturity = 16

Current Price = $45 * PVIFA(6.5%, 16) + $1,000 * PVIF(6.5%, 16)
Current Price = $45 * (1 - (1/1.065)^16) / 0.065 + $1,000 / 1.065^16
Current Price = $804.64

Answer b.

Face Value = $1,000

Annual Coupon Rate = 9%
Annual Coupon = 9% * $1,000
Annual Coupon = $90

Annual Interest Rate = 13%
Time to Maturity = 8

Current Price = $90 * PVIFA(13%, 8) + $1,000 * PVIF(13%, 8)
Current Price = $90 * (1 - (1/1.13)^8) / 0. 13 + $1,000 / 1.13^8
Current Price = $808.05