Question

The Seaside Inn has bonds outstanding with a par value of $1,000 each and a 4.30 percent coupon. The bonds mature in 7.5 years and pay interest semiannually. What is the current value of each of these bonds if the yield to maturity is 5.0 percent?

$1,004.36

$938.40

$956.67

$988.55

$1,009.47

Answer 1

Given,

Par value = $1000

Coupon rate = 4.30%

Years to maturity = 7.5 years

Yield to maturity = 5.0% or 0.05

Solution :-

Semi annual coupon payment (C) = $1000 x 4.30% x 1/2 = $21.50

Semi annual periods (n) = 7.5 years x 2 = 15

Semi annual yield to maturity (r) = 0.05/2 = 0.025

Now,

Current value of these bonds

= C/r x [1 - (1 + r)^-n] + [par value x (1 + r)^-n]

= $21.50/0.025 x [1 - (1 + 0.025)^-15] + [$1000 x (1 + 0.025)^-15]

= $860 x [1 - (1.025)^-15] + [$1000 x (1.025)^-15]

= $860 x [1 - 0.6904655568] + [$1000 x 0.6904655568]

= $860 x 0.3095344432 + [$690.4655568]

= $266.199621152 + $690.4655568

= $956.67