Question

What is the fair value of a $1000 face value, fixed coupon bond with a coupon rate of 3.7%, yield to maturity of 4.0%, semi-annual coupon payments and 8 years to maturity?

A. $887.24

B. 998.03

C. 979.63

D. 968.17

Answer 1

Bond Value = C * [( 1 - ( 1 + R)^-N)]/R + FV/ ( 1 + R)^N

Where, R = Yield per period

N = Number of periods

FV = Face value

C = Coupon payment per period

Coupon Payment = Face Value * Coupon rate * ( 1 / Number of coupon payment in a year)

= 1000 * 3.7% * ( 1 /2)

= 37 * ( 1 /2)

= $18.5

Number of periods = 8 *2

= 16

Rate ( Yield per period ) = 4% / 2

= 2%

Bond Value = 18.5 * [( 1 - ( 1 +2%)^ -16] / 2% + 1000 / ( 1 + 2%)^16

= 18.5 * ( 1 - (1.02)^-16)/ 0.02 + 1000 / ( 1.02)^16

= 18.5 * ( 1 - 0.728445) / 0.02 + (1000/ 1.37278570)

= (18.5 * 13.57775) + 728.445816

= 251.188375 + 728.445816

Bond Value = 979.63 [ Option C is the correct option]