A coupon bond that pays interest semi-annually has a par value of $1,000,matures in 5 years,and has a yield to maturity of 10%.The intrinsic value of the bond today will be ________ if the coupon rate is 12%.

Question

Quizplus · Accepted Answer

When the coupon rate is 12%, the bond will pay $60 in interest semi-annually (i.e. $1,000 x 12% / 2).

Using the formula for calculating the intrinsic value of a bond:

Intrinsic value = (C / Y) x [1 - 1 / (1 + Y)^n] + M / (1 + Y)^n

where: 
C = coupon payment = $60 
Y = yield to maturity = 10% / 2 = 5% 
n = number of periods = 5 x 2 = 10 
M = par value = $1,000

Plugging in the values, we get:

Intrinsic value = ($60 / 5%) x [1 - 1 / (1 + 5%)^10] + $1,000 / (1 + 5%)^10 
= $1,077.22

Therefore, the answer is D.

A Coupon Bond That Pays Interest Semi-Annually Has a Par