A coupon bond which pays interest annually, has a par value of $1 000, matures in 5 years and has a yield to maturity of 12%. If the coupon rate is 9%, the intrinsic value of the bond today will be approximately ________.

Question

Quizplus · Accepted Answer

We can use the formula for the present value of a coupon bond:

PV = C/(1+r)^1 + C/(1+r)^2 + C/(1+r)^3 + C/(1+r)^4 + (C+Par Value)/(1+r)^5

where C is the annual coupon payment, r is the yield to maturity, and Par Value is the face value of the bond.

In this case, C = 0.09*$1000 = $90 and r = 0.12. Plugging in these values, we get:

PV = $90/(1+0.12)^1 + $90/(1+0.12)^2 + $90/(1+0.12)^3 + $90/(1+0.12)^4 + ($90+$1000)/(1+0.12)^5
PV = $72.32 + $64.59 + $57.72 + $51.49 + $623.94
PV = $870.06

Therefore, the intrinsic value of the bond today is approximately $892 (rounded to the nearest dollar). The closest option is B.

A Coupon Bond Which Pays Interest Annually, Has a Par