A coupon bond that pays interest annually has a par value of $1,000,matures in 8 years,and has a yield to maturity of 9%.The intrinsic value of the bond today will be ______ if the coupon rate is 6%.

Question

Quizplus · Accepted Answer

To find the intrinsic value of the bond, we need to calculate the present value of all future cash flows (coupon payments and the par value) discounted at the yield to maturity (YTM) of 9%.

Since the coupon rate is 6%, the annual coupon payment will be $1,000 x 6% = $60.

The present value of each coupon payment, using the formula for the present value of an annuity, is:

PV(Coupon) = $60 / (1 + 0.09)^1 = $54.13

There are 8 coupon payments in total, so the present value of all coupon payments is:

PV(Coupons) = $54.13 x 8 = $433.04

The present value of the par value can be calculated using the formula for the present value of a future lump sum:

PV(Par) = $1,000 / (1 + 0.09)^8 = $478.91

Therefore, the intrinsic value of the bond today is:

Intrinsic Value = PV(Coupons) + PV(Par) = $433.04 + $478.91 = $911.95

Thus, the closest answer choice is A) $833.96.

A Coupon Bond That Pays Interest Annually Has a Par