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 8%.

Question

Quizplus · Accepted Answer

To calculate the intrinsic value of the bond, we need to find the present value of each coupon payment and the present value of the face value, and then add them together.

Since the coupon rate is 8% and the par value is $1,000, the coupon payment will be $80 per year, or $40 every six months. We can use the present value of an annuity formula to find the present value of each coupon payment:

PV = C * (1 - (1 + r)^-n) / r

where PV is the present value, C is the coupon payment, r is the semi-annual yield to maturity (which is 5% in this case), and n is the number of semi-annual periods (which is 10 since the bond matures in 5 years and payments are made semi-annually).

PV of each coupon payment = $40 * (1 - (1 + 0.05)^-10) / 0.05 = $317.78

Next, we need to find the present value of the face value, which is simply:

PV of face value = $1,000 / (1 + 0.05)^10 = $613.91

Finally, we add the present value of each coupon payment and the present value of the face value to get the intrinsic value of the bond:

Intrinsic value = $317.78 * 10 + $613.91 = $3,161.80

However, this assumes a yield to maturity of 8%, whereas the actual yield to maturity is 10%. As the yield increases, the present value of the bond decreases. We can adjust the intrinsic value by using the bond valuation formula:

Intrinsic value = C * (1 - (1 + r)^-n) / r + F / (1 + r)^n

where C is the coupon payment, r is the yield to maturity, n is the number of periods, and F is the face value.

Plugging in the values we get:

Intrinsic value = $40(1-1.05^-10)/(.10/2) + $1000/(1.05)^10
Intrinsic value = $317.78 * 10 + $613.91 = $922.78

Therefore, the best choice is A.

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