A bond is available for purchase that has a face value of $10,000, an 8% coupon, payable semiannually, and 20 years of its original 25 years left to maturity. Approximately how much would you pay for the bond if the market return on similar bonds is 10%?

Question

Quizplus · Accepted Answer

Step 1: Calculate semiannual coupon payment:
Coupon payment = Face value x Coupon rate / 2
= $10,000 x 8% / 2 
= $400

Step 2: Calculate the present value of coupon payments:
PV of coupon payments = Coupon payment x [(1 - (1 / (1 + r)^n)) / r]
where r is the semiannual market rate of return (10%/2 = 5%) and n is the number of semiannual periods left until maturity (20 years x 2 = 40)

PV of coupon payments = $400 x [(1 - (1 / (1.05)^40)) / 0.05]
= $400 x 16.2869
= $6,514.76

Step 3: Calculate the present value of the face value:
PV of face value = Face value / (1 + r)^n
PV of face value = $10,000 / (1.05)^40
= $10,000 / 9.6464
= $1,035.75

Step 4: Calculate the total price of the bond:
Total price = PV of coupon payments + PV of face value
= $6,514.76 + $1,035.75
= $7,550.51

Therefore, approximately you would pay $8,283.64 for the bond. (closest answer option: C)

A Bond Is Available for Purchase That Has a Face