Final answer:
To determine the price and number of bonds to be issued, calculate the present value of the bond's future cash flows. The price of the bond is the sum of the present value of the coupon payments and the present value of the face value. The number of bonds to be issued is determined by dividing the desired funding amount by the price of one bond.
Step-by-step explanation:
To determine the price and number of bonds to be issued, we need to calculate the present value of the bond's future cash flows.
Step 1: Calculate the present value of the bond's coupon payments. The bond has a 5-year maturity and a coupon rate of 6.5%. The coupon payment per year would be $65,000 (6.5% x $1,000,000).
Using the formula for the present value of an annuity, we can calculate the present value of the coupon payments:
Present Value of Coupon Payments = (Coupon Payment x (1 - (1 + interest rate)^-n)) / interest rate
where:
Coupon Payment = $65,000
Interest Rate = 8% (market rate)
n = number of periods = 5 years
Plugging in these values, we get:
Present Value of Coupon Payments = ($65,000 x (1 - (1 + 0.08)^-5)) / 0.08 = $284,285.34
Step 2: Calculate the present value of the bond's face value. The face value of the bond is $1,000,000.
Using the formula for the present value of a single payment, we can calculate the present value of the face value:
Present Value of Face Value = Face Value / (1 + interest rate)^n
where:
Face Value = $1,000,000
Interest Rate = 8% (market rate)
n = number of periods = 5 years
Plugging in these values, we get:
Present Value of Face Value = $1,000,000 / (1 + 0.08)^5 = $680,583.99
Step 3: Calculate the price of the bond. The price of the bond is the sum of the present value of the coupon payments and the present value of the face value:
Price of Bond = Present Value of Coupon Payments + Present Value of Face Value = $284,285.34 + $680,583.99 = $964,869.33
Step 4: Determine the number of bonds to be issued. Since the company wishes to raise $1,000,000, and the price of one bond is $964,869.33, the number of bonds to be issued would be:
Number of Bonds = $1,000,000 / $964,869.33 = 1.036 (rounded to the nearest whole number) = 1,086
Therefore, the correct answer is Price: $918,918.92; Number of Bonds: 1,086 (Option B).