ABC Enterprises issues $400,000 of bonds paying a stated interest rate of 7%. The bonds are due in 10 years, with interest payable annually each year on Jan. 1st. When the bonds are issued, other bonds of similar risk and maturity are paying 11% (i. e. the discount rate or market interest rate is 11%) alculate the issuance (selling) price of this bond (int. payment) (factor)-- Present value of interest payments (annuity portion) Present Value of Bond Principal (single sum value) Total Present Value, or selling price 400,000 (principal)* (factor) Is the bond issued at a premium, discount, or face value (par)?

Present value of interest payments = $164,897.83

Present value of bond principal = $140,874.83

Total present value = $305,772.66

The bond was issued at premium.

Explanation:

Face value of the bond = $400,000

Interest rate = 7%

Annual interest payable = 7% of 400000

                    = $28,000

Present value adjusts the value of a future payment into today’s dollars.

We calculate the present value of annual payment of $28,000 for a period of 10years. This is an annuity and we shall calculate using the present value of annuity formula. We also find the present value of bond principal paid at the end of 10years.

Where:

I = annual interest payable = $28,000

r = discount rate or market interest rate = 11%

n = number of years = 10 years

Where:

P = Lump sum at maturity = $400000

r = discount rate = 11%

n = maturity period = 10 years

Total present value = 164897.83 + 140874.83

Total present value = $305,772.66

Since total present value is less than the face value of the bond of $400,000, it is safe to conclude that the bond was issued at a premium.

answer; ///retained

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