Ultimate Butter Popcorn issues 5%, 15-year bonds with a face amount of $58,000. The market interest rate for bonds of similar risk and maturity is 5%. Interest is paid semiannually. At what price will the bonds issue

So, the bonds will issue at par which means that they will issue at their face value of $58000

Explanation:

If the coupon rate paid by the bond and the market interest rates are same, the bonds are always issued at par. We can check this through the following.

To calculate the price of the bond, we need to first calculate the coupon payment per period. We assume that the interest rate provided is stated in annual terms. As the bond is a semi annual bond, the coupon payment, number of periods and semi annual YTM will be,

Coupon Payment (C) = 0.05 * 1/2 * 58000 = $1450

Total periods (n)= 15 * 2 = 30

r or YTM = 5% * 1/2 = 2.5% or 0.025

The formula to calculate the price of the bonds today is attached.

Bond Price = 1450 * [( 1 - (1+0.025)^-30) / 0.025]  +  58000 / (1+0.025)^30

Bond Price = $58000

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