# How to calculate the issue price of a bond

The issue price of a bond is based on the relationship between the interest rate that the bond pays and the market interest rate being paid on the same date. The basic steps required to determine the issue price are:

1. Determine the interest paid by the bond. For example, if a bond pays a 5% interest rate once a year on a face amount of \$1,000, the interest payment is \$50.

2. Find the present value of the bond. To continue with the example, if the bond matures in five years, its present value factor is 0.74726, as taken from a table for the present value of 1 due in n periods, and based on the market interest rate of 6%. The present value of the bond is therefore \$747.26.

3. Calculate present value of interest payments. To continue with the example, the present value of an ordinary annuity of 1 at 6% for five years is 4.21236. When we multiply this present value factor by the annual interest payment of \$50, we arrive at a present value of \$210.62 for the interest payments.

4. Calculate bond price. The price of the bond should be \$957.88, which is the sum of the present value of the bond repayment that is due at its maturity in five years, and the present value of the related stream of future interest payments.

Since the price of the bond is less than its face value, it is evident that the interest rate being paid on the bond is lower than the market rate. Investors are therefore bidding its price down in order to achieve an effective interest rate that matches the market rate. If the result of this calculation had instead been a price higher than the face value of the bond, then the interest rate being paid on the bond would be higher than the market rate.

When a bond issuer sells bonds at a discount from their face value, it records a debit in the amount of the discount, a debit to the cash account, and a credit to the bonds payable account for the full face value of the bonds. It then amortizes the discount over the remaining period of the bond, which results in an increase in the recognized amount of interest expense.

When a bond issuer sells bonds at a premium to their face value, it records a debit to the cash account, a credit to the bonds payable account for the full face value of the bonds, and a credit in the amount of the premium. It then amortizes the premium over the remaining period of the bond, which results in a reduction in the recognized amount of interest expense.

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