# How to calculate the present value of a bond

A bond is a fixed obligation to pay that is issued by a corporation or government entity to investors. The issuer may have an interest in paying off the bond early, so that it can refinance at a lower interest rate. If so, it can be useful to calculate the present value of the bond. The steps to follow in this process are listed below. First, we need to use several assumptions as we work through the calculation steps. The assumptions are:

• The bond amount is \$100,000
• The maturity date of the bond is in five years
• The bond pays 6% at the end of each year

With this information, we can now compute the present value of the bond, as follows:

1. Determine the interest being paid on the bond per year. In this case, the amount is \$6,000, which is calculated as \$100,000 multiplied by the 6% interest rate on the bond.
2. Consult the financial media to determine the market interest rate for similar bonds. These bonds have the same maturity date, stated interest rate, and credit rating. In this case, the market interest rate is 8%, since similar bonds are priced to yield that amount. Since the stated rate on our sample bond is only 6%, the bond is being priced at a discount, so that investors can buy it and still achieve the 8% market rate.
3. Go to a present value of \$1 table and locate the present value of the bond's face amount. In this case, the present value factor for something payable in five years at a 6% interest rate is 0.7473. Therefore, the present value of the face value of the bond is \$74,730, which is calculated as \$100,000 multiplied by the 0.7473 present value factor.
4. Go to a present value of an ordinary annuity table and locate the present value of the stream of interest payments, using the 8% market rate. This amount is 3.9927. Therefore, the present value of the stream of \$6,000 interest payments is \$23,956, which is calculated as \$6,000 multiplied by the 3.9927 present value factor.
5. Add together the two present value figures to arrive at the present value of the bond. In this case, it is \$98,686, which is calculated as the \$74,730 bond present value plus the \$23,956 interest present value.

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