A bond is a type of loan. When you buy a bond from its issuer, whether a corporation or government entity, you are actually lending the issuer money that it has to pay back with interest. You can also buy and sell already-issued bonds at the current market price from a broker. The yield of the bond is the total return -- the repayment of the loan amount plus periodic interest payments -- you'll receive if you hold the bond until it matures. The higher a bond's price, the lower its yield.
Bond Price Conventions
A bond's price multiplied by the bond factor -- the value at maturity divided by 100 -- equals the amount you will actually pay for the bond. For example, a bond with a price of 100 and a factor of 10 will cost $1,000 to buy, omitting commission. A price of 100 is called par. A discount bond sells for less than par, whereas a premium bond sells above the par price. A bond's price may be expressed as a decimal or a fraction. For example, the U.S. Treasury might sell a 30-year bond at a discount for a price of 98.375. Bond traders usually quote bond prices in fractions, such as 1/32 of a dollar. The 30-year Treasury Bond's price would be expressed as 98 6/32, which is written as 98'06.
Pricing a Bond
The price of a bond is based on the following parameters:
- C = coupon payment, the amount of interest periodically paid to the bondholder. Bonds typically pay interest quarterly, semi-annually or annually.
- n = number of coupon payments periods remaining until the bond matures
- i = the required rate of interest per period. This is not necessarily the stated interest rate for the bond, but rather the prevailing interest rate demanded by buyers of new, similar bonds
- M = value at maturity, also known as the face value. This is the principle amount repaid by the bond issuer on the bond's maturity date.
The bond's price is figured as the present value of the bond's cash flows. A bond that pays a fixed coupon at equal intervals has a price determined by the following formula:
Bond Price = C/(1+i) + C/(1+i)2 + ... + C/(1+i) n + M/(1+i) n
This present value is the sum of the cash flows, with each flow discounted by the required interest rate. That is, the longer it takes to receive a cash flow, the smaller its present value. Although the equation looks intimidating, it is easily solved using an Excel spreadsheet.
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Pricing a Bond in Excel
Select the PV function from the Financial Functions menu.
Enter the parameters for required interest rate (Rate), coupon payment (Pmt), number of remaining periods (Nper) and the value at maturity (Fv).
Divide the result by the bond factor, which is M/100.
This procedure won't produce correct results if the period length or coupon payment varies. You can use the Excel Price function for uneven cash flows.
Suppose you want to price a 10-year semiannual $1,000 face-value bond that pays interest twice a year at an annual rate of 4 percent. The stated interest rate per period is 2 percent, because there are two periods per year. However, the prevailing interest rate is 6 percent per year, or 3 percent per period. Each interest payment is ((4%/2) x $1,000) or $20. The number of periods left are (2/year) x (10 years), or 20. Enter Rate = .03, Pmt = 20, Nper = 20 and Fv of 1,000. Excel calculates the PV as $851.23. The bond factor is the face value of $1,000 divided by $100, or 10. Divide the PV by the bond factor to get the bond price, 85.123.