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# An Introduction to Bond Valuation

Bonds

The value of a bond is the present value of the discounted expected cash flows. So to value the bond we’ll need information on the cash flows and discount rate. This information is summarized in the:

• Coupon rate
• Par (or face) value
• Years to maturity
• Payment period (usually semiannual)
• Yield-to-Maturity (YTM)

## Cash Flow Structure

Given the previous information, we know the cash flow structure and the rate at which to discount the cash flows. For example, say a bond has a 5% coupon rate, a $1000 par value, 10 years to maturity, makes payments annually, and lastly has a 8% YTM (we’ll define YTM in greater detail a little later on). • Then the bond will pay 0.05(\$1000) = \$50 every year for 10 years, with an additional$1000 in year 10. In other words, the cash flows are $50 in years 1 through 9, and$1050 in year 10.
Year12345678910
$50$50 $50$50 $50$50 $50$50 $50$1050

## Bond Value

To find the value of the bond we simply sum the present value of each individual cash flow. So we sum the values in the table below. Note 1.08 = (1 + YTM) where the yield-to-maturity is 8%.

Year12345678910
\frac{\$50}{1.08} \frac{\$50}{1.08^{2}} \frac{\$50}{1.08^{3}} \frac{\$50}{1.08^{4}} \frac{\$50}{1.08^{5}} \frac{\$50}{1.08^{6}} \frac{\$50}{1.08^{7}} \frac{\$50}{1.08^{8}} \frac{\$50}{1.08^{9}} \frac{\$50}{1.08^{10}}

## Semiannual vs Annual Values

Above, in the section on Semiannual Interest, we asked whether the effective semiannual rate was always lower than the effective annual rate. The answer is:

• If the bond is trading at a discount (YTM above the coupon rate), then switching from annual to semiannual will lower the value of the bond.

• However, if the bond is trading at a premium (YTM below the coupon rate), then switching from annual to semiannual will raise the value of the bond.

The reason is due to compounding. When we switch from annual to semiannual we are now compounding the rate—and compounding has a larger effect on higher rates. So it has a larger effect on the YTM or coupon, depending on which is higher.

## Credits and Collaboration

Click the following links to see the codeline-by-line contributions to this presentation, and all the collaborators who have contributed to 5-Minute Finance via GitHub.

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Intro: Bond Valuation