# How to Price Bonds: Formula & Calculation Video

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• 0:04 How Does a Bond Work?
• 1:17 Factors that Impact…
• 2:24 Determining the Price…
• 4:55 Three Ways to Price a Bond
• 5:56 Lesson Summary
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Lesson Transcript
Instructor: Lori Forrest

Lori has taught college Finance, Operations and Business courses for over five years. She has a master's degree in both Accounting and Project Management.

A bond is a loan an investor makes to a company or government entity for a set period of time and an agreed upon interest rate. This lesson will discuss how to determine the price of a bond using the present value of cash flows over time.

## How Does a Bond Work?

Rebekah wants to expand her travel agency business, so she asks each investor to pay her \$1000. She promises to pay each investor \$100 a year for three years and return their \$1000 at the end of that three years. Is this a fair deal? To answer that, we'll look at what bonds are, learn how to price them, and help Steve (one of Rebekah's potential investors) decide if she is offering a fair deal.

For an investor, bonds are like IOUs. A bond is a loan an investor makes to a company or government for a set period of time and an agreed upon interest rate. The companies or government entities that issue the bonds periodically make interest payments to investors; in Rebekah's case, this will be once a year. The companies or government entities also agree to pay back investors the face value of the bond once it reaches maturity, like Rebekah promising to return Steve's \$1000 after three years.

There are three main categories of bonds:

1. Corporate bonds
2. Municipal bonds issued by state and local governments
3. U.S. Treasury bonds issued by the federal government

## Factors that Impact Pricing Bonds

Rebekah is pricing the bond at \$1000, but how does Steve know what that \$1000 he's paying now for the bond will be worth in the future? Steve has to think about what Rebekah is offering to repay in addition to the \$1000, how long he'll have to wait for his money, and how reliable she is.

He needs to explore three factors:

• First is the coupon rate is the interest rate paid on a bond. Steve's \$1000 bond pays \$100 per year, so it has a coupon rate of 10%. Investors should compare the coupon rate to the going market rate, or the interest rate most investors can expect in a similar bonds market.
• Next, Steve needs to consider duration, which is the length of time the bond will be held to maturity. The longer the bond is held, the more likely it will be affected by changes in the market.
• And finally, credit quality relates to the issuer's expected ability to repay the coupon at face value as agreed. Bonds backed by the U.S. government have a lower coupon rate because the government usually has a higher credit rating than, say, someone like Rebekah who may have a higher risk of defaulting on payments.

## Determining the Price of a Bond

Determining the price of a bond requires adding up the present values of all future payments from the bond. The basic idea of present value is the sooner we get money, the more valuable it is.

Let's put it this way: would you rather have \$100 today or three years from now? Most investors, including Steve, would rather have \$100 today because they could invest it and earn interest. The present value of \$100 today is, of course, \$100, but what about the present value of the first \$100 payment that Steve can expect from Rebekah in a year?

The present value of future payments depends on what Steve could get if he invested his money elsewhere. Steve does his research and finds that the going market rate is 7%. He can find the present value of that first \$100 bond payment he'll receive a year from now by using the present value formula:

PV = FV / ((1+r)^n)

The future value (FV) of the first bond payment is \$100, the annual interest rate (r) based on the market is 7% (.07), and the number of periods between today and payout (n) is one year.

PV = \$100 / ((1 + .07)^1) = \$93.46

The \$100 that Steve will get 1 year from now is worth \$93.46 today. Let's find the present value for the second \$100 payment that Steve will receive two years from now:

PV = \$100 / ((1 + .07)^2) = \$87.34

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