Bonds, in general, are simply debt instruments that allow businesses, or the government, to finance their capital needs by finding investors who agree to loan them an amount in exchange for interest for a period, before returning the principal amount of the loan in full. There are specific rates and periods that the bond issuer and investor agree to.

Though the numbers may appear confusing at first, breaking down the important figures and some simple calculations can help make the math behind corporate bonds a bit easier to understand. Especially when it comes to figuring out which corporate bonds are worth investing in and which do not offer a high enough return on investment (ROI).

### Key Takeaways

- Bond math may seem intractable, but it is necessary to compute a bond's value, riskiness, and yield.
- Before computing a bond's metrics, several pieces of terminology need to be understood and disambiguated.
- Here we will go over basic bond math terms including coupon, duration, and yield-to-maturity.

### Defining Some Important Terms

** Current yield: **This refers to the current yield a corporate bond provides based specifically on its market price and coupon rate as opposed to basing it on par or face value (see below). This yield is determined by taking the bond’s annual interest and dividing that amount by its current market price. To make this clear, consider this simple example: a $1,000 bond that sells for $900 and pays a 7% coupon (that’s $70 a year), would have a current yield of 7.77%. This is $70 (annual interest) divided by $900 (current price).

** Yield to call: **The yield to call refers to the bond’s yield if it’s redeemed at the first possible call date instead of its date of maturation. The date used in this calculation is typically the earliest possible call date, not the final date where it reaches full value. It’s not uncommon for prudent investors to determine both a corporate bond’s yield to call and yield to maturation before making a final decision about investing in a bond. A range of possible yields become evident with the yield to call on the low end. Whereas, the yield to maturity is used to determine the possible high-end yield of the bond. According to Standard & Poor's, the yield to call will assume that corporate bond is held until the call date and that the reinvested cash is done so at the same rate as the original yield to call.

** Yield to Maturity (YTM): **This refers to the interest rate for equating a bond’s price to its present cash flow value. When the phrase yield to maturity

*is used, this means it’s assumed that the corporate bond will be held until it matures. Additionally, this term also assumes all interim cash flows are reinvested at an equivalent rate to the yield upon maturation. If the corporate bond isn’t held to maturity, or the cash flows become reinvested at different rates from the yield to maturity rate, then the investor's yield will differ from the yield to maturity. It's important to note that the calculation for a yield to maturity includes consideration for any capital losses, gains or income investors experience when holding a bond all the way to maturation.*

** Yield to Worst (YTW): **This refers to the lowest possible yield a corporate bond can generate. This measure is typically called before maturity.

** Duration: **This measures a bond’s sensitivity to changes in interest rates. Duration specifically refers to the weighted average term that it takes a security’s cash flows to mature. This average term is weighted specifically by the present cash flow value’s percentage of the security’s price. This means that the longer, or greater, the duration of a bond is, the more vulnerable it is to changes in interest rates. According to S&P, duration is therefore used to estimate what exactly changes in a bond’s price in percentage given a 1% fluctuation in the interest rate. For example: if a corporate bond’s duration is 3, then it would be expected to move by 3% for every 1% that the interest rate moves.

### Other Factors to Be Considered

** Maturity date: **The date of maturation is the date you receive your principal investment back on a corporate bond. It also, therefore, determines how long you will receive interest payments on that capital. Of course, there are some exceptions to how this works. For example, some bonds or securities are considered callable. This means the issuer of the bond can pay back the principal at specific times they before the actual maturity. Without any doubt, it is important for investors to determine if a corporate bond is callable before the investment in such securities.

** Coupon: **This refers to the annual amount of interest a bond pays out and is often expressed as a percentage of the bond’s face value. This means a $1,000 corporate bond that has a fixed 6% coupon pays $60 a year for the duration of the bond. Most interest payments are made semiannually. So in this example, investors would likely receive a $30 payment, twice a year. As mentioned above, there is also a current yield that can deviate from the coupon, which is also called the nominal yield in contrast to the current yield. This comes about because bonds, once issued, can be traded and resold, which may cause their value to fluctuate. It is important to keep in mind that changes in the current yield do not affect the coupon as the face value, and annual payments are fixed from the date of issuance.

** Par Value: **This is the bond’s face value—the amount written in the issuer’s corporate charter. This amount is of particular importance for fixed-income bonds where it is used to determine the bond’s value upon maturation as well as the number of coupon payments until that time. The normal par value for a bond is either $100 or $1,000. The current market price of any corporate bond may be above or below the par value at any time depending on many different factors like the current interest rate, the credit rating of the bond’s issuer, the quality of the corporation and the time to maturity.

** The current price (or buying price): **This only refers to the amount an investor pays for the corporate bond (or any other security). For investors, this is the important amount as the current price ultimately determines their potential ROI. If the buying price is much higher than the par value, then the opportunity most likely does not present as great a possibility of returns.

** Coupon frequency and the date of interest payment:** It's important that all investors are aware of the coupon frequency as well as the exact dates of interest payments on the corporate bonds they hold in their portfolio. This information can be found for instance in the prospectus of the issuer.

### The Bottom Line

Using the information mentioned above, investors can precisely determine the cash flows coming in by the interest payments of different corporate bonds. As noted, most corporate bonds pay out semiannually; however, the alternatives are annually or quarterly: a corporate bond (annual coupon frequency) with a $1,000 face value and a fixed 6% coupon pays out $60 once a year at the predetermined date of interest payment.

A corporate bond (quarterly coupon frequency) with a $1,000 face value and a fixed 6% coupon pays out $15 four times a year, also at the predetermined dates of interest payment. In fact, by gathering the relevant data for all corporate bonds in a portfolio, investors may obtain a clear payout structure for their portfolio as they receive precise information on the date and amount of each interest coupon they will receive. By summing up accordingly, the investor will be able to determine for instance the exact amount of monthly interest received. These are excellent methods to find out important figures.