# The Relationship Between Yield to Maturity and Internal Rate of Return

Bonds and other fixed-income investments -- that is, investments that provide regular, equal payments -- are commonly quoted according to their effective interest rate, known as "yield to maturity." All investments, meanwhile, have an internal rate of return, or the total return earned by investors. A closer look at yield to maturity and internal rate of return reveals that in the case of fixed-income investments, they are one and the same.

## IRR

In simple terms, the internal rate of return, or IRR, is the return you will be getting from an investment if you assume that everything you get back is equal to everything you put in. For example, say an investment requires \$1,000 upfront and will pay you \$500 in one year and \$750 in two years. The IRR of this investment is about 15.139 percent. In other words, over the two-year term of the investment, your money will earn a return of 15.139 percent a year. The math works like this: You invest \$1,000. After a year, that's grown 15.139 percent to \$1,151.39. The investment then pays you \$500, dropping the total to \$651.39. After another year, that amount grows 15.139 percent -- to \$750, the amount of your final payment.

## Bonds

Bonds provide two kinds of cash flows: regular interest payments, known as coupon payments, and a face-value payment at maturity, the time when the bond comes due. For example, a five-year bond with a face value of \$1,000 and a 6 percent coupon rate would pay you \$60 every year -- 6 percent of \$1,000. Those payments would continue for five years, and at the end of the fifth year, you'd also get the \$1,000 face value as the maturity payment.

## YTM

Bonds don't usually sell at face value. That's because bonds have to provide a return that's competitive with other investments. The coupon and maturity payments don't change, but by adjusting the price of the bond, you can effectively change the return generated by the bond. For example, if the bond in the previous example sold at its face value of \$1,000 (known as selling "at par"), it would generate a 6 percent annual return. But if it sold at \$950, the \$60 coupon payments and the \$1,000 maturity payment would represent a roughly 7.23 percent annual return. This "effective return" based on the price paid is the bond's yield to maturity, or YTM, often called just the yield.

## Relationship

The yield to maturity of a bond is the interest rate that equates the price of the bond with the cash flows you receive from that bond -- the rate you are getting if you assume that "what you get back" is equal to "what you put in" when you bought the bond. That also happens to be the exact definition of the internal rate of return of an investment. YTM, therefore, is simply another term for the IRR of a bond.