# The Difference Between the IRR & the Yield to Maturity i Jupiterimages/Comstock/Getty Images

Many investments, such as bonds and capital infusions, are designed to return a certain cash flow over time. To measure the success of an investment and compare it to others, use an interest rate calculation that determines the return on your investment.

## Yield to Maturity

Yield to Maturity, or YTM, is a measure used to determine the annual return generated by a bond's interest payments, or coupons. A \$1,000 bond, for example, with a bond rate of 6 percent and semi-annual coupons, pays interest of \$30 every six months. You're earning 3 percent every six months, making the YTM in this example equal to 1.03^2 - 1 = 6.09 percent. Your annual yield to maturity is higher than the bond rate because you receive your coupon payments every 6 months rather than once a year.

## Bond Price

To purchase that same bond with an 8 percent yield to maturity, calculate the market price with the formula: C * [1-(1/(1+i)^n] / i + MV / (1+i)^n, where C is the coupon amount, n is the number of coupons remaining, PV is the bond's maturity value and i equals (1+YTM)^(1/f) - 1, where f is the frequency of the coupons (2 for semi-annual, 4 for quarterly, 12 for monthly). The market price of the bond is the present value of the cash flows, or coupons, plus the present value of the bond's maturity value, using a discount factor equal to your desired yield to maturity. The price of a \$1,000 bond with \$30 semi-annual coupons payable for another 10 years at a desired YTM of 8 percent would be: \$30 * [1-(1/1.0392)^20] / 0.0392 + \$1,000 / 1.0392^20 = \$410.50 + \$463.19 = \$873.69. You pay less than the \$1,000 par value of the bond because you wish to earn a higher YTM than the bond's 6.09 percent original YTM.

## IRR

The Internal Rate of Return -- IRR -- measures the interest rate a capital infusion must earn to break even based on projected cash flows. With an investment of \$C in a business and expected cash flows of CF(1), CF(2), CF(3) and CF(4) at the end of the next four years, the IRR would be the value of i solved in the following: C = CF(1)/(1+i) + CF(2)/(1+i)^2 + CF(3)/(1+i)^3 + CF(4)/(1+i)^4.

## Calculating IRR

The IRR is the interest rate at which the present value of the future expected cash flows equals your current capital infusion. A number of IRR calculators are available online that allow for quick calculation of an IRR. Suppose you wanted to know the IRR for an investment of \$1,000 with projected cash flows of \$300 in each of the next four years. The interest rate at which the present value of the expected cash flows equal \$1,000 is 7.72 percent.