How to Calculate Yield to Maturity

Consider the following equation:

Where:

• P is the bond price
• C is the periodic coupon payment
• N is the number of years to maturity
• M is the (face value) payment at maturity
• y is the “risk-adjusted discount rate” (or yield to maturity, or IRR)

In the above equation, we solve for y, which is the yield to maturity of the bond.

It’s a trial and error process, and you need a spread sheet or a calculator to calculate YTM.

Let’s take a simple example to understand how YTM is calculated. Consider a $1,000 par bond, with 8% coupon and 7 years to maturity. The price of the bond is $1,112.96. Assume that the bond pays coupon semi-annually.

C = $40

N = 2 x 7 = 14

M (face value) = $1,000

P = $1,112.96

Plugging all these numbers in the above equation, we calculate y = 3.00%

In excel you can use Goal Seek to get the YTM. You can also use a calculator such as Texas Instrument BA II to calculate YTM.

Since this bond paid semi-annual coupon, the y we calculated is the semi-annual YTM. We use the bond-equivalent yield convention to calculate the annual YTM. So, YTM = 3.00x 2 = 6%

On the other hand, the effective annual yield is (1.03)2 – 1 = 6.09%

Again, note that YTM is a bond equivalent yield (BEY) which is calculated by applying simple interest rules. So, we annualize the rate by multiplying, instead of using raise to the power. For semi-annual yield, we double the semi-annual yield. For quarterly yield, we will quadruple the quarterly yield.

YTM is a preferred yield measure over current yield because it considers both interest income and capital gains for calculating the returns from the bond. It also includes the reinvestment income.