Yield to Maturity (YTM) Calculator

What is Yield to Maturity (YTM)?

Yield to Maturity (YTM) is a comprehensive measure of a bond's total return, assuming the bond is held until it matures. It takes into account the bond's current market price, par value, coupon interest rate, and time to maturity. YTM is expressed as an annual rate and is considered a long-term bond yield expressed as an annual rate.

The YTM Formula

The formula for calculating YTM is:

\[P = \sum_{t=1}^{n} \frac{C}{(1+YTM/m)^{t}} + \frac{F}{(1+YTM/m)^{n}}\]

Where:

• P = Current bond price
• C = Coupon payment
• F = Face value (par value)
• n = Number of periods
• m = Number of compounding periods per year
• YTM = Yield to Maturity (what we're solving for)

Step-by-Step YTM Calculation

1. Gather the necessary information: bond's face value, current price, coupon rate, years to maturity, and payment frequency.
2. Set up the YTM equation using the gathered information.
3. Since the equation can't be solved algebraically for YTM, use a numerical method (like Newton-Raphson or trial and error) to find the YTM that satisfies the equation.
4. Iterate until you find a YTM that makes the present value of all the bond's cash flows equal to its current price.
5. Express the final YTM as an annual percentage rate.

Example Calculation

Let's calculate the YTM for a bond with the following characteristics:

• Face Value: $1,000
• Current Price: $950
• Coupon Rate: 5% (annual)
• Years to Maturity: 3
• Payments: Semi-annual

Using these values, we set up our equation:

\[950 = \sum_{t=1}^{6} \frac{25}{(1+YTM/2)^{t}} + \frac{1000}{(1+YTM/2)^{6}}\]

Solving this equation numerically (which our calculator does automatically), we find:

YTM ≈ 6.76%

Visual Representation

The green portion represents the bond's face value ($1,000), and the blue portion represents the additional yield (6.76%) that an investor would receive by holding the bond to maturity.