Introduction

In this chapter, we will explore the concept of Yield-to-Maturity (YTM) calculation in greater detail. YTM is a critical metric for bond investors as it represents the annualized rate of return an investor can expect to receive if the bond is held until maturity. Understanding how to calculate YTM is essential for assessing the attractiveness of a bond investment. In this chapter, we will learn how to compute a bond’s YTM when we have the bond’s structure and its market price. We will walk through the steps involved in this calculation and provide practical examples to illustrate the process.

Calculating YTM

The Yield-to-Maturity (YTM) of a bond is the discount rate at which the present value of all future cash flows from the bond, including coupon payments and the face value (par value) at maturity, equals the bond’s current market price. In other words, YTM is the rate that makes the bond’s price equal to the sum of its future cash flows, adjusted for the time value of money.

The formula to calculate YTM for a bond is as follows:

$$YTM = \frac{C+\frac{(F-P)}{n}}{\frac{(F+P)}{2}}$$

Where:

• $YTM$ is the yield to maturity.
• $C$ is the annual coupon payment.
• $F$ is the face value (par value) of the bond.
• $P$ is the current market price of the bond.
• $n$ is the number of years to maturity.

Example: Suppose you have a bond with the following characteristics:

• Face Value (F): USD 1,000
• Annual Coupon Payment (C): USD 80
• Current Market Price (P): USD 950
• Time to Maturity (n): 5 years

Using the YTM formula:

$$YTM = \frac{80+\frac{(1,000-950)}{5}}{\frac{(1,000+950)}{2}}$$ $$YTM = \frac{80+\frac{50}{5}}{\frac{(1,950)}{2}}$$ $$YTM = \frac{80+10}{975}$$ $$YTM = \frac{90}{975}$$ $$YTM \approx 0.092$$

So, the YTM for this bond is approximately 9.2%.