Yield to Maturity for Bonds - How to Calculate Yield to Maturity - Executive MBA

This post I'll be talking about Yield to Maturity for Bonds. So before we being, we need to know what Bonds are in the first place. If you are reading this, I'm sure that you already know that a firm can raise money in two ways

• Debt
• Equity

Bonds. Courtesy: Financial Star

Bonds are a type of Debt Financing Tools that a government/firm can use to raise funds. Debt ways of financing differ from the equity way in a way, the borrower has to return the principal along with the interest that was agreed upon at the time of issuance of the bond. You might ask How is Bond different from a loan ? The major difference between a bond and a loan is that Bonds are tradable while loans aren't. In case of bonds there are a few terms that we need to know before we proceed:

• Time to Maturity: This is the time period post which the entire principal amount will be returned
• Coupon Amount: The interest is awarded in the form of coupons at regular intervals.
• Face Value: This is the final amount that the buyer of the bond will get after the term is over.
• Market Price: Market price is the price at which the bond is currently trading at.

There are two types of bonds, one are call the Zero-Coupon Bond or discount bond while the other is the Coupon Bond. From the names itself, I'm sure you would have guessed it, the zero-coupon bond is a bond where there are no interests(coupon) paid out and only the principal is paid at the end. While for a coupon bond, the principal along with the interest is paid.

What is Yield to Maturity ?

Yield to Maturity helps us arrive at the rate/yield of a bond based on its current market price. So it will help us answer a question "What will be the rate of return is the market price of a bond is Rs 920 with a face value of Rs 1000 after a period of 10 years ?"

Since we have two types of bonds, there are two ways to calculate YTM. First we will calculate the YTM for a zero-coupon bond.

How to Calculate YTM for Zero Coupon Bond ?

Example: A 180 day T- bill (Treasury Bill) is trading in the market for Rs. 96. The face value of the T- bill is Rs. 100. What is the bond yield equivalent for this T- bill? Assume 1 year = 360 days.

For a zero-coupon bond, the formula to calculate the YTM is quite straight forward as there are no coupons involved. The formula is as follows:

Yield to Maturity = (((Face Value - Market Price) / Market Price)/ Time (in years))

For our question, we have the face value as Rs 100, Market Price as Rs 96 and the time as 180 days. Note that the time is in days and we want it in years. Hence we do (180/360). Putting all these values in the formula, we get the answer as 8.33%

How to Calculate YTM for Coupon Bond ?

Example: The price of a bond is Rs 920 with a face value of Rs 1000 which is the face value of many bonds. Assume that the annual coupons are Rs 100, which is a 10% coupon rate, and that there are 10 years remaining until maturity. 

For a Coupon Bond, the formula to calculate the YTM is as follows:

Yield to Maturity = (c / r) x (1 - (1/(1+r)^n)+(f/(1+r)^n)) where,

c - Coupon Rate

r - Required Rate of Return

n - Time Period

f - Face Value

For this question, I'm going to be using excel to calculate the Yield to Maturity:

There are again two ways of solving this:

• Applying the same formula in Excel. In the image below, please note that the YTM field is pre-filled with a dummy value. This will be later updated using the Goal Seek feature of Microsoft Excel / Libre Office. I've calculate all the parts of the formula shared above separately to ensure you understand it.

Filling the values as per the question.

Using the Goal Seek feature.

Using the Goal Seek feature, we arrive at the Yield of Maturity as 11.38%.

• The second way of solving this example using the built-in excel function is using the =RATE() function. The rate function requires the parameters: Time(NPER), Coupon Amount(PMT), Market Price(PV), Face Value (FV). Thus replacing all the values in the formula we get =RATE(10, (10%*1000),-920,1000) = 11.38%

I have spent some considerable time understanding this and have penned this down so that others might benefit from this. I feel the best way to understand anything is to teach someone and in this case I'm writing it down with an intention of teaching some one. That is all about Yield to Maturity for Bonds and how to calculate Yield to Maturity. This is a part of my Executive MBA program at NMIMS Hyderabad. Keep reading my other posts to know more about my experiences and review of the Executive PGDM program at NMIMS Hyderabad.

Hope this helps !