LESSON 8: VALUE A BOND – YIELD TO MATURITY (YTM)

## LESSON OBJECTIVES

1. Understand simple interest.
2. Understand compounding interest.
3. Understand current yield.
4. Understand yield to maturity.

## LESSON SUMMARY

In this lesson the end goal is really to learn about yield to maturity, which is a function of compounding interest. However, to grasp this, the easiest thing is to first understand Simple Interest. Imagine that you have a 5% bond with a par value of \$1,000. As an investor, you will receive \$25 bi-annually in coupon payments. Simple interest can be understood easily since it’s that simple.

Oftentimes, bonds will not be held from the time it’s issued to the time of maturity by the same bond investor. Current yield is a reflection of bonds changing in price, and is a neat measure when bonds change hands. Since the coupon will be the same, your current yield will change. For instance, you pay \$1,200 for a coupon of \$50, and your yield is 4.2% (50/1,200).

In other words, Yield to maturity is a combination of the current yield and compound interest. Yield to maturity discloses the annual return you, as an investor, can expect to receive for your bond investment until the bond expires (matures). It combines the loss or gain the investor incurs if paying a different price than the par value for the bond with the coupon payment.

To gain expert knowledge in bonds I highly recommend the book titled The Bond Book, by Annette Thau. Be sure to check out the reviews on Amazon to see third party endorsements and concerns before simply taking my recommendation.

Related: Bond Value and Yield to Maturity

## YIELD TO MATURITY CALCULATOR

Coupon (\$): * This is the total coupons recieved for 1 year.

Par Value (\$):

Years to Maturity:

Market Price (\$):

Yield to Maturity (%):

## NEW VOCABULARY

Coupon Yield
This yield is determined when the bond is issued. The Coupon yield is calculated by taking the coupon payments for 1 year and dividing them by the par/face value.

Current Yield
The current yield reflects the return when a bond changes in price. A 5% bond with a par value of \$1,000 that trades for \$1,200 would have a current yield of: 50/1,200 = 4.2%.

Yield To Maturity
The yield to maturity is perhaps the most important number to look at in bond investing. It tells you the return you can expect to receive from the bond investment starting from today until the bond matures.

Simple Interest
The simple interest is a simple measure of the return the investor gets from a bond. 5% of a \$1,000 bond is \$50 each year.

Compound Interest
The compound interest is the process of reinvesting returns gained from a bond or any other security that starts the effect of compounding interest.

## LESSON TRANSCRIPT

Backtracking to the second lesson, Jesse was a bond investor who had his bond from Real Estates Empire. Jesse can value his bond in two different ways. Firstly, he can take a good look at the simple interest and then the compound interest. While the coupon yield and current yield come under the simple interest, the yield to maturity comes under the compound interest. The Yield to maturity is the focus of this lesson.

This lesson will show why all three of these are different and why the yield to maturity is the most important to understand here.

First, let’s discuss the simple interest. To understand the concept, add up all the value of the coupons. Do not assume reinvesting of all the coupons. Simply collect the 25-dollar payment throughout the entire term of the bond. Again, just add up the coupons to get the simple interest.

Jesse would have \$50 for 2 coupons, \$75 after the third coupon, and so on. As you continue, we arrive at coupon 60 where Jesse had \$1,500 from all the coupons. To get this, just take the number of coupons. For the 30-year bond, it’s 60 coupons. Multiply that with the account payment, which is \$25.

Simple interest = # of coupons x coupon payment
\$1,500 = 60 x 25

The key to understanding this is simple. If Jesse would just buy the bond on the very first day and hold it until its maturity, the value of the investment would be \$1,500. We won’t count the \$1,000 he bought and initially the \$1,000 he gets back at the end, because it will value all those coupon payments and that’s the money he made on the investment.

The coupon yield is under simple interest and is nothing more than taking a year’s worth of those coupon payments.

Coupon yield = 1 year coupon payment / Par value
5% = \$50 / \$1,000

The current yield on a bond is typically a bond that has been on the market for a few years. If you want to buy on the very first day, you have to look at the price you’re buying that bond for compared to the coupon payment. To calculate the current yield, take the coupon payment you received for one year and divide it with the price you bought the bond for. If Jesse wanted to buy this bond, regardless of the duration of the time that passed after the initial issue was paid, there could be one year in the bond or there could be 25 years left. The current yield is taking that coupon, which in the first scenario, will be \$50. Divide it by the price (Let’s say the price needed to be paid is \$1,200.) We get a current yield of 4.25. That’s 50 divided by 1,200. See the table below:

 Price: \$1200 Price: \$1000 Price: \$800 Coupon: \$50 Coupon: \$50 Coupon: \$50 Current yield: 4.2% Current yield: 5% Current yield: 6.3.%

We’re talking about the same exact bond. There is no difference in the bond; just the price he’s buying that bond at and how that price affects the yield because he’s getting it at a more expensive price. The problem with the current yield is it doesn’t account for the amount of money that you lose or gain whenever the bond matures.

Let’s look at this first one we have: Jesse bought the bond for \$1,200. The current yield is 4.2%. What about the \$200 he will lose when the bond matures? When the bond matures, he will only get \$1,000 back, because that’s the Par value. This does not account for that loss when you sell the bond. Likewise, when you take a good look at what you get, which is \$800, regardless of how long he holds it when the bond matures, the bonds will be worth \$1,000. That \$200 profit isn’t calculated into that percent. When we talk about yield to maturity that comes in to place. Just so you know, when someone puts you a current yield, it’s not accounting for that difference between the price you will pay and the Par value when the bond matures.

Compound interest on a bond. Assume that Jesse bought the bond as soon as it was issued. Jesse would receive \$25 after the first 6 months. For the second coupon, which is 6 months later, he will receive another \$25 check. The difference is that for the first coupon of \$25, we will assume that Jesse invested that \$25 into another investment. It has nothing to do with this bond, but he pushed that money in another investment, which will provide the same interest rate he’s receiving on this bond, which is 5%. That’s the biggest consumption, because in 6 months, let’s assume Jesse bought this bond and he gets his first coupon, then when he receives that first coupon, there is no guarantee that he will be able to reinvest that first \$25 payment into another 5% yielding security. That’s where you’ve given the compound interest in figuring out what this bond is worth. There is a little bit of guess work.

Let’s assume that whatever coupon yield he had is what he can reinvest this coupon back into the same rate. After he received the first \$35 payment, let’s assume that he invested that into a really different investment—something that will make 5%. As we look at the second coupon, that initial 25% has matured into \$26, and then he receives the second \$25 coupon for a total of \$51. Jesse now has \$51 that’s maturing at a 5% interest rate as he’s waiting for the third coupon, which will be another \$25 payment. Each one of these coupons, assuming that the previous total is compounding at 5%, will keep compounding and he will actually have \$3,400 when he gets to the 60th coupon at the end where he receives his last coupon payment.

Let’s compare the simple interest versus the compound interest. The simple interest for the total duration, from the first day the last day after 30 years, will fetch him \$1500 according to the calculation. When you look at the compound interest, it is \$3,400 if it’s reinvested in 5% for each coupon. That’s a pretty big difference — it more than doubles the money on a bond. Under the compound interest, let’s look at the yield of maturity.

We are not accounting for the difference somebody would pay for a bond versus what the bond would be redeemed for whenever it reaches its term. That’s the face value paid back to the investor and the yield to maturity accounts for. Not only does it compound the interest, but it also accounts for the difference between the price that you pay and the face value.

These numbers are important because it wraps all the variables together. It gives you a real estimate of what you will get if you buy any bond and hold it until maturity.

 Price: \$2000 Price: \$1000 Price: \$800 Coupon: \$50 per month Coupon: \$50 per month Coupon: \$50 per month Years remaining: 15 Years remaining: 15 Years remaining: 15 Coupon Payments: \$1,098 Coupon Payments: \$1,098 Coupon Payments: \$1,098 Gain/Loss: \$-200 Gain/Loss: \$0 Gain/Loss: \$200 Difference: \$898 Difference: \$1098 Difference: \$1298

Assume that Jesse purchases a 30-year bond that has been on the market for 15 years. There are 15 years remaining until the bonds mature. Each one of these scenarios is exactly the same. The only difference is the price Jesse’s paying for each one of these bonds. The first one, he will pay for the premium of the bond, meaning he’s paying more than the Par value. He pays \$1,200. The coupon payment he will receive over the next 15 years amounts to \$1,098 if he’s reinvesting each coupon on 5%. The coupon is \$1,098. He will lose \$200 on the fact that he paid a premium for the bond. Whenever it matures, he will get \$1,000 and lose \$200 there.

That \$200 comes right off the top of his coupon payments for a difference of \$898. If he bought this bond at this price and holds it until maturity, he will make \$898. The yield would actually be 3.3% for that purchase price, which is significantly lower than the 5% coupon that you might think when you look at a simple interest and coupon yield perspective.

Let’s go to the second one. Jesse bought \$1,000 Par bond with 15 years remaining until maturity. The coupon that he’d received would be the same – \$1,098, but he has no gain or loss from the purchase price. The difference is \$1,098 and the yield to maturity is 5%.

When buying for the same price of the Par value, coupon yield is exactly what is says on the bond. When we look at buying a bond that’s selling at a discount, coupon payments are the same and the Par value is gaining, because you bought it for \$800. You’ll get \$1,000 back when the bond matures, which means that you’ll receive \$200 and the difference is \$1298. . Your yield to maturity on that bond is 7.2% a year although it’s a 5% coupon bond. You can see the amount of difference based on the price you’re buying these bonds for. Anytime you’re paying a premium for a bond, your yield to maturity will be much different than what your coupon yield is. Understanding yield to maturity is the most important thing you can do when understanding how to value a bond.

The equation to figure out the yield to maturity is a complex equation, but we made it easy at Buffett Books. We have a calculator on this page and you can go down there and there are practical exercises. That will show how to use the calculator. You can try this up for yourself and see that using the calculator solves the really hard math problem.

Assuming that the bond has been on the market for 15 years and that there are 15 years remaining until the bond becomes mature. Let’s says we bought that bond for \$800. The coupon yield is still 5%. To figure it out, just take the coupon payment for the year divided by the par value. Let’s say 5%. The \$1,000 bond price is 5% and the \$1,200 would be 5%. That’s really misleading when somebody gives you a code based off a coupon and that doesn’t mean anything because the price you pay will drastically affect your yield.

Let’s look at the current yield. To find out, take the coupon payments for 1 year and divide it by the price you’re paying. The first one for \$800 was 6.3%, for the \$1,000 it was 5%, and for \$1,200 it was 4.2%. Those aren’t really numbers, so when we go down to the yield to maturity, this is actually accounting for the difference of the price we’re paying and accounting for what we’ll receive for the phase value of the bond.

The numbers get more different than what you saw before with the current yield where the \$800 bond will give you a 7.2% return, which is high. The \$1,000 bond price will get you 5%. The \$1,200 will give you 3.3%, which is significantly low. That is 1.7% lower than what you’d be expecting when looking at the coupon itself.

I recommend you go back and re-watch this video if you didn’t understand anything. Go back to the lessons under this unit if you still really don’t understand.

In this lesson, we began to understand the important terms that truly value a bond. Since most investors will never hold a bond throughout the entire term, understanding how to value the asset becomes very important. As we get into the second course of this website, a thorough understanding of these terms is needed. So, be sure to learn it now and then jump ahead.

We learned that there are two ways to look at the value of a bond – simple interest and compound interest. As an intelligent investor, you’ll really want to focus on understanding compound interest. The term that was really important to understand in this lesson was yield to maturity. It was really important because it accounted for almost every variable we could consider when determining the true value (or intrinsic value) of the bond. Yield to Maturity estimates the total amount of money you will earn over the entire life of the bond, but it actually accounts for all coupons, interest-on-interest, and gains or losses you’ll sustain from the difference between the price you pay and the par value.