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LESSON SUMMARY
In this lesson we learn how to calculate the value of a bond. The value of a bond is partly determined by the coupon, which is the money you get from holding the bond, and partly the term which defines for how long you can hold the bond. Further, the value is determined by the face value which is the amount of money you receive by the end of the term, and last but not the least, by the interest rate. This lesson has the following points:
1) What is the relationship between interest rates and the value of bond: The easiest way to think about interest rates when you buy a newly issued bond is to assume that the coupon rate is the same as the interest rate. Imagine that the interest rate is 5%, so you expect to get 5% coupon. Now assume that interest rate declines to 4% on the day after you buy the bond. What does that do to the value of your bond? It increases! This is very intuitive. You get 5% while all new investors can only expect to get 4% return on their investment.
2) What is the relationship between the interest rate, the term and the value of the bond: The concept that interest rates and bond prices always go in each direction is also valid when you account for the term. The remaining period of the term rather determines the magnitude of the change in the bond price. The reason is simple. If you get 5% on your bond and everyone only gets 4% it’s more valuable if you can hold that bond for 20 years than only 1 year.
LESSON TRANSCRIPT
Take note that you need to refer to the video while reading this in order to fully understand this lesson.
BOND PRICES WITH INTEREST RATES
Math really makes the head hurt for most people, but Buffett Books has made it easy. A bond calculator does the entire hard math, so instead of focusing on the equation, focus on the fundamentals and why the numbers move in a certain direction.
Here’s a practical example. You purchased one bond in the year 2012 and the Par value for that bond was a thousand dollars with a 5% coupon and a 30-year term.
Now, if that didn’t make any sense, go back to the very first course here at Buffett Books and take those lessons to understand what those terms mean and then come back to this lesson.
See what happens to that bond. Try to figure out what that market price will do for that bond one year later as interest rates change. You are holding your 5% bond one year later and interest rates have dropped, which is a good thing. Interest rates drop down to 4% and the FED is now issuing a thousand-dollar bond with a term of 30 years at a 4% coupon. What is the value of the 5% bond you’re holding now?
You’re now holding a more valuable asset, but there are only 29 years until it matures, while the other one is 30. Figure out your bond’s worth using the bond calculator here at Buffett Books. First, put in the values. The first value is the coupon which is in a dollar amount. Look at the bond that you purchased in 2012 which had a 5% coupon. The bond calculator will only take the values in dollars, so you need to convert. A 5% coupon with a thousand-dollar Par value is 50 dollars. Put that in.
BUFFETT’S BOOKS BOND CALCULATOR
The bond calculator is only for an annual calculation, so sometimes you’ll have to go to a more advanced calculator. This is just to basically give you a general idea of how these market prices change with interest rates.
Just add up the coupons for the year which should be 50 dollars. You’d probably receive two $25 coupons. Now the Par value is just a thousand, make sure you don’t put any dollar sign in there. Just put the numbers. For the years, since you bought it and held it for 1 year, your years to maturity are 29 years. Now the new interest rate of the bond that you will compare these two is 4%. That interest rate went down. All you got to do is put in 4. Don’t put any decimal. Just put it as 4. Hit calculate. As you can see, the bond price increased. Your bond is worth 1169 dollars.
The reason you could sell it for premium is because the best that somebody can get is 4%. If you’d add up all those coupon payments for the next 29 years of that 4% bond, the price would equal 1169 with the 5% bond. That’s why you’re able to charge a premium for it.
What would happen if you changed the years to maturity so that there are only a few years left until this bond became mature? Would you see that bond price go up or down?
Let’s put that in the bond calculator – 1 year left. This would be like you held this bond for 29 years and there’s only one year left on this 5% bond. You’re comparing it to a bond that has a 4% coupon. The price goes down to $1009. The price goes down so much, because if a person bought this 5% bond from you with only 1 year left, what would they get back when the bond matures? They only get the Par face value back – $1000 only. They’re only reaping the benefits of buying a bond that’s only paying 1% more than what they can get for a year. That’s why you see that price change. You see it only goes up by 9 to 10 dollars.
However, when the bond has a lot of terms left on it and those interest rates go down, the value increases a lot, especially if you’re only holding it for 1 year.
If the interest rates went down to 3%, it’s almost a 1400-dollar bond. You don’t gain $400 in one year because you had such a drastic change in your interest rate. As those interest rates go down, the bond price goes up. Go ahead and look at it in another scenario.
Assume that you still bought the same bond in 2012 which was a 5% coupon. This time, instead of the coupon on the newly issued bonds in 2013, and so than being 4%, let’s say that the interest rates went up and now they’re 6%. Just come back over here in the bond calculator. Your coupon is still the same, your Par value is still the same, and you still have 29 years left before maturity, because you only advanced 1 year, but the interest rate is 6%. What do you think will happen to that bond price? The bond price went down below the Par value. It’s only worth 864 dollars. As those interest rates rise on you, if you’re buying a bond that is really low-interest rates, that interest rate rises, and that bond will become worthless. That is really important to understand as you invest in bonds and stocks. You got to be buying these assets at the right time.
How you can buy these assets at the right time? It’s going back to the previous lesson, lesson 3, where you learned about yield curves. When you see that inverse yield curve or that yield curve is flat, that’s the time to be in the bond market, because you’re buying those bonds at a high-interest rate and the FED is telling you on the yield curve that they expect interest rates to go down over a long period of time. When you see that, you’re buying those bonds at a high coupon with the anticipation that the interest rates will drop and you will see a change in the market price. Get capital to take and then invest that in the stock market when stocks are really cheap.
CALCULATE BOND MARKET PRICE EASILY
Use the bond calculator to your advantage. Put those coupon payments in there, see what that bond price would change to, and really learn the ins and outs. You don’t really have to fully understand the bond calculator; you just have to understand how it changes the interest rates and how it changes with the term.
When you combine this lesson with the previous lesson about the yield curve, you’ll find yourself really starting to analyze how these markets move and how the value of these assets change whether it’s a bond or a stock, and how they are related and how they all work together. Go ahead and play with the bond calculator and really try to understand how the term affects the bond and how the interest rates affect t the bond.
In this lesson, students learned how to apply the BuffettsBooks.com bond calculator. You learned that as interest rates increase, the value of a bond decreases. Similarly, when interest rates decrease, the value of a bond decreases.
When using the bond calculator, it becomes evident that the term of the security changes as it approaches maturity. Since a premium or discount paid for a bond cannot be recuperated through coupon payments, short-term bonds are less affected by changes in interest rates compared to long-term bonds. This idea of changing interest rates can be taken advantage of by intelligent investors if they purchase high-yielding long-term bonds. In order to find a high-yielding, long-term bond, an investor can implement the ideas learned in lesson 3 of this unit.
LESSON VOCABULARY
Bond Market Price
This is the ever-changing price that a bond trades for on secondary markets.
