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Economics: Price of Bonds and the Interest Rate


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About this Lesson

  • Type: Video Tutorial
  • Length: 12:58
  • Media: Video/mp4
  • Use: Watch Online & Download
  • Access Period: Unrestricted
  • Download: MP4 (iPod compatible)
  • Size: 139 MB
  • Posted: 03/29/2010

This lesson is part of the following series:

Economics: Full Course (269 lessons, $198.00)
Economics: Banking, Spending, Saving and Investing (19 lessons, $30.69)
Economics: Financial Markets (4 lessons, $8.91)

This economics video lesson will teach you about the Price of Bonds and the Interest Rate. Taught by Professor Tomlinson, this lesson was selected from a broader, comprehensive course, Economics. This course and others are available from Thinkwell, Inc. The full course can be found at The full course covers economic thinking, markets, consumer choice, household behavior, production, costs, perfect competition, market models, resource markets, market failures, market outcomes, macroeconomics, macroeconomic measurements, economic fluctuations, unemployment, inflation, the aggregate expenditures model, banking, spending, saving, investing, aggregate demand and aggregate supply model, monetary policy, fiscal policy, productivity and growth, and international examples.

Steven Tomlinson teaches economics at the Acton School of Business in Austin, Texas. He graduated with highest honors from the University of Oklahoma and earned a Ph.D. in economics at Stanford University. Prof. Tomlinson's academic awards include the prestigious Texas Excellence Teaching Award given by the University of Texas Alumni Association and being named "Outstanding Core Faculty in the MBA Program" several times. He has developed several instructional guides and computerized educational programs for economics.

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This lesson is about bonds, financial securities, a way of lending and borrowing. We are going to look in this lesson at how bonds work and also about the relationship between the price of bonds and the return on investment. As it turns out, there is an inverse relationship between the price you pay for a bond and the return you get on your money.
Let's start by defining a bond with its characteristics. This financial security has as one of its defining characteristics its face value. The face value is the number with respect to which interest is calculated. For almost all bonds, the face value is equal to $1000. The second determinant of a bond is its coupon rate. The coupon rate determines the interest payment. For instance, if we took the unusually high coupon rate of 20%, then 20% of a $1,000 would be the annual coupon payment on this bond, which would be equal to $200. Whether the bond pays its coupon payment annually or whether it pays half of it every six months, it's still going to be given to you by this percentage. This bond pays you 20% of the face value each year in interest payments. Holding this bond is going to entitle you to a $200 check each year during the life of the bond. The third characteristic of a bond is its maturity date, and the maturity date is the date upon which the holder of the bond is entitled to receive the face value. For instance, if the maturity date of this bond is tomorrow, then tomorrow I am going to get $1000 from the issuer of the bond. A final characteristic of a bond is its tax treatment. Will the interest that I receive from this investment be taxed by the federal government and by state and local governments? If you buy a corporate bond, you will have to pay all taxes on income you receive from it. If you buy a U.S. Treasury Bond, on the other hand, you may be exempt from most state and local income taxes. Finally, if you buy a municipal bond--that is, a bond issued by a state government, a county government, a school district--those bonds are almost always exempt from federal income taxes.
Let's suppose that you purchase a bond today that matures exactly one year from now, and let's suppose that that bond is going to entitle you to a payment of $1,200. Let's suppose further that that $1,200 is the sum of the $1,000 face value and a $200 interest payment. That is, it's a bond with a coupon rate of 20%. Well, how would you calculate your return on this particular security? It depends on how much you pay for the bond. Let's suppose that you pay the face value of a $1,000 with this bond. That means you've put $1,000 into savings by purchasing this instrument. That means that $1,000 of what you get back is just repaying what you put in. We call that the principal--what you put in and what you will get back. The remaining money is your reward for having made the investment; that is, the remaining money $200 counts as interest. Now, if you are able to get this bond for a smaller price, that is, you have put less in, more of the repayment will count as interest. And that means a better return on your investment. On the other hand, if you pay a higher price to purchase this bond, then a smaller percentage of what you get back counts as interest and the return on the bond isn't so good.
Let's look now at the inverse relationship between the price you pay for a bond and the return you get on that investment, and we are going to stick with our simple case of a one-year bond that pays $1,200 one year from today. Let's remember that the bond is defined by its face value, its coupon rate, and its time to maturity. And we are going to represent that definition in this simple visual setup. We are going to create a seesaw and we have got a horizon here and a fulcrum that's sitting waiting for our teeter-totter. The horizon is made up of those fixed components of the bond, that is, the face value of $1,000, the coupon rate of 20%, and multiplying 20% by a 1000 we get the coupon payment of $200. But these are just the definitional aspects of the bond. To see really what's in it for you, we have got to look at what you actually pay to get this bond, because frequently the price will differ from the face value. Suppose for a moment that you actually purchase this bond at its face value of $1,000. Well, a year from now when you get $1,200, $1,000 of that is going to repay your initial investment. That leaves $200 worth of interest for an interest rate of 20%. When you pay the face value for a bond, your rate of return or interest rate is equal to the coupon rate.
Suppose now instead you pay a price that's less than the face value. If that's the case, we will get the following setup. Suppose you pay $900 to get this bond. A year from now you are still going to get 1,200 back, so 1,200 minus your initial investment of 900 means $300 of that is interest. Because you are paying less to get the bond, more of the money that's coming back to you counts as interest because less of it is counting as repayment. When the price is $900, then the $300 interest payment divided by $900 gives you an interest rate of 33 1/3%. Anytime the price you pay for a bond is less than the face value, then the rate of return on that bond for you will be greater than the coupon rate.
Now the converse is also true. Suppose now instead of getting the bond at a discount, you actually had to pay a premium to get this bond, that is, the price you pay is greater than the face value. Suppose in fact that the price you pay for this bond is equal to $1,050. Now, a year from now you are still going to get $1,200, 1,200 minus 1,050 leaves you with interest of only $150. Because you are paying more to get the bond, more of that $1,200 counts as repayment of your original investment and less of it counts as interest. $150 worth of interest on a principal of 1,050 means that the interest rate you calculate at only 14.28%.
So far, we have been talking about a mathematical relationship. When the price you pay for a bond goes up then mathematically the return you get on that investment will fall. What determines the price you actually pay for any given bond? And this will be driven by alternative investment opportunities. What's the opportunity cost of buying this particular bond? Well it means you are not putting your money into another investment opportunity. As you look around at comparably risky investments, other investments that are like this, you are going to be comparing the rate of return you could get on those investments with the rate of return that this investment offers. And the price of the bond will adjust to make them equal, that is, if this is a relatively unattractive investment, no one is going to buy it and the price is going to fall. On the other hand, if everyone wants it, because the return is high, the price will be bid up. And remember, when the price changes, so does the rate of return. Let's suppose that the market interest rate is equal to 33 1/3%, that is, you can get 33 1/3% on a comparably risky investment somewhere else. Well in that case, you will never pay at $1,000 for this bond because that would be a return of only 20%. Because this bond has to match the market rate of 33 1/3% for anyone to be willing to buy it, the price of this bond is going to fall to $900. This bond is going to sit undesired, unpurchased until the price falls low enough that the interest rate on the bond is comparable to what you can earn on something else. On the other hand, when market interest rates are low then this bond looks very attractive, and so if the market interest rate is 14.28%, everyone wants to buy this bond until the price is bid up to 1,050. At that point, this bond is just as desirable, just as attractive, just as profitable investment as those other investments available in the market. When the market interest rate rises, the price of the bond will fall to make this return equal to the market. When the market rate falls, the price of this bond will rise to make the rate equal to that of the market.
An important concept in the study of financial instruments is the time value of money. The time value of money is the relationship between the value of money today and the value of money in the future. The value of money today is the present value of money and the value of money at some point in the future is the future value of money. The connection between the present and the future is the interest rate. Let's look at some examples, first, of the future value of money.
If you have taken amount of money in the present, V0, and put it in the bank, then one year from today you are going to have that amount plus interest. Multiply V0 by 1 plus the interest rate and you get V1, the future value of money a year from now. One specific example, $1,000 put in the bank for one year at 10% interest is worth $1,100 a year from now. You can extend this principal into the future indefinitely by taking account of compounding interest. For instance, for every year you leave the money in the bank, multiply by an additional 1 plus the interest rate. So the value two years from the present will be the value at the end of one year multiplied once again by 1 plus the interest rate. So if we take the relationship from the first line, plug it in here, we get the equation that says the future value of money at some point in years into the future is equal to the present value, multiplied by 1 plus the interest rate raised to the n^th power; 2 for 2 years, 3 for 3 years and so forth.
The present value of money is the same story told in reverse. Let's suppose now that we take this top-line equation and divide both sides by 1 plus the interest rate; then we will get the present value formula. That is, suppose we are not going to receive our $1,000 until a year from now. How much can we borrow today if we are going to repay the loan out of that $1,000 one year in the future? Well, you can't borrow the full $1,000 because you are going to have to pay the money back with interest, so you have to discount the money, leaving room for interest to accumulate. That's what we mean here by dividing the future value by 1 plus the interest rate. As an example, suppose we are going to get $1,000 a year from now. Dividing by 1 plus the interest rate that we have to pay on the loan, 1 plus 10%, gives us a present value of about $909. That means if you borrow $909 today at a 10% interest rate, then you will owe $1000 to the bank a year from now just in time to repay the loan with the $1000 that you are going to receive.
Present value means taking money that you are going to receive in the future and discounting it back to the present, leaving room for interest to accumulate when you want to borrow the money today. And you can project that concept through any number of periods by using the relationship we saw before. For instance, if you are not going to receive the money until two years from now, you got to use one plus i raised to the 2^nd power in order to allow two years worth of compound interest to accumulate.
You can see then there are all kinds of interesting relationships between the present and the future that are mediated through the interest rate. Bond prices and interest rates are inversely related and understanding the present value of money helps make that even clearer. When the interest rate goes up, then the present value is going to fall. That's another way of thinking about how that seesaw tells us about bond prices and interest rates and the connection between them.
Money: Banking, Spending, Saving, and Investing
Financial Markets
The Price of Bonds and the Interest Rate Page [1 of 2]

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