Yield to maturity sounds pretty scary, right? I've seen students cringe when they hear the term. However, once you realize that calculating the yield to maturity on a bond is just a simple time value of money problem, it will become your new best friend. Naturally, a good grasp of annuities will be necessary for this tutorial.
So what in the world is yield to maturity? Simply put, it is the rate of return that you would earn if you bought a bond today and held it until the bond matured. If you dig a little deeper, you'll find out that it is also the internal rate of return of the bond. So now that we know what the term means, let's take a look at how we calculate it with our financial calculator.
Whenever you see a question that asks you to find the yield to maturity of a bond, you need to think of the letter I. Since we can think of a bond as just a time value of money problem in disguise, we solve for I to get the yield to maturity. Let's take a look at a problem to illustrate this point.
Sample Problem
Family Moving Company has recently issued 10 year bonds with a 5% coupon rate. The bonds make annual coupon payments and are currently selling for $950 in the market. What is the yield to maturity of these bonds?
Solution
We can draw a timeline to see what's going on with this bond. Your timeline should look like this:
In year 0, or today, we pay $950 for this bond. The bond has a 5% coupon rate, so every year we receive a $50 coupon payment. Finally, in 10 years when the bond matures, we will receive par value of $1,000. To find the yield to maturity, we just need to solve for I/YR in our financial calculator.
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Nice work! You just found that the yield to maturity is 5.67% for this bond! There are a few points to clear up here. At time 0, we pay $950 for the bond. Since this is a cash outflow, it must go into the calculator as a negative number. We will receive the payments and the par value at the end as cash inflows, so both of these values are positive. Calculating yield to maturity really is that easy! Try some of these practice problems on your own to make sure you've got it.
Practice Problem 1
CardCounter Casino has bonds on the market with 15 years left to maturity. The bonds make semiannual coupon payments and have a coupon rate of 16%. If the current market price of these bonds is $1,085, what is the yield to maturity?
Solution
If you got a yield to maturity of 14.59%, you're doing a great job! If not, there were a few tricks in this one that might have got you. Since the bonds make semiannual coupon payments, you'll need to set P/Y=2 and N=30. Also, you'll find out that the bonds make $160 in coupon payments annually, so they will make $80 payments semiannually.
Practice Problem 2
Taco Town issued 30 year bonds 22 years ago. The bonds now sell in the market for $915, make semiannual coupon payments, and have a coupon rate of 11.5%. What is the yield to maturity?
Solution
Tough question, eh? 13.26% is the correct answer. The bonds have 8 years left until maturity but with semiannual coupon payments, N=16. Whenever we deal with bonds, we're only going to worry about the time that is left. Also, the bonds pay $115 per year in coupon payments, but since the bonds are semiannual, divide by 2 to get PMT=57.50.
That's all for this one, folks. If you have any questions, get a good discussion going on our forum.