Here we are going to take a look at two different ways to calculate bond yield: current yield and yield to maturity (YTM). Let’s take a look at calculating current yield first.
How to Calculate Current Yield
We can calculate the yield on a bond investment using the current yield as long as we know the annual cash inflows of the investment and the market price of the security. Current yield is simply the current return an investor would expect if he/she held that investment for one year, and this yield is calculated by dividing the annual income of the investment by the investment’s current market price. The formula is shown below:
Where:
- Annual Income = amount the investment returns in a year
- Current Market Price = amount the asset is worth at present day
Current yield is usually calculated for bonds, where the annual income is the coupon paid out, but the yield could also be calculated for stocks, where the annual income is the dividend paid out, or really for any asset that pays out annually. In any case, the current market price is the price someone would be willing to pay for the asset whether that price is at a premium or a discount.
How to Calculate Yield to Maturity
Yield to maturity (YTM) is similar to current yield, but YTM accounts for the present value of a bond’s future coupon payments. In order to calculate YTM, we need the bond’s current price, the face or par value of the bond, the coupon value, and the number of years to maturity. The formula for calculating YTM is shown below:
Where:
- Bond Price = current price of the bond
- Face Value = amount paid to the bondholder at maturity
- Coupon = periodic coupon payment
- n = number of time periods until maturity
The yield to maturity is the discount rate that equates the present value of all future cashflows of the bond (coupon payments and payment of face value) and the current price of the bond. We must assume that all payments are made on time, and we must assume that the bond is held to maturity. We can recognize that, because all of the coupon payments are the same, we can rewrite the formula by breaking it down into the present value of an annuity and the present value of the face value of the bond. The rewritten formula is shown below:
The left half of the right side of the equation is the present value of all the coupon payments, i.e. the present value of an annuity where the payment is the coupon and the rate is the YTM, and the right half of the right side of the equation is the present value of the face value of the bond.
In either situation, there is not an easy way to calculate YTM. You can either take a “plug and chug” approach, or you may use a calculator. It may seem an obvious choice to most, but for those looking for more of a challenge, the “plug and chug” approach is an interesting exercise. There are also a few clues that can point us to good starting values so that we aren’t simply guessing, although that works as well. If we want to be smart about our first guess, we can take a look at the current bond price compared to the face value of the bond. If the current market price is less than the face value, then the bond is said to be selling at a discount. Contrarily, if the current market price is greater than the face value of the bond, then the bond is said to be selling at a premium. Intuitively, if the bond is selling at a discount, then we know that the YTM is going to be greater than the coupon rate, and if the bond is selling at a premium, then the YTM is going to be less than the coupon rate. A third situation is that when the current market price is equal to the face value. This would imply that the YTM is equal to the coupon rate. To understand these concepts, think about plugging different rates into the first form of the YTM equation. If the YTM is greater than the coupon rate, then the denominator of each cash flow will increase, so the sum of those cash flows will be less than the face value of the bond (and hence will sell at a discount). If the YTM is less than the coupon rate, then the denominator of each cash flow will decrease, so the sum of those cash flows will be greater than the face value of the bond (and hence will sell at a premium).
Let’s take a look at an example below to understand how to calculate current yield as well as YTM.
Example
Suppose you just bought a bond for $965 that matures in three years, pays semiannual coupon payments at 4.2%, and has a face value of $1,000. This means that twice per year, your bond will pay out 4.2%/2 of $1,000, which is $21 every six months. What is your bond’s current yield and YTM?
We can start with the current yield calculation, as that will be a much easier task. To calculate current yield, we must know the annual cash inflow of the bond as well as the current market price. The bond pays out $21 every six months, so this means that the bond pays out $42 every year. The current market price of the bond is how much the bond is worth in the current market place. You just bought the bond, so we can assume that its current market value is $965. Now that we have our two inputs to the equation, we just need to plug the inputs in and solve. The work is shown below:
This means that if you bought the bond at its current market price and held it for one year, your current return you would expect is 4.35%.
Now let’s take a look at how to calculate the bond’s yield to maturity. Remember, this yield assumes that all payments are paid on time and the bond is held to maturity. We must first determine the cash flows. Every six months, the bond pays out coupons of $21, and the bondholder receives these payments for three years, which means there is a total of six coupon payments, i.e. the number of periods is six. Also, at the end of three years, the bondholder receives the face value of $1,000. So, we have all of our parts for the equation, which are the bond price of $965, the coupon of $21, the number of periods of six, and the face value of $1,000. Now, we must take a shot at a guess for YTM. Let’s take a look at our equation first, however.
Remember that, because our coupon payments are paid out semiannually, we must halve the YTM in our equation. We know that the price of the bond is below the face value of the bond. This means that our first guess should be above our coupon rate because the cash inflows need to be discounted more than they would at the rate required to reach the face value. Since the coupon rate is 4.2%, let’s try 5%. When you plug in 5% to YTM in the equation, the right side of the equation is $977.97. Because this is greater than the price of the bond, we need to guess something higher than 5%. Let’s try 5.5%. When you plug in 5.5% to YTM in the equation, the right side of the equation is $964.49. This is close, but it is below $965, so we need to guess a value lower than 5.5%. After a few iterations, you will see that 5.481% gives you a value very close to $965. This means that our yield to maturity is 5.481%.
While both current yield and yield to maturity are useful metrics to look at when valuing bonds. The current yield helps investors calculate the profitability of the investment, so an investor would be able to narrow down a list of bonds based on those that generate good returns each year. Yield to maturity helps investors maximize profits, since the YTM formula assumes that investors are reinvesting the coupons earned each period.