![]() Remember, this yield assumes that all payments are paid on time and the bond is held to maturity. Now let’s take a look at how to calculate the bond’s yield to maturity. 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 that we have our two inputs to the equation, we just need to plug the inputs in and solve. You just bought the bond, so we can assume that its current market value is $965. The current market price of the bond is how much the bond is worth in the current market place. The bond pays out $21 every six months, so this means that the bond pays out $42 every year. To calculate current yield, we must know the annual cash inflow of the bond as well as the current market price. We can start with the current yield calculation, as that will be a much easier task. What is your bond’s current yield and YTM? This means that twice per year, your bond will pay out 4.2%/2 of $1,000, which is $21 every six months. 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. Let’s take a look at an example below to understand how to calculate current yield as well as YTM. 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). 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). To understand these concepts, think about plugging different rates into the first form of the YTM equation. This would imply that the YTM is equal to the coupon rate. A third situation is that when the current market price is equal to the face value. 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. 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. If the current market price is less than the face value, then the bond is said to be selling at a discount. 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. 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. 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. You can either take a “plug and chug” approach, or you may use a calculator. In either situation, there is not an easy way to calculate YTM. ![]() 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. The left half of the right side of the equation is the present value of all the coupon payments, i.e. ![]() 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. We must assume that all payments are made on time, and we must assume that the bond is held to 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. n = number of time periods until maturity. ![]()
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