Yield to maturity is the total return expected to be earned on a bond if it is held until it matures. The yield to maturity is expressed as an annual percentage rate. The yield to maturity formula is used to calculate the return on a bond based on its current market price. The yield of maturity calculation is based on the assumption that the investors buys the bond at the current market price and hold it until maturity.
Yield to maturity = (C+ ((FV-PV) / t) /((FV+PV) / 2 ))
Where C is the coupon payment, FV is the face value, PV is the Present value and t is the number of years until maturity.
To get a better understanding of the Yield to maturity formula and how it works, let’s look at an example. Let’s take an example where we buy 5% coupon bond with $100000 that matures in 5 years and will pay interest twice a year, e.g. it will pay $2500 every 6 months until the maturity. Now if the market price of the bond drops to $95,753 the actual yield to maturity will increase to roughly 6% . This is taking into account the $5,000 additional profit that the investor will make because he is going to receive $10,000 at the end of the maturity and he has paid only the $95,000 market price.
If we take the above example and make the Yield to maturity calculation exact , we’ll get:
Yield to maturity = (5,000+((100,000 - 95,000))/5) /((100,000 + 95,000) / 2) = (5,000+1,000) / 97,500 = 6.15%
This will we our actual yield to maturity if we buy the bond at price of $95,000 and hold it until maturity.
The main reason why we need to calculate the actual yield to maturity is the fact that it is a lot more real representative of the return expected to get we we decide to hold the bond until its maturity data. The other obvious reason is that because the yield to maturity is more absolute measure it allows us to compare different bonds with different coupon prices and different market prices in a more meaningful way. It also useful for it allows the investor to get more understanding of how changes in make prices changes the portfolio return because when bond prices drop the yield of the bonds rise and vice versa.