# Yield to Maturity Concept

The yield to maturity (YTM) of a bond represents the annual rate of return for the full life of the bond. The YTM assumes the investor will hold the bond to maturity, and that all interest payments will (hypothetically) be reinvested at the YTM rate.

For example, a bond with a maturity of 10 years and a YTM of 5% implies that buying this bond and holding it for the full ten years would give the investor an annual return of 5% on the invested capital.

Given the bond’s price, par value, maturity date, coupon rate and coupon payment schedule, the YTM represents the time value of money – incorporating the aforementioned variables – that sets the bond price equal to the present value of the future payments of the bond, including coupon payments and principal redemption. The YTM is equal to the bond’s discount rate and internal rate of return.

## Define Yield to Maturity

Yield to maturity is the implied annual rate of return on a long-term interest-bearing investment, such as a bond, if the investment is held to maturity and all interest payments are reinvested at the YTM rate.

### Current Yield Calculation

The current yield of a bond differs from the yield to maturity. The current yield of a bond represents the implied return on the bond for one year, given the coupon payments and the current market price. For example, if an investor buys a bond for \$95 with an annual coupon payment of \$5, the current yield for that bond would be 5.26% (.0526 = 5/95). The current yield formula is:

Current Yield = Annual Payment/Current Market Price

### Yield to Maturity – Bond Price

If a bond’s yield to maturity is greater than its current yield, the bond is selling at a discount, or a price less than par value. If YTM is less than current yield, the bond is selling at a premium, or a price above the par value. If YTM equals current yield, the bond is selling at par value.

Discount Price – Yield to Maturity > Current Yield

Premium Price – Yield to Maturity < Current Yield

Par Value Price – Yield to Maturity = Current Yield

### Bond Yield To Maturity Formula

The formula for a bond’s yield to maturity is complicated and solving it mathematically often requires a process of trial and error. It is possible to get an approximate YTM for a bond using a bond yield table. The best way to compute the YTM for a bond is to use a financial calculator. Using a financial calculator, punching in four out of five of the relevant variables (price, par value, maturity, coupon payment, YTM) will give you the fifth variable.

To calculate the bond’s YTM, solve this formula for YTM:

Price = Coupon Payment x 1/YTM (1 – (1/((1+YTM)^Time Periods)) + Future Value/((1 + YTM)^Time Periods) See Dates