# Yield to Maturity

## What is “Yield to Maturity”?

The Yield-to-Maturity (YTM) is the total rate of return on a bond if it is held until maturity. It assumes all coupon and principal amounts are paid as scheduled and the investor is able to reinvest the coupon payments at the same yield. In other words, YTM is the internal rate of return (IRR) of an investment in a bond based on the aforesaid assumptions. The YTM is also referred to as “yield-to-redemption” or “book yield”.

The YTM helps investors compare different bonds and their expected returns and enables them to determine which bonds they should add to their portfolios i.e. which bonds are good investments. Further, the YTM can be used to compare various bonds with different maturities and coupons, as it is expressed as an annual rate regardless of the bond’s term to maturity.

## Key Learning Points

- The “Yield-to-Maturity” is the internal rate of return of an investment or bond
- The formula used to approximate the YTM of a bond includes the face value and the current market price of a bond, coupon payments on the same, and years to maturity
- The YTM takes into account the capital gain or loss that occurs when the investor receives the par or face value of the bond upon maturity
- The YTM of a bond with a face value of US$1,000, maturity of 10 years, and a coupon rate of 8% has been calculated using the “yield” function in Excel

## YTM – Formula, Capital Gain, and Loss

Typically, the formula used to approximate the YTM of a bond is given below:

YTM (%) = __C + (FV – PV/T)__

FV + PV/2

C = Coupon or interest payment on the bond

FV = Face value of the bond

PV = Current price or value of the bond

T = Years to maturity

This formula is used to determine a bond’s YTM according to its most recent market price.

The YTM is different from the current yield of a bond, which is the bond’s annual coupon payment divided by the current or present price at which the bond is selling (i.e. current yield = annual interest payment/current market price of the bond).

For bonds that sell above par or face value (i.e., bonds that sell at a premium), the YTM is less than the coupon rate and current yield. On the other hand, for bonds that sell at a discount (i.e., a bond selling below its par or face value), its YTM is greater than the coupon rate and current yield.

Next, an investor who has purchased a bond at a premium (discount) will lose (gain) money as the bond will eventually fall (rise) in value to its par or face value at maturity. The YTM of a bond held until maturity takes into account the aforesaid built-in capital gain or loss that occurs when the investor receives the par or face value of the bond upon maturity. This is why the YTM is a better measure of the investment return on a bond.

With reference to YTM, it is important to know that there is an inverse relationship between a bond’s price and interest rates. If interest rates rise (fall) then bond prices fall (rise), all else staying equal. Therefore, when bond prices fall or go lower, it means a higher YTM and if bond prices rise, it means a lower YTM.

## YTM – An Example

Given below is the calculation of the yield to maturity (YTM) of a bond with a par value of US$1,000, coupon rate of 8%, and maturity of 10 years. The market price of the bond is US$1,050 and the frequency of coupon payments is paid annually.

From the aforesaid information, the YTM (7.3%) has been calculated by using the “Yield” function of Microsoft Excel. Its constituents are:

YTM (0.0727892) = Yield (settlement, maturity, rate, price, redemption, frequency, basis)

Or, 0.0727892 * 100 =7.3%.

The settlement date is the date at which the investor purchases the bond and the maturity date is the date at which the bond matures. Further, the rate is the coupon rate and the price is the Actual Price/Par Value *100. Moreover, the redemption value is the value received by an investor at maturity as a percentage of the par value of the bond (which is assumed here as 100% of par value).

Frequency refers to the number of times an investor receives the coupon payment in a year and the basis controls how days are counted and defaults to zero.