Yield to Maturity (Definition) | How to Calculate YTM?

Yield to Maturity Definition

Yield to maturity (YTM) is the expected return on a bond that an investor will receive if it is held until the maturity date of the bond. In other words, it refers to the returns that a bond will fetch considering all payments made on time throughout the life of the bond. Redemption Yield or Book Yield are other terms which are used to mention yield to maturity. It equates the bond’s present value of future cash flows (periodic coupon payments and principal amount at maturity) to the market value of the bond. It is expressed as an annual rate even though it is a long term bond yield.

It can be calculated for bonds as wells as other long term fixed interest-paying securities like gilts. Unlike current yield which measures the present value of the bond whereas the yield to maturity measures the value of the bond at the end of the term of a bond.

Yield to Maturity Formula

YTM considers the effective yield of the bond which is based on compounding. The below formula focuses on calculating the approximate yield to maturity whereas calculating the actual YTM will require trial and error by considering different rates in the current value of the bond until price matches the actual market price of the bond. Nowadays, there are computer applications that facilitate easy calculation of the yield to maturity of the bond.

Approx Yield to Maturity = [C+ (F-P) / n] / [(F+P) / 2]

Where,

C = Coupon Payment
F = Face Value
P = Price
n = Years to maturity

In the below formula of the present value of the bond, yield to maturity (r) can be calculated.

Present Value of Bond = [C / ( 1+r )] + [C / ( 1+r )^2] . . . . . . [C / ( 1+r )^ t ] + [F / ( 1+r )^ t ]

To calculate yield to maturity of a bond, the present value of the bond needs to be known. In this way, yield to maturity (r) can be calculated in reverse with the help of the present value of the bond formula.

Example of Yield to Maturity

ABC Inc issues a bond with face value $1500 and the discounted price is $1200. The annual coupon for the bond is 10% which is $150 per annum. The bond will mature after 10 years.

Approx Yield to Maturity = [C+ (F-P) / n] / (F+P) / 2
= [150 + ($1500 – $1200) / 10] / ($1500 + $1200) / 2
= 13.33%

The approximate yield to maturity for the bond is 13.33% which is above the annual coupon rate by 3%.

Using this value as yield to maturity (r), in the present value of the bond formula would result in the present value to be $1239.67; this price is somewhat close to the current price of the bond which is $1200.

When a bond is purchased at a discounted rate the present value of the yield to maturity is high. In this example, the present value of the bond is lower than the value calculated by the present value formula which is $1239.67. By this, we can confirm that the YTM is above 13.33%

By means of trial and error, the actual YTM, in this case, is 13.81% which is calculated by adjusting the estimated rate to match the present value of the bond with the price of the bond.

With technological advancement, YTM can be calculated using various computer applications and websites.

Advantages

Yield to maturity allows an investor to compare the present value of the bond with other investment options in the market.
Time value of money is taken into consideration while calculating YTM which helps in better analysis of the investment with regards to a future return.
It promotes making credible decisions as to whether investing in the bond will fetch good returns as compared to the value of the investment at the current state.

Disadvantages

Yield to maturity (YTM) considers coupon payments will be reinvested whereas, in reality, the reinvestment rate tends to vary.
The impact of factors like sinking funds, call options or put options within a bond structure are ignored in the YTM.
Taxes paid are not accounted in the yield to maturity (YTM) calculations and hence can depict an incorrect image of the reality.
It does not consider the costs involved in purchasing or selling the bonds.
The calculation requires a lot of trial and error which is time-consuming and requires a lot of guesswork with regards to what value can be used to bring the price of the bond and the current value to be in line.

Important Points

A bond that is bought at discount has a higher yield to maturity (YTM) than its current yield since the present value of the bond is lower.
A premium bond has a lower YTM than its current yield since the present value of the bond is higher.
It is more reliable than current yield since it considers the time value of money.
Yield to call and yield to put are variations to YTM depending on whether the bond is callable or puttable respectively.

Conclusion

Yield to maturity is the rate of return that a bond will fetch the investor if the bond is held until its maturity.
An investor can estimate whether buying a bond is worth the investment by looking at the yield to maturity for the bond.
Various factors including time value of money are considered while calculating YTM.
Yield to maturity (YTM) can be calculated for bonds as well as other long term fixed interest-paying securities. Bond investments can be corporate bonds, municipal bonds, treasury bonds to name a few.