# Yield to Maturity

Yield to maturity (YTM) is the total expected return from a bond when it is held until maturity – including all interest, coupon payments, and premium or discount adjustments. The YTM formula is used to calculate the bond’s yield in terms of its current market price and looks at the effective yield of a bond based on compounding. This differs from the simple yield using a dividend yield formula.

Put simply, yield to maturity is the internal rate of return (IRR) of a bond investment if you hold the bond until maturity and all payments made as scheduled and reinvested at the same rate.

YTM is also known as the redemption yield or the book yield and is expressed as a percentage which tells investors what their return on investment would be if they purchase the bond and hold it until maturity.

It’s difficult to calculate the exact YTM, but in the formulas below we’ll look at how you can calculate the approximate yield to maturity of a bond.

## Yield to Maturity Formula

$YTM = \dfrac{ C + \dfrac{F-P}{n} }{ \dfrac{F+P}{2}}$
• C = Coupon/interest payment
• F = Face value
• P = Price
• n = Years to maturity

This is the most accurate formula because yield to maturity is the interest rate an investor would earn by reinvesting every coupon payment from the bond at a constant rate until the bond reaches maturity.

If you had a discount bond which does not pay a coupon, you could use the following formula instead:

$YTM = \sqrt[n]{ \dfrac{Face\: Value}{Current\: Value} } - 1$

## Yield to Maturity Examples

The bond has a price of $920 and the face value is$1000. The annual coupons are at a 10% coupon rate ($100) and there are 10 years left until the bond matures. What is the yield to maturity rate? $YTM = \dfrac{ \100 + \dfrac{\1{,}000-\920}{10} }{ \dfrac{\1{,}000+\920}{2}} = 11.25\%$ The approximate yield to maturity of this bond is 11.25%, which is above the annual coupon rate of 10% by 1.25%. You can then use this value as the rate (r) in the following formula: $Bond\: Value = C \bigg( \dfrac{1 - (1 + r)^{-n} }{r} \bigg) + \dfrac{F}{(1+r)^{n}}$ • C = future cash flows/coupon payments • r = discount rate (the yield to maturity) • F = Face value of the bond • n = number of coupon payments Let’s use the figures from above to work out the value of the bond, assuming the coupon payments are made once per year: $Bond\: Value = \1{,}000 \bigg( \dfrac{ 1 - (1 + 11.25\%)^{10} }{11.25\%} \bigg) + \dfrac{ \1{,}000 }{ (1+11.25\%)^{10} } = \927.15$ Here we can see that the current fair valuation of the bond is$7.15 more than the purchase price, and this current value will increase over time as the length to maturity reduces.

## Yield to Maturity Conclusion

When calculating inflation, the below points are worth bearing in mind as a quick recap of what it is, why it’s used, and how to use it:

• Yield to maturity formula is for calculating the bond based yield on its current market price rather than the straightforward yield which is discovered utilizing the profit yield equation.
• To calculate yield to maturity, the bond price or bond’s current value must already be known.
• A better return to maturity will have a lower present worth or price tag of a bond.
• Investors like to utilize unique projects to limit the conceivable YTMs as opposed to computing through experimentation, as the counts required to decide YTM can be very protracted and tedious.
• When the bond is assumed to be called, yield to call (TYC) is being used.
• YTC and yield to put (YTP) are similar to each other. The only difference is that the hold of a put bond can choose to sell the bond back to the issuer with a fixed priced depending on the terms of the bond.
• When a bond has multiple options, yield to worst (YTW) calculation can be used.
• YTM estimations, as a rule, don’t represent charges that an investor pays on the bond.

## Yield to Maturity Calculator

You can use the yield to maturity calculator below to work out both the YTM and the current value of a bond investment.