How To Calculate The Yeld To Maturity, Or Yield To Maturity

The yield to maturity of a bond (in English Yield to Maturity) is the total income, made up of principal plus interest, which is obtained by keeping the security until its maturity. It is expressed in the form of a percentage and informs investors about the possible gain that can be obtained by buying and keeping the bond, until it is paid by the company that issued it. . It is difficult to calculate the yield to maturity exactly, but you can approximate a value using the yield table or one or more online calculators.

Calculate an Estimated Return on Maturity

Come Calcolare lo Yeld to Maturity, o Rendimento a Scadenza

Collect all the information. To calculate the approximate yield, you need to know the coupon value, the face value of the bond, the price paid and the number of years to maturity. These factors are entered into the formula

ApproxYTM=(C+((FP)/n))/(F+P)/2{displaystyle ApproxYTM=(C+((F-P)/n))/(F+P)/2}

.

C = coupon value, ie the interest paid each year to the holder of the security;

F = nominal value or total value of the bond;

P = price paid by the investor to purchase the security;

n = number of years to maturity.

Come Calcolare lo Yeld to Maturity, o Rendimento a Scadenza

Calculate an estimate of the yield to maturity. Suppose you bought a bond with a face value of $ 1000 to $ 920. The interest rate is 10% and matures over 10 years. The coupon is $ 100 (

$1000x0,10=$100{displaystyle $1000×0,10=$100}

), the face value is $ 1000 and the price paid is $ 920; the years to maturity are 10.

Use the formula:

($100+(($1000$920)/10))/($1000+$920)/2{ displaystyle ( $ 100 + (( $ 1000 – $ 920) / 10)) / ( $ 1000 + $ 920) / 2}

.

Thanks to these calculations, you can get an approximate yield to maturity of 11.25%.

Come Calcolare lo Yeld to Maturity, o Rendimento a Scadenza

Check the correctness of the calculation. Enter the percentage you found in the equation and solve it by isolating P, the price of the bond. It is likely that you will not get the same value, since the yield to maturity you have calculated is only an estimate; therefore define if you are satisfied with the data you have obtained or if you need more precise ‘information.

Use the formula

P=C((1(1/(1+i)n))/i)+M/((1+i)n){displaystyle P=C*((1-(1/(1+i)^{n}))/i)+M/((1+i)^{n})}

, where P is the security price, C is the coupon value, i is the percentage of yield to maturity, M the face value and n the number of coupons.

If you substitute 11.25% for the return variable and solve the equation for P (the stock price) you get $ 927.15.

A lower percentage of annuity leads to the calculation of a higher price. The price of the bond you get when you put the yield of 11.25% into the formula is too high, which means that the estimate is somehow too low.

Calculate Return to Maturity for Trials and Errors

Come Calcolare lo Yeld to Maturity, o Rendimento a Scadenza

Collect the information and enter it into the formula. You must know the face value of the security and the current one, that is the purchase price; furthermore, you must know the exact amount of coupons you will receive and their number until expiry. Once you have all this data, you can enter it into the formula:

P=C((1(1/(1+i)n))/i)+M/((1+i)n){displaystyle P=C*((1-(1/(1+i)^{n}))/i)+M/((1+i)^{n})}

, where P is the purchase price of the bond, C is the coupon value, i is the yield to maturity, M is the face value and n is the number of the coupons.

For example, suppose you bought a $ 100 stock at a price of $ 95.92 that pays 5% interest every 6 months for 30 months.

Every 6 months you receive a coupon of $ 2.50 (

$1000,050,5=$2,50{ displaystyle $ 100 * 0.05 * 0.5 = $ 2.50}

).

If there are 30 months to maturity and the coupons are paid every six months, that means you get 5.

Enter the data in the formula:

95,92=2,5((1(1/(1+i)5))/i)+100/((1+i)5){displaystyle 95,92=2,5*((1-(1/(1+i)^{5}))/i)+100/((1+i)^{5})}

.

At this point, you need to solve the equation for i by trial and error; enter different values ​​of i until you find the correct price.

Come Calcolare lo Yeld to Maturity, o Rendimento a Scadenza

Estimate the interest rate by considering the relationship between the yield and the price of the security. You don’t have to make random guesses to know the probable value of the interest rate; Since the bond is issued at a discounted price, you know that the yield to maturity is greater than the coupon rate. In this case, the coupon interest rate is 5%, you can then start using a larger value to solve the equation for P.

Remember, though, that you are using an estimate of i for half-yearly payments; this means you have to divide the interest rate by 2.

In the previous example, start by considering the annual interest rate and increase it by one percentage point up to 6%; divide it by two (3%, as the payments are semiannual) and enter it into the formula to get a figure of P of $ 95.

This is too high, as the purchase price is $ 95.92.

Take the annual interest rate and add another percentage point, up to 7%. Divide it by 2 (3.5%, as payments are semiannual) and enter the value in the formula to get P = $ 95.

The result is too low, but at this point you know that the yield to maturity is a value between 6% and 7% or between 3% and 3.5%, if you consider a semiannual basis.

Come Calcolare lo Yeld to Maturity, o Rendimento a Scadenza

Reduce the interval to determine the precise interest rate. Enter values ​​between 6% and 7% in the formula. Start with 6.9% and gradually reduce the figure by a tenth percent at a time; in this way, you get an accurate calculation of the yield to maturity.

For example, when you use the value 6.9% (3.45% on a semiannual scale), you get P = $ 95.70. You are getting close to real value, but not close enough.

Reduce the percentage by one-tenth and use 6.8% (3.4% on a semiannual scale) and you get P = $ 95.92.

The result is exactly the purchase price of the stock, so you know with certainty that its yield at maturity is 6.8%.

Understanding the Meaning of Yield to Maturity

Come Calcolare lo Yeld to Maturity, o Rendimento a Scadenza

Use this information to determine if a bond is a good investment or not. People who buy securities often want to determine the yield, that is, a minimum income, before concluding the deal. By calculating the yield to maturity, you can understand if a specific security meets investors’ expectations, which vary from person to person; however, these calculations provide hard data to compare the value of different bonds.

Come Calcolare lo Yeld to Maturity, o Rendimento a Scadenza

Learn about changes in yield to maturity. Companies that issue bonds may choose to let them grow to maturity. This causes the yield to decrease; they can also “recall ” the security, ie refund it before the natural expiration date or, alternatively, they can buy it back before the expiration date.

Yield to call (YTC) – literally “return on call ” – indicates the rate of return between the current one and that of the moment in which the is paid in advance ‘obligation.

Yield to put (YTP) calculates the rate of return until the issuer repurchases the security.

Come Calcolare lo Yeld to Maturity, o Rendimento a Scadenza

Understand the limits of the data. The yield to maturity does not take into account the taxes or costs of buying and selling the security; these charges actually lower the yield of a ‘bond. Furthermore, investors should remember that these calculations are only an estimate, as market fluctuations also have a significant impact on the value of the security.

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