# How to Calculate Yield to Maturity, or Expiry Return

How to Calculate Yield to Maturity. The yield on the maturity of a bond (in English Yield to Maturity ) is the total income, composed of capital plus interest, which is obtained by keeping the security until its expiry. It is expressed as a percentage and informs investors about the possible gain that is obtained by buying and retaining the obligation 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 Expiry Estimate

1) Collect all information.
To calculate the approximate yield, you have to know the value of the coupon, the bond’s face value, the price paid and the number of years to maturity. These factors are included in the formula{\ Displaystyle ApproxYTM = (C + ((FP) / n)) / (F + P) / 2}.
C = the value of the coupon, ie the interest paid each year to the defending champion;
F = nominal value or total value of the obligation;
P = price paid by the investor to purchase the security;
n = number of years at expiry.

2) Calculate an estimate of yield to maturity.
Suppose you bought a bond with a face value of \$ 1000 to \$ 920. The interest rate is 10% and matures in 10 years. The coupon is \$ 100 ({\ display style \ \$ 1000×0.10 = \ \$ 100}), the face value is \$ 1000 and the price paid is \$ 920; the years to maturity are 10.
Take advantage of the formula: {\ displaystyle (\ \$ 100 + ((\ \$ 1000 – \ \$ 920) / 10)) / (\ \$ 1000 + \ \$ 920) / 2}.
Thanks to these calculations, you can get an approximate value of the yield at maturity of 11.25%.

3) 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 do 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) </ math>, where P is the price of the stock , C is the value of the coupon, i is the percentage of the yield to maturity, M the nominal value and the number of coupons.
.) If you replace 11.25% of the yield variable and resolve the equation for P (the price of the stock) you get \$ 927.15.
.) A lower percentage of rent leads to the calculation of a higher price. The price of the bond you get when you insert 11.25% in the formula is too high, which means that the estimate is somewhat too low.

## Calculate the Expiration Return for Attempts and Errors

4) Collect the information and enter it into the formula.

You must know the nominal value of the title and the current one, that is the purchase price; in addition, you must know the exact amount of the coupons you will receive and their number until expiry. Once you have all these data, you can enter them in the formula:{\ display style P = C * ((1- (1 / (1 + i) ^ {n})) / i) + M / ((1 + i) ^ {n})}, where P is the purchase price of the bond, C is the value of the coupons, i is the yield at maturity, M is the nominal value en is the number of coupons. For example, suppose you have purchased a \$ 100 bond at the price of \$ 95.92 which pays 5% interest every 6 months for 30 months.
Every 6 months, you receive a coupon of \$ 2.50 ({\ displaystyle \ \$ 100 * 0.05 * 0.5 = \ \$ 2.50}).
If there are 30 months until expiration and the coupons are paid every six months, it means you receive 5.
Enter the data in the formula: {\ displaystyle 95.92 = 2.5 * ((1- (1 / (1 + i) ^ {5})) / i) +100 / ((1 + i) ^ {5})}.
At this point, you must solve the equation for proceeding by trial and error; enter different values of I until you find the correct price.

5) Estimate the interest rate by considering the relationship between the yield and the price of the security.

You do not have to make random assumptions to know the probable value of the interest rate; since the bond is issued at a discounted price, you know that the yield at maturity is greater than the coupon rate. In this case, the coupon interest rate is 5%, so you can start using a larger value to solve the equation for P.
Remember, however, that you are using an estimate of I for half-yearly payments; this means that 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%, since the payments, are half-yearly) and enter it into the formula to obtain a P figure of \$ 95.
This is too high a result since the purchase price is \$ 95.92.
Take the annual interest rate and add another percentage point, up to 7%. Divide by 2 (3.5%, since the payments, are half-yearly) 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 semi-annual basis.

6) 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 one-tenth percentage at a time; in this way, you get a precise calculation of the yield at maturity.
For example, when you use 6.9% (3.45% six-monthly), you get P = \$ 95.70. You are approaching real value, but not enough.
Reduce the percentage by one-tenth and use 6.8% (3.4% on a six-monthly scale) and 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 equal to 6.8%.

Understanding the meaning of the Expiration Return

7) Use this information to determine if an obligation is a good investment or not.

People who buy securities often want to determine the yield, ie a minimum income, before concluding the deal. By calculating the yield at maturity, you can understand if a specific security meets the expectations of investors, which vary from person to person; however, these calculations provide concrete data to compare the value of different bonds.

8) Learn changes in yield to maturity.
Companies that issue bonds may choose to let them grow until maturity. This causes the yield to decrease; they can also “recall” the title, that is, repay it before the natural expiry date or, alternatively, they can buy it back before the date of extinction.
Yield to call (YTC) – literally “call return” – indicates the yield rate between the current rate and the rate at which the bond is paid in advance.
Yield to put (YTP) calculates the rate of return until the issuing company recovers the security.

9) Understand the data limits.
The yield to maturity does not take into account taxes or costs of buying and selling the security; these expenses actually lower the yield of an obligation. In addition, investors should remember that these calculations are only an estimate, given that even market fluctuations have a significant impact on the value of the stock.