What is Yield to Maturity?

Yield to Maturity Formula

YTM considers the effective yieldEffective YieldEffective yield is a yearly rate of return at a periodic interest rate proclaimed to be one of the effective measures of an equity holder’s return as it takes compounding into its due consideration, unlike the nominal yield method.read more of the bond, which is based on compoundingCompoundingCompounding is a method of investing in which the income generated by an investment is reinvested, and the new principal amount is increased by the amount of income reinvested. Depending on the time period of deposit, interest is added to the principal amount.read more. 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 the price matches the actual market price of the bond. Nowadays, computer applications facilitate the easy calculation YTM of the bond.

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

Where,

  • C is the Coupon.F is the Face Value of the bond.P is the current market price.n will be the years to maturity.

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The formula below calculates the bond’s present value. If you have the bond’s present value, you can calculate the yield to maturity (r) in reverse using iterations.

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

Step by Step Calculation of Yield to Maturity (YTM)

Examples

Example #1

Assume that the bond’s price is $940, with the face value of the bond at $1000. The annual coupon rate is 8%, with a maturity of 12 years. Based on this information, you must calculate the approximate yield to maturity.

  • Gather information on the bond-like its face value, months remaining to mature, the bond’s current market price, and the bond’s coupon rate. Now calculate the annual income available on the bond, which is mostly the coupon, and it could be paid annually, semi-annually, quarterly, monthly, etc. Accordingly, the calculation should be made. Also, one needs to amortize the discount or premium, which is a difference between the face value of the bond and the current market price over the bond’s life. The numerator of the YTM formula will be the sum of the amount calculated in steps two and step 3. The denominator of the YTM formula will be the average price and face value. When one divides step 4 by step 5 value, it shall be the approximate yield on maturity.

Solution:

Use the below-given data for the calculation of YTM.

We can use the above formula to calculate approximate yield to maturity.

Coupons on the bondCoupons On The BondCoupon bonds pay fixed interest at a predetermined frequency from the bond’s issue date to the bond’s maturity or transfer date. The holder of a coupon bond receives a periodic payment of the stipulated fixed interest rate.read more will be $1,000 * 8%, which is $80.

Yield to Maturity (Approx) = (80 + (1000 – 94) / 12 ) / ((1000 + 940) / 2)

YTM will be –

Example #2

FANNIE MAEFANNIE MAEFannie Mae, i.e., Federal National Mortgage Association is a United States government-sponsored enterprise (GSE) which was founded in the year 1938 by congress to boost the secondary mortgage market during the great depression which involves financing for the mortgage lenders thereby providing access to affordable mortgage financing in all the markets at all times.read more is one of the famous brands trading in the US market. The government of the US now wants to issue a 20 year fixed semi-annually paying bond for their project. The price of the bond is $1,101.79, and the face value of the bond is $1,000. The coupon rate is 7.5% on the bond. Based on this information, you are required to calculate the approximate yield to maturity on the bond.

Use the below-given data for the calculation of yield to maturity.

Coupon on the bond will be $1,000 * 7.5% / 2 which is $37.50, since this pays semi-annually.

Yield to Maturity (Approx) = ( 37.50 + (1000 – 1101.79) / (20 * 2) )/ ((1000 + 1101.79) / 2)

This is an approximate yield on maturity, which shall be 3.33%, which is semiannual.

Annual YTM will be –

Example #3

Mr. Rollins has received the lump sum amount from the lottery. He is a risk-averse person and believes in low risk and high return. He approaches a financial advisor, and the advisor tells him he is the wrong myth of low risk and high returns. Then Mr. Rollins accepts that he doesn’t like risk, and a low-risk investmentLow-risk InvestmentLow-risk investments are the financial instruments with minimal uncertainties or chances of loss to the investors. Although such investments are safe, they fail to offer high returns to the investors. read more with a low return will do. The advisor gives him two investment options, and the details of them are below:

Option 1

Coupon on the bond will be $1,000 * 9% / 2 which is $45, since this pays semi-annually.

Yield to Maturity (Approx) = (45 + (1000 – 1010) / (10 * 2)) / (( 1000 +1010 )/2)

This is an approximate yield on maturity, which shall be 4.43%, which is semiannual.

Therefore, the annual Yield on maturity shall be 4.43% * 2, which shall be 8.86%.

Option 2

Coupon on the bond will be $1,000 * 8.50% / 2 which is $42.5, since this pays semi-annually.

Yield to Maturity (Approx) = (42.50 + (1000 – 988) /(10 * 2))/ (( 1000 +988 )/2)

This is an approximate yield on maturity, which shall be 4.34%, which is semiannual.

Annual Yield to Maturity will be –

Therefore, the annual Yield on maturity shall be 4.34% * 2, which shall be 8.67%.

Since the YTM is higher in option 2; hence the advisor is correct in recommending investing in option 2 for Mr. Rollins.

Relevance and Uses

  • Yield to maturity allows an investor to compare the bond’s present value with other investment options in the market.TVMTVMThe Time Value of Money (TVM) principle states that money received in the present is of higher worth than money received in the future because money received now can be invested and used to generate cash flows to the enterprise in the future in the form of interest or from future investment appreciation and reinvestment.read more (Time value of money) is taken into consideration while calculating YTM, which helps in better analysis of the investment about a future return.It promotes making credible decisions as to whether investing in the bond will fetch good returns compared to the value of the investment at the current state.

This has been a guide to Yield to Maturity (YTM). Here we discuss how to calculate the bond yield to maturity using its formula along with practical examples and a downloadable excel template. You can learn more about economics from the following articles –

  • Yield to Call CalculationYield To Call CalculationYield to call is the return on investment for a fixed income holder if the underlying security, such as a callable bond is held until the pre-determined call date rather than the maturity date.read moreCurrent Yield of a Bond CalculationCurrent Yield Of A Bond CalculationThe current yield formula essentially calculates the yield on a bond based on the market price instead of face value. The current yield of bond= Annual coupon payment/current market priceread moreYield to WorstYield To WorstThe yield to worst (YTW) is the minimum yield that can be received on a bond, assuming the issuer doesn’t default on any of its payments. YTW makes sense for bonds where the issuer exercises its options like calls or prepayments. YTW = risk free rate + credit risk premium
  • read moreCalculate Yield in ExcelCalculate Yield In ExcelThe Yield Function in Excel is an in-built financial function to determine the yield on security or bond that pays interest periodically. It calculates bond yield by using the bond’s settlement value, maturity, rate, price, and bond redemption.read more