Yield to Maturity

What is Yield to maturity?

Yield to Maturity refers to the expected returns an investor anticipates after keeping the bond intact till the maturity date. In other words, a bond’s expected returns after making all the payments on time throughout the life of a bond. Unlike current yieldThe 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 moreThe 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 more, which measures the present value of the bond, 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 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 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 the price matches the actual market price of the bond. Nowadays, there are computer applications that facilitate the easy to calculate 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.
Yield-to-Maturity-Formula

You are free to use this image on your website, templates etc, Please provide us with an attribution linkHow to Provide Attribution?Article Link to be Hyperlinked
For eg:
Source: Yield to Maturity (wallstreetmojo.com)

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)

The steps to calculate Yield to Maturity are as follows.

  1. Gathered the information on the bond-like its face value, months remaining to mature, the current market price of the bond, the coupon rate of the bond.

  2. 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. and accordingly, the calculation should be made.

  3. 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 life of the bond.

  4. The numerator of the YTM formula will be the sum of the amount calculated in steps 2 and step 3.

  5. The denominator of the YTM formula will be the average of price and face value.

  6. When one divides step 4 by step 5 value, it shall be the approximate yield on maturity.

Examples

You can download this Yield to Maturity (YTM) Formula Excel Template here – Yield to Maturity (YTM) Formula Excel Template

Example #1

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

Solution:

Use the below-given data for calculation of YTM

Example 1

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 Formula Example 1.1

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

YTM will be –

Example 1.2

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 that are trading in the US market. The government of the US now wants to issue 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.

Solution:

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

Yield to Maturity Formula Example 2

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

 Example 2.1

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

YTM will be –

Yield to Maturity Formula Example 2.2

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

Annual YTM will be –

Example 2.3

Example #3

Mr. Rollins has received the lump sum amount in the form of 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 that he is the wrong myth of low risk and high returns. Then Mr. Rollins accepts that he doesn’t like risk, and 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:

Yield to Maturity Formula Example 3

Both the coupons pay semi-annually. Now Mr. Rollins is perplexed which bond to select. He asks Advisor to invest in option 2 as the price of the bond is less, and he is ready to sacrifice a 0.50% coupon. However, Advisor tells him instead to invest in option 1.

You are required to validate the advice made by the advisor.

Solution:

Option 1

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

 Example 3.1.0

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

YTM will be –

Yield to Maturity Formula Example 3.2

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

Annual YTM will be –

 Example 3.3

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 Formula Example 3.4

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

 Example 3.5

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

Annual Yield to Maturity will be –

Yield to Maturity Formula Example 3.6

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

Since the yield on maturity 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 present value of the bond with other investment options in the market.
  • TVM (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

Recommended Articles

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