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Calculating Yield to Maturity Using the Bond Price
The yield to maturity is the discount rate that returns the bond's market price: YTM = [(Face value/Bond price)1/Time period]1.
Learning Objective

Calculate a bond's yield to maturity
Key Points
 To achieve a return equal to YTM (i.e., where it is the required return on the bond), the bond owner must buy the bond at price P0, hold the bond until maturity, and redeem the bond at par.
 If a bond's coupon rate is less than its YTM, then the bond is selling at a discount. If a bond's coupon rate is more than its YTM, then the bond is selling at a premium. If a bond's coupon rate is equal to its YTM, then the bond is selling at par.
 Formula for yield to maturity: Yield to maturity(YTM) = [(Face value/Bond price)1/Time period]1.
Term

discount rate
The interest rate used to discount future cash flows of a financial instrument; the annual interest rate used to decrease the amounts of future cash flow to yield their present value.
Full Text
YTM
The yield to maturity is the discount rate which returns the market price of the bond. YTM is the internal rate of return of an investment in the bond made at the observed price.
USD Yield Curve
2005 USD yield curve
To achieve a return equal to YTM (i.e., where it is the required return on the bond), the bond owner must buy the bond at price P_{0}, hold the bond until maturity, and redeem the bond at par.
If the yield to maturity for a bond is less than the bond's coupon rate, then the (clean) market value of the bond is greater than the par value (and vice versa). If a bond's coupon rate is less than its YTM, then the bond is selling at a discount. If a bond's coupon rate is more than its YTM, then the bond is selling at a premium. If a bond's coupon rate is equal to its YTM, then the bond is selling at par.
Calculating YTM
Formula for yield to maturity: Yield to maturity(YTM) = [(Face value/Bond price)^{1/Time period}]1
As can be seen from the formula, the yield to maturity and bond price are inversely correlated.
Consider a 30year, zerocoupon bond with a face value of $100. If the bond is priced at an annual YTM of 10%, it will cost $5.73 today (the present value of this cash flow, 100/(1.1)30 = 5.73). Over the coming 30 years, the price will advance to $100, and the annualized return will be 10%.
What happens in the meantime? Suppose that over the first 10 years of the holding period, interest rates decline, and the yieldtomaturity on the bond falls to 7%. With 20 years remaining to maturity, the price of the bond will be 100/1.0720, or $25.84. Even though the yieldtomaturity for the remaining life of the bond is just 7%, and the yieldtomaturity bargained for when the bond was purchased was only 10%, the return earned over the first 10 years is 16.25%. This can be found by evaluating (1+i) from the equation (1+i)10 = (25.842/5.731), giving 1.1625.
Over the remaining 20 years of the bond, the annual rate earned is not 16.25%, but rather 7%. This can be found by evaluating (1+i) from the equation (1+i)20 = 100/25.84, giving 1.07. Over the entire 30 year holding period, the original $5.73 invested increased to $100, so 10% per annum was earned, irrespective of any interest rate changes in between.
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Key Term Reference
 Interest
 Appears in these related concepts: Interest Compounded Continuously, Your Areas of Interest, and Tax Considerations
 Yield to maturity
 Appears in these related concepts: Reinvestment Risk, Duration, and Other Features
 bond
 Appears in these related concepts: Factors Affecting the Price of a Bond, Current Maturities of LongTerm Debt, and Preferred Stock
 cash flow
 Appears in these related concepts: Calculating the NPV, Interpreting the NPV, and Defining the Cash Flow Cycle
 discount
 Appears in these related concepts: The Discount Rate, Par Value at Maturity, and Present Value, Multiple Flows
 interest rate
 Appears in these related concepts: Greenspan Era, The Financial Account, and Determinants of investment
 investment
 Appears in these related concepts: Functions of Corporate Finance, The Role of the Financial System, and GDP Equation in Depth (C+I+G+X)
 market value
 Appears in these related concepts: Lower of Cost or Market, Maximizing Value Without Harming Stakeholders, and Maximizing Shareholder and Market Value
 maturity
 Appears in these related concepts: Types of Financial Markets, Accounting for Interest Earned and Principal at Maturity, and Maturity
 par
 Appears in these related concepts: Characteristics of Bonds, Call Provisions, and Accounting for Preferred Stock
 par value
 Appears in these related concepts: Par Value, Convertible Stock, and Equity Finance
 period
 Appears in these related concepts: Frequency of Sound Waves, Sine and Cosine as Functions, and Tangent as a Function
 premium
 Appears in these related concepts: The Term Structure, Redeeming Before Maturity, and Health Insurance
 present value
 Appears in these related concepts: Capital Leases vs. Operating Leases, Calculating Values for Different Durations of Compounding Periods, and Present Value and the Time Value of Money
 required return
 Appears in these related concepts: Impact of Dividend Policy on Clientele, Differences Between Required Return and the Cost of Capital, and The Capital Asset Pricing Model
 return
 Appears in these related concepts: Dollar Returns, Comparing the Fields of Finance, Economics, and Accounting, and Disadvantages of the Payback Method
 yield
 Appears in these related concepts: Bonds Payable and Interest Expense, Stock Warrants, and Calculating the Yield of an Annuity
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Source: Boundless. “Calculating Yield to Maturity Using the Bond Price.” Boundless Finance. Boundless, 08 Aug. 2016. Retrieved 26 Aug. 2016 from https://www.boundless.com/finance/textbooks/boundlessfinancetextbook/bondvaluation6/valuingbonds68/calculatingyieldtomaturityusingthebondprice3101033/