Yield to maturity

Examples of Yield to maturity in the following topics:

• Yield to Maturity

  • The formula for yield to maturity:
  • Yield to maturity (YTM) = [(Face value / Present value)1/Time period]-1
  • Yield to worst: when a bond is callable, puttable, exchangeable, or has other features, the yield to worst is the lowest yield of yield to maturity, yield to call, yield to put, and others.
  • Development of yield to maturity of bonds of 2019 maturity of a number of Eurozone governments.
  • Classify a bond based on its market value and Yield to Maturity

• Calculating Yield to Maturity Using the Bond Price

  • The yield to maturity is the discount rate which returns the market price of the bond.
  • 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.
  • Suppose that over the first 10 years of the holding period, interest rates decline, and the yield-to-maturity on the bond falls to 7%.
  • Even though the yield-to-maturity for the remaining life of the bond is just 7%, and the yield-to-maturity bargained for when the bond was purchased was only 10%, the return earned over the first 10 years is 16.25%.

• Chapter Questions

  • A T-bill has a face value of $20,000 with a yield to maturity of 3%, and this bill matures in 270 days.
  • If the yield to maturity is 5% and the bond matures in three years, calculate the market value of this bond.
  • If the yield to maturity is 20% and the bond matures in three years, compute the market value of this bond.
  • If you expect the central bank to lower interest rates, define a good investment strategy.
  • If the bond matures in 3 years with a face value of $5,000, calculate your yield-to-maturity (YTM).

• Yield to Maturity and Rate of Return

  • If investors hold the bond until maturity, then we call the discount rate the yield to maturity.Economists consider yield to maturity the most accurate measure of the interest rates because the yield to maturity allows investors to compare different bonds.For example, you want to buy a coupon bond today for a market price of $1,600.Bond pays $400 interest per year and matures in three years.Finally, the bond pays $1,000 on the maturity date.Consequently, we calculate your yield to maturity of 14.11% in Equation 6.You can compare this yield toother investments and choose the investment with the greatest yield.
  • Yield to maturity generates two important rules on bonds, which are:
  • Market interest rate (or yield to maturity) and the market price (or present value) of the securities are inversely related.For example, if you examine the present value formula, the interest rate, or yield to maturity is located in the denominators of the fractions.Thus, the market price falls as the interest rate rises, and vice versa.
  • If a bond has a shorter maturity, subsequently, its price will fluctuate less for a change in the market interest rate.We show this by an example.
  • You can become confused by the terms used throughout this book.We use yield to maturity, discount rate, and interest rate interchangeably, and you can interpret these terms to mean an interest rate.However, a rate of return differs because investors could sell their securities before they matured.Thus, the rate or return includes the interest rate and capital gains or losses.A capital gain is an investor sells a financial security for greater price, while a capital loss is an investor sells a financial security for a lower price.Investors do not want capitallosses, but they can occur.For instance, an investor must sell an asset whose market price has dropped because he or she needs cash quickly.Thus, the present value still works for capital gains and losses.Finally, if the investor holds onto the security onto the maturity date, then the rate of return equals the yield to maturity.

• The "Bond Yield Plus Risk Premium" Approach

  • We can estimate the value of a company's equity by adding its risk premium to the yield to maturity on the company's long-term debt.
  • A company's long-term debt has a yield to maturity of 6%.
  • BYPRP allows us to estimate the required return on an equity by adding the equity's risk premium to the yield to maturity on company's long-term debt.
  • In the BYPRP approach, we use a bond's yield to maturity, which is the discount rate at which the sum of all future cash flows from the bond (coupon payments and principal payments) are equal to the price of the bond.
  • A hypothetical graph showing yield to maturities (or internal rates of return) for corresponding present values.

• Par Value at Maturity

  • A bond selling at par has a coupon rate such that the bond is worth an amount equivalent to its original issue value or its value upon redemption at maturity.
  • Federal government bonds tend to have much higher face values at $10,000.
  • Together with coupon payments, the par value at maturity is discounted back to the time of purchase to calculate the bond price.
  • F = face value, iF = contractual interest rate, C = F * iF = coupon payment (periodic interest payment), N = number of payments, i = market interest rate, or required yield, or observed/ appropriate yield to maturity, M = value at maturity, usually equals face value, P = market price of bond.
  • Bond price is the present value of coupon payments and the par value at maturity.

• Characteristics of Bonds

  • The issuer has to repay the nominal amount on the maturity date.
  • The length of time until the maturity date is often referred to as the term or maturity of a bond.
  • short term (bills): maturities between one to five year (instruments with maturities less than one year are called money market instruments)
  • It usually refers either to the current yield, or running yield, which is simply the annual interest payment divided by the current market price of the bond.
  • It can also refer to the yield to maturity or redemption yield, which is a more useful measure of the return of the bond, taking into account the current market price, and the amount and timing of all remaining coupon payments and of the repayment due on maturity.

• Using the Yield Curve to Estimate Interest Rates in the Future

  • A yield is the return an investor will receive by holding a bond to maturity.
  • The line on a yield curve chart plots the interest rate of bonds at set times and gives the relation between the interest rate to be paid to the bond holder and the time to the maturity of the bond.
  • The yield curve is normal, meaning that yields rise as maturity lengthens (i.e., the slope of the yield curve is positive).
  • Investors price these risks into the yield curve by demanding higher yields for maturities further into the future.
  • Note that this graph follows the pattern of a "normal yield curve," where yields rise as maturity lengthens, indicating that the investors believed the Federal Reserve was going to raise interest rates in the future.

• The Yield Curve

  • A yield curve shows the relation between interest rate levels (or cost of borrowing) and the time to maturity.
  • The curve shows the relation between the (level of) interest rate (cost of borrowing) and the time to maturity, known as the "term," of the debt for a given borrower in a given currency.
  • The yield curve is normal meaning that yields rise as maturity lengthens (i.e., the slope of the yield curve is positive).
  • A flat yield curve is observed when all maturities have similar yields, whereas a humped curve results when short-term and long-term yields are equal and medium-term yields are higher than those of the short-term and long-term.
  • Because of the term premium, long-term bond yields tend to be higher than short-term yields, and the yield curve slopes upward.

• Term Structure of Interest Rates

  • Economists plot U.S. government securities by the market interest rates and maturity, which they call a yield curve.
  • Economists use three theories to explain why the yield curve has these two characteristics.
  • Consequently, the yield curve slopes upward because the investors add the term premium to long maturity bonds.
  • Economists use the yield curve to predict economic activity.
  • Although many economists and analyst use the yield curve to forecast recessions, the yield curve is not a perfect predictor.