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Measuring Yield What is Yield? The purpose of any investment is to enhance the wealth of the holder. When an investor purchases a bond he seeks to earn a return that compensates him for his risk exposure and foregone consumption. Investors use yield measurements to quantify a bond’s expected return. Yield is the percentage return a bond is expected to earn at a given price and is used to compare the prospects of one fixed income investment to another. There are several methods of measuring yield. Each method provides a different, but valuable perspective of a bond’s potential return on investment. Note: A comprehensive yield measurement should take into account all of a bond’s sources of cash flow. In addition, it should consider the effect of the time value of money.
Nominal (Coupon) Yield Nominal Yield, or Coupon Yield, is a bond’s annual coupon rate relative to its face value. For example, a bond with a 5% coupon rate has a nominal yield of 5%. It is important to understand that nominal yield is a measure of coupon income relative to face value, not market price. Nominal Yield is derived from the following formula:
Current Yield Current Yield is a simple measurement that calculates the expected return a bond will earn from coupon interest relative to the bond’s market value. It ignores the returns earned from capital gains and reinvestment income. Current Yield is expressed by the following formula:
Consider a semi-annual coupon bond with a $1,000 face value, a $950 market value, and a 10% coupon rate. The bond’s current yield equates to 10.53%. If the bond’s market value decreases to $920 its yield will rise to 10.87%. Notice that the bond’s current yield moves inversely to its price. A bond’s current yield will increase as its price declines and vice versa.
Current yield is commonly used to compare the expected coupon return of one bond with another. However, because it does not measure the returns earned from capital gains and reinvestment income, it does not provide a true measurement of a fixed income investment’s total expected return. Yield-to-Maturity Generally, when investors talk about yield they are referring to yield-to-maturity. Recall that a bond is valued by discounting its future cash flows at a discount rate. Yield-to-maturity is the discount rate that will make the sum of the present values of a bond’s cash flows equal to the market value of the bond. A bond’s yield-to-maturity is known as its internal rate of return. Yield-to-maturity calculates a bond’s total expected rate of return because it takes into account coupon interest, capital gains, reinvestment income, and the effect of the time value of money. Thus, YTM allows investors to compare bonds with different coupons and maturities. YTM is based on two assumptions: (1) the investor holds the bond until maturity, and (2) the investor reinvests the coupon payments in securities that offer the same rate of return. Yield-to-Maturity is a complex calculation. An approximate measurement of a bond’s yield-to-maturity can be derived from the following formula:
Alternatively, a precise measurement of a bond’s yield-to-maturity can be calculated using the Bond Valuation functions of a Hewlett Packard 12C.
Consider the following example: A semi-annual coupon bond has a $1,000 face value, an 8% coupon rate, and 10 years remaining until maturity. Suppose the bond is purchased on January 1, 2002 for $1,090 or 109. Calculate the bond’s yield-to-maturity.
Consider a second example: Calculate the YTM of a semi-annual coupon bond with a $1,000 face value, a $970 market value, a 7% coupon rate, and five years remaining until maturity.
Reinvestment Income It is important to reiterate that the yield-to-maturity calculation is based on the assumption that the investor reinvests the coupon payments in securities that offer the same rate of return. In reality, coupon returns will generally be invested in different securities with different yields. If the reinvestment yield is lower than the initial bond’s YTM, total return will be less than the initial bond’s YTM. If the reinvestment yield is higher than the initial bond’s YTM, total return will exceed the initial bond’s YTM. Questions: 1. Calculate the coupon yield of a bond with a $1,000 face value, a $900 market value, and a 12% coupon rate. 2. Bond A, a semi-annual coupon bond, has a $1,000 face value, a $1,050 market value, and a coupon rate of 10%. Bond B, a semi-annual coupon bond, has a $5,000 face value, $4,786 market value, and a coupon rate of 8%. Which bond offers the largest coupon yield? 3. Calculate the YTM of a semi-annual coupon bond with a $1,000 face value, a $950 market value, a 4% coupon rate, and four years remaining until maturity. 4. Calculate the YTM of a semi-annual coupon bond with a $5,000 face value, a $4,800 market value, a 6% coupon rate, and four years remaining until maturity. 5. Bond A, a semi-annual coupon bond, has a $1,000 face value, a $1,070 market value, a 6% coupon rate, and four years remaining until maturity. Bond B, a semi-annual coupon bond, has a $1,000 face value, a $980 market value, a 7% coupon rate, and 2 years remaining until maturity. Which bond offers the largest YTM? Answers: 1. 13.34% Current Yield = 12/90 = .1334 or 13.34%
2.
Bond A Bond A:
Current Yield = 10/105 = .095 or 9.5% 3. 5.41% PMT = 4, PV = 95, 1.012000 ENTER, 1.012004 f YTM 4. 7.17% PMT = 6, PV = 96, 1.012000 ENTER, 1.012004 f YTM
5. Bond B Bond
A: PMT = 6, PV = 107, 1.012000 ENTER, 1.012004 f
YTM All
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