Yield to Maturity (YTM)

*Yield to Maturity (YTM)The yield to maturity is the discount rate that makes the present value of the bonds promised interest and principal equal to the bonds observed market price.Note that the yield to maturity will be equal to the coupon rate if the bond is selling for its face value. For premium bonds, the current yield > YTM.For discount bonds, the current yield < YTM.

*The Mills Company bond, which currently sells for P1,080, has a 10% coupon interest rate and P1,000 par value, pays interest annually, and has 10 years to maturity. What is the bonds YTM?P1,080 = P100 x (PVIFAkd,10yrs) + P1,000 x (PVIFkd,10yrs)Yield to Maturity (YTM) YTM = 8.77%

*Yield to Maturity (YTM): Semiannual Interest Assuming that the Mills Company bond pays interest semiannually, what is the YTM?YTM = 8.78%

*Effective Annual Rate (EAR)

*Bond Valuation: Four Key RelationshipsFirst Relationship:The value of bond is inversely related to changes in the yield to maturity.

Bond Value Drops

YTM = 12%YTM rises to 15%Par valueP1,000P1,000Coupon rate12%12%Maturity date5 years5 yearsBond ValueP1,000P899.44

*Bond Valuation: Four Key Relationships

*Bond Valuation: Four Key RelationshipsSince future interest rates cannot be predicted, a bond investor is exposed to the risk of changing values of bonds as interest rates change.

The risk to the investor that the value of his or her investment will change is known as interest rate risk.

*Bond Valuation: Four Key RelationshipsSecond Relationship: The market value of a bond will be less than its par value if the yield to maturity is above the coupon interest rate and will be valued above par value if the yield to maturity is below the coupon interest rate.

*Bond Valuation: Four Key Relationships When a bond can be bought for less than its par value, it is called discount bond. For example, buying a P1,000 par value bond for P950.

Bonds will trade at a discount when the yield to maturity on the bond exceeds the coupon rate.

*Bond Valuation: Four Key Relationships When a bond can be bought for more than its par value, it is called premium bond. For example, buying a P1,000 par value bond for P1,110.

Bonds will trade at a premium when the yield to maturity on the bond is less than the coupon rate.

*Bond Valuation: Four Key RelationshipsThird Relationship: As the maturity date approaches, the market value of a bond approaches its par value.

Regardless of whether the bond was trading at a discount or at a premium, the price of bond will converge towards par value as the maturity date approaches.

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*Bond Valuation: Four Key RelationshipsFourth Relationship: Long term bonds have greater interest rate risk than short-term bonds.

While all bonds are affected by a change in interest rates, long-term bonds are exposed to greater volatility as interest rates change.

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Determinants of Interest Rates

*Determinants of Interest RatesAs we observed earlier, bond prices vary inversely with interest rates.

Therefore in order to understand bond pricing we need to know the determinants of interest rates.

*Real Rate of Interest and the Inflation PremiumQuotes of interest rates in the financial press are commonly referred to as the nominal (or quoted) interest rates.

Real rate of interest adjusts the nominal rate for the expected effects of inflation.

*Real Rate of Interest and the Inflation PremiumThe nominal interest rate on a note or bond can be thought of as including four basic components:The real rate of interest rate of increase in purchasing power experienced over time.An inflation premium premium for the expected increase in prices of goods and services in the economy over the term of the bond/note.The default premium a premium to reflect the risk of default by the borrower.A maturity premium a premium that reflects the term structure of interest rates. In general, longer maturity debt has higher rate.

*Fisher EffectThe relationship between the nominal rate of interest, rnominal , the anticipated rate of inflation, rinflation , and the real rate of interest is known as the Fisher effect. It is captured in the following equation: (1 + rnominal) = (1 + rreal)(1 + rinflation)

rearranging the terms, we can solve for rreal:

*Fisher EffectWe can also solve for rnominal:

(1 + rnominal) = (1 + rreal)(1 + rinflation)

*Fisher Effect Example: What is the real rate of interest if the nominal rate of interest is 10% and the anticipated rate of inflation is 3%?

rreal = {(1+.10) (1+.03)} 1= .0680 or 6.80%

*Checkpoint 9.5Solving for the Real Rate of InterestYou have managed to build up your savings over the three years following your graduation from college to a respectable P10,000 and are wondering how to invest it. Your banker says they could pay you 5% on your account for the next year. However, you recently saw on the news that the expected rate of inflation for next year is 3.5%. If you are earning a 5% annual rate of return but the prices of goods and services are rising at a rate of 3.5%, just how much additional buying power would you gain each year? Stated somewhat differently, what real rate of interest would you earn if you made the investment?

*The Term Structure of Interest RatesThe relationship between interest rates and time to maturity with risk held constant is known as the term structure of interest rates or the yield curve.

Figure 9-3 illustrates a hypothetical yield curve of US Treasury Bonds.

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*Shifts in the Yield CurveThe term structure of interest rates changes over time as expectations regarding each of the three factors that underlie interest rates change.

Figure 9-4 shows the yield curve one day before 911 attack and again two weeks later.

*Shifts in the Yield Curve