Chapter 11 Bond Valuation Bond valuation We value

Chapter 11 Bond Valuation

Bond valuation • We value securities by discounting their future cash flows to today to obtain its present value. • Valuation of a security involves two tasks: 1. Forecast its future cash flow 2. Determine its discount rate (the required rate of return) • The future cash flows from a bond are known (coupons+principal), as long as there is no default. • The key for bond valuation then is to determine its discount rate. Copyright © 2014 Pearson Education, Inc. All rights reserved. 11 -2

Determine the discount rate • The required rate of return =[Real rate of return + Expected inflation premium] + Risk premium • The first two terms in the bracket is captured by the Treasury yield, which we usually label as riskfree. • Term risk premium: Bond yields at longer maturities tend to be higher on average than at shorter maturities. This is driven by the interest rate variation. • Credit risk premium: Bonds that have a higher chance of default tend to have a larger credit yield spread. • Tax: Some bonds are tax free, in which case one would ask for a lower return Copyright © 2014 Pearson Education, Inc. All rights reserved. 11 -3

Major Bond Sectors • Bond market is comprised of a series of different market sectors: – U. S. Treasury issues – Municipal bonds – Corporate bonds – Sovereign bonds • Differences in interest rates between the various market sectors are called yield spreads Copyright © 2014 Pearson Education, Inc. All rights reserved. 11 -4

Factors Affecting Yield Spreads • Municipal bond rates are usually 20 -30% lower than corporate bonds due to tax-exempt feature • Treasury bonds have lower rates than corporate bonds due to no default risk • The lower the credit rating (and higher the default risk), the higher the interest rate • Revenue municiple bonds yield more than general obligation municiple bonds due to higher risk • Freely callable bonds yield higher than noncallable bonds • Bonds with longer maturities generally yield more than shorter maturities Copyright © 2014 Pearson Education, Inc. All rights reserved. 11 -5

Determine credit risk • Credit risk is the key driver of yield spreads • How to determine credit risk? – It is the risk that borrower cannot afford to pay the debt and its interest. • What determines the borrower’s capability to pay back the debt? – Does the company has too much debt relative to asset: leverage ratio = Debt/Asset – Does the company make enough money each year to pay off its interest expense: Interest coverage ratio =Operating Income/Interest expense • Credit rating is largely based on these two metrics – +some other metrics such as liquidity. Copyright © 2014 Pearson Education, Inc. All rights reserved. 11 -6

Term Structure of Interest Rates and Yield Curves • Term Structure of Interest Rates: relationship between the interest rate or rate of return (yield) on a bond and its time to maturity • Yield Curve: a graph that represents the relationship between a bond’s term to maturity and its yield at a given point in time Copyright © 2014 Pearson Education, Inc. All rights reserved. 11 -7

Figure 11. 2 Two Types of Yield Curves Copyright © 2014 Pearson Education, Inc.

Theories on Shape of Yield Curve • Slope of yield curve affect by: – Investors’ expectations regarding the future behavior of interest rates – Risk premiums: Long bonds are riskier and demand higher returns on average) – Convexity: Drives longer-term bond yield down because bond-rate relation is nonlinear. – Supply and demand for bonds of different maturities Copyright © 2014 Pearson Education, Inc. All rights reserved. 11 -9

Theories on Shape of Yield Curve (cont’d) • Expectations Hypothesis – Shape of yield curve is based upon investor expectations of future behavior of interest rates – When investors expect interest rates to go up, they will only purchase long-term bonds if those bonds offer higher yields than short-term bonds; hence the yield curve will be upward sloping – When investors expect interest rates to go down, they will only purchase short-term bonds if those bonds offer higher yields than long-term bonds; hence the yield curve will be downward sloping Copyright © 2014 Pearson Education, Inc. All rights reserved. 11 -10

Interpreting Shape of Yield Curve • Upward-sloping yield curves result from: – Expectation of rising interest rates – Lender preference for shorter-maturity loans – Greater supply of shorter-term loans • Flat or downward-sloping yield curves result from: – Expectation of falling interest rates – Lender preference for longer-maturity loans – Greater supply of longer-term loans Copyright © 2014 Pearson Education, Inc. All rights reserved. 11 -11

Basic Bond Investing Strategy • If you expect interest rates to increase, buy short-term bonds • If you expect interest rates to decrease, buy long-term non-callable bonds Copyright © 2014 Pearson Education, Inc. All rights reserved. 11 -12

The Pricing of Bonds • Bonds are priced according to the present value of

The Pricing of Bonds (cont’d) • Bond prices are driven by market yields • Appropriate yield at which the bond should sell is determined before price of the bond – Required rate of return is determined by market, economic and issuer characteristics – Required rate of return becomes the bond’s market yield – Market yield becomes the discount rate that is used to value the bond Copyright © 2014 Pearson Education, Inc. All rights reserved. 11 -14

The Pricing of Bonds (cont’d) • Bond prices are comprised of two components: – Present value of the annuity of coupon payments, plus – Present value of the single cash flow from repayment of the principal at maturity • Compounding refers to frequency coupons are paid – Annual compounding: coupons paid once per year – Semi-annual compounding: coupons paid every six months Copyright © 2014 Pearson Education, Inc. All rights reserved. 11 -15

The Pricing of Bonds (cont’d) • Bond Pricing Example: – What is the market price of a $1, 000 par value 20 year bond that pays 9. 5 % compounded annually when the market rate is 10%? Copyright © 2014 Pearson Education, Inc. All rights reserved. 11 -16

Ways to Measure Bond Yield • Current yield • Yield-to-Maturity • Yield-to-Call • Expected

Current Yield • Simplest yield calculation • Only looks at current income Copyright ©

Yield-to-Maturity • Most important and widely used yield calculation • True yield received if the bond is held to maturity • Assumes all interest income is reinvested at rate equal to market rate at time of YTM calculation—no reinvestment risk • Calculates value based upon PV of interest received and the appreciation of the bond if held until maturity • Difficult to calculate without a financial calculator Copyright © 2014 Pearson Education, Inc. All rights reserved. 11 -19

Yield-to-Maturity (cont’d) • Yield-to-Maturity Example: – Find the yield-to-maturity on a 7. 5 % ($1, 000 par value) bond that has 15 years remaining to maturity and is currently trading in the market at $809. 50? Copyright © 2014 Pearson Education, Inc. All rights reserved. 11 -20

Yield-to-Call • Similar to yield-to-maturity • Assumes bond will be called on the first call date • Uses bonds call price (premium) instead of the par value • True yield received if the bond is held to call Copyright © 2014 Pearson Education, Inc. All rights reserved. 11 -21

Yield-to-Call (cont’d) • Yield-to-Call Example: – Find the yield-to-call of a 20 -year, 10. 5 % bond (annual payment) that is currently trading at $1, 204, but can be called in 5 years at a call price of $1, 085? Copyright © 2014 Pearson Education, Inc. All rights reserved. 11 -22

Expected Return • Used by investors who expect to actively trade in and out of bonds rather than hold until maturity date • Similar to yield-to-maturity • Uses estimated market price of bond at expected sale date instead of the par value Copyright © 2014 Pearson Education, Inc. All rights reserved. 11 -23

Expected Return (cont’d) • Expected Return Example: – Find the expected return on a 7. 5% bond (semi-annual payment) that is currently priced in the market at $809. 50 but is expected to rise to $960 within a 3 -year holding period? Copyright © 2014 Pearson Education, Inc. All rights reserved. 11 -24

Bond Duration • Bond Duration: A measure of bond price sensitivity to interest rate changes. • Macauley duration: Weighted average maturity of all cash flows, with the weight given by the present value of the cash flow, divided by the current bond price. MD=sum(t*w) Copyright © 2014 Pearson Education, Inc. All rights reserved. 11 -25

Bond Duration • Modified duration: Macauley duration/(1+y), measures the percentage change in bond value per change in interest rate • Example: A bond as a Macauley duration of 7. 00 and is priced to yield 5%. If the market interest rate goes up so that the yield goes up to 5. 5%, the percentage change in the bond price is: -7*(5. 5%-5%)/(1+5%)=-3. 33% The bond price will go down by 3. 33%. Copyright © 2014 Pearson Education, Inc. All rights reserved. 11 -26

The Concept of Duration • Generally speaking, bond duration possesses the following properties: – Bonds with higher coupon rates have shorter durations – Bonds with longer maturities have longer durations – Bonds with higher YTM lead to shorter durations • The bond duration as a sensitivity measure works better for small rate moves, but may not work well for large moves due to convexity effects. Copyright © 2014 Pearson Education, Inc. All rights reserved. 11 -27

Measuring Duration • Steps in calculating Macauley duration – Step 1: Find present value of each coupon or principal payment – Step 2: Divide this present value by current market price of bond – Step 3: Multiple this ratio by the year in which the bond makes each cash payment – Step 4: Repeat steps 1 through 3 for each year in the life of the bond then add up the values computed in Step 3 Copyright © 2014 Pearson Education, Inc. All rights reserved. 11 -28