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Chapter 9

Learning Objectives Principles Used in This Chapter

1.Overview of Corporate Debt2.Valuing Corporate Debt3 B d V l ti F K R l ti hi3.Bond Valuation: Four Key Relationships4.Types of Bonds5.Determinants of Interest Rates

1. Identify the key features of bonds and describe the difference between private and public debt markets.

2. Calculate the value of a bond and relate it to the yield to maturity on the bond.D ib th f k b d l ti3. Describe the four key bond valuation relationships.

4. Identify the major types of corporate bonds.5. Explain the effects of inflation on interest rates

and describe the term structure of interest rates.

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Principle 1: Money Has a Time Value.◦ Debt securities require that the borrower repay the

lender over time so cash flows have to be adjusted for time value of money.

Principle 2: There is a Risk-Return Tradeoff.◦ The rate used to discount future cash flows depends

on the risk of default by the borrower.

Principle 3: Cash Flows Are the Source of Value◦ Debt securities provide value to the lender through

the interest payments on the outstanding loan amount and the repayment of the loan balanceamount and the repayment of the loan balance itself.

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There are two main sources of borrowing for a corporation:

1. Loan from a financial institution K i d b i i i i l h ldKnown as private debt, since it is privately held

2. Bonds Known as public debt since bonds can be traded in public financial markets

Smaller firms choose to raise money from banks in the form of loans because of the high costs associated with issuing bonds.

f ll f Larger firms generally raise money from banks for short-term needs and depend on the bond market for long-term financing needs.

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Firms also raise money by selling debt securities to individual investors and financial institutions such as mutual funds.

d ll d b h bl In order to sell debt securities to the public, the issuing firm must meet the legal requirements as specified by the securities laws.

Corporate bond is a debt security issued by corporation that has promised future payments and a maturity date.

f h f f l h d f If the firm fails to pay the promised future payments of interest and principal, the bond trustee can classify the firm as insolvent and force the firm into bankruptcy.

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Bond ratings indicate the default risk ◦ The probability that the firm will make the promised

payments.

Bond ratings affect the rate of return that Bond ratings affect the rate of return that lenders require of the firm and the firm’s cost of borrowing.

Consistent with Principle 2 (There is a Risk-Return Tradeoff), the lower the bond rating, the higher the risk of default and higher the rate of return demanded in the capital market.

Bond iss es are rated not companies◦ Bond issues are rated, not companies A company may have several bonds with different ratings

Bond ratings are provided by three rating agencies – Moody’s, Standard & Poor’s, and Fitch Investor Services.

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The value of corporate debt is equal to the present value of the contractually promised principal and interest payments (the cash flows) discounted back to the present using the market’s required yieldthe market s required yield.

The valuation of corporate debt relies on the first three basic principles of finance:

◦ Principle 1: Money Has a Time Value.P i i l 2 Th i Ri k R t T d ff◦ Principle 2: There is a Risk-Return Tradeoff.◦ Principle 3: Cash Flows are the Source of Value.

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Step 1: Determine the amount and timing of bondholder cash flows. The total cash flows equal the promised interest payments and principal payment.

Annual Interest = Par value × coupon rate

Example 9.1: The annual interest for a bond with coupon interest rate of 7% and a par value of $1,000 is equal to $70, (.07 × $1,000 = $70).

Step 2: Estimate the appropriate discount rate on a similar risk bond. ◦ The discount rate is the return the bond will yield if

it is held to maturity and all bond payments are made.made.

Discount rate can be either calculated or obtained from various sources (such as Yahoo! Finance).

Step 3: Calculate the present value of the bond’s interest and principal payments from Step 1 using the discount rate estimated in step 2.

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We can think of YTM as the discount rate that makes the present value of the bond’s promised interest and principal equal to the bond’s observed market price.

Calculating the Yield to Maturity on a Corporate BondCalculate the yield to maturity for the following bond issued by Ford Motor Company (F) with a price of $744.80, where we assume that interest payments are made annually at the end of each year and the bond has a maturity of exactly 11 years.exactly 11 years.

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Calculate the YTM on the Ford bond where the bond price rises to $900 (holding all other things equal).

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YTM=?

YearsCash flow -$900 $65 $65 $65 $1,065

0 1 2 3 … 11

Purchase price = $900 Interest payments = $65 per year for years 1-11 Final payment = $1,000 in year 11 of principal.

We can use equation 9-2a to find YTM. YTM is the rate that makes the present value of all future expected cash flows equal to the current market price.

We can also solve for YTM using a calculator and a spreadsheet.

Using Mathematical Equation

It is cumbersome to solve for YTM by hand using the equation. It is more practical to use the financial calculator or the spread sheet.

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Using Financial CalculatorEnter:

N = 11 I/Y = 7.89PV = -900PMT = 65FV = 1,000

The yield to maturity on the bond is 7.89%. The yield is higher than the coupon rate of interest of 6.5%. Since the coupon rate is lower than the yield to maturity, the bond is trading at a price below $1 000 We call this atrading at a price below $1,000. We call this a discount bond.

Market yield to maturity is regularly reported by a number of investor services and is quoted in terms of credit spreads or spreads to Treasury bonds.

Table 9-4 contains some examples of yield spreads.

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The spread values in table 9-4 represent basis points over a US Treasury security of the same maturity as the corporate bond. For example, a 30-year Ba1/BB+ corporate bond has a spread of 275 basis points over a i il 30 US T b dsimilar 30-year US Treasury bond.

Thus this corporate bond should earn 2.75% over the 4.56% earned on treasury yield or 7.31%.

The yield to maturity calculation assumes that the bond performs according to the terms of the bond contract or indenture. Since corporate bonds are subject to risk of default, the promised yield to maturity may not bethe promised yield to maturity may not be equal to expected yield to maturity.

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Example 9.2 Consider a one-year bond that promises a coupon rate of 8% and has a principal (par value) of $1,000. Further assume the bond is currently trading for $850 What is the promised yield to maturity?$850. What is the promised yield to maturity?

Promised YTM = {(Interest year 1 + Principal) ÷ (Bond Value)} – 1

= {($80+$1,000) ÷ ($850)} – 1

= 27.06%

The yield of 27.06% is based on the assumption of no default.

Assume there is a 40% probability of default h b d d f h b d d f l hon this bond and if the bond defaults, the

bondholders will receive only 60% of the principal and interest owed. What is the expected YTM on this bond?

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YTMdefault = {(Interest year 1 + Principal)} ÷ (Bond Value)} – 1

= {($80+$1000) × .60} ÷ ($850)} – 1

= -23.76%

= (27.06 × .60) + (-23.76 × .40)= 6.73%

The financial press quotes promised yield and not expected YTM.

Valuing a Bond IssueConsider a $1,000 par value bond issued by AT&T (T) with a maturity date of 2026 and a stated coupon rate of 8.5%. On January 1, 2007, the bond had 20 years left to maturity, and the market’s required yield to maturity for similar rated debt was 7.5%. If the market’s required yield to maturity on a comparable risk bond is 7.5%, what is the value y y p ,of the bond?

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Calculate the present value of the AT&T bond should the yield to maturity for comparable risk bonds rise to 9% (holding all other things equal).

i= 9%Years

C h fl $85 $85 $85 $1 085

0 1 2 3 … 20

Cash flows $85 $85 $85 $1,085

PV of allCash flows =?

$85 annualinterest $85 interest

+ $1,000 Principal

Here we know the following:◦ Annual interest payments = $85◦ Principal amount or par value = $1,000◦ Time = 20 years◦ YTM or discount rate = 9%

We can use the above information to determine the value of the bond by discounting future interest and principal payment to the present.

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Using Mathematical Equation

Bond Value = $ 85{[1-(1/(1.09)20] ÷ (.20)} + $1,000/(1.09)20

= $85 (9.128) + $178.43= $954.36

Using a Financial Calculator Enter:◦ N = 20◦ 1/y = 9.0

PMT 85◦ PMT = 85◦ FV = 1000◦ PV = 954.36

The value of AT&T bond falls to $954.36 when the yield to maturity for comparable risk bond rises to 9%. The bonds are now trading at a discount as the coupon rate on AT&T bonds is lower than the market yieldbonds is lower than the market yield.

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An investor who buys AT&T bonds at its current discounted price will earn a promised yield to maturity of 9%.

Corporate bonds typically pay interest to bondholders semiannually.

Double the number of periods Have 2 payments per year◦ Have 2 payments per year

Divide the interest rate by 2 Everything else is the same

When you compute YTM, need to multiply by 2

We can adapt Equation (9-2a) from annual to semiannual payments as follows:

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Valuing a Bond Issue That Pays Semiannual InterestReconsider the bond issued by AT&T (T) with a maturity date of 2026 and a stated coupon rate of 8.5%. AT&T pays interest to bondholders on a semiannual basis on January 15 and July 15. On January 1, 2007, the bond had 20 years left to maturity. The market’s required yield to maturity for a similarly rated debt was 7.5% per year or 3.75% for six months. What is the value of the bond?

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Table 9-7 contains a listing of major types of long-term debt securities that are sold in the public financial market.

The differences among the various types of bond are based on the following bond attributes:g◦ Secured versus Unsecured, ◦ Priority of claim, ◦ Initial offering market, ◦ Abnormal risk, ◦ Coupon level, ◦ Amortizing or non-amortizing, and ◦ Convertibility.

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As we observed earlier, bond prices vary inversely with interest rates.

Therefore in order to understand bond pricing d k h d fwe need to know the determinants of interest

rates.

Quoted interest rates are nominal (or quoted) interest rates.

There are four determinants of quoted rates◦ Real interest rate (inflation-free)◦ Inflation premium◦ Inflation premium◦ Risk premium ◦ Maturity premium

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Real rate of interest adjusts the nominal rate for the expected effects of inflation.◦ The relationship between the nominal and real

interest rates is called the Fisher equation

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

◦ rreal = rnominal – rinflation is “close enough” for low inflation rates

The interest rate that a firm’s bonds pay must also offer a default premium◦ For the risk that the issuer will fail to repay interest

and principal in a timely manner.

As before:

Bond relationship 4: Long-term bonds are more sensitive to interest rate changes.

Maturity premium is the compensation that d d f binvestors demand for bearing interest rate

risk on long-term bonds.

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The 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.

The term structure of interest rates changes over time as expectations regarding each of the three factors that underlie interest rates change.

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The yield curve is generally upward sloping but it can assume different shapes i.e. downward sloping or flat.

ll d ff h f ld Figure 9-5 illustrates different shapes of yield curves at different dates.