M09 titman 2544318_11_fin_mgt_c09

Copyright © 2011 Pearson Prentice Hall. All rights reserved.

Debt Valuation and Interest Rates

Chapter 9

Copyright © 2011 Pearson Prentice Hall. All rights reserved.9-2

Slide Contents

• Learning Objectives• Principles Used in This Chapter

1.Overview of Corporate Debt2.Valuing Corporate Debt3.Bond Valuation: Four Key Relationships4.Types of Bonds5.Determinants of Interest Rates

• Key Terms


Learning Objectives

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.

3. Describe the four key bond valuation relationships.


Learning Objectives (cont.)

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.


Principles Used in This Chapter

• 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.


Principles Used in This Chapter (cont.)

• 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 balance itself.


9.1 Overview of Corporate Debt


Corporate Borrowings

• There are two main sources of borrowing for a corporation:

1. Loan from a financial institution (known as private debt)

2. Bonds (known as public debt since they can be traded in public financial markets)


Corporate Borrowings (cont.)

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

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


Borrowing Money in the Private Financial Market

• Financial Institutions are an important source of capital for corporations. The loan might be used to finance firm’s day-to-day operations or it might be used for the purchase of equipment or property.

• Such loans are considered private market transactions since it only involves the two parties to the loan.


Borrowing Money in the Private Financial Market (cont.)

• In the private financial market, loans are typically floating rate loans i.e. the interest rate is periodically adjusted based on a specific benchmark rate.

• The most popular benchmark rate is the London Interbank Offered Rate (LIBOR)



• LIBOR is the daily interest rate that is based on the interest rates at which banks offer to lend in the London wholesale or interbank market.

– Interbank market is the market where banks loan each other money.



• A typical floating rate loan will specify the following:– The spread or margin between the loan rate

and the benchmark rate expressed as basis points.

– A maximum and a minimum annual rate, to which the rate can adjust, called the ceiling and floor.

– A maturity date– Collateral



• For example, a corporation may get a 1-year loan with a rate of 300 basis points (or 3%) over LIBOR with a ceiling of 11% and a floor of 4%.



Checkpoint 9.1

Calculating the Rate of Interest on a Floating Rate LoanThe Slinger Metal Fabricating Company entered into a loan agreement with its bank to finance the firm’s working capital. The loan called for a floating rate that was 25 basis points (.25%) over an index based on LIBOR. In addition, the loan adjusted weekly based on the closing value of the index for the previous week within the bounds of a maximum annual rate of 2.5% and a minimum of 1.75%. Calculate the rate of interest for the weeks 2 through 10.


Checkpoint 9.1


Checkpoint 9.1


Checkpoint 9.1


Checkpoint 9.1


Checkpoint 9.1: Check Yourself

Consider the same loan period as above but change the spread over LIBOR from .25% to .75%. Is the ceiling rate or floor rate violated during the loan period?


Step 1: Picture the Problem

• The graph on the next slide shows the LIBOR index (series 1), LIBOR plus the spread of 75 basis points (series 2) the ceiling rate (series 3), and the floor rate (series 4).


Step 1: Picture the Problem (cont.)


Step 2: Decide on a Solution Strategy

• We have to determine the floating rate for every week and see if it exceeds the ceiling or falls below the floor.

• Floating rate on Loan = LIBOR for the previous week + spread of .75%



• The floating rate on loan cannot exceed the ceiling rate of 2.5% or drop below the floor rate of 1.75%.

– If the floating rate falls below the floor, the rate will be reset at the floor rate.

– If the floating rate exceeds the ceiling, the rate will be reset at the ceiling rate.


Step 3: SolveLIBOR LIBOR +

Spread (.75%)

Loan Rate

2/29/2008 1.98%

3/7/2008 1.66% 2.73% 2.50%

3/14/2008 1.52% 2.44% 2.41%

3/21/2008 1.35% 2.27% 2.27%

3/28/2008 1.60% 2.10% 2.10%

4/4/2008 1.63% 2.35% 2.35%

4/11/2008 1.67% 2.38% 2.38%

4/18/2008 1.88% 2.42% 2.42%

4/25/2008 1.93% 2.63% 2.50%

5/2/2008 2.68% 2.50%

Ceiling Violated


Step 3: Solve (cont.)

• The table shows the ceiling is violated during the first week and last two weeks of the loan period. The floor rate is never violated.


Step 4: Analyze

• The ceiling is the maximum rate charged on the loan while floor is the minimum rate charged on the loan. If the ceiling or floor rates are violated, the loan rate is reset to the ceiling rate or the floor rate.

• If there were no ceiling, the loan rate would have been 2.73% during the first week of the loan, and 2.63% and 2.68% during the last two weeks of the loan.


Borrowing Money in the Public Financial Market

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

• In order to sell debt securities to the public, the issuing firm must meet the legal requirements as specified by the securities laws.


Borrowing Money in the Public Financial Market

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

• 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.


Basic Bond Features

• The basic features of a bond include the following:– Bond Indenture– Claims on Assets and Income– Par or Face Value– Coupon Interest Rate– Maturity and Repayment of Principal– Call Provision and Conversion Features



Bond Ratings and Default Risk

• Bond ratings indicate the default risk i.e. the probability that the firm will make the promised payments.

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


Bond Ratings and Default Risk (cont.)

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



9.2 Valuing Corporate Debt


Valuing Corporate Debt

• 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 yield.


Valuing Corporate Debt (cont.)

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

– Principle 1: Money Has a Time Value.– Principle 2: There is a Risk-Return Tradeoff.– Principle 3: Cash Flows are the Source of Value.


Step-by-Step: Valuing Bonds by Discounting Future Cash Flows

• 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-by-Step: Valuing Bonds by Discounting Future Cash Flows (cont.)

• Step 2: Estimate the appropriate discount rate on a similar risk bond. Discount rate is the return the bond will yield if it is held to maturity and all bond payments are made.

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


Step-by-Step: Valuing Bonds by Discounting Future Cash Flows (cont.)

• 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.


Calculating a Bond’s Yield to Maturity (YTM)

• 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.


Checkpoint 9.2

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.


Checkpoint 9.2


Checkpoint 9.2


Checkpoint 9.2



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



YTM=?

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

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

0 1 2 3 … 11



• 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.


Step 3: Solve

• 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.



• Using Financial Calculator

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



• Using an Excel Spreadsheet

• YTM = RATE(nper, pmt,pv,fv)= RATE (11,65,-900,1000)= 7.89%


Step 4: Analyze

• 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 a discount bond.


Using Market Yield to Maturity Data

• 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.


Using Market Yield to Maturity Data (cont.)

• 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 similar 30-year US Treasury bond.

• Thus this corporate bond should earn 2.75% over

the 4.56% earned on treasury yield or 7.31%.



Promised Returns versus Expected Yield to Maturity

• 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 be equal to expected yield to maturity.


Promised Returns versus Expected Yield to Maturity (cont.)

• 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?



• 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 on 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?



• 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.


Checkpoint 9.3

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 of the bond?


Checkpoint 9.3


Checkpoint 9.3


Checkpoint 9.3



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

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

0 1 2 3 … 20

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.


Step 3: Solve


• 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– FV = 1000– PV = 954.36




• Bond Value = PV (rate, nper, pmt, fv)= PV (.09,20,85,1000)= $954.36


Step 4: Analyze

• 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 yield.


Step 4: Analyze (cont.)

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


Semiannual Interest Payments

• Corporate bonds typically pay interest to bondholders semiannually. We can adapt Equation (9-2a) from annual to semiannual payments as follows:


Checkpoint 9.4

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?


Checkpoint 9.4


Checkpoint 9.4


Checkpoint 9.4


Checkpoint 9.4



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



i= 9%Periods

Cash flow $42.5 $42.5 $42.5 $1,042.50

0 1 2 3 … 40

PV=?

$42.50 Semiannualinterest

$42.5 interest + $1,000 Principal

40 6-monthperiods



• Here we know the following:– Semiannual interest payments = $42.50– Principal amount or par value = $1,000– Time = 20 years or 40 periods– YTM or discount rate = 9% or 4.5% for 6-

months

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


Step 3: Solve


• Bond Value

= $ 42.5{[1-(1/(1.045)40] ÷ (.20)} + $1,000/(1.045)40

= $42.5 (18.40) + $171.93 = $954



• Using a Financial Calculator• Enter:

– N = 40– 1/y = 4.50– PMT = 42.50– FV = 1000– PV = 954




• Bond Value = PV (rate, nper, pmt, fv)= PV (.045,40,42.5,1000)= $954


Step 4: Analyze

• Using semi-annual compounding we get a value of $954 for AT&T bonds. This is very close to the value of $954.26 found using annual compounding.


9.3 Bond Valuation: Four Key Relationships


Bond Valuation: Four Key Relationships

• First Relationship The value of bond is inversely related to changes in the yield to maturity.

YTM = 12% YTM rises to 15%

Par value $1,000 $1,000Coupon rate 12% 12%Maturity date 5 years 5 yearsBond Value $1,000 $899.44

Bond Value Drops


Bond Valuation: Four Key Relationships (cont.)



• Since 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.



• Second 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.



• There are two sources of return from bond investment:– Periodic interest payments– Capital gain or loss when the bond is sold



• When a bond can be bought for less than its par value, it is called discount bond. For example, buying a $1,000 par value bond for $950.

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



• When a bond can be bought for more than its par value, it is called premium bond. For example, buying a $1,000 par value bond for $1,110.

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



• Third 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.





• Fourth 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.



9.4 Types of Bonds


Types of Bonds

• 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: Secured versus Unsecured, Priority of claim, Initial offering market, Abnormal risk, Coupon level, Amortizing or non-amortizing, and Convertibility.


Types of Bonds (cont.)

• Secured versus Unsecured

– Secured bonds have specific assets pledged to support repayment of the bond.

– Unsecured bond are referred to as debentures.

– Bonds secured by lien on real property is called a mortgage bond.



• Priority of Claim– The priority of claim refers to the order of

repayment when the firm’s assets are distributed, as in the case of liquidation.

– Secured bonds are paid first followed by debentures; Among debentures, subordinated debentures have lower priority than secured debt and unsubordinated debentures.



• Initial Offering Market

– Bonds are classified by where they were originally issued (in the domestic bond market or not).

– For example, Eurobonds are issued in a foreign country but are denominated in domestic currency. For example, a US corporation issuing bonds in Germany in US dollars.



• Abnormal Risk

– Junk, or high-yield, bonds have a below-investment grade bond rating. These bonds have a high risk of default as the firms that issued these bonds are facing severe financial problems.



• Coupon Level

– Bonds with a zero or very low coupon are called zero coupon bonds.

– These bonds are issued at substantial discounts from their par value and promise to repay a zero or very low coupon rate each year. The par value is repaid at the maturity of the bond.



• Amortizing or Non-Amortizing

– The payments from amortizing bonds, like a home mortgage, include both the interest and principal.

– The payments from a non-amortizing bonds include only interest. At maturity, the bonds repay the par value of bond.



• Convertibility

– Convertible bonds are debt securities that can be converted into a firm’s stock at a pre-specified price.



9.5 Determinants of Interest Rates


Determinants of Interest Rates

• As 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 Premium

• Quotes 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 Premium (cont.)

• The nominal return or interest rate on a note or bond can be thought of including four basic components:


Fisher Effect

• The 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.


Fisher Effect (cont.)

• Example 9.3 What will be 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

= .0679 or 6.79%



• We can approximate the real rate of interest as follows:

• Real Rate of Interest≈ Nominal interest rate – Inflation

premium


Checkpoint 9.5

Solving 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 $10,000 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?


Checkpoint 9.5



Assume now that you expect that inflation will be 5% over the coming year and want to analyze how much better off you will be if you place your savings in an account that also earns just 5%. What is the real rate of return in this circumstance?



• Let us assume that the prices of goods and services today is $1.00 per unit.

• With a 5% inflation, these goods and services will cost $1.05.

• Thus, $10,500 expected in the savings account at the end of the year will buy you only 10,000 units (10,500/1.05) at the end of the year.



Year 0 Year 1

Savings Account Balance $10,000.00 $10,500.00

Price Index (5% inf lat ion) $1.00 $1.05

Purchasing Power (units) 10,000.00 10,000.00



• We can estimate the real rate of interest by using equation 9-4b.


Step 3: Solve

• rreal = {(1+.05) ÷ (1+.05)} – 1

= 0%


Step 4: Analyze

• Here the nominal rate of interest is equal to the expected rate of inflation. Therefore, the real rate of return is equal to zero i.e. there is no increase in purchasing power from investing the savings at 5%.


Checkpoint 9.6

Solving for the Nominal Rate of InterestAfter considering a number of investment opportunities, you have decided that you should be able to earn a real return of 2% on your $10,000 in savings over the coming year. If the expected rate of inflation is expected to be 3.5% over the coming year, what nominal rate of return must you anticipate in order to earn the 2% real rate of return?


Checkpoint 9.6


Checkpoint 9.6



If you anticipate that the rate of inflation will now be 4% next year, holding all else the same, what rate of return will you need to earn on your savings in order to achieve a 2% increase in purchasing power?



• Let us assume that the prices of goods and services today is $1.00 per unit.

• If the expected rate of inflation is 4% and you want to be able to purchase 2% more, you will need to earn a nominal rate of interest on your savings that will allow you to buy 10,200 units at $1.04 each.



Year 0 Year 1

Savings Account Balance $10,000.00 $10,608

Price Index (5% inf lat ion) $1.00 $1.04

Purchasing Power (units) 10,000.00 10,200.00

Real rate (% increase in purchasing power)

2%

Interest rate of6.08% solvedin step 3



• Here we know the real rate of interest and the expected rate of inflation.

• We can use the Fisher model found in equation 9-4a to determine the nominal rate of interest.


Step 3: Solve

• rnominal =.02 + .04 + (.02 × .04)

= .0608 or 6.08%


Step 4: Analyze

• In order to achieve a 2% increase in purchasing power in the face of a 4% rate of inflation, you must earn a 6.08% rate on your savings.


Default Premium

• In addition to accounting for the time value of money and inflation, the interest rate that a firm’s bonds pay must also offer a default premium i.e. risk that the issuer will fail to repay interest and principal in a timely manner.


Maturity Premium – The Term Structure of Interest Rates

• Long-term bonds are more sensitive to interest rate changes.

• Maturity premium is the compensation that investors demand for bearing interest rate risk on long-term bonds.


Maturity Premium – The Term Structure of Interest Rates (cont.)

• 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.



Shifts in the Yield Curve

• The 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 (cont.)

• We observe a significant shift in the yield curve in figure 9-4 for short-term interest rates.

• Investors shifted their funds to the safety of Treasury securities, pushing up the prices and bringing down the yields.


Shifts in the Yield Curve (cont.)

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

• Figure 9-5 illustrates different shapes of yield curves at different dates.



Key Terms

• Amortizing bond• Bond rating• Bond indenture• Call provision• Collateral• Conversion feature


Key Terms (cont.)

• Convertible bond• Corporate bond• Coupon interest rate• Credit spread• Current yield• Debenture• Default premium


Key Terms (cont.)

• Discount bond• Eurobonds• Fisher effect• Fixed rate loan• Floating rate bonds• Floating rate• Inflation premium


Key Terms (cont.)

• Interest rate risk• Junk (high-yield) bonds• LIBOR• Maturity premium• Mortgage bonds• Nominal (or quoted) rate of interest• Non-amortizing bond


Key Terms (cont.)

• Par or face value of a bond• Private market transaction• Premium bond• Real rate of interest• Recovery rate• Secured debt• Spread to Treasury


Key Terms (cont.)

• Subordinated debentures• Term structure of interest rates• Transaction loans• Unsubordinated debentures• Yield curve• Yield to maturity• Zero coupon bond

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