Interest Rate and Bond Valuation
Page 2: Interest Rate
Discuss the general features, yields, prices, ratings, popular types, and international issues of corporate bonds.
Describe interest rate fundamentals, the term structure of interest rates, and risk premiums.
Review the legal aspects of bond financing and bond cost.
Understand the key inputs and basic models used in the bond valuation process.
Apply the basic valuation model to bonds, and describe the impact of required return and time to maturity on bond values.
Explain yield to maturity (YTM), its calculation, and the procedure used to value bonds that pay interest semiannually.
Page 3: Interest Rate Fundamentals
Interest rate is usually applied to debt instruments such as bank loans or bonds.
It is the compensation paid by the borrower of funds to the lender.
From the borrower's point of view, it is the cost of borrowing funds.
Required return is the cost of funds obtained by selling an ownership interest.
Liquidity preference is the general tendency for investors to prefer short-term and more liquid securities.
Page 4: Real Rate of Interest
The real rate of interest is the rate that creates equilibrium between the supply of savings and the demand for investment funds.
It changes with changing economic conditions, tastes, and preferences.
Central Banks can initiate actions to increase the supply of credit in the economy, resulting in a lower real rate of interest and stimulating economic expansion.
Page 5: Nominal or Actual Rate of Interest (Return)
The nominal rate of interest is the actual rate of interest charged by the supplier of funds and paid by the demander.
It differs from the real rate of interest due to inflation and risk.
Investors demand a higher nominal rate of return if they expect inflation, which is called the expected inflation premium (IP).
Investors also demand a higher nominal rate of return on risky investments, known as the risk premium (RP1).
Page 8: Example Nominal and Real Rate of Interest
An example is given to illustrate the difference between nominal and real rate of interest.
Marilyn Carbo has $10 and can buy 40 pieces of candy today.
She could invest the $10 at a nominal rate of interest of 7% for one year.
After one year, she would have $10.70, but inflation would have increased the cost of candy by 4%.
Marilyn's real rate of return is 3%, which represents the increase in her buying power.
Page 9: Term Structure of Interest Rate
Term structure of interest rates refers to the relationship between the maturity and rate of return for bonds with similar levels of risk.
Yield curve is a graphic depiction of the term structure of interest rates.
It provides information on how rates vary between short-, medium-, and long-term bonds and can indicate future interest rate trends.
Page 13: Yield Curves
Yield curves can be upward-sloping, downward-sloping, or flat, depending on the interest rate environment.
The shape of the yield curve may affect a firm's financing decisions.
A downward-sloping yield curve may lead to reliance on cheaper, long-term financing, but there is a risk of future interest rate decreases.
An upward-sloping yield curve may lead to the use of cheaper, short-term financing, but there is a risk of rising interest rates and difficulty in refinancing short-term loans.
Page 14: Theories of Term Structure
There are three main theories of term structure: Market Segmentation Theory, Expectations Theory, and Liquidity Preference Theory.
The Expectations Theory suggests that the yield curve reflects investor expectations about future interest rates.
An expectation of rising interest rates results in an upward-sloping yield curve, while an expectation of declining rates results in a downward-sloping yield curve.
Page 16: Expectations Theory
Investors believe that interest rates will decline in the future
A 5-year Treasury note currently offers a 3% annual return
Investors expect the rate on a 5-year Treasury note to be 2.5% in 5 years
According to the expectations theory, the return that a 10-year Treasury note has to offer today is 2.75%
The yield curve is downward sloping
Page 17: Liquidity Preference Theory
Long-term rates are generally higher than short-term rates
Short-term investments are perceived as more liquid and less risky
Borrowers must offer higher rates on long-term bonds to entice investors away from short-term securities
Borrowing on a long-term basis reduces uncertainty about future borrowing costs
Page 18: Market Segmentation Theory
The market for loans is segmented based on maturity
The supply and demand for loans within each segment determine prevailing interest rates
The slope of the yield curve is determined by the relationship between prevailing rates in each market segment
Page 19: Conclusion on Term Structure Theories
The slope of the yield curve is affected by interest rate expectations, liquidity preferences, and the equilibrium of supply and demand in the short- and long-term market segments
Upward-sloping yield curves result from expectations of rising interest rates, lender preferences for shorter-maturity loans, and a greater supply of short-term loans relative to demand
Downward-sloping yield curves result from the opposite conditions
Page 20: Risk Premiums - Issuer and Issue Characteristics
The nominal rate of interest for a security includes the risk-free rate, inflation expectations premium, and risk premium
Risk premiums vary based on specific issuer and issue characteristics
Page 21: Risk Premiums - Issuer and Issue Characteristics
Risk premiums consist of issuer- and issue-related components such as business risk, financial risk, interest rate risk, liquidity risk, tax risk, default risk, maturity risk, and contractual provision risk
Securities issued by firms with a high risk of default and long-term maturities with unfavorable contractual provisions have the highest risk premiums and returns
Page 22: Debt-Specific Issuer- and Issue-Related Risk Premium Components
Default risk refers to the possibility that the issuer of debt will not pay the contractual interest or principal as scheduled
Maturity risk refers to the fact that the longer the maturity, the more the value of a security will change in response to a given change in interest rates
Contractual provision risk includes conditions in a debt agreement or stock issue that can reduce or increase risk
Page 23: Corporate Bonds
Coupon interest rate is the percentage of a bond's par value that will be paid annually as interest
Corporate bonds are long-term debt instruments indicating that a corporation has borrowed money and promises to repay it in the future
Most bonds have maturities of 10 to 30 years and a par value of $1,000
Page 24: Legal Aspects of Corporate Bonds
A bond indenture is a legal document that specifies the rights of bondholders and the duties of the issuing corporation
It includes descriptions of interest and principal payments, standard and restrictive provisions, sinking-fund requirements, and security interest provisions
The borrower must maintain accounting records, supply audited financial statements, pay taxes and other liabilities, and maintain facilities
Page 25: Legal Aspects of Corporate Bonds
Restrictive covenants are provisions in a bond indenture that place operating and financial constraints on the borrower
Standard provisions specify recordkeeping and general business practices that the bond issuer must follow to protect bondholders against increases in borrower risk
Page 26: Restrictive Covenants
Restrictive covenants include requirements for minimum liquidity, limitations on cash dividend payments, prohibition of selling accounts receivable, constraints on subsequent borrowing, and fixed-asset restrictions
Page 27: Violation of Restrictive Covenants
Violation of any standard or restrictive provision gives bondholders the right to demand immediate repayment of the debt
Bondholders evaluate violations to determine if they jeopardize the loan and can choose to demand repayment, continue the loan, or alter the terms of the bond indenture
Page 28: Sinking-Fund Requirements and Security Interest Trustee
Sinking-fund requirements are a provision for the systematic retirement of bonds prior to their maturity
Security interest specifies collateral pledged against the bond and how it is maintained
A trustee acts as a "watchdog" on behalf of bondholders and can take actions if the terms of the indenture are violated
Page 29: Impact of Bond Maturity, Cost of Bonds to the Issuer, Impact of the Cost of Money, Impact of Offering Size, Impact of Issuer's Risk
The longer the maturity of the bond, the less accuracy there is in predicting future interest rates and the greater the bondholders' risk.
Greater chance of default for longer-term bonds.
Bond flotation and administration costs per dollar borrowed decrease with increasing offering size.
Larger offerings result in greater risk of default, increasing the risk to bondholders.
The greater the issuer's default risk, the higher the interest rate.
Risk can be reduced through appropriate restrictive provisions in the bond indenture.
Bondholders must be compensated with higher returns for taking greater risk.
The cost of money in the capital market determines a bond's coupon interest rate.
The rate on U.S. Treasury securities of equal maturity is used as the lowest-risk cost of money.
A risk premium is added to the basic rate to reflect factors such as maturity, offering size, and issuer's risk.
Page 30: General Features of a Bond Issue
Convertible bonds: Bondholders can change each bond into a stated number of shares of common stock.
Call Feature: Issuer has the opportunity to repurchase bonds at a stated call price prior to maturity.
Call Premium: The amount by which a bond's call price exceeds its par value.
Stock Purchase Warrants: Instruments that give holders the right to purchase a certain number of shares of the issuer's common stock at a specified price over a certain period of time.
Page 31: Stock Purchase Warrants, Call Feature, Call Premium
Stock Purchase Warrants enable the issuer to pay a slightly lower coupon interest rate.
Call Feature allows an issuer to call an outstanding bond when interest rates fall and issue a new bond at a lower interest rate.
Callable bonds have a higher interest rate than noncallable bonds of equal risk to compensate bondholders for the risk of having the bonds called away from them.
Page 32: Bond Yield, Current Yield
Current Yield: A measure of a bond's cash return for the year, calculated by dividing the bond's annual interest payment by its current price.
Current yield indicates the cash return for the year from the bond but does not measure the total return.
Yield, or rate of return, on a bond is frequently used to assess a bond's performance over a given period of time.
Three widely cited bond yields: Current Yield, Yield to Maturity, Yield to Call.
Page 33: Bond Prices, Data on Selected Bonds
Bond trading and price data are not readily available to individual investors.
Bonds are quoted as a percentage of par value.
Corporate bonds are quoted in dollars and cents.
Bond prices represent the final price at which the bond traded on the current day.
Yield to Maturity (YTM) is the compound annual rate of return earned on the bond if held to maturity.
Page 34: Bond Ratings, Moody's and Standard & Poor's Bond Ratings
Independent agencies assess the riskiness of publicly traded bond issues.
Ratings reflect the likely payment of bond interest and principal.
High-quality bonds provide lower returns than lower-quality bonds.
Expected ratings of a bond issue affect salability and cost.
Page 35: Common Types of Bonds, Debentures, Income Bonds
Debentures: Unsecured bonds that only creditworthy firms can issue.
Income Bonds: Payment of interest is required only when earnings are available.
Subordinated Debentures: May have other unsecured bonds subordinated to them.
Page 36: Common Types of Bonds, Mortgage Bonds, Equipment Trust Certificates, Collateral Trust Bonds
Mortgage Bonds: Secured by real estate or buildings.
Equipment Trust Certificates: Used to finance "rolling stock" like airplanes, trucks, boats, railroad cars.
Collateral Trust Bonds: Secured by stock and/or bonds owned by the issuer.
Page 37: Common Types of Bonds
Floating-rate bonds
Debt rated Ba or lower by Moody's or BB or lower by Standard & Poor's
Used by rapidly growing firms to obtain growth capital
Often used to finance mergers and takeovers
High risk bonds with high yields
Junk bonds
High risk bonds with high yields
Often yield 2% to 3% more than the best-quality corporate debt
Zero- (or low-) coupon bonds
Issued with no or very low coupon rate
Sold at a large discount from par
Investor's return comes from gain in value
Callable at par value
Adjustable-rate bonds
Stated interest rate adjusted periodically within stated limits
Popular when future inflation and interest rates are uncertain
Tend to sell at close to par due to automatic adjustment to changing market conditions
Some issues provide for annual redemption at par at the option of the bondholder
Page 38: Common Types of Bonds (continued)
Bonds that can be redeemed at par
Option for bondholder to redeem at specific dates or when certain actions are taken by the firm
Yield is lower than non-putable bonds
Extendible notes
Short maturities, typically 1 to 5 years
Can be renewed for a similar period at the option of holders
Similar to a floating-rate bond
Page 39: International Bond Issues
Foreign bond
Bond issued by a foreign corporation or government
Denominated in the investor's home currency and sold in the investor's home market
Eurobond
Bond issued by an international borrower
Sold to investors in countries with currencies other than the bond's denomination
Two principal financial markets for international bond issues: Eurobond market and foreign bond market
Largest foreign-bond markets: Japan, Switzerland, and the United States
Page 40: Valuation Fundamentals
Valuation
Process that links risk and return to determine the worth of an asset
Applies to various assets such as bonds, stocks, income properties, etc.
Three key inputs to the valuation process:
Cash flows (returns)
Timing
Measure of risk, which determines the required return
Page 41: Cash Flows (Returns)
Cash flow estimates for three assets:
Stock in Michaels Enterprises
Expect to receive cash dividends of $300 per year indefinitely
Oil well
Expect to receive cash flow of $2,000 at the end of year 1, $4,000 at the end of year 2, and $10,000 at the end of year 4
Well to be sold at the end of year 4
Original painting
Expect to sell the painting in 5 years for $85,000
Value of an asset depends on the cash flow(s) it is expected to provide over the ownership period
Page 42: Timing
Cash flow estimates must be combined with timing of the cash flows
Greater risk can lower the value of a cash flow
Risk can be incorporated by using a higher required return or discount rate
Page 43: Valuation Fundamentals (continued)
Example of valuing an original painting in two scenarios:
Certainty scenario
Painting contracted to be sold for $85,000 in 5 years
Use risk-free rate of 3% as the required return
High-risk scenario
Painting's sale price in 5 years could range between $30,000 and $140,000
Use a 15% required return
Required return captures risk and can be subjective
Page 44: Basic Valuation Model
Value of any asset is the present value of all future cash flows it is expected to provide
Value is determined by discounting the expected cash flows back to their present value
Required return is used as the appropriate discount rate
Page 45: Valuation Fundamentals (continued)
Example of valuing assets using the valuation equation:
Michaels Enterprises stock: $300 / 0.12 = $2,500
Oil well investment: value estimated using a 20% required return
Painting: expected $85,000 lump sum payment in 5 years discounted at 15%
Page 47: Bond Valuation
Basic valuation equation can be customized for valuing specific securities
Bonds are long-term debt instruments used by business and government to raise money
Most corporate bonds pay interest semiannually, have an initial maturity of 10 to 30 years, and have a par value of $1,000
Page 48: Bond Valuation (continued)
Example of a bond issued by Mills Company
Investors receive $100 annual interest and $1,000 par value at the end of the tenth year
Page 49: Basic Bond Valuation
The value of a bond is the present value of the payments its issuer is obligated to make until it matures.
The basic model for bond valuation is given by an equation.
Bond value can be calculated using a financial calculator or a spreadsheet.
Page 50: Bond Valuation Example
Tim Sanchez wants to determine the current value of the Mills Company bond.
The bond has an annual interest payment of $100, a coupon interest rate of 10%, a par value of $1,000, and a maturity of 10 years.
The bond value computations are depicted on a timeline.
Page 51: Bond Valuation Example using Spreadsheet
The bond value, annual interest, and required return are entered into a spreadsheet.
The bond value is calculated using the PV function in Excel.
The result is a negative value, indicating the price that must be paid to acquire the bond.
Page 52: Bond Value Behavior
The value of a bond in the marketplace is rarely equal to its par value.
Bonds can be valued below par (discount) or above par (premium) due to various economic forces and the passage of time.
Required return and time to maturity impact bond value.
Page 53: Required Returns and Bond Values
When the required return on a bond differs from the coupon interest rate, the bond's value will differ from its par value.
The required return can be influenced by changes in economic conditions or the firm's risk.
When the required return is greater than the coupon interest rate, the bond sells at a discount.
When the required return falls below the coupon interest rate, the bond sells at a premium.
Page 54: Required Returns and Bond Values (Continued)
The bond's value equals its par value when the required return equals the coupon interest rate.
The bond's value can be calculated using the equation provided.
Page 55: Required Returns and Bond Values (Continued)
The inverse relationship between bond value and the required return is shown in a figure.
As the required return increases, the bond value decreases, and vice versa.
Page 56: Time to Maturity and Bond Values
The value of a bond approaches its par value as time moves closer to maturity.
Time to maturity affects bond value when the required return is different from the coupon interest rate.
Constant required returns and changing required returns are factors to consider.
Page 57: Time to Maturity and Bond Values (Continued)
The behavior of bond values over time is depicted in a figure.
The bond's value approaches its par value as the discount or premium declines with the passage of time.
Page 58: Time to Maturity and Bond Values (Continued)
Rising interest rates decrease bond values, causing concern for bondholders.
Shorter maturities have less interest rate risk compared to longer maturities.
Changing required returns impact bond values differently based on the time to maturity.
Page 59: Time to Maturity and Bond Values (Continued)
The effect of changing required returns on bond values with different maturities is illustrated using the example of Mills Company's bond.
The impact on bond value caused by a given change in the required return is less for shorter time to maturity.
Page 60: Yield to Maturity (YTM)
Yield to maturity is the compound annual rate of return earned on a bond held to maturity.
When the bond value differs from par, the yield to maturity differs from the coupon interest rate.
The YTM can be found using a financial calculator, Excel spreadsheet, or trial and error.
Page 61: Yield to Maturity (YTM) Example
Earl Washington wants to find the YTM on Mills Company's bond.
The bond's cash flows are entered into an Excel spreadsheet.
Excel's internal rate of return function is used to calculate the YTM, which equates the bond's price to the present value of its cash flows.
Page 62: YIELD TO MATURITY (YTM)
Earl Washington wants to find the YTM on Mills Company's bond.
Bond details:
Selling price: $1,080
Coupon interest rate: 10%
Par value: $1,000
Interest payment frequency: Annually
Time to maturity: 10 years
Page 63: SEMIANNUAL INTEREST AND BOND VALUES
Steps to convert annual interest to semiannual interest:
Divide the annual interest by 2.
Multiply the number of years to maturity by 2 to get the number of 6-month periods to maturity.
Divide the required stated annual return for similar-risk bonds that pay semiannual interest by 2 to get the semiannual rate.
To value bonds paying interest semiannually, the present value needs to be found.
Formulas for annual and semiannual interest payments are provided.
Page 64: SEMIANNUAL INTEREST AND BOND VALUES Example
Example using the Mills Company bond:
Bond pays interest semiannually.
Required stated annual return (rd) is 12% for similar-risk bonds with semiannual interest.
The value of the Mills Company bond with semiannual interest at a required return of 12% can be calculated using the provided equation or an Excel spreadsheet.
When comparing the value with semiannual interest ($887.00) to the value with annual interest, it is lower. This is because the bond sells at a discount.
Bonds selling at a premium will have a higher value with semiannual