Chapter 6 interest rate & bond valuation

 Explain and apply yield to maturity YTM to value semi annual interest paying bonds...  Risk Free Rate: The required return on a risk free asset Treasury bonds.. Term Structure Of Int

Learning Goals:

 Understand the fundamentals of interest rates.

 Describe the term structure of interest rates and risk premiums.

 Understand the legal aspects of bond financing and bond cost.

 Describe general features of bonds.

 Explain and apply the bond valuation model.

 Explain and apply yield to maturity (YTM) to value semi annual interest paying bonds.



Interest Rate Fundamentals

 Interest rates act as a regulating device that control the flow of funds between suppliers and demanders.

 Interest Rate: The compensation paid by a borrower

of funds to the lender, expressed as a percentage.

 Required Rate Of Return: The cost of funds to a

supplier/lender Reflects the lender’s expected rate

of return on an investment.

Interest Rate Fundamentals

 Real Rate Of Interest: The rate where demand (for

investment funds) equals supply (of savings funds) in the absence of inflation or liquidity preferences.

Assumed to be stable and around 1 – 2%.

 Risk Free Rate: The required return on a risk free

asset (Treasury bonds).

Includes the real rate of interest and the inflationary expectation.

Interest Rate Fundamentals

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Nominal Rate Of Interest

 Is the actual rate of interest charged by the lender and paid by the borrower.

 Includes inflation and risk components.

 Is calculated by:

[Equation 6.1]

Where:

r 1 = Nominal (actual) rate of return

r * = Real rate of interest

Term Structure Of Interest

Rates

 Is the relationship between interest rates and their time to maturity.

 Can be graphically depicted on a yield curve.

 The yield to maturity is the annual rate of return

earned by a debt security held to maturity.

 At any point in time the yield curve will show the relationship between the debt’s remaining time to maturity and its yield to maturity.

 Three types of yield curves:

1 Downward Sloping (Inverted) – longer term

borrowing is cheaper than short term.

2 Upward Sloping (Normal) – short term

borrowing is cheaper than longer term.

3 Flat – longer and short term borrowing costs are

similar.

Term Structure Of Interest

Rates – Yield Curves

 Used to explain the general shape of the yield curve.

 Three Theories:

1 Expectation Theory: The yield curve reflects

investor expectations about future interest rates and inflation.

2 Liquidity Preference Theory: Long term rates will

tend to be higher than short term rates.

3 Market Segmentation Theory: The market for

loans is segmented on the basis of maturity and that the supply and demand for loans within each segment determine its prevailing interest rate.

Term Structure Of Interest

Rates – Theories

Risk Premiums

 Vary with specific issuer and issue characteristics.

 Includes a number of issuer and issue related

 Coupon Interest Rate: The percentage of a bond’s

par value that will be paid annually as interest

[generally paid in two semi annual instalments].

 The longer the maturity, the higher the coupon rate.

 The larger the issue, the lower the coupon rate.

 The riskier the issuer, the higher the coupon rate.

Legal Aspects Of Bonds

 Bond Trust Deed: A legal document that specifies

the rights of the bondholders and the responsibilities

of the issuing corporation

Legal Aspects & Costs Of

Issuing Bonds

 Trustee:

 The cost of issuing bonds (rate of interest payable) is affected by a number of factors, including:

 Maturity

 Offering size

 Issuer’s risk

Features Of A Bond & Interest

Rate Securities Issue

 Conversion Feature: Allows bondholders to convert

their bonds to a stated number of shares.

 Call Feature: Allows issuers to repurchase bonds

prior to maturity at a set (call) price.

 Share Price Warrants: Give bondholders the right to

purchase a certain number of shares at a specified price over a certain period of time.

Common Interest Rate

Securities

 Floating rate notes

 Convertible notes

 Hybrid debt securities

 Asset backed securities

Bond Quotations & Ratings

 Quotations: Information on bonds, shares and

other securities, including as current price data and statistics on recent price behaviour.

 Bond Ratings: Derived from financial ratios and

cash flow analysis to assess the likely payment

of bond interest and principal

Informs investors about the risk profile of the

issuer.

Bond Ratings

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 Collateral Trust Bonds

 Equipment Trust Certificates

Unsecured

Secured

 The process that links risk and return to

determine the worth of an asset.

 Three key inputs:

1 Cash Flows

2 Timing

3 Risk/Required Return

The Basic Valuation Model

n

nr

CF r

CF r

CF V

) 1 (

) 1 ( ) 1

21

10

The Basic Valuation Model

The Basic Valuation Model

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Bond Valuation

 The value of a bond is the present value of all future cash flows the issuer is contractually obliged to

make between now and maturity

[Equation 6.7a]

Where:

B 0 = Value of the bond at time 0

I = Annual interest paid in dollars

r d = Required rate of return

M = Par value in dollars

n = Number of years to maturity

) (

)

0 I PVIFA rd n M PVIF rd n

Bond Valuation

Bond Value Behaviour

 Discount: The amount by which a bond sells below

its par value.

 Premium: The amount by which a bond sells above

its par value.

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 Time To Maturity: As the bond approaches

maturity, its value will approach par

 Changing Required Return: Changes in market

interest rates will change the required return and consequently the value of the bond.

Bond Value Behaviour

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 Yield To Maturity: The rate of return that investors

earn if they buy a bond at a specific price and hold

it until maturity.

 Semi Annual Interest: Uses a similar process to

compounding interest semi annually, except we are finding present value rather than future value.

Bond Value Behaviour