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Valuing bonds Cheat Sheet by

Valuing bonds

Formula key

= Asset's price today (at time 0)
= Cash flow expected at time t
= time
= required return. Discount rate that reflects the asset's risk.
= Assets life / period it distri­butes cash flows
= Coupon payment amount
= par value maturity amount

Required rate of return

The rate of return that investors expect or require an investment to earn given its risk.
Riskier = higher the return required by investors in the market­place
Purchase of investment means investor loses the opport­unity to invest their money in another asset. Opport­unity cost.
Po = CF1/(1 + r)1 + CF2/(1 + r)2 + ... + CFn/(1 + r)n

Asset valuation basics

In a market economy, ownership of an asset confers rights to stream of benefits generated by asset.
Benefits may be tangible, such as interest payments on bonds, or intang­ible, e.g. viewing a beautiful ring
Asset value = present value of all its future benefits
Finance theory focuses on tangible benefits, usually cash flows an asset pays over time
e.g. landlord. Incoming = Rental payments from tenants. Outgoing = Liabil­ities for mainta­ining premises, paying taxes, etc.
When selling an asset the market price should equal present value of all future net cash flows
Step 1:
Estimate $$ an investment distri­butes over time
Step 2:
Discount expected cash payments using time value of money maths
Therefore pricing an asset requires knowledge of
its future benefits
the approp­riate discount rate to convert future benefits into a present value
If an assets future benefits are uncertain then investors will apply a larger rate when discou­nting those benefits to present value
An inverse relati­onship exists between risk and value
Investors will pay a higher price for investment with more credible promise.
Riskier invest­ments must offer higher returns
Marginal benefit of owning an asset = right to receive cash flows it pays
Marginal cost = opport­unity cost of committing funds to this asset rather than to an equally risky altern­ative

Bond features

Floati­ng-rate bonds
Bonds that make coupon payments that vary through time. The coupon payments are usually tied to a benchmark market interest rate
also called variab­le-rate bonds
provide some protection against interest rate risk
If market interest rates increase, then eventu­ally, so do the bond’s coupon payments
Makes borrowers future cash obliga­tions unpred­ictable
Risk is transf­erred from buyer to issuer
London Interbank Offered Rate (LIBOR)
The interest rate that banks in London charge each other for overnight loans. Widely used as a benchmark interest rate for short-term fl oatingrate debt.
Cash rate
Rate Aus banks charge each other for overnight loans
The difference between the rate that a lender charges for a loan and the underlying benchmark interest rate
Also called the credit spread
to the benchmark interest rate, according to the risk of the borrower
Lenders charge higher spreads for less credit­worthy borrowers
Capital indexed bonds / inflation linked bonds
Issued by Aus govt, face value changes each year with inflation
Unsecured debt
Debt instru­ments issued by an entity backed only by faith and credit score of borrowing company
Subord­inated unsecured debt
Debt instru­ments issued by an entity which is backed only by the credit of the borrowing entity which is paid only after senior debt is paid
The specifi c assets pledged to secure a loan.
Mortgage bonds
A bond secured by real estate or buildings
Collateral trust bonds
A bond secured by financial assets held by a trustee
Usually backed by property
Equipment trust certif­icates
A bond often secured by various types of transp­ort­ation equipment
Pure discount bonds
Bonds that pay no interest and sell below par value. Also called zero-c­oupon bonds.
Conver­tible bond
A bond that gives investors the option to convert their bonds into the issuer’s common stock.
Exchan­geable bonds
Bonds issued by corpor­ations which may be converted into shares of a company other than the company that issued the bonds.
Bonds that the issuer can repurchase from investors at a predet­ermined price known as the call price
Call price
The price at which a bond issuer may call or repurchase an outsta­nding bond from investors
Putable bonds
Bonds that investors can sell back to the issuer at a predet­ermined price under certain conditions
Sinking fund
A provision in a bond indenture that requires the borrower to make regular payments to a third-­party trustee for use in repurc­hasing outsta­nding bonds, gradually over time
Protective covenants
Specify requir­ements that the borrower must meet as long as bonds remain outsta­nding

Bond Vocabulary

Fundam­ent­ally, a bond is just a loan
Bonds make intere­st-only payments until they mature
The amount of money on which interest is paid
Maturity date
The date when a bond’s life ends and the borrower must make the fi nal interest payment and repay the principal.
Par value (bonds)
The face value of a bond, which the borrower repays at maturity
Typically $1,000 for corporate bonds
A fixed amount of interest that a bond promises to pay investors
Usually semian­nually
A legal document stating the conditions under which a bond has been issued
Specifies dollar amount of coupon
Specifies when the borrower must make coupon payments
Coupon rate
The rate derived by dividing the bond’s annual coupon payment by its par value.
Coupon yield
The amount obtained by dividing the bond’s coupon by its current market price (which does not always equal its par value). Also called current yield
Might have additional features:
Call feature allows the issuer to redeem the bond at a predet­ermined price prior to maturity
Conversion feature grants bondho­lders right to redeem bonds for a predet­ermined number of shares of stock in borrowing firm
A bond that sells for more than its par value
Selling at a better than market return
As more investors buy the price goes up
Yield to maturity
The discount rate that equates the present value of the bond’s cash flows to its market price
A bond sells at a discount when its market price is less than its par value
Might be offset with a built-in gain at maturity

Changes in Issuer Risk

When macroe­conomic factors change
Yields may change simult­ane­ously on a wide range of bonds
Return on a particular bond can also change as market reassesses borrower's default risk (risk issuer could default on payments)
Changes may be positive or negative

Issuer types

Treasury bonds
Debt instru­ments issued by the federal government with maturities of up to 30 years
Corporate bonds
Issued by corpor­ations
Finance new invest­ments
Fulfil other needs
Range from 1 - 100 years
Under 10 years usually called a note means the same
Most corporate bonds have a par value of $1,000 and pay interest semian­nually
Australian government bonds
Issued by Australian government

Bond Markets

Larger than the stock market
Bond Price Quotations
bond prices are quoted as a percentage of par values
Yield spread
The diff erence in yield to maturity between two bonds or two classes of bonds with similar maturities
Basis point
1/100 of 1 percent; 100 basis points equal 1.000 percent
Bond ratings
Letter ratings assigned to bonds by specia­lized agencies that evaluate the capacity of bond issuers to repay their debts. Lower ratings signify higher default risk.
Junk bonds
Bonds rated below investment grade. Also known as high-yield bonds

Basic bond valuing equation

Bond makes a fixed coupon payment each year
Po = C / (1 + r)1 + C / (1 + r)2 + ... + C / (1 + r)n + M / (1 + r)n

Semiannual Compou­nding

Most bonds make 2 payments a year
Po = (C / 2) / (1 + r)1 + (C / 2) / (1 + r)2 + ... + (C / 2) / (1 + r)2n + M / (1 + r)2n

Factors affecting bond prices

A bonds market price changes frequently as time passes
Term to maturity
Whether a bond sells at a discount or a premium, its price will converge to par value (+ final interest payment) as maturity date draws near.
Economic Forces
Most important factor is prevailing market interest rate
Required return
When required return on a bond changes, bonds price changes in opposite direction
Higher bonds required return = lower its price, and vice versa
General lessons
Bond prices and interest rates move in opposite directions
Prices of long-term bonds display greater sensit­ivity to changes in interest rates than do prices of short-term bonds

Interest Rate Risk

Risk that changes in market interest rates will move bond price
Interest rates fluctuate widely, so investors must be aware of interest rate risk
Inherent in these instru­ments
Inflation is a main factor
Important because
When investors buy financial assets, they expect these invest­ments to provide a return that exceeds inflation rate.
Investors want to achieve a better standard of living by saving and investing their money
If asset returns do not exceed inflation investors are not better off for having invested
Real return
Bond yields must offer investors a positive real return
Approx­imately equals difference between stated or nominal return and inflation rate

Bond Markets

Many types of bonds in modern financial markets
Many bonds provide a steady, predic­table stream of income
Others have exotic features that make returns volatile and unpred­ictable
Bond trading occurs in either primary or secondary market
Primary market trading
Initial sale of bonds by firms or government entities
Might be through auction process
With help of investment bankers who assist bond issuers with design, marketing, and distri­bution of new bond issues
Once issued in primary market, investors trade them with each other in secondary market
Often purchased by instit­utional investors who hold bonds for a long time
Secondary market
Because instit­utions hold bond for a long time, trading in bonds can be somewhat limited
But bond market is large which means investors have a wide range of choices


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