Valuing bonds Cheat Sheet (2024)

Po

= Asset's price today (at time 0)

CFn

= Cash flow expected at time t

t

= time

r

= required return. Discount rate that reflects the asset's risk.

n

= Assets life / period it distri­butes cash flows

$C

= Coupon payment amount

$M

= par value maturity amount

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.

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

Certainty

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

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

Spread

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

Collateral

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

Debentures

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.

Callable

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

Fundam­ent­ally, a bond is just a loan

Bonds make intere­st-only payments until they mature

Principal

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

Coupon

A fixed amount of interest that a bond promises to pay investors

Usually semian­nually

Indenture

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

Premium

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

Discount

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

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

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

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

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

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

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