Formula key
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 |
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 |
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 |
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 |
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 |
Bond Vocabulary
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 |
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 |