# Valuing bonds Cheat Sheet by NatalieMoore

Valuing bonds

### 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

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