Tài chính doanh nghiệp - Measuring and calculating interest rates and financial asset prices

Money and Capital Markets6C h a p t e rEighth EditionFinancial Institutions and Instruments in a Global MarketplacePeter S. RoseMcGraw Hill / IrwinSlides by Yee-Tien (Ted) FuMeasuring and Calculating Interest Rates and Financial Asset Prices Learning Objectives To learn how to measure and calculate interest rates and the prices of financial assets.To understand the relationship between the interest rate on a financial instrument and its market value.To look at the many different ways that banks and other lending institutions calculate the interest rates they charge borrowers for loans. Learning Objectives To determine how interest rates or yields on deposits in banks, credit unions, and other depository institutions are figured.Units of MeasurementFor Interest Rates and Security PricesThe interest rate is the price that is charged to a borrower for the loan of money. Interest Fee required by the lender forrate on = the borrower to obtain credit  100loanable Amount of credit madefunds available to the borrowerInterest rates are usually expressed as annualized percentages. However, both 360-day and 365-day years are commonly used. The compounding terms may also differ.Units of MeasurementFor Interest Rates and Security PricesA basis point equals 1/100 of a percentage point.Example10.5% = 10% + 50 basis points, or 1050 basis pointsUnits of MeasurementFor Interest Rates and Security PricesThe prices of common and preferred stock are measured today in many markets in terms of dollars and decimal fractions of a dollar (or some other currency unit).Example$40.25 per share (versus $40 1/4 in the recent past)Units of MeasurementFor Interest Rates and Security PricesBond prices are usually expressed in points and fractions of a point, with each point representing $1 on a $100 basis or $10 for a $1000 bond.ExampleA bond priced at 97 is selling for $97 on a $100 basis, or $970 for each $1000 in face value.Units of MeasurementFor Interest Rates and Security PricesSecurity dealers usually quote two prices for an asset.The higher ask price is the dealer’s selling price, while the lower bid price is the dealer’s buying price.The difference between the bid and ask prices – known as the spread – provides the dealer’s return for creating a market for the security.Measures of the Rate of Return (Yield)On a Financial AssetThe coupon rate of a security is the contracted interest rate that the security issuer agrees to pay at the time the security is issued.ExampleA bond with a par value of $1000 and a coupon rate of 9% pays an annual coupon of $90.Measures of the Rate of Return (Yield)On a Financial AssetThe current yield of a security is the ratio of the annual income (dividends or interest) generated by the security to its market value.ExampleThe current yield of a share of common stock selling for $30 in the market and paying an annual dividend of $3 to the shareholder is $3/$30 = 0.10, or 10%.Measures of the Rate of Return (Yield)On a Financial AssetThe yield to maturity of a financial asset is the rate of interest that the market is prepared to pay today for the financial asset.It is the rate that equates the purchase price (P) with the present value of all the expected annual net cash flows (CF) from the asset.Measures of the Rate of Return (Yield)On a Financial AssetA bond trades at a discount from par if its price is less than its par value, i.e. if its current yield to maturity is higher than its coupon rate. A bond trades at a premium over par if its price is more than its par value, i.e. if its current yield to maturity is lower than its coupon rate. A bond trades at par if its price equals its par value, i.e. if the current market interest rate on comparable securities equals its coupon rate. Measures of the Rate of Return (Yield)On a Financial AssetThe holding-period yield is the rate of return from an investment over its actual or planned holding period.It is the discount rate equalizing the purchase price (P0) of a financial asset with all the discounted net cash flows (CF) received from the asset from the time the asset is purchased until the time it is sold (in period n).Yield-Asset Price RelationshipsThe price of a security and its yield or rate of return are inversely related – a rise in yield implies a decline in price, while a fall in yield implies a rise in the security’s price.This inverse relationship can be seen by noting that investing funds in financial assets can be viewed from two different perspectives –  the borrowing and lending of money, and  the buying and selling of securities.Yield-Asset Price RelationshipsEquilibrium Security Prices and Interest Rates (Yields)InterestRateLoanable FundsrEQEDemand(borrowing)Supply(lending)PriceSecuritiesPEVEDemand(lending)Supply(borrowing)Interest-Rate DeterminationSecurity Price DeterminationYield-Asset Price Relationships demand for loanable fundsInterestRateLoanable FundsDSInterest-Rate Determination  supply of securitiesD’PriceSecuritiesSecurity Price DeterminationDSS’Yield-Asset Price Relationships supply of loanable fundsInterestRateLoanable FundsDSInterest-Rate Determination  demand for securitiesPriceSecuritiesSecurity Price DeterminationDSS’D’Interest RatesCharged or Paid by Institutional LendersThe simple interest method assesses interest charges on a loan only for the period of time that the borrower has actual use of the borrowed funds.Interest = principal  rate  termThe more frequently a borrower makes repayments on a loan, the lesser the total interest will be.Interest RatesCharged or Paid by Institutional LendersIn the add-on rate approach, interest is calculated on the full principal of the loan, and the sum of interest and principal payments is divided by the number of payments to determine the dollar amount of each payment.In a single payment loan, the simple interest and add-on methods give the same interest rate. However, as the number of installment payments increases, the borrower pays a higher effective rate under the add-on method.Interest RatesCharged or Paid by Institutional LendersThe discount method determines the total interest charged to the customer on the basis of the amount to be repaid. However, the borrower receives as proceeds of the loan only the difference between the total amount owed and the interest bill.Hence, the effective interest rate is Interest paid  100 Net loan proceedsInterest RatesCharged or Paid by Institutional LendersEach monthly payment of a home mortgage loan first covers in full the monthly interest on the outstanding principal. The remainder is then applied to the principal of the loan, such that the amount owed is reduced progressively.The monthly payment whereL = total amount owedr = annual loan interest ratet = number of years of the loanInterest RatesCharged or Paid by Institutional LendersThe U.S. Consumer Credit Protection Act of 1968 (Truth in Lending) requires lending institutions to calculate and tell the borrower the annual percentage rate (APR) he or she is actually paying. The constant ratio formula usually gives a close approximation to the true APR.m = number of payments in a yearc = annual interest costN = total number of paymentsP = principal of the loanInterest RatesCharged or Paid by Institutional LendersThe compounding of interest means that the lender or depositor earns interest income on both the principal amount and any accumulated interest.The formula for calculating the future value of a financial asset earning compound interest is:FV = future value of the assetP = principal value of the assetr = annual interest ratem = annual compounding frequencyt = term of the asset in yearsInterest RatesCharged or Paid by Institutional LendersThe U.S. Truth in Savings Act of 1991 requires depository institutions to use the daily average balance in a customer’s deposit over each interest-crediting period to determine the customer’s annual percentage yield (APY) for that deposit account.wherei = interest earnedb = daily average balanced = term in daysMoney and Capital Markets in CyberspaceThe measurement or calculation of interest rates is a popular subject on many websites. See, for example, ReviewUnits of Measurement for Interest Rates and Security PricesDefinition of Interest RatesBasis PointsSecurity PricesChapter ReviewMeasures of the Rate of Return, or Yield, on a Loan, Security, or other Financial AssetCoupon RateCurrent YieldYield to MaturityHolding-Period YieldYield-Asset Price RelationshipsChapter ReviewInterest Rates Charged or Paid by Institutional LendersSimple Interest RateAdd-On Rate of InterestDiscount MethodHome Mortgage Interest RateAnnual Percentage Rate (APR)Compound InterestAnnual Percentage Yield (APY)