Tài chính doanh nghiệp - Chapter 6: Measuring and calculating interest rates and financial asset prices

Chapter 6Measuring and Calculating Interest Rates and Financial Asset Prices Learning Objectives To explore the important relationships between the interest rates on bonds and other financial instruments and their market value or price.To look at the many different ways lending institutions may calculate the interest rates they charge borrowers for loans.To determine how interest rates or yields on deposits in banks, credit unions, and other depository institutions are figured.IntroductionMany different interest-rate measures attached to different types of financial assets have been developed, leading to considerable confusion, especially for small borrowers and savers.In this chapter, we will examine the methods most frequently used to measure interest rates and the prices of financial assets in the money and capital markets.Units of MeasurementFor Interest Rates and Asset 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 Asset 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 Asset 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 Asset 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 Asset PricesMany security dealers who act as “market makers” 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 interest rate on a loan or other financial asset is not necessarily a true reflection of the yield or rate of return actually earned by the lender during the life of the asset.Some borrowers may default on all or a portion of their promised payments.The market value of the financial asset may rise or fall.Measures of the Rate of Return (Yield)On a Financial AssetThe perpetuity rate is the return on a financial instrument that never matures, but promises a fixed income to its holder every year ad infinitum into the future.Annual rate of return on a perpetual financial instrument = Annual cash flow promised . current price or present valueMeasures of the Rate of Return (Yield)On a Financial AssetThe coupon rate of a bond or some other debt 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 financial asset is the ratio of the annual income (dividends or interest) generated by the asset 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 (YTM) 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 m).Measures of the Rate of Return (Yield)On a Financial AssetExampleA 5-year corporate bond has a face value of $1,000. Its promised annual coupon rate is 10% and it pays $50 in interest every 6 months. The bond is currently selling for $900.Yield to maturity  12.8%Measures of the Rate of Return (Yield)On a Financial AssetExampleShares of common stock issued by General Electric Corporation are currently selling for $40 per share. Dividends of $2 per share are expected each year. An investor plans to hold the stock for two years and then sell out at an expected price of $50 per share.Holding period yield  16.5%Measures of the Rate of Return (Yield)On a Financial AssetThe bank discount rate is widely used for short-term loans and securities traded daily in the money market on which there is no intermediate payment before the asset matures.The discount rate =face value  purchase price  360 days/year . face value days to maturityThe YTM-equivalent return measure =face value  purchase price  365 days/year . purchase price days to maturityYield-Asset Price RelationshipsThe price of a financial asset (especially for a bond or some other debt security) and its yield or rate of return are inversely related – a rise in yield implies a decline in price, and vice versa.This principle can be reinforced 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 financial assets.Yield-Asset Price RelationshipsEquilibrium Asset Prices and Interest Rates (Yields)InterestRateLoanable FundsrEQEDemand(borrowing)Supply(lending)PriceAssetsPEAEDemand(lending)Supply(borrowing)Interest-Rate DeterminationAsset Price DeterminationYield-Asset Price Relationships demand for loanable fundsInterestRateLoanable FundsDSInterest-Rate Determination  supply of securitiesD’PriceAssetsAsset Price DeterminationDSS’Yield-Asset Price Relationships supply of loanable fundsInterestRateLoanable FundsDSInterest-Rate Determination  demand for securitiesPriceAssetsAsset Price DeterminationDSS’D’Yield-Asset Price RelationshipsInterest rates and corporate stock (equity) prices also frequently move in opposite directions (though by no means is this always the case).For example, if interest rates rise, bonds and other debt instruments now offering higher yields become more attractive relative to stocks, resulting in increased stock sales and declining equity prices.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 loan 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 APR, which measures the yearly cost of credit, includes not only interest costs but also any transaction fees or service charges imposed by the lender.Interest 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 daysMarkets on the NetBankrate.com at www.bankrate.comCompare Interest Rates at www.compareinterestrates.comFederal Reserve System at www.federalreserve.govFinancial Power Tools at www.financialpowertools.comMarkets on the NetInterest Rate Calculator at www.interestratecalculator.comLocal Bank Rates on Loans and Savings at www.digitalcity.comThe Credit Card Analyzer at www.creditcardanalyzer.comChapter ReviewIntroductionUnits of Measurement for Interest Rates and Asset PricesCalculating and Quoting Interest RatesBasis PointsPrices of Stocks and BondsChapter ReviewMeasures of the Rate of Return, or Yield, on a Loan, Security, or other Financial AssetRate of Return on a Perpetual Financial InstrumentCoupon RateCurrent YieldYield to MaturityHolding-Period YieldBank Discount RateChapter ReviewYield-Asset Price RelationshipsInterest Rates and the Prices of Debt SecuritiesInterest Rates and Stock PricesChapter ReviewInterest Rates Charged by Institutional LendersSimple Interest RateAdd-On Rate of InterestDiscount Loan MethodHome Mortgage Interest RateAnnual Percentage Rate (APR)Compound InterestAnnual Percentage Yield (APY) on Deposits