1、Chapter 5Interest Rates第1頁，共66頁。Chapter Outline5.1 Interest Rate Quotes and Adjustments5.2 Application: Discount Rates and Loans5.3 The Determinants of Interest Rates5.4 Risk and Taxes5.5 The Opportunity Cost of Capital第2頁，共66頁。Learning ObjectivesDefine effective annual rate and annual percentage ra

2、te.Given an effective annual rate, compute the n-period effective annual rate.Convert an annual percentage rate into an effective annual rate, given the number of compounding periods.Describe the relation between nominal and real rates of interest.Given two of the following, compute the third: nomin

3、al rate, real rate, and inflation rate.第3頁，共66頁。Learning Objectives (contd)Describe the effect of higher interest rates on net present values in the economy.Explain how to choose the appropriate discount rate for a given stream of cash flows, according to the investment horizon.Discuss the determina

4、nts of the shape of the yield curve.Explain why Treasury securities are considered risk free, and describe the impact of default risk on interest rates.Given the other two, compute the third: after-tax interest rate, tax rate, and before-tax interest rate.第4頁，共66頁。5.1 Interest Rate Quotes and Adjust

5、mentsThe Effective Annual RateIndicates the total amount of interest that will be earned at the end of one yearConsiders the effect of compoundingAlso referred to as the effective annual yield (EAY) or annual percentage yield (APY)第5頁，共66頁。5.1 Interest Rate Quotes and Adjustments (contd)Adjusting th

6、e Discount Rate to Different Time PeriodsEarning a 5% return annually is not the same as earning 2.5% every six months.General Equation for Discount Rate Period Conversion(1.05)0.5 1= 1.0247 1 = .0247 = 2.47%Note: n = 0.5 since we are solving for the six month (or 1/2 year) rate第6頁，共66頁。Textbook Exa

7、mple 5.1第7頁，共66頁。Textbook Example 5.1 (contd)第8頁，共66頁。Alternative Example 5.1ProblemSuppose an investment pays interest quarterly with the interest rate quoted as an effective annual rate (EAR) of 9%. What amount of interest will you earn each quarter? If you have no money in the bank today, how muc

8、h will you need to save at the end of each quarter to accumulate $25,000 in 5 years?第9頁，共66頁。Alternative Example 5.1SolutionFrom Equation 5.1, a 9% EAR is approximately equivalent to earning (1.09)1/4 1 = 2.1778% per quarter. To determine the amount to save each quarter to reach the goal of $25,000

9、in five years, we must determine the quarterly payment, C:第10頁，共66頁。Annual Percentage RatesThe annual percentage rate (APR), indicates the amount of simple interest earned in one year.Simple interest is the amount of interest earned without the effect of compounding.The APR is typically less than th

10、e effective annual rate (EAR).第11頁，共66頁。Annual Percentage Rates (contd)The APR itself cannot be used as a discount rate.The APR with k compounding periods is a way of quoting the actual interest earned each compounding period:第12頁，共66頁。Annual Percentage Rates (contd)Converting an APR to an EARThe EA

11、R increases with the frequency of compounding.Continuous compounding is compounding every instant.第13頁，共66頁。Annual Percentage Rates (contd)A 6% APR with continuous compounding results in an EAR of approximately 6.1837%.Table 5.1 Effective Annual Rates for a 6% APR with Different Compounding Periods第

12、14頁，共66頁。Textbook Example 5.2第15頁，共66頁。Textbook Example 5.2 (contd)第16頁，共66頁。Alternative Example 5.2ProblemA firm is considering purchasing or leasing a luxury automobile for the CEO. The vehicle is expected to last 3 years. You can buy the car for $65,000 up front , or you can lease it for $1,800 p

13、er month for 36 months. The firm can borrow at an interest rate of 8% APR with quarterly compounding. Should you purchase the system outright or pay $1,800 per month?第17頁，共66頁。Alternative Example 5.2 (contd)SolutionThe first step is to compute the discount rate that corresponds to monthly compoundin

14、g. To convert an 8% rate compounded quarterly to a monthly discount rate, compound the quarterly rate using Equations 5.3 and 5.1:第18頁，共66頁。Alternative Example 5.2 (contd)SolutionGiven a monthly discount rate of 0.66227%, the present value of the 36 monthly payments can be computed:Paying $1,800 per

15、 month for 36 months is equivalent to paying $57,486 today. This is $65,000 - $57,486 = $7,514 lower than the cost of purchasing the system, so it is better to lease the vehicle rather than buy it.第19頁，共66頁。5.2 Application: Discount Rates and LoansComputing Loan PaymentsPayments are made at a set in

16、terval, typically monthly.Each payment made includes the interest on the loan plus some part of the loan balance.All payments are equal and the loan is fully repaid with the final payment.第20頁，共66頁。5.2 Application: Discount Rates and Loans (contd)Computing Loan PaymentsConsider a $30,000 car loan wi

17、th 60 equal monthly payments, computed using a 6.75% APR with monthly compounding. 6.75% APR with monthly compounding corresponds to a one-month discount rate of 6.75% / 12 = 0.5625%.第21頁，共66頁。5.2 Application: Discount Rates and Loans (contd)Computing Loan PaymentsFinancial Calculator Solution 第22頁，

18、共66頁。5.2 Application: Discount Rates and Loans (contd)Computing the Outstanding Loan BalanceOne can compute the outstanding loan balance by calculating the present value of the remaining loan payments.第23頁，共66頁。Textbook Example 5.3第24頁，共66頁。Textbook Example 5.3 (contd)第25頁，共66頁。5.3 The Determinants

19、of Interest RatesInflation and Real Versus Nominal RatesNominal Interest Rate: The rates quoted by financial institutions and used for discounting or compounding cash flowsReal Interest Rate: The rate of growth of your purchasing power, after adjusting for inflation第26頁，共66頁。5.3 The Determinants of

20、Interest Rates (contd)The Real Interest Rate第27頁，共66頁。Textbook Example 5.4第28頁，共66頁。Textbook Example 5.4 (contd)第29頁，共66頁。Alternative Example 5.4ProblemIn the year 2008, the average 1-year Treasury Constant Maturity rate was about 1.82% and the rate of inflation was about 0.28%. What was the real in

21、terest rate in 2008?第30頁，共66頁。Alternative Example 5.4SolutionUsing Equation 5.5, the real interest rate in 2008 was:(1.82% 0.28%) (1.0028) = 1.54%Which is (approximately) equal to the difference between the nominal rate and inflation: 1.82% 0.28% = 1.54%第31頁，共66頁。Figure 5.1 U.S. Interest Rates and I

22、nflation Rates,19602009第32頁，共66頁。Investment and Interest Rate PolicyAn increase in interest rates will typically reduce the NPV of an investment.Consider an investment that requires an initial investment of $10 million and generates a cash flow of $3 million per year for four years. If the interest

23、rate is 5%, the investment has an NPV of: 第33頁，共66頁。Investment and Interest Rate Policy (contd)If the interest rate rises to 9%, the NPV becomes negative and the investment is no longer profitable: 第34頁，共66頁。Monetary Policy, Deflation, and the 2008 Financial CrisisWhen the 2008 financial crisis stru

24、ck, the Federal Reserve responded by cutting its short-term interest rate target to 0%. While this use of monetary policy is generally quite effective, because consumer prices were falling in late 2008, the inflation rate was negative, and so even with a 0% nominal interest rate the real interest ra

25、te remained positive. 第35頁，共66頁。The Yield Curve and Discount RatesTerm Structure: The relationship between the investment term and the interest rateYield Curve: A graph of the term structure第36頁，共66頁。Figure 5.2 Term Structure of Risk-Free U.S. Interest Rates, November 2006, 2007, and 2008第37頁，共66頁。T

26、he Yield Curve and Discount Rates (contd)The term structure can be used to compute the present and future values of a risk-free cash flow over different investment horizons.Present Value of a Cash Flow Stream Using a Term Structure of Discount Rates第38頁，共66頁。Textbook Example 5.5第39頁，共66頁。Textbook Ex

27、ample 5.5 (contd)第40頁，共66頁。Alternative Example 5.5ProblemCompute the present value of a risk-free three-year annuity of $500 per year, given the following yield curve:第41頁，共66頁。Alternative Example 5.5SolutionEach cash flow must be discounted by the corresponding interest rate:第42頁，共66頁。The Yield Cur

28、ve and the EconomyInterest DeterminationThe Federal Reserve determines very short-term interest rates through its influence on the federal funds rate, which is the rate at which banks can borrow cash reserves on an overnight basis. All other interest rates on the yield curve are set in the market an

29、d are adjusted until the supply of lending matches the demand for borrowing at each loan term. 第43頁，共66頁。The Yield Curve and the EconomyInterest Rate ExpectationsThe shape of the yield curve is influenced by interest rate expectations. An inverted yield curve indicates that interest rates are expect

30、ed to decline in the future. Because interest rates tend to fall in response to an economic slowdown, an inverted yield curve is often interpreted as a negative forecast for economic growth. Each of the last six recessions in the United States was preceded by a period in which the yield curve was in

31、verted.The yield curve tends to be sharply increasing as the economy comes out of a recession and interest rates are expected to rise. 第44頁，共66頁。Figure 5.3 Short-Term Versus Long-Term U.S. Interest Rates and Recessions第45頁，共66頁。Textbook Example 5.6第46頁，共66頁。Textbook Example 5.6 (contd)第47頁，共66頁。5.4

32、Risk and TaxesRisk and Interest RatesU.S. Treasury securities are considered “risk-free.” All other borrowers have some risk of default, so investors require a higher rate of return.第48頁，共66頁。Figure 5.4 Interest Rates on Five-Year Loans for Various Borrowers, March 2009第49頁，共66頁。Textbook Example 5.7

33、第50頁，共66頁。Textbook Example 5.7 (contd)第51頁，共66頁。After-Tax Interest RatesTaxes reduce the amount of interest an investor can keep, and we refer to this reduced amount as the after-tax interest rate.第52頁，共66頁。Textbook Example 5.8第53頁，共66頁。Textbook Example 5.8 (contd)第54頁，共66頁。5.5 The Opportunity Cost

34、of CapitalOpportunity Cost of Capital: The best available expected return offered in the market on an investment of comparable risk and term to the cash flow being discountedAlso referred to as Cost of Capital第55頁，共66頁。Chapter QuizWhat is the difference between and EAR and an APR quote?Why cant the

35、APR itself be used as a discount rate?What is an amortizing loan?What is the difference between a nominal and real interest rate?Why do corporations pay higher interest rates on their loans then the U.S. government?第56頁，共66頁。Chapter Quiz (contd)How do taxes affect the interest earned on an investmen

36、t? What about the interest paid on a loan?What is the opportunity cost of capital?第57頁，共66頁。Chapter 5Appendix第58頁，共66頁。Continuous Rates and Cash FlowsDiscount Rate of a Continuously Compounded APRSome investments compound more frequently than daily. As we move from daily to hourly to compounding eve

37、ry second, we approach the limit of continuous compounding, in which we compound every instant.The EAR for a Continuously Compounded APR第59頁，共66頁。Continuous Rates and Cash Flows (contd)Discount Rate of a Continuously Compounded APRAlternatively, if we know the EAR and want to find the corresponding continuously compounded APR, the formula is:The Continuously Compounded APR for an EARContinuously compounded rates are not often used in practice.第60頁，共66頁。Continuous Rates and Cash Flows (contd)Continuously Arri