《公司理财第七版chap005》由会员分享，可在线阅读，更多相关《公司理财第七版chap005（28页珍藏版）》请在金锄头文库上搜索。
1、5-2,Money has a time value. It can be expressed in multiple ways:A dollar today held in savings will grow.A dollar received in a year is not worth as much as a dollar received today.,Time Value of Money,5-3,Future Values,Future Value: Amount to which an investment will grow after earning interest.Le
2、t r = annual interest rate Let t = # of yearsSimple Interest Compound Interest,5-4,Simple Interest: Example,Interest earned at a rate of 7% for five years on a principal balance of $100.Example - Simple InterestToday Future Years1 2 3 4 5 Interest Earned Value 100 Value at the end of Year 5: $135,7
3、107,7 114,7 121,7 128,7 135,5-5,Interest earned at a rate of 7% for five years on the previous years balance.Example - Compound InterestToday Future Years1 2 3 4 5 Interest Earned Value 100,Compound Interest: Example,7 107,7.49 114.49,8.01 122.50,8.58 131.08,9.18 140.26,Value at the end of Year 5 =
4、$140.26,5-6,The Power of Compounding,Interest earned at a rate of 7% for the first forty years on the $100 invested using simple and compound interest.,5-7,Present Value,What is it?,Why is it useful?,5-8,Present Value,Present Value:,Discount Rate:,Discount Factor:,Recall: t = number of years,5-9,Pre
5、sent Value: Example,Always ahead of the game, Tommy, at 8 years old, believes he will need $100,000 to pay for college. If he can invest at a rate of 7% per year, how much money should he ask his rich Uncle GQ to give him?,Note: Ignore inflation/taxes,5-10,The PV formula has many applications. Given
6、 any variables in the equation, you can solve for the remaining variable.,Time Value of Money (applications),5-11,Present Values: Changing Discount Rates,Discount Rates,The present value of $100 to be received in 1 to 20 years at varying discount rates:,5-12,PV of Multiple Cash Flows,The present val
7、ue of multiple cash flows can be calculated:,Recall: r = the discount rate,5-13,Multiple Cash Flows: Example,Your auto dealer gives you the choice to pay $15,500 cash now or make three payments: $8,000 now and $4,000 at the end of the following two years. If your cost of money (discount rate) is 8%,
8、 which do you prefer?,* The initial payment occurs immediately and therefore would not be discounted.,5-14,Perpetuities,Let C = Yearly Cash Payment PV of Perpetuity:,What are they?,Recall: r = the discount rate,5-15,Perpetuities: Example,In order to create an endowment, which pays $185,000 per year
9、forever, how much money must be set aside today if the rate of interest is 8%?What if the first payment wont be received until 3 years from today?,5-16,Annuities,What are they? Annuities are equally-spaced, level streams of cash flows lasting for a limited period of time.,Why are they useful?,5-17,P
10、resent Value of an Annuity,Let: C = yearly cash paymentr = interest rate t = number of years cash payment is received,The terms within the brackets are collectively called the “annuity factor.”,5-18,Annuities: Example,You are purchasing a home and are scheduled to make 30 annual installments of $10,
11、000 per year. Given an interest rate of 5%, what is the price you are paying for the house (i.e. what is the present value)?,5-19,Future Value of Annuities: Example,You plan to save $4,000 every year for 20 years and then retire. Given a 10% rate of interest, how much will you have saved by the time
12、 you retire?,5-20,Annuity Due,How does it differ from an ordinary annuity?,What is it?,Recall: r = the discount rate,How does the future value differ from an ordinary annuity?,5-21,Annuities Due: Example,Example: Suppose you invest $429.59 annually at the beginning of each year at 10% interest. Afte
13、r 50 years, how much would your investment be worth?,5-22,Interest Rates: EAR & APR,What is EAR?What is APR?How do they differ?,5-23,*where MR = monthly interest rate,EAR & APR Calculations,Effective Annual Interest Rate (EAR):,Annual Percentage Rate (APR):,5-24,EAR and APR: Example,Given a monthly
14、rate of 1%, what is the Effective Annual Rate(EAR)? What is the Annual Percentage Rate (APR)?,5-25,Inflation,What is it?,What determines inflation rates?,What is deflation?,5-26,Inflation and Real Interest,Exact calculation:,Approximation:,5-27,Inflation: Example,If the nominal interest rate on your interest-bearing savings account is 2.0% and the inflation rate is 3.0%, what is the real interest rate?,5-28,Appendix A: Inflation,Annual U.S. Inflation Rates from 1900 - 2010,
