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1、,Chapter 2,FundamentalsofCorporateFinanceNinth Edition,Present Value,The Objectives of The Firm,and Net Present Value,Time value of money,A dollar today is worth more than a dollar tomorrow.The dollar today can be invested to start earning interest immediately,Present and Future Value,Present ValueV
2、alue today of a future cash flow.,Future ValueAmount to which an investment will grow after earning interest,Simple and Compound interest,Simple interest Interest is not reinvested,is earned each period only on the original principal.,Compound interestInterest means earning interest on interest.,Dis
3、count Factors and Rates,Discount RateInterest rate used to compute present values of future cash flows.,Discount FactorPresent value of a$1 future payment.,Suppose you invest$1000 for one year at 5%per year.What is the future value in one year?Interest=1000(.05)=50Value in one year=principal+interes
4、t=1000+50=1050Future Value(FV)=1000(1+.05)=1050Suppose you leave the money in for another year.How much will you have two years from now?FV=1000(1.05)(1.05)=1000(1.05)2=1102.50,Future Values,Future Value of$100=FV,FV=PV(1+r)tFV=future valuePV=present valuer=period interest rate t=number of periodsFu
5、ture value interest factor=(1+r)t,Quick Quiz,What is the difference between simple interest and compound interest?Suppose you have$500 to invest and you believe that you can earn 8%per year over the next 15 years.How much would you have at the end of 15 years using compound interest?How much would y
6、ou have using simple interest?,5C-9,Future Values,Example-FVWhat is the future value of$100 if interest is compounded annually at a rate of 6%for five years?,Future Values,Example-FVWhat is the future value of$400,000 if interest is compounded annually at a rate of 5%for one year?,5-12,Present Value
7、s,How much do I have to invest today to have some amount in the future?FV=PV(1+r)tRearrange to solve for PV=FV/(1+r)tWhen we talk about discounting,we mean finding the present value of some future amount.When we talk about the“value”of something,we are talking about the present value unless we speci
8、fically indicate that we want the future value.,Quick Quiz Part II,What is the relationship between present value and future value?Suppose you need$15,000 in 3 years.If you can earn 6%annually,how much do you need to invest today?If you could invest the money at 8%,would you have to invest more or l
9、ess than at 6%?How much?,5C-13,Present Value,Present Value,Discount Factor=DF=PV of FV$1Discount Factors can be used to compute the present value of any cash flow.,Question,If the present value of$150 paid at the end of one year is$130,what is the one-year discount factor?What is the discount rate?C
10、alculate the one-year discount factor DF1 for discount rates of(a)10 percent,(b)20 percent,and(c)30 percent,Valuing an Office Building,Step 1:Forecast cash flowsCost of building=C0=370,000Sale price in Year 1=C1=420,000Step 2:Estimate opportunity cost of capitalIf equally risky investments in the ca
11、pital marketoffer a return of 5%,thenCost of capital=r=5%,Valuing an Office Building,Step 3:Discount future cash flowsStep 4:Go ahead if PV of payoff exceeds investment,Net Present Value,Risk and Present Value,Higher risk projects require a higher rate of returnHigher required rates of return cause lower PVs,Risk and Present Value,Risk and Net Present Value,
