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1、,Chapter 2,Fundamentals of Corporate Finance Ninth 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
2、 Value Value today of a future cash flow.,Future Value Amount 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 interest Interest means earning interest on in
3、terest.,Discount Factors and Rates,Discount Rate Interest rate used to compute present values of future cash flows.,Discount Factor Present 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) = 50 Value in one
4、 year = principal + interest = 1000 + 50 = 1050 Future Value (FV) = 1000(1 + .05) = 1050 Suppose 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)t FV = future value
5、 PV = present value r = period interest rate t = number of periods Future 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 w
6、ould you have at the end of 15 years using compound interest? How much would you have using simple interest?,5C-9,Future Values,Example - FV What is the future value of $100 if interest is compounded annually at a rate of 6% for five years?,Future Values,Example - FV What is the future value of $400
7、,000 if interest is compounded annually at a rate of 5% for one year?,5-12,Present Values,How much do I have to invest today to have some amount in the future? FV = PV(1 + r)t Rearrange to solve for PV = FV / (1 + r)t When we talk about discounting, we mean finding the present value of some future a
8、mount. When we talk about the “value” of something, we are talking about the present value unless we specifically 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% annual
9、ly, how much do you need to invest today? If you could invest the money at 8%, would you have to invest more or less than at 6%? How much?,5C-13,Present Value,Present Value,Discount Factor = DF = PV of FV $1 Discount Factors can be used to compute the present value of any cash flow.,Question,If the
10、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? Calculate 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 flows Cost o
11、f building = C0 = 370,000 Sale price in Year 1 = C1 = 420,000 Step 2: Estimate opportunity cost of capital If equally risky investments in the capital market offer a return of 5%, then Cost of capital = r = 5%,Valuing an Office Building,Step 3: Discount future cash flows Step 4: Go ahead if PV of payoff exceeds investment,Net Present Value,Risk and Present Value,Higher risk projects require a higher rate of return Higher required rates of return cause lower PVs,Risk and Present Value,Risk and Net Present Value,
