6Present Value Discount Factor = DF = PV of $1 Discount Factors can be used to compute the present value of any cash flow.
7Valuing 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 capital marketoffer a return of 5%, thenCost of capital = r = 5%
8Valuing an Office Building Step 3: Discount future cash flowsStep 4: Go ahead if PV of payoff exceeds investment
12Net Present Value RuleAccept investments that have positive net present valueExampleUse the original example. Should we accept the project given a 10% expected return?
13Rate of Return RuleAccept investments that offer rates of return in excess of their opportunity cost of capitalExampleIn the project listed below, the foregone investment opportunity is 12%. Should we do the project?
14Multiple Cash Flows For multiple periods we have the Discounted Cash Flow (DCF) formula
15Net Present Values - $370,000 $20,000 $ 420,000 Present Value Year 0 20,000/1.12420,000/1.122Total= $17,900= $334,800= - $17,300Year-$370,000
16Short CutsSometimes there are shortcuts that make it very easy to calculate the present value of an asset that pays off in different periods. These tools allow us to cut through the calculations quickly.
17Short CutsPerpetuity - Financial concept in which a cash flow is theoretically received forever.
18Short CutsPerpetuity - Financial concept in which a cash flow is theoretically received forever.
19Present Values Example What is the present value of $1 billion every year, for all eternity, if you estimate the perpetual discount rate to be 10%??
20Present Values Example - continued What if the investment does not start making money for 3 years?
21Short CutsAnnuity - An asset that pays a fixed sum each year for a specified number of years.AssetYear of Payment…..t t + 1Present ValuePerpetuity (first payment in year 1)Perpetuity (first payment in year t + 1)Annuity from year 1 to year t
22Present Values Example Tiburon Autos offers you “easy payments” of $5,000 per year, at the end of each year for 5 years. If interest rates are 7%, per year, what is the cost of the car?5,0005,0005,0005,0005,000YearPresent Value at year 0
23Short CutsAnnuity - An asset that pays a fixed sum each year for a specified number of years.
24Annuity Short Cut Example You agree to lease a car for 4 years at $300 per month. You are not required to pay any money up front or at the end of your agreement. If your opportunity cost of capital is 0.5% per month, what is the cost of the lease?
25Annuity Short Cut Example - continued You agree to lease a car for 4 years at $300 per month. You are not required to pay any money up front or at the end of your agreement. If your opportunity cost of capital is 0.5% per month, what is the cost of the lease?
26Annuity Short Cut Example The state lottery advertises a jackpot prize of $295.7 million, paid in 25 installments over 25 years of $ million per year, at the end of each year. If interest rates are 5.9% what is the true value of the lottery prize?
27FV Annuity Short CutFuture Value of an Annuity – The future value of an asset that pays a fixed sum each year for a specified number of years.
28Annuity Short Cut Example What is the future value of $20,000 paid at the end of each of the following 5 years, assuming your investment returns 8% per year?
29Constant Growth Perpetuity g = the annual growth rate of the cash flow
30Constant Growth Perpetuity NOTE: This formula can be used to value a perpetuity at any point in time.
31Constant Growth Perpetuity ExampleWhat is the present value of $1 billion paid at the end of every year in perpetuity, assuming a rate of return of 10% and a constant growth rate of 4%?
32PerpetuitiesA three-year stream of cash flows that grows at the rate g is equal to the difference between two growing perpetuities.
33Effective Interest Rates Effective Annual Interest Rate - Interest rate that is annualized using compound interest.Annual Percentage Rate - Interest rate that is annualized using simple interest.26
34Effective Interest Rates exampleGiven a monthly rate of 1%, what is the Effective Annual Rate(EAR)? What is the Annual Percentage Rate (APR)?27
35Effective Interest Rates exampleGiven a monthly rate of 1%, what is the Effective Annual Rate(EAR)? What is the Annual Percentage Rate (APR)?28
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