Present value Future dollars into the present Suppose someone promises to pay you $100 one year from now What is the maximum amount you should be willing to pay today for such a promise? You are forgoing the interest that you could earn on the money that is being loaned
6 Present Value: Future Dollars into the Present • Suppose someone promises to pay you $100 one year from now. • What is the maximum amount you should be willing to pay today for such a promise? • You are forgoing the interest that you could earn on the money that is being loaned
Present value Future dollars into the present The present value of a future amount of money is the maximum amount you would be willing to pay today for the right to receive the money in the future
7 Present Value: Future Dollars into the Present • The present value of a future amount of money is the maximum amount you would be willing to pay today for the right to receive the money in the future
Present value Present dollars into the future Define R=amount to be received in future r=rate of return on investment T=years of investment The present value(Pv) of the investment is R PV= 1+r 8
8 Present Value: Present Dollars into the Future • Define – R=amount to be received in future – r=rate of return on investment – T=years of investment • The present value (PV) of the investment is: ( ) PV R r T = 1+
Present value Future dollars into the present In previous equation, r is often referred to as the discount rate, and(1+r)- is the discount factor Finally consider a promise to pay a stream of money, SRo today, SR, one year from now, and so on for T years? R1 R P=R0+ T (1+n)(+)2(1+ 9
9 Present Value: Future Dollars into the Present • In previous equation, r is often referred to as the discount rate, and (1+r)-T is the discount factor. • Finally consider a promise to pay a stream of money, $R0 today, $R1 one year from now, and so on, for T years? ( ) ( ) ( ) PV R R r R r R r T T = + + + + + + + 0 1 2 2 1 1 1
Present value Future dollars into the present Present value is an enormously important concept A$1,000,000 payment 20 years from now is only worth today 376889ir=.05 $148,644r=.10 10
10 Present Value: Future Dollars into the Present • Present value is an enormously important concept • A $1,000,000 payment 20 years from now is only worth today: – $376,889 if r=.05 – $148,644 if r=.10