《公共经济学 Public Economics》课程PPT教学讲稿（英文版）Chapter 11 Cost-Benefit Analysis Public Economics

Chapter 11-Cost-Benefit Analysis Public economics

1 Chapter 11 – Cost-Benefit Analysis Public Economics

Introduction Cost-benefit analysis is a set of practical procedures for guiding public expenditure decisions

2 Introduction • Cost-benefit analysis is a set of practical procedures for guiding public expenditure decisions

Present value Project evaluation usually requires comparing costs and benefits from different time periods Dollars across time periods are not immediately comparable, because of inflation and returns in the market

3 Present Value • Project evaluation usually requires comparing costs and benefits from different time periods • Dollars across time periods are not immediately comparable, because of inflation and returns in the market

Present value Present dollars into the future Suppose you invest $100 today in the bank At the end of year 1, it is worth(1+ 05)X$100 or$105 At the end of year 2, it is worth(1+05)x$105, or$11025 The interest compounds over time. that is the interest is also earning interest

4 Present Value: Present Dollars into the Future • Suppose you invest $100 today in the bank – At the end of year 1, it is worth (1+.05)x$100, or $105 – At the end of year 2, it is worth (1+.05)x$105, or $110.25 – The interest compounds over time, that is the interest is also earning interest

Present value Present dollars into the future Define R=initial investment amount r=rate of return on investment T=years of investment The future value(F of the investment is T FV=R(1+r

5 Present Value: Present Dollars into the Future • Define – R=initial investment amount – r=rate of return on investment – T=years of investment • The future value (FV) of the investment is: FV R( r) T = 1+

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