第8章 成本—收益分析（课件）- 《财政学（第十版）》同步教学（人大版）

COST-BENEFIT ANALYSIS Chapter 8 1 Projecting Present Dollars into the Future R=$ T=years r=interest rate How much will $1000 earn in 2 years at an interest rate of 10%? R0 = $1000 R1 = $1000*(1+.01) = $1010 R2 = $1010*(1+.01) = $1020.10 R2 = $1000*(1+.01)2 = $1020.10 RT = R0*(1+r)T 8-2 2 one click per line Projecting Future Dollars into the Present How much will $1000 earned in 2 years at an interest rate of 10% be worth today? Since RT = R0*(1+r)T R0 = RT/(1+r)T Present Value discount rate discount factor Low r – more future-oriented and benefits projects in which returns are concentrated further into the future High r – more present-oriented and benefits projects in which returns are concentrated closer into the future 8-3 3 5 lines visible 1st click – 6th line 7th click – “Present Value” 8th click – “discount rate” 9th click ‘ discount rate arrow disappears, bracket appears, “discount factor” Present Value of a Stream of Money 8-4 4 Inflation How to incorporate inflation – price level increases – into the procedure? Given: ∏ = inflation rate However, (1+∏) terms cancel out, leaving the PV equation from previous slide! CAUTION: $ values and r values must be measured consistently – if real values are used for R, the r must be measured in real terms 8-5 5 Private Sector Project Evaluation Present Value Criterion Annual Net Return PV of R&D vs. Advertising Year R&D Advertising r = R&D Advertising 0 $1,000 -$1,000 0 $150 $200 1 600 0 0.01 128 165 2 0 0 0.05 46 37 3 550 1,200 0.07 10 -21 Note choice of r is critical: Low r benefits Advertising; High r benefits R&D. 8-6 6 Private Sector Project Evaluation Internal Rate of Return Project Year 0 Year 1 ρ Profit PV X -$100 $110 10% $4 3.77 Y -$1,000 $1,080 8% $20 18.87 IRR: Discount rate that would make a project’s NPV zero This criterion is flawed when comparing projects of much differing sizes. Although X has the higher IRR, Y yields the higher profit. Note that the PV criteria, us