In this chapter, the following content will be discussed: Cost-Benefit analysis is used to evaluate potential public sector projects; present value of future expected costs and benefits must be calculated in order to allow correct comparisons; although the IRR and B-C Ratio are used to evaluate projects, the NPV criterion has fewer biases and problems; | COST-BENEFIT ANALYSIS Chapter 8 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) = $ R2 = $1000*(1+.01)2 = $ RT = R0*(1+r)T 8- one click per line Projecting Future Dollars into the Present How much will $1000 earned in 2 years at an interest rate of 10% be worth today? Since RT = R0*(1+r)T R0 = RT/(1+r)T Present Value discount rate discount factor Low r – more future-oriented and benefits projects in which returns are concentrated further into the future High r – more present-oriented and benefits projects in which returns are concentrated closer into the future 8- 5 lines visible 1st click – 6th line 7th click – “Present Value” 8th click – “discount rate” 9th click ‘ discount rate arrow disappears, bracket appears, “discount factor” Present Value of a Stream of Money 8- Inflation How to incorporate . | COST-BENEFIT ANALYSIS Chapter 8 Projecting Present Dollars into the Future R=$ 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) = $ R2 = $1000*(1+.01)2 = $ RT = R0*(1+r)T 8- 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- 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- 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- 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 0 128 165 2 0 0 46 37 3 550 1,200 10 -21 Note choice of r is critical: Low r benefits Advertising; High r benefits R&D. 8- Private Sector Project Evaluation Internal Rate of Return Project Year 0 Year 1 ρ Profit PV X -$100 $110 10% $4 Y -$1,000 $1,080 8% $20 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, using r=6%, .
