Chapter 7: Cost-Benefit Analysis
 Present Value Calculations and Alternatives
 Public Sector Discount Rate
 Calculating Public Costs and Benefits
 Cost-Benefit Analysis Errors
 Distribution
 Uncertainty
         Math- Compound Interest
   Investment: $100  
   Interest rate: 2%
                               Year  Calc.         Amount
   Derived Formula:
                                   1          100   100.00
     S = P (1+r)t                  2 100*1.02       102.00
                                   3 100*1.022      104.04
   S = value after t 
     years                         4 100*1.023      106.12
   P = principle                   5 100*1.024      108.24
     amount
   r = interest rate
   t = years
   Compound Interest Example
 The City loans $2 million to a local sports 
  team, to be paid back in 10 years at 
  3% interest.  How much will the City 
  get?
 S = P (1+r)t 
 S = $2 million (1+0.03)10
 S = $2.69 million
  
     Math - Present Value 
 How much do I have to invest now to 
  have a given sum of money in the 
  future?
 How much is a future amount worth 
  now?
       PV = S/[(1+r)t]
 PV = present value (money invested 
  now)
 S = sum needed in future
 r = real, compound interest rate
 t = years
  
         Present Value Example 
  If the City wins their bid for the Video 
    Games Olympics (VGO) in 5 years, 
    they will gain $10 billion in economic 
    activity.  What is the present value of 
    that gain if interest rates are 4%?
                 t
  PV = S/[(1+r)]
                               5
  PV = $10 billion/[(1+0.04) ]
  PV = $8.22 billion