1. Chapter 6 – Capital Budgeting, Pubic Infrastructure, and Project Evaluation 1. What is a capital budget 2. Capital budget process 3. Accounting for the time value of money: Discounting & Compounding 4. Cost-Benefit Analysis

2. Capital expenditures  Assets purchased that are expected to provide services (both private and public) for several years  Benefits from a project will extend into the future without additional purchases  Spending is directed toward increasing the “public capital stock”

3. Capital budget  Separate budget that attempts to match borrowing to support net worth of the public sector  Focuses exclusively on project that: 1. Have long life (ten+ years) 2. Have a high price tag relative the resources of the governing unit 3. Represent non-recurrent costs

4. Justifications for having a separate capital budget  Improves inter-generational equity. By borrowing, allows future generations to pay for project that benefit them.  Stabilizes tax rates when project is large relative to tax revenues  Requires special attention to decision making since capital projects are permanent and more important to avoid error  Help to manage limited fiscal resources

5. Capital budgets and levels of government  Most important at local and state level, rather than federal  Reasons against including capital budget in the federal spending include: A separate capital budget will bias toward deficit spending since all items can be called “future investments” At fed level, no single project is likely to destabilize tax rates since federal revenue pool is so large Fed govt. does not need careful analysis of all capital spending since it does not have to concerned about its debt rating (bond rating) as do local and state govts. Some suggest it would just allow another way to hide spending

6. The Capital-Budgeting Process  Aims to constrain financial impact of capital asset acquisition on the overall budget while still providing infrastructure 1. Capital asset inventory 2. Capital-improvement plan 3. Long-term financial analysis 4. Integration into the annual budget 5. Execution

7. 1. Capital asset inventory  Gathers information about capital facilities owned by government and when replacement (and how much) is needed Age of facilities Assessment of condition Degree of use Capacity Replacement cost

8. 2. Capital-improvement plan  Identifies the capital expenditure projects appropriate for the next 6 years  List of projects proposed by both govt. agencies and private entities  Provides both justification and cost estimates  Scheduling is important to fit project into existing community or state planning & avoiding waste

9. 3. Long-term financial analysis  Coordinates spending on long-term projects with local capacity  Examines extent to which cost sharing occurs (other govt. agencies, transfer funds, private entities)  Measures spending against debt structures (existing debt)  Examines debt structure to use to finance new projects (more borrowing, what type of bond issue, capital reserve funds (special funds), or current revenue sources.

10. 4. Integration into the annual budget  Involves determining how capital project fit within annual budget priories  Measures the impact of project (is a project about to be retired? Are there vulnerable populations?)  Assesses the degree of support  Assigns a formal ranking within annual budget

11. 5. Execution  Specific attention is given to rules on bidding, procurement, etc. for private contractors  Controls to keep project on schedule  Cost monitoring to keep costs within budget and on schedule

12. Accounting for the time value of money  If I borrowed $1,000 today how much would you want me to pay back tomorrow?  In 1 year?  In 10 years  In 50 years?

13. Time Value of Money  As time passes what happens to the value of money? 1. May lose value (purchasing power) due to inflation 2. Could have been used for other purposes today rather than put off to the future 3. It has opportunity costs (there are competing uses for money)

14. Future Value (FV)  If I have money now and invest it at a given rate of return, how much will it be worth in the future?  Finds the future value of a present present investment Value now Value then Year 1 Year 2 Year 3

15. Thinking about future value (FV)  If you put $100 in the bank every year for three years how much will it be worth? ? Year 1 Year 2 Year 3 $100

16. Present Value (PV)  If I have money in the future, how much is that worth to me today? Or how much would I need to invest today in order to attain that future quantity?  Present value of future investment (PV) Value now Value then Year 1 Year 2 Year 3

17. Thinking about present value  If a project gives $100 of benefits every year for 3 years, what is the present value (PV) of that project? ? Year 1 Year 2 Year 3 $100

18. Calculating Present Value – multiple periods and compounding  Multiple period investments may earn either simple interest or compound  Simple Interest: Amount at end of period = Original principal + Interest earned in period 1 + Interest earned in period 2 + Interest earned in period n…

19. Calculating Present Value –single period  Amount at end of period = Original principal + Interest earned  Example: Invested $1,000 at 5% interest rate, end of the year $1,050 FV 1 = PV (1+r) FV 1 = 1,000 (1+.05) FV 1 = 1,000 (1.05) = $1,050

20. Calculating Present Value – multiple periods and compounding  Compound Interest: Amount at end of period = Original principal + Interest earned in period 1 + Interest earned in period 2 and interest on the interest earned in period 1 + Interest earned in period n and interest on the interest earned in period n-1

21. Ex: Compound Interest One period: FV 1 = PV 1 (1+r) = PV(1.05) [ same as simple interest ] Two periods: FV 2 = PV 1 (1+r)(1+r) = PV(1+r) 2 Three periods: FV 3 = PV 1 (1+r)(1+r)(1+r) = PV(1+r) 3

22. Future Value (FV)  Compounding along a time line PV FV PV(1+r) PV(1+r)(1+r) PV(1+r)(1+r)(1+r)

23. General Compounding Formula Compounding: FV n = PV(1+r) n Example: What would the future value be of an investment of $1,000 for 5 years earning 5% compound interest yearly? So n=5, PV=1,000, r=.05 FV 5 = 1,000(1.05) 5 = 1,276.28

24. Compounding over Multiple Periods Example: What would the future value be of an investment of $1,000 for 5 years earning 5% compound interest bi-annually? n = 10 FV 10 = 1,000(1.05) 10 = 1,628.90

25. Present Value (PV)  Whereas FV needs interest, PV uses a “discount rate”  Discounting adjusts the sum to be received in the future to the present- value equivalent  The discount rate is often set to the interest rate that could be earned if the money was spent in an alternative investment. It can also represent the amount of risk a government entity is willing to take on, or be legally mandated.

26. Calculating Discount Rate General Formula: PV = FV n /(1+r) n Example 1: What is the present value of $1,000 received one year from now given a discount rate of 5%? PV = FV 1 /(1+r) 1 PV = $1,000 / (1+.05) = $952.88

27. Calculating Discount Rate Example 2: What is the present value of $1,000 received 10 years from now given a discount rate of 5%? PV = FV 10 /(1+r) 10 PV = $1,000 / (1+.05) 10 = $613.91 As the number of years increases, or the discount rate increases, the PV value decreases

28. Evaluating the present value of a project  If a project gives $100 of benefits every year for 3 years, and the discount rate is 5%, what is the present value (PV) of that project? Or put another way, how much should you pay for the project today?

29. Evaluating the present value of a project  General Formula: PV=FV n /(1+r) n  PV 1 =FV 1 /(1+r) 1 =100/(1.05) 1 =95.24  PV 2 =FV 2 /(1+r) 2 =100/(1.05) 2 =90.70  PV 3 =FV 3 /(1+r) 3 =100/(1.05) 3 =86.38 PV Year 1 Year 2 Year 3 100/(1.05) 1 100/(1.05) 2 100/(1.05) 3 95.24 90.70 86.38 ______ 272.32

30. Using PV to compare projects Received at end of year: Project A:Project B: 11,000480 2300480 31,000480 40 50 Total:2,3002,400

31. Using PV to compare projects Year:Project A: Discount:Discounted Amount: Project B: Disc Amount: 11,0001,000/(1.1) 1 909480436 2300300/(1.1) 2 248480396 31,0001,000/(1.1) 3 751480360 400/(1.1) 4 0480328 500/(1.1) 5 0480298 Total2,3001,9082,4001,818

32. Annuity Formula  When a project has a constant stream of benefits over a number of periods a short cut is the use of the annuity formula:  PV = S[1-1/(1+r) n ]/r S=Annual flow of benefits, r=discount rate Using the info from Project B:  PV=480[1 – 1/(1.10) 5 ] /.10  PV Project B = $1,819

33. Cost-Benefit Analysis  Method of making decisions about whether a project is worth its cost  Can be used to compare similar projects (water purification or a reservoir for a new water source) or different projects (new fire station vs. re-surfacing a road)  Estimates if the gains to society (benefits) are greater than the total sacrifice (costs)  If not, then the project is probably not worth doing

34. Elements of Cost-Benefit Analysis (CBA)  Five steps for conducting a CBA 1. Categorizing project objectives 2. Estimation of project’s benefits 3. Estimates project costs 4. Discount cost and benefit flows over time at appropriate discount rate 5. Present results useable to decision- makers

35. Project Objectives  What are the desirable results that will occur from the project  Follows the “incremental principle” that only costs that change because of a decision are considered  Analysis must focus on the factors that are different if the project occurs  Example (p. 253) Labor, cost of recycle rack are new costs Operation, maintenance are NOT new

36. Estimating Benefits  Requires estimating value from changes from the existence of the project over the entire life of the project  Difficulty in estimating benefits cannot be an excuse for indecision  Various methods possible: Controlled experiment on sample population Use of mathematical and computer Modeling  Outputs of the project are valued in terms of monetary value to allow comparison across different project benefits

37. Valuing projects that save lives  How can a value be assigned to projects that save lives?  Governments make decisions that affect public safety, health and involve high degrees of risk. To compare projects requires putting a dollar value on lives.  Methods: Live insurance face value Earnings lost method – estimates lost value from a lifetime of employment Willingness to pay – estimates willingness to take on extra risk

38.  What if one project with a low cost ($) saves travel time and another with higher cost ($$$) saves a couple of lives ?  Normal criteria would favor the lower cost project

39.  Methods for determining benefits include:  Inferred value Ex: effect of a park on real estate values  Travel costs Ex: value of protecting a resource estimated according to willingness to pay to visit it  Contingent valuation-uses surveys Problems include:  Overstatements  Sensitivity to question order/wording  Inconsistent responses  Difficult to verify

40. Estimates project costs  Costs need to include all those of path not taken 1. Negative effects of the project  Ex: traffic delays, environmental damage, increased crime, etc. 2. Needs to include opportunity costs (alternative uses)  If no other feasible use, then opportunity costs are zero  If opportunity costs, needs to include lost use (ex: land used for a public building rather than alternative use)

41. Discount cost and benefit flows over time at appropriate discount rate  Since there is no easy way to use market rates, public projects use one of two discount rates  1. Uses the interest rate government must pay  2. Opportunity costs of displaced private activity (opportunity costs of use of taxes)

42. Four methods for evaluating projects:  Net Present Value (NPV)  Benefit-Cost Ratio (BCR)  Payback Period  Internal Rate of Return (IRR)

43. Net Present Value  Compares the value of the flow of benefits from a project to the cost of the initial investment NPV = Benefit 1 / (1.1) 1 + Benefit 2 / (1.1) 2 + Benefit n / (1.1) n – Initial investment

44. Example: Comparing Three Projects Project Capital cost Yr 1Disc value yr 1 Yr 2Disc value yr 2 Yr 3Disc value yr 3 A10,000 10,000/ (1.1) 1 = 9,090 0000 B10,0007,0007,000 / (1.1) 1 = 6,364 3,0003,000 / (1.1) 2 =2,479 00 C10,0003,0003,000/ (1.1) 1 = 2,727 5,0005,000 / (1.1) 2 =4,132 7,0007,000 / (1.1) 3 =5,259 Annual Net Benefits: 10% Discount value

45. Calculating NPV Project A: NPV = 9,090 – 10,000 = -910 Project B: NPV = 6,364 + 2,479 – 10,000 = -1,157 Project C: NPV = 2,727 + 4,132 + 5,259 – 10,000 = 2,118 Decision Criteria: Only a project that provides a positive NPV should be accepted

46. Benefit-Cost Ratio (BCR) BCR = Sum of Benefits / Sum of Costs Project A: 9,090 / 10,000 = 0.91 Project B: ( 6,364 + 2,479) / 10,000 = 0.88 Project C: ( 2,727 + 4,132 + 5,259) / 10,000 = 1.2 Decision Criteria: Accept projects when BCR>1

47. Payback Period  Payback period – number of years it takes to payback the original investment  Project A: Initial investment 10,000 Benefits yr 1: 10,000 Payback period: 1 year  Project X: Initial investment 10,000 Benefits yr 1: 3,000 yr 2: 4,000 yr 3: 4,000 Payback period: 3 years

48. Problems with Payback Period  Does not account for the time value of money  Only useful for quick project estimates or internal criteria

49. Internal Rate of Return (IRR)  Estimates the discount rate for a project given an stream of benefits and an initial investment by setting future flow of benefits equal to costs  Initial Investment = Sum of Benefits n / (1+r) n  10,000 = 3,000/(1+r) + 4,000/(1+r) 2 + 7,000/(1+r) 3

50. Calculating Internal Rate of Return (IRR) 10,000 = 3,000/(1+r) + 4,000/(1+r) 2 + 7,000/(1+r) 3 Can only be calculated computer, calculator or trial & error Try 10%: 3,000/(1.1)+ 4,000/(1.1) 2 + 7,000/(1.1) 3 = 2,727 + 3,306 + 5,259 = 11,292 > 10,000 So increase the discount rate, try 16%: 3,000/(1.16) + 4,000/(1.16) 2 +7,000/(1.16) 3 =2,586 + 2,973 + 4,485 = 10,043 nearly equal to 10,000 So IRR is 16%

51.  IRR is primarily used as an internal measure against a given rate  Such as, projects are only accepted if the IRR is at least 12%  Smaller the discount rate used, the higher the estimate of the benefits from a project  Set a given rate of return from any investment