CAPITAL BUDGETING Infrastructure & Project Evaluation

Making decisions having significant future net benefits or costs CAPITAL BUDGETINGInfrastructure & Project Evaluation

JUSTIFYING PUBLIC SPENDING • Spending/Proposing agencies are responsible for justifying their proposals (I.e., presenting the case for spending in ABC terms) • Budget analysts are supposed to guarantee that the proper justification has been provided

Exercise 3.7

As a Practical Matter If this proposal were consistent with executive priorities, we would stop here: • The dollar values are small • The activities are more or less reversible • Estimating program benefits would be prohibitively costly

But The following is also true: • Present Value of the workforce commitment is approximately $6million, excluding hiring and training costs • Overheads are probably of roughly the same magnitude • Some benefits can be estimated • e.g., savings to state from reductions in future assistance. If teams would counsel 4000 battered spouses a year, they would pay for themselves if they reduced future assistance by $100 on average.

Public Sector Project Assessment should take all benefits and costs to public into account Federal Gov. treats consequences to itself as costs Consequences for citizens as benefits Hence, revenues are negative costs and payments by citizens negative benefits REVENUE TO GOVERNMENT ≤ COST TO CITIZENS

The welfare of an entity's stakeholders will be maximized by the implementation of all policy choices that generate positive net-present values. Timing of benefits or costs accruing from a policy choice is generally of no importance -- so long as benefits/ costs are properly discounted. The source of financing does not matter -- shouldn’t influence capital budgeting decisions, value will be the same regardless of whether an activity is financed with debt, fund balances, or taxes TWO ASSUMPTIONS

Together these two assertions imply that all capital budgeting decisions should be governed by cost-benefit analysis, which says: do it whenever benefits exceed costs

As Practical Matters • Some projects have greater value when deferred than at present • State and Local Governments are often Liquidity constrained (as are many of their citizens), which means that they may have to make tradeoffs

CONVERTING FUTURE VALUE TO PRESENT VALUE Making decisions having significant future benefits or costs means looking at consequences from where we are right now: converting future benefit/cost flows to PRESENT VALUES

Discounting Future values are converted to present values by means of a discount rate. That is, future nominal benefits are worth less than present benefits of equal magnitude -- the WIMPY principal • Inflation • Markets tell us that people demand compensation for forgoing current consumption

Mechanics of Discounting I PV = FV in yeart / [1+r]^t Where PV = Present Value FV = Future Value (real or nominal) t = Year r = Discount Rate (real or nominal)

Mechanics of Discounting II For a Stream of Benefits from year 1 to year t, SUM [add up] all the present values for all net future values Where t = 3 PV = (FV in year1/ [1+r]^1) + (FV in year2/ [1+r]^2) + (FV in year3/ [1+r]^3)

Three Ways to Find PVs • Solve the equation with a regular calculator(or use FV tables from an accounting text). • Use a financial calculator. • Use a spreadsheet.

What’s the PV of $100 due in 3 years if i = 10%? Finding PVs is discounting; it’s the reverse of compounding. 0 1 2 3 10% 100 PV = ?

3 1    PV = $100    1.10   = $100 0.7513 = $75.13.

Spreadsheet Solution • Use the PV function: see spreadsheet. = PV(Rate, Nper, Pmt, FV) = PV(0.10, 3, 0, -100) = 75.13

What is the PV of this uneven benefit stream? 4 0 1 2 3 10% 100 300 300 -50 90.91 247.93 225.39 -34.15 530.08= PV

Spreadsheet Solution A B C D E 1 0 1 2 3 4 2 100 300 300 -50 3530.09 Excel Formula in cell A3: =NPV(10%,B2:E2)

Perpetuities PV = NBF / r Where NBF = a specified annual net-benefit flow For example: $186k / .03 = $6.2m

Alternative Discount Rates • Market rate = r + i + b + y Where r = real, risk-free rate i = the expected rate of inflation b = project specific (nondiversifiable) risk y = income tax adjustment • Nominal risk-free rate [n] = r + i

Use of Alternative Discount Rates • Use real rate [r] with real FVs • For example, where you are using current costs to estimate future costs • Use nominal rate [n] with nominal FVs • For example, where you are making identical nominal principal and interest payments each year WHAT NOMINAL RATE SHOULD YOU USE?

Use of Alternative Discount Rates • Use real rate [r] with real FVs • For example, where you are using current costs to estimate future costs • Use nominal rate [n] with nominal FVs • For example, where you are making identical nominal principal and interest payments each year Borrowing rate on tax-exempt, general-purpose bonds of similar Maturities.

Annualizing Capital Costs • Since US government budget is formulated one year at a time, the budget tends to be biased against delivery methods requiring up-front investments • The proper solution is converting everything to PV • However, there is a reasonable alternative, which is the annualizing capital costs

Mechanics of Annualizing Annual Cost of a Capital Asset = P [r + d - a] Where P = Purchase Price [replacement cost] d = Depreciation rate [wear and tear + obsolescence] a = Appreciation rate

Borrowing Cost as a Proxy for Capital Consumption • Principal plus interest • Simplify by laying out an amortization schedule • Charge that amount to programs • Sock it way to replace asset

CAPITAL BUDGETING Infrastructure & Project Evaluation