Class 4 Benefit Cost Analysis Reference source for the slides: http://www.agecon.purdue.edu/staff/shively/courses/AGEC406/index.htm

Benefit-Cost Analysis First of two related lectures: 1. Overview of benefit-cost analysis 2. Specific benefit-cost tools

Static vs. dynamic efficiency Static efficiency is defined as maximization of net benefits for a single time period. Many economic decisions that occur over time are a series of static decisions. Example: Shopping for Food Choose groceries each week, consume them, then start over again next week.

Static vs. dynamic efficiency A dynamic decision is one in which current decisions have impacts on net benefits arising in the future. Many economic decisions with environmental implications are dynamic. Example: Forestry If you choose to harvest trees this year, harvesting next year is no longer an option.

Benefit-Cost Analysis What is benefit-cost analysis? BCA is an economic technique used to: 1.Evaluate a project or investment over time 2. Compare the merits of a set of projects BCA is conducted by comparing economic benefits of an activity with economic costs of an activity.

Key Point As a tool for economic analysis, BCA seeks to examine potential actions with the objective of increasing well being... …seeking an activity or use that provides greater benefit than cost, or the greatest benefit among competing uses.

Key Point Decisions are typically not made on the basis of BCA alone… but BCA can be useful for providing information on economic features of projects or activities, and can therefore be useful for informing the debate.

BCA in a timeless world Dam construction Costs: Materials = $500,000 Labor = $600,000 Total Cost = $1,100,000

BCA in a timeless world Dam construction Benefits: Recreation = $400,000 Flood control = $300,000 Electricity = $500,000 Total Benefit =$1,200,000

BCA in a timeless world Dam construction Total Benefit =$1,200,000 Total Cost = 1,100,000 Net Benefit = 100,000 Benefit exceeds cost, so dam appears to be a good investment

BCA as “Approach” To know whether society should build the dam, other information may be needed: 1. Are there non-economic impacts? 2. What is the opportunity cost of the dam?

Time and Discounting Often the benefits and costs of a project accrue at different times. The technique used to deal with this issue is discounting.

Discounting Discounting is a technique used to convert all benefits and costs to a common point in time, usually the present. The value of a project, expressed in terms of the present, is called the Present Value.

Discounting Discounting is based on the premise that a dollar of benefit received today is worth more than a dollar of benefit received in the future. The bias arises because current resources can be invested. Discounting is the opposite of compounding.

Discounting The rate at which a current value is compounded is called the interest rate. The rate at which a future value is discounted is called the discount rate.

Computing a present value PV = Pt / (1 + r)t PV = present value Pt = value at time t r = interest (discount) rate t = year in which Pt is realized

BCA with discounting Dam revisited Total Benefits accrue when dam is finished (t = 1) Total Costs accrue at start of construction (t = 0) Discount rate = 10% Should the dam be built?

Dam construction revisited Total Benefits accrue when dam is finished (t = 1), so Pt = $1,200,000 and PV of benefit is: $1,200,000 / (1+0.10)1 = $1,090,909 Total Costs accrue at start of construction (t = 0), so Pt = $1,100,000 and PV of benefit is: $1,100,000 / (1+0.10)0 = $1,100,000 PV(B) < PV(C) The dam shouldn’t be built.

Why the reversal? Total Benefits accrue in the future (i.e. when dam is finished). The process of discounting reduces the value of those benefits because they occur in the future. Because the merit of a project can hinge on the choice of discount rate, it can be a source of debate. There is no simple rule for choosing a discount rate. Often a “well known” interest rate is used.

Key Points Whenever benefits and costs accrue at different points in time, amounts should be converted to present values for comparison. BCA is a decision-support tool, not a decision-making tool. Discounting can be used regardless of the length of time under consideration, but discounting has implications for equity.

Three BCA tools: 1. Net Present Value (NPV) 2. Benefit-Cost Ratio (BCR) 3. Net Present Value (NPV)

Net Present Value (NPV) NPV is the current value of all net benefits associated with a project Net benefit is simply the sum of benefits minus the sum of costs. The net present value of benefits is the present value of those net benefits. The net benefits are converted to present value by discounting.

NPV Formula

Key Point If the project has a NPV > 0, then it is worth considering on its economic merits. If the project has a NPV < 0, then it fails to return benefits greater than the value of the resources used.

NPV Example -50/(1+.1)0 + 0/(1+.1)1 + 50/(1+.1)2 = -8.68

Benefit Cost Ratio (BCR) BCR is computed as the PV of Benefits divided by the present value of Costs. Discounted benefits and discounted costs are calculated and summed separately, then divided.

BCR Formula

Key Point If the project has a BCR > 1, then it is worth considering on its economic merits. If the project has a BCR < 1, then it fails to return benefits larger than its costs.

BCR Example Num. = 100/(1.1)0 + 100/(1.1)1 +100/(1.1)2 = 273.54 Den. = 150/(1.1)0 + 100/(1.1)1 +50/(1.1)2 = 282.22 BCR = 273.54/282.22 = 0.97 < 1

Internal Rate of Return (IRR) The IRR is the maximum interest rate that could be paid for the project resources that would leave enough money to cover investment costs and still allow society to break even. The IRR is the discount rate at which the PVof benefits equals the present value of costs.

IRR Formula PV(Benefits) = PV(Costs) Use algebra or a spreadsheet Solve for the IRR by finding i that solves: PV(Benefits) = PV(Costs) Use algebra or a spreadsheet

Key Point The IRR must exceed the chosen discount rate for the project to be accepted.

IRR Example 100/(1 + i)0 + 100/(1 + i)1 +100/(1 + i)2 = 150/(1 + i)0 + 100/(1 + i)1 +50/(1 + i)2 i = 0

Advantages of BCA 1. Provides a framework 2. BCA is quantitative 3. BCA is based on facts 4. The methods provide clarity 5. Results allow comparability

Disadvantages of BCA 1. Requires valuation 2. Discount rate sensitivity 3. Plagued by uncertainty 4. Silent on equity 5. BCA is anthropocentric