Slide 1Benefit-Cost MeasuresThree BCA tools:Net Present Value (NPV)NPV FormulaKey PointNPV ExampleBenefit Cost Ratio (BCR)BCR FormulaSlide 10BCR ExampleInternal Rate of Return (IRR)IRR FormulaSlide 14IRR ExampleAdvantages of BCADisadvantages of BCAAGEC/FNR 406 LECTURE 10 Rice drying on the Philippine National HighwayBenefit-Cost MeasuresLecture Goals:1. Present three tools of benefit-cost analysis2. Discuss advantages and disadvantages of BCADon’t neglect to review the BCA packet!Three BCA tools: 1. Net Present Value (NPV) 2. Benefit-Cost Ratio (BCR) 3. Net Present Value (NPV)Net Present Value (NPV)The net present value of benefits is the present value of those net benefits.Net benefit is simply the sum of benefits minus the sum of costs. NPV is the current value of all net benefits associated with a project The net benefits are converted to present value by discounting.NPV Formula  TtttttrCostBenefitNPV11Key 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 Time Benefit Cost Net Benefit0 100 150 -501 100 100 02 100 50 50all 300 300 0-50/(1+.1)0 + 0/(1+.1)1 + 50/(1+.1)2 = -8.68Benefit 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    TttttTttttrCostrBenefitBCR1111Key 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 ExampleNum. = 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 = 282.22BCR = 273.54/282.22 = 0.97 < 1Internal 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 Solve for the IRR by finding i that solves:PV(Benefits) = PV(Costs)Use algebra or a spreadsheetKey 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 = 0Advantages of BCA1. Provides a framework2. BCA is quantitative3. BCA is based on facts4. The methods provide clarity5. Results allow comparabilityDisadvantages of BCA1. Requires valuation 2. Discount rate sensitivity 3. Plagued by uncertainty 4. Silent on equity5. BCA is