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## AGEC/FNR 406 LECTURE 10

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**AGEC/FNR 406**LECTURE 10 Rice drying on the Philippine National Highway**Benefit-Cost Measures**Lecture Goals: 1. Present three tools of benefit-cost analysis 2. Discuss advantages and disadvantages of BCA Don’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)**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.**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.**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 = 282.22BCR = 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**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)2i = 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