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129 A p p e n d i x B Equivalent annual net benefit (EANB) initializes the net present value (NPV) of different service life projects as a series of equivalent annual payments allowing comparison. It computes the amount needed to pay off a specified sum (NPV) in a series of equal periodic (e.g., annual) payments. The formula is given by NPV multiplied by a capital recovery factor and is shown below. The rule is to select NPV (given in Equation B1 where r is the discount rate): EANB r r r NPVn1 1 (B1)( ) ( )= + â + â Example 1: â¢ Project A: 10 years, NPV = $216 million. â¢ Project B: 5 years. NPV = $83 million. At 7%, the EANB for Project A = $30.8 million and Project B = $20.2 million. Choose Project A. Common Multiples of Project Duration (CMPD) (or rolling over the shorter period): A second method of comparing projects of unequal duration is to compute the NPV using the least common multiple of all asset lives. Example 2: â¢ Project A: 10 years with NPV of $10,000; i = 3%. â¢ Project B: 15 years with NPV of $20,000; i = 3%. The least common multiple = 30 years. This implies that 3 project As = 2 project Bs. Equivalency implies that for Project A, the NPV of $10,000 will cover the 10 years. Another $10,000 will cover the next 10 years, and the third $10,000 is received 20 years later (to span 30 years). Discount as follows: â¢ Project A: NPV = $10,000 + $10,000/(1.03)10 + $10,000/(1.03)20 = $22,978. â¢ Project B: NPV = $20,000 + $20,000/(1.03)15 = $32,837. Decision: Project A NPV < Project B NPVâAccept Project B. Compare Two Alternative Modal Strategies with Different Service Life: In this case, each alternative has been examined as a mutually exclusive option with its own NPV and both can be used to address the problem using EANB Table B1 shows a comparison of two alternatives, each with a different service life. Projects with Different Service Lives (EANB and CMPD)
130 Guide for Conducting Benefit-Cost Analyses of Multimodal, Multijurisdictional Freight Corridor investments Example 3: Question: How does the more expensive and longer lasting strategy compare with the shorter but less expensive strategy? Solution is to compare the NPV of these two mutually exclusive options using EANB or CMPD. Benefit, Costs Discount Rate 5% Modal Strategy 1 (Service life 75 years) Modal Strategy 1 (Service 50 life years) Discounted cost ($ million) $7440 $9143 Discounted Benefits ($ million) $9584 $10,638 NPV $2144 $1496 EANB (NPV) $111 > $73 Table B1. EANB of two alternative strategies.