Annual Equivalent Worth Criterion Lecture No.17 Professor C. S. Park Fundamentals of Engineering Economics Copyright © 2005

Which Brand Would you Pick? Brand A Brand B $55/Year$85/Year $799 $699 How Would you calculate the hourly operating cost?

Chapter 6 Annual Equivalence Analysis  Annual equivalent criterion  Applying annual worth analysis  Mutually exclusive projects

Chapter Opening Story Capstone Turbine Corporation Manufacturer of micro- turbine (mini-Power Plant) At Issue: Economics of MicroCHP

Annual Worth Analysis Principle: Measure an investment worth on annual basis Benefit: By knowing the annual equivalent worth, we can: Seek consistency of report format Determine the unit cost (or unit profit) Facilitate the unequal project life comparison

Example 6.1 Computing Equivalent Annual Worth $15 $3.5 $5 $12 $ A = $ AE(12%) = $6.946(A/P, 15%, 6) = $1.835 $ PW(15%) = $6.946 $9.0 $10

Annual Equivalent Worth - Repeating Cash Flow Cycles $500 $700 $800 $400 $500 $700 $800 $400 $1,000 Repeating cycle

First Cycle: PW(10%) = -$1,000 + $500 (P/F, 10%, 1) $400 (P/F, 10%, 5) = $1, AE(10%) = $1, (A/P, 10%, 5) = $ Both Cycles: PW(10%) = $1, $1, (P/F, 10%, 5) $400 (P/F, 10%, 5) = $1, AE(10%) = $1, (A/P, 10%,10) = $304.87

Annual Equivalent Cost When only costs are involved, the AE method is called the annual equivalent cost. Revenues must cover two kinds of costs: Operating costs and capital costs. Capital costs Operating costs + Annual Equivalent Costs

Capital (Ownership) Costs Def: Owning an equipment is associated with two transactions—(1) its initial cost (I) and (2) its salvage value (S). Capital costs: Taking these items into consideration, we calculate the capital costs as: N 0 N I S CR(i)

VehicleValue after three years Monthly lease Acura MDX 4WD$21, Toyota 4Runner 4WD 4-door Limited (with moonroof) $18, Lexus RX300 2 WD$18, GMC Envoy 4WD 4door SLT (with Bose audio, CD changer and moonroof) $15, Mitsubishi Montero 4WD 4 door Limited $15, Ford Explorer 4WD 4-door Eddie Bauer edition (with moonroof, rear air and third seat) $14, Isuzu Trooper 4WD 4-door Limited $11, Source: Automotive Lease Guide

SEGMENTBEST MODELSASKING PRICE PRICE AFTER 3 YEARS Compact carMini Cooper$19,800$12,078 Midsize carVolkswagen Passat $28,872$15,013 Sports carPorsche 911$87,500$48,125 Near luxury carBMW 3 Series$39,257$20,806 Luxury carMercedes CLK$51,275$30,765 MinivanHonda Odyssey $26,876$15,051 Subcompact SUVHonda CR-V$20,540$10,681 Compact SUVAcura MDX$37,500$21,375 Full size SUVToyota Sequoia$37,842$18,921 Compact truckToyota Tacoma$21,200$10,812 Full size truckToyota Tundra$25,653$13,083

Example - Capital Cost Calculation for Mini Cooper Given: I = $19,800 N = 3 years S = $12,078 i = 6% Find: CR(6%) $19,800 $12,

Example 6.2