Applying the Annual Worth Analysis - Bilkent University

Applying the Annual Worth Analysis - Bilkent University

Applying Annual Worth Analysis Lecture No. 20 Chapter 6 Contemporary Engineering Economics Copyright 2016 Contemporary Engineering Economics, 6e, GE Park Copyright 2016, Pearson Education, Ltd. All Rights Reserved Annual Worth Analysis Principle: Measure an Annual Equivalent Conversion investments worth on an annual basis. Benefits: By knowing the annual equivalent worth, we can: oSeek consistency of report format. oDetermine the unit cost (or unit profit). oFacilitate the unequal project life comparison.

Contemporary Engineering Economics, 6e, GE Park Copyright 2016, Pearson Education, Ltd. All Rights Reserved Fundamental Decision Rules For Single Project: For Mutually Exclusive Alternatives: If AE(i) > 0, accept the investment. If AE(i) = 0, remain indifferent to the investment. If AE(i) < 0, reject the investment. Contemporary Engineering Economics, 6e, GE Park Service projects: Select the alternative with the minimum annual equivalent cost (AEC). Revenue projects: Select the alternative with the maximum AE(i). Copyright 2016, Pearson Education, Ltd. All Rights Reserved Example 6.1: Economics of Installing a Feed-water Heater Install a 150MW unit Initial cost = $1,650,000 Service life = 25 years Salvage value = 0 Expected improvement in fuel efficiency = 1% Fuel cost = $0.05kWh Load factor = 85% Determine the annual worth for installing the unit at i = 12%. If the fuel cost increases at the annual rate of 4%, what is AE(12%)? Contemporary Engineering Economics, 6e, GE Park Copyright 2016, Pearson Education, Ltd. All Rights Reserved Solution: Calculation of Annual Fuel Savings Required input power before adding the second unit

150,000kW 272,727kW 0.55 Required input power after adding the second unit 150,000kW 267,857kW : 0.56 Reduction in energy . consumption 272,727kW 267,857kW = 4,870 kW Annual Operatioperating ng hours = (365)(24)(0.85) hours =7,446 hours/year Contemporary Engineering Economics, 6e, GE Park

Annual Fuel Savings Afuel savings (reduction in fuel requirement) (fuel cos t) (operating hours per year) =(4,870kW) ($0.05/kWh) 7,446 hours/year =$1,813,101/year Copyright 2016, Pearson Education, Ltd. All Rights Reserved Solution: Annual Worth Calculations (a) with constant fuel price Cash Flow Diagrams PW(12%) $1,650,000 $1,813,101(P / A,12%,25) $12,570,403 AE(12%) $12,573,321(A / P ,12%,25) $1,602,726 (b) with escalating fuel price A1 =$1,813,101 PW (12%) $1,650,000 $1,813,101(P / A1 ,4%,12%,25) $17,459,783 AE(12%) $17,459,783(A / P ,12%,25) $2,226,122

Contemporary Engineering Economics, 6e, GE Park Copyright 2016, Pearson Education, Ltd. All Rights Reserved Repeating Cash Flow Cycles First Cycle PW(12%) $1,000,000 [($800,000 $100,000(A G ,12%,4)](P A ,12%,4) $1,000,000 $2,017,150. $1,017,150. Repeating Cycles AE 12% = $1,017,150 A P , 12%, 4 = $334,880. Contemporary Engineering Economics, 6e, GE Park Copyright 2016, Pearson Education, Ltd. All Rights Reserved Example 6.3: Comparing Alternatives Contemporary Engineering Economics, 6e, GE

Park Copyright 2016, Pearson Education, Ltd. All Rights Reserved Solution Required assumptions The service life of the selected alternative is required on a continuous basis. Each alternative will be replaced by an identical asset that has the same costs and performance. Model A PW 15% = $22,601 AEC 15% = $22,601 A P , 15%, 3 = $9,899. Model B PW 15% = $25,562 AEC 15% = $25,562 A P , 15%, 4 = $8,954. Contemporary Engineering Economics, 6e, GE Park Copyright 2016, Pearson Education, Ltd. All Rights Reserved When only costs are

involved, the AE method is called the annual equivalent cost (AEC). Revenues must cover two kinds of costs: operating costsand capital costs. Annual Equivalent Costs Annual Equivalent Cost (AEC) Capital costs + Operating costs Annual equivalent cost = Capital cost + Operating costs Contemporary Engineering Economics, 6e, GE Park Copyright 2016, Pearson Education, Ltd. All Rights Reserved Capital (Ownership) Cost Def: Owning equipment 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: S 0 N I 0 1 2 3 CR(i) I(A / P , i , N) S(A / F , i , N) (I S)(A / P , i , N) iS Contemporary Engineering Economics, 6e, GE Park CR(i) Copyright 2016, Pearson Education, Ltd.

All Rights Reserved N Cost of Owning a Vehicle SEGMENT BEST MODELS ASKING PRICE PRICE AFTER 3 YEARS Compact car Mini Cooper $19,800 $12,078 Midsize car Volkswagen Passat

$28,872 $15,013 Sports car Porsche 911 $87,500 $48,125 Compact Luxury car BMW 3 Series $39,257 $20,806 Luxury car Mercedes CLK $51,275

$30,765 Minivan Honda Odyssey $26,876 $15,051 Subcompact SUV Honda CR-V $20,540 $10,681 Compact SUV Acura MDX $37,500 $21,375

Full size SUV Toyota Sequoia $37,842 $18,921 Compact truck Toyota Tacoma $21,200 $10,812 Full size truck Toyota Tundra $25,653 $13,083 Contemporary Engineering Economics, 6e, GE Park

Copyright 2016, Pearson Education, Ltd. All Rights Reserved Example: Capital Cost (Mini-Cooper) Capital Recovery Cost Given: o o o o $12,078 0 I = $19,800 N = 3 years S = $12,078 i = 6% Find: CR(6%) 1 2

3 $19,800 CR(i) = (I -S) (A/P , i , N) + iS CR(6%) = ($19,800 - $12,078) (A/P , 6%, 3) + (0.06)$12,078 = $3,614 Contemporary Engineering Economics, 6e, GE Park Copyright 2016, Pearson Education, Ltd. All Rights Reserved Example 6.4: Required Annual Revenue Cost of Owning and Operating Given: o o o o I = $20,000 S = $4,000 N = 5 years i= 10%

Find: See if an annual revenue of $5,000 is large enough to cover both the capital and operating costs. Contemporary Engineering Economics, 6e, GE Park $4,000 Capital cost 0 1 2 3 4 5 $20,000 +

0 1 2 3 4 5 $500 Operating cost Copyright 2016, Pearson Education, Ltd. All Rights Reserved Solution Need additional revenue in the amount of $120.76 to justify the investment Contemporary Engineering Economics, 6e, GE Park Copyright 2016, Pearson Education, Ltd. All Rights Reserved

Where to Apply the AE Analysis Unit cost (or profit) calculation Outsourcing (makebuy) decision Pricing the use of an asset Contemporary Engineering Economics, 6e, GE Park Copyright 2016, Pearson Education, Ltd. All Rights Reserved Unit Cost (Profit) Calculation Step 1: Determine the number of units (annual volume) to be produced (or serviced) each year over the life of the asset. Step 2: Determine the annual equivalent cost (or worth) of owning and operating the asset. Step 3: Divide the equivalent cost (worth) by the annual volume. Contemporary Engineering Economics, 6e, GE Park Copyright 2016, Pearson Education, Ltd.

All Rights Reserved Example 6.5: Unit Profit per Machine Hour When Annual Operating Hours Remain Constant Hours Project Cash Flows and Operating Contemporary Engineering Economics, 6e, GE Park Copyright 2016, Pearson Education, Ltd. All Rights Reserved Example 6.6: Unit Profit per Machine Hour When Annual Operating Hours Fluctuate $35,560 $37,360 $31,850 $34,400 3 4

0 1 2 $76,000 Year 1 3,500 hours Year 2 4,000 hours Contemporary Engineering Economics, 6e, GE Park Year 3 1,700

hours Year 4 2,800 hours Copyright 2016, Pearson Education, Ltd. All Rights Reserved Make or Buy Decision Step 1: Determine the time span(planning horizon) for which the part (or product) will be needed. Step 2: Determine the annual volumeof the part (or product). Step 3: Obtain the unit costof purchasing the part (or product) from an outside firm. Step 4: Determine the equipment, manpower, and all other resources required to make the part (or product). Contemporary Engineering Economics, 6e, GE Park Copyright 2016, Pearson Education, Ltd. All Rights Reserved

Step 5: Estimate the net cash flows associated with the make option over the planning horizon. Step 6: Compute the annual equivalent cost of producing the part (or product). Step 7: Compute the unit cost of making the part (or product) by dividing the annual equivalent cost by the required annual volume. Step 8: Choose the option with the minimum unit cost. Contemporary Engineering Economics, 6e, GE Park Copyright 2016, Pearson Education, Ltd. All Rights Reserved Example 6.7: Outsourcing Production of Electric Compressors Investment and Other Financial Date Related to Outsourcing Electric compressor: $42 per unit Required investment: $325,000 Salvage value: $60,000

Service life: 7 years Annual maintenance cost: $120,000 MARR: 18% Contemporary Engineering Economics, 6e, GE Park Copyright 2016, Pearson Education, Ltd. All Rights Reserved Pricing the Use of an Asset The cost per square foot for owning and operating a real property (example, user fee) The cost of using a private car for business (cost per mile) The cost of flying a private jet (cost per seat) The cost of using a parking deck (cost per hour) Contemporary Engineering Economics, 6e, GE Park Copyright 2016, Pearson Education, Ltd. All Rights Reserved Example 6.8: Pricing an Apartment Rental Fee Investment Problem: Building a 50-unit apartment

complex o Land investment cost = $1,000,000 o Building investment cost = $2,500,000 o Annual upkeep cost = $150,000 o Property taxes and insurance = 5% of o o o o total investment Occupancy rate = 85% Study period = 25 years Salvage value = Only land cost can be recovered in full Interest rate = 15% At Issue: How to price the monthly rental per unit? Contemporary Engineering Economics, 6e, GE Park Copyright 2016, Pearson Education, Ltd. All Rights Reserved

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