ch6 aw analysis_rev2
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Ch6 aw analysis_rev2TRANSCRIPT
Annual Worth AnalysisAnnual Worth Analysis
Chapter 6
04/08/232
Objectives• Using AW for different life alternatives without
repeating CFD’s.• AW of permanent alternatives (capitalized cost
analysis…from Chapter 5)
Annual Worth Analysis
• AW is easy to understand by any individual acquainted with annual amounts, that is, dollars per year.
• AW = PW(A/P,i,n) = FW(A/F,i,n)• The n in the factors is the number of years for
equal-service comparison.
04/08/233
Annual Worth Analysis• When alternatives being compared have
different lives, the AW method makes the assumptions that
• 1. The services provided are needed for at least the LCM of the lives of the alternatives.
• 2. The selected alternative will be repeated for succeeding life cycles in exactly the same manner as for the first life cycle.
• 3. All cash flows will have the same estimated values in every life cycle.
Example
Example – cont.
Example – cont.
Capital Recovery and AW
• The annual worth (AW) value for an alternative is comprised of two components:
• capital recovery for the initial investment P at a stated interest rate (usually the MARR) and the equivalent annual amount A. The symbol CR is used for the capital recovery component. In equation form,
AW = -CR-A• Both CR and A have minus signs because they
represent costs.
Capital Recovery and AW• The recovery of an amount of capital P committed to an asset,
plus the time value of the capital at a particular interest rate, is a very fundamental principle of economic analysis.
• Capital recovery is the equivalent annual cost of owning the asset plus the return on the initial investment.
• The AI P factor is used to convert P to an equivalent annual cost.
• If there is some anticipated positive salvage value S at the end of the asset's useful life, its equivalent annual value is removed using the A I F factor.
CR = -[P(A/P,i,n) - S(A/F,i,n)]
Example
Example• The AOC is A = $ - 0.9 per year,• The present worth P in year 0 of the two separate investment
amounts of $8 and $5 is determined before multiplying by the A/ P factor.– CR = - [8.0 + 5.0(P/ F,12%,1)](A / P,12%,8) -0.5(A / F,12%,8)= - [12.46](0.2013) - 0.040= $ - 2.47
– It means that each and every year for 8 years, the equivalent total revenue must be at least 2.47 to recover the initial PW investment and MARR of 12 %.
– Total AW = -2.47-0.9 = -3.37 mil