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