2 Annual Equivalent Worth Criterion AE worth criterion provides a basis for measuring investment worth by determining equal payments on annual basis.Knowing that any lump-sum cash amount can be converted into a series of equal annual paymentsFind the net present worth of the original series and then multiply this amount by the capital-recovery factor:AE (i)=PW (i) x (A/P, i, N)We use this formula to evaluate the investment worth of projects. Therefore, AE criterion provides basis for evaluating a project that is consistent with the PW criterion.
4 Benefits of AE Analysis In the real world situations, AE analysis is preferred, or demanded, over NPW analysisConsider that even corporations issue annual reports and develop yearly budgets.For these purposes, a company may find it useful to present the annual cost or benefit of ongoing project rather than its overall cost or benefit. More specifically;When consistency of report formats is desiredFinancial managers and engineering managers use annual reports and submit project analysis annual basis that is easy use by other members of the corporation and stock holders.When there is a need to determine unit costs or profitsProjects must be broken into unit cost (or profits) for easy comparison with alternatives.When project lives are unequal
5 Annual Equivalent Cost When only costs are involved, the AE method is called the annual equivalent cost method.Revenues must cover two kinds of costs: Operating costs and capital costs.CapitalcostsAnnual Equivalent Costs+Operatingcosts
6 Operating costs are incurred by operation of physical plant or equipment needed to provide service; examples include the costs of items; labor, & raw materials.Capital recovery costs ( or ownership costs) are incurred by purchasing assets to be used in production and service.Normally, Capital costs are nonrecurring (one time costs), where as operating costs recur as long as an asset is owned.Annual equivalent of a capital cost is given special name: Capital Recovery cost, designated CR (i).
7 Capital (Ownership) Costs Definition: Owning equipment is associated with two transactions - (1) its initial cost (I) and (2) its salvage value (S).Capital costs: Taking these items into account, we calculate the capital costs as:SNINCR(i)
12 Applying Annual Worth Analysis Unit Cost (Unit Profit) CalculationTo obtain a unit profit (or cost), we may proceed as follows:Determine the number of units to be produced (or service) each year over the life of the asset.Identify the cash flow series associated with production or serviceover the life of the asset.3. Calculate the present worth of the project cash flow series at a given interest rate and then determine the equivalent annual worth.Divide the equivalent annual worth by the number of units to be produced or serviced during each year.
13 Example 6.3 Equivalent Worth per Unit of Time $24,400$55,760$27,340$75,000Operating Hours per Year2,000 hrs.PW (15%) = $3553AE (15%) = $3,553 (A/P, 15%, 3)= $1,556Savings per Machine Hour= $1,556/2,000= $0.78/hr.
14 SummaryAnnual equivalent worth analysis, or AE, is—along with present worth analysis—one of two main analysis techniques based on the concept of equivalence. The equation for AE isAE(i) = PW(i)(A/P, i, N).AE analysis yields the same decision result as PW analysis.The capital recovery cost factor, or CR(i), is one of the most important applications of AE analysis in that it allows managers to calculate an annual equivalent cost of capital for ease of itemization with annual operating costs.
15 The equation for CR(i) is CR(i)= (I – S)(A/P, i, N) + iS,where I = initial cost and S = salvage value.AE analysis is recommended over NPW analysis in many key real-world situations for the following reasons:1. In many financial reports, an annual equivalent value ispreferred to a present worth value.2. Calculation of unit costs is often required to determinereasonable pricing for sale items.3. Calculation of cost per unit of use is required toreimburse employees for business use of personal cars.