(c) 2001 Contemporary Engineering Economics 2 Annual Equivalent Worth (AE) Analysis 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 payment Find 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. ( Example 8.1 )
(c) 2001 Contemporary Engineering Economics 3 Benefits of AE Analysis In the real world situations, AE analysis is preferred, or demanded, over NPW analysis Consider that 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.
(c) 2001 Contemporary Engineering Economics 4 Capital Cost versus Operating Cost When only costs are involved, the AE method is sometimes called the annual equivalent cost method. In this case we have two kinds of costs: operating costs and capital costs. Capital costs Operating costs + Annual Equivalent Costs
(c) 2001 Contemporary Engineering Economics 5 Operating costs are incurred by operation of physical plant or equipment needed to provide service, i.e. labor, & raw materials. Capital recovery costs ( or ownership costs) are incurred by purchasing assets to be used in production and service. Usually 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).
(c) 2001 Contemporary Engineering Economics 6 Capital (Ownership) Costs The cost of owning an equipment is associated with two transactions, (1) its initial cost (I) and (2) its salvage value (S). Capital costs: Taking into these sums, we calculate the capital costs as: 0 1 2 3 N 0 N I S CR(i)
(c) 2001 Contemporary Engineering Economics 7 Example - Capital Cost Calculation Given: I = $200,000 N = 5 years S = $50,000 i = 20% Find: CR(20%) $200,000 $50,000 5 0
(c) 2001 Contemporary Engineering Economics 8 Example 8.3 Justifying an investment based on AE Method Given: I = $20,000, S = $4,000, N = 5 years, i = 10% Find: see if an annual revenue of $4,400 is enough to cover the capital costs. Solution: CR(10%) = $4,620.76 Conclusion: Need an additional annual revenue in the amount of $220.76.
(c) 2001 Contemporary Engineering Economics 9 Applying Annual Worth Analysis To obtain a unit profit (or cost), we may proceed as follows: Unit Cost (Profit) Calculation ( Example 8.4) 1. Determine the number of units to be produced (or service) each year over the life of the asset. 2. Identify the cash flow series associated with production or service over 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. 4. Divide the equivalent annual worth by the number of units to be produced or serviced during each year. Unequal Service Life Comparison (Example 8.5)
(c) 2001 Contemporary Engineering Economics 10 Example 8.4 Equivalent Worth per Unit of Time 0 1 2 3 $24,400 $55,760 $27,340 $75,000 Operating Hours per Year 2,000 hrs. PW (15%) = $3553 AE (15%) = $3,553 (A/P, 15%, 3) = $1,556 Savings per Machine Hour = $1,556/2,000 = $0.78/hr.
(c) 2001 Contemporary Engineering Economics 11 Summary Annual 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 is AE(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.
(c) 2001 Contemporary Engineering Economics 12 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 is preferred to a present worth value. 2. Calculation of unit costs is often required to determine reasonable pricing for sale items. 3. Calculation of cost per unit of use is required to reimburse employees for business use of personal cars.