Engineering Economics. John Ayers September 17, 2004

Engineering Economics Why is it important? Value and Interest Cash Flow Diagrams and Patterns Equivalence of Cash Flow Patterns Evaluating Alternatives Break-Even Analysis Income Tax and Depreciation Inflation Conclusion

Why do we care about Engineering Economics? Engineering designs are intended to produce good results. They are accompanied by undesirables (costs). If outcomes are evaluated in dollars, and “good” is defined as profit, then decisions will be guided by engineering economics. This process maximizes goodness only if all outcomes are anticipated and can be monetized. $

Value and Interest The “value” of money depends on the amount and when it is received or spent. 12 $1000 $1166 Example: What amount must be paid to settle a current debt of $1000 in two years at an interest rate of 8% ? Solution: $1000 ( ) ( ) = $1166

Cash Flow Diagrams P-Pattern 123n “present” F-Pattern 123n “future” A-Pattern 123n “annual” G-Pattern 123n “gradient”

Equivalence of Cash Flow Patterns To FindGivenMultiply ByFormula FP PF AP AG

Example: A new circuit board component insertion tool will save $50,000 in production costs each year and will have a life of seven years. What is the highest price that can be justified for the tool using a 12% interest rate? Solution: P 50k

Evaluating Alternatives Annual Equivalent Cost Comparisons Present Equivalent Cost Comparisons Incremental Approach Rate of Return Comparisons Benefit/Cost Comparisons Minimum Attractive Rate of Return (MARR): The lowest rate of return that the organization will accept.

Annual Equivalent Cost Comparison Incomes are converted to an A-pattern. Costs are converted to an A-pattern. The costs are subtracted from the incomes to determine the ANEV. Mutually Exclusive Alternatives – choose the one with highest ANEV Independent Alternatives – choose all with positive ANEV ANEV: Annual Net Equivalent Value

Example: A new circuit board component insertion tool is needed. Which should you buy? Solution: The ANEV is calculated for each: ModelPriceAnnual MaintenanceSalvage ValueLife JACO$220k$20k$30k10 years Cheepo$100k$35k05 years JACO: Cheepo: JACO

Present Equivalent Cost Comparison Incomes and costs are converted to P-patterns. The costs are subtracted from the incomes to determine the PNEV. Mutually Exclusive Alternatives – choose the one with highest PNEV Independent Alternatives – choose all with positive PNEV PNEV: Present Net Equivalent Value, also called “life cycle cost,” “present worth,” “capital cost,” and “venture worth.”

Incremental Approach For a set of mutually exclusive alternatives, only the differences in amounts need to be considered. ModelPriceAnnual MaintenanceSalvage ValueLife JACO$220k$20k$30k10 years Cheepo$100k$35k05 years JACO- Cheepo: JACO

Rate of Return Method ANEV or PNEV is formulated From this, we solve for the interest rate that will give zero ANEV or PNEV This interest rate is the ROR of the alternative For mutually exclusive alternatives, the one with the highest ROR is chosen For independent alternatives, all with a ROR greater than MARR are accepted ROR: Rate of Return on Investment

Benefit/Cost Comparisons The benefit/cost ratio is determined from For mutually exclusive alternatives, the one with the highest B/C is chosen. For independent alternatives, all with B/C > 1 are accepted. The MARR is used to determine the numerator (benefits).

Break-Even Analysis Break-even point: the value of an independent variable such that two alternatives are equally attractive. For values above the break-even point, one alternative is preferred. For values below the break-even point, the other is preferred. Break-even analysis is useful when dealing with a changing variable (such as MARR).

Income Tax and Depreciation Businesses pay the IRS a tax: Depreciation: method of charging the initial cost of an asset against more than one year. An asset is depreciable if : –It is used to produce income, –Has a life greater than one year, but –Decays, wears out, becomes obsolete, or gets used up. ACRS: Accelerated Cost Recovery System, used by IRS since 1980.

Inflation The buying power of money changes with time. Inflation, if anticipated, can be put to good use by fixing costs and allowing income to rise by –Entering long-term contracts for materials or wages –Purchasing materials long before they are needed –Stockpiling product for sale later.

Conclusion For-profit enterprises exist to make money. Non-profit entities also make decisions to maximize the goodness of outcomes by assigning dollar values. Your engineering decisions will be shaped by economics. $