Engineering Economics John Ayers September 17 2004 Engineering

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. Example: What amount must be paid to settle a current debt of $1000 in two years at an interest rate of 8% ? Solution: $1000 (1 + 0. 08) = $1166 $1000 1 2 $1166

Cash Flow Diagrams P-Pattern F-Pattern A-Pattern G-Pattern 1 1 2 2 3 3 n n “present” “future” “annual” “gradient”

Equivalence of Cash Flow Patterns To Find Given Multiply By F P P F A P A G Formula

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? 50 k 50 k Solution: 1 P 2 3 4 5 6 7

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: Annual Net Equivalent Value

Example: A new circuit board component insertion tool is needed. Which should you buy? Model Price Annual Maintenance Salvage Value Life JACO $220 k $30 k 10 years Cheepo $100 k $35 k 0 5 years Solution: The ANEV is calculated for each: 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: 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. Model Price Annual Maintenance Salvage Value Life JACO $220 k $30 k 10 years Cheepo $100 k $35 k 0 5 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. $