ENGINEERING ECONOMICS

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ENGINEERING ECONOMICS Factor Name Coverts Symbol Formula Sgle Paymet Compoud Amout to F gve P (F/P, %, ) ( + ) Sgle Paymet Preset Worth to P gve F (P/F, %, ) ( + ) Uform Seres to A gve F (A/F, %, ) Skg Fud + Captal Recovery to A gve P (A/P, %, ) Uform Seres Compoud Amout Uform Seres Preset Worth Uform Gradet Preset Worth Uform Gradet Future Worth Uform Gradet Uform Seres to F gve A (F/A, %, ) to P gve A (P/A, %, ) to P gve G (P/G, %, ) to F gve G (F/G, %, ) to A gve G (A/G, %, ) ( ) ( + ) ( + ) ( + ) + + ( ) ( ) ( + ) ( + ) ( + ) ( + ) ( + ) NOMENCLATURE AND DEFINITIONS A... Uform amout per terest perod B... Beeft BV... Book value C... Cost d... Iflato adjusted terest rate per terest perod D j... Deprecato year j F... Future worth, value, or amout f... Geeral flato rate per terest perod G... Uform gradet amout per terest perod... Iterest rate per terest perod e... Aual effectve terest rate m... Number of compoudg perods per year... Number of compoudg perods; or the expected lfe of a asset P... Preset worth, value, or amout r... Nomal aual terest rate S... Expected salvage value year Rsk Rsk s the chace of a outcome other tha what s plaed to occur or expected the aalyss. NON-ANNUAL COMPOUNDING m r m e = b + l - BREAK-EVEN ANALYSIS By alterg the value of ay oe of the varables a stuato, holdg all of the other values costat, t s possble to fd a value for that varable that makes the two alteratves equally ecoomcal. Ths value s the break-eve pot. Break-eve aalyss s used to descrbe the percetage of capacty of operato for a maufacturg plat at whch come wll just cover expeses. The payback perod s the perod of tme requred for the proft or other beefts of a vestmet to equal the cost of the vestmet. Subscrpts j... at tme j... at tme... F/G = (F/A )/ = (F/A) (A/G) ENGINEERING ECONOMICS

INFLATION To accout for flato, the dollars are deflated by the geeral flato rate per terest perod f, ad the they are shfted over the tme scale usg the terest rate per terest perod. Use a flato adjusted terest rate per terest perod d for computg preset worth values P. The formula for d s d = + f + ( f) DEPRECIATION Straght Le C - S Dj = Modfed Accelerated Cost Recovery System (MACRS) Dj = (factor) C A table of MACRS factors s provded below. BOOK VALUE BV = tal cost Σ D j TAXATION Icome taxes are pad at a specfc rate o taxable come. Taxable come s total come less deprecato ad ordary expeses. Expeses do ot clude captal tems, whch should be deprecated. CAPITALIZED COSTS Captalzed costs are preset worth values usg a assumed perpetual perod of tme. Captalzed Costs = P = A BONDS Bod value equals the preset worth of the paymets the purchaser (or holder of the bod) receves durg the lfe of the bod at some terest rate. Bod yeld equals the computed terest rate of the bod value whe compared wth the bod cost. RATE-OF-RETURN The mmum acceptable rate-of-retur (MARR) s that terest rate that oe s wllg to accept, or the rate oe desres to ear o vestmets. The rate-of-retur o a vestmet s the terest rate that makes the beefts ad costs equal. BENEFIT-COST ANALYSIS I a beeft-cost aalyss, the beefts B of a project should exceed the estmated costs C. B C 0, or B/C Year 0 MACRS FACTORS Recovery Perod (Years) 0 Recovery Rate (Percet). 0.00. 0.00..00..00..0..0................. ENGINEERING ECONOMICS

ENGINEERING ECONOMICS Factor Table - = 0.0% 0 0 0 0 0 0 00 0.0 0.0 0. 0.0 0. 0.0 0. 0.0 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.0 0.0 0.00 0. 0. 0. 0. 0.0 0. 0. 0. 0.0 0.0..0.0....0..0 0.0........0..0 0......... 0.0.0.0.0. 0.......0..... 0.00...0..00...,0.,.,..000.000.0.00.0.00.0.00.0.0.0.0.00.0.0.0.0.0.0.0.0.0.....0....000.00.00.00.0.0.. 0.0......... 0..00..0.0..00...00..000 0.0 0. 0. 0.00 0. 0. 0. 0. 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.00 0.0 0.0 0.0 0.0 0.00 0.0 0.0 0.0 0.0 0. 0. 0. 0.0 0. 0.0 0. 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.00 0.0 0.0 0.00 0.0 0.0 0.0 0.0 0.0 0.0 0.00 0.0 0.0 0.0 0.00 0. 0...00..0....0.0.0.0.0.0.0..0.. 0. 0.0..0....00. Factor Table - =.00% 0 0 0 0 0 0 00 0.0 0.0 0.0 0.0 0. 0.0 0. 0. 0. 0.0 0. 0. 0. 0.00 0. 0. 0. 0.0 0. 0. 0. 0.0 0. 0. 0. 0. 0. 0.00 0.0 0. 0.0.0.0.00.....0. 0....00.....0.0.0.0 0...0.0...0.0 0.0..0.0.0.... 0.0 0....0 0. 0...0..0..00.00..00..,.0,0..000.00.00.00.00.0.0.0.0.0.....0....0.0..........0.000.00.00.00.0... 0....0..0..0. 0.0.00......... 0..000 0.0 0.00 0. 0.00 0. 0. 0.0 0. 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.00 0.0 0.0 0.00 0.00 0.0 0.0 0.0 0.0 0.00 0.0 0.0 0.0 0. 0.00 0. 0.0 0. 0. 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.00 0.0 0.0 0.00 0.00 0.0 0.0 0.0 0.0 0.00 0.0 0.0 0.00 0. 0...0.0.0....00..0......0.. 0.0 0..0......

0 ENGINEERING ECONOMICS Factor Table - =.0% 0 0 0 0 0 0 00 0. 0.0 0. 0. 0. 0. 0.00 0. 0. 0. 0. 0. 0.0 0. 0. 0.0 0. 0. 0. 0. 0. 0.0 0.00 0. 0. 0. 0. 0.0 0.0 0. 0.........0. 0.0 0.0.....0....00.0.0 0.00 0..0...0. 0.0..0...0.. 0...0... 0..00. 0.0... 00.000.00.0.0...,.0.00.00.0.0.0.0.0...0.....0.0.0.0.0....0..0..0.0..0.00.0.00...0.. 0.0..0..0...0 0....0... 0.00.....00.00 0. 0. 0. 0.0 0. 0. 0. 0. 0.0 0.0 0.0 0.0 0.0 0.0 0.00 0.0 0.0 0.00 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0. 0. 0. 0. 0.0 0. 0. 0.0 0.0 0.0 0.0 0.00 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.00 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.00 0.00 0. 0.0..0..0..00.........0..00.0.0 0. 0......00. Factor Table - =.00% 0 0 0 0 0 0 00 0.0 0. 0. 0. 0.0 0.0 0.0 0. 0. 0.0 0.0 0. 0.0 0. 0.0 0. 0. 0.00 0. 0.0 0. 0. 0. 0. 0.0 0. 0. 0. 0.0 0.0 0.0...0..0.0.... 0...0....0...0.0.......0.0 0....0.0.0..0......0. 0....00...0.0....0.,..000.00.0.0.0.....0.......00.....0..0.0..00..0..000.00..00.0..0. 0....0... 0.0..0...0.0 0..00 0. 0.00..0..000 0.0 0. 0. 0. 0. 0. 0. 0. 0. 0.0 0.0 0.0 0.0 0.0 0.0 0.000 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0. 0. 0. 0. 0. 0. 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.000 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.00 0.00 0.0 0...0..0....0....0.0...0..0.0 0. 0. 0..0. 0.0..

ENGINEERING ECONOMICS Factor Table - =.00% 0 0 0 0 0 0 00 0. 0. 0.0 0. 0. 0.0 0. 0.0 0.0 0. 0. 0. 0.00 0. 0. 0. 0. 0. 0. 0. 0. 0.0 0.0 0.0 0. 0.0 0.0 0.0 0.0 0.0 0.......00...0.0.. 0.......0.0...0..0....00 0..0.0..0.0.0.0. 0........ 0.. 0..0..0.00 0.0.0....000.0........0..00...00.0..0.0........00.0 0. 0.0.000....0.. 0..00..0.. 0.0.......0..0..0.0..0,..000 0.0 0.0 0. 0. 0.0 0. 0. 0. 0. 0. 0.0 0.00 0.0 0.0 0.0 0.0 0.00 0.0 0.0 0.0 0.0 0.0 0.0 0.00 0.0 0.00 0.0 0.0 0.00 0.0 0.0 0. 0. 0.0 0. 0.0 0.0 0.0 0.0 0.0 0.00 0.0 0.0 0.0 0.0 0.00 0.0 0.0 0.0 0.0 0.0 0.0 0.00 0.0 0.00 0.00 0.00 0.000 0.0 0..0.......00.0....0.0.0..0..0........00 Factor Table - =.00% 0 0 0 0 0 0 00 0. 0.00 0. 0. 0. 0.00 0. 0. 0. 0. 0. 0.0 0. 0. 0. 0. 0. 0.0 0.0 0. 0. 0. 0. 0.0 0.0 0. 0.0 0.0 0.00 0.00 0...0.....0.0.0....0. 0.0 0. 0.....0.0.0...0... 0.00........0.0 0......0..0.0.. 0.00 0......0.0.000..0....0...0..0..0..0...0.0..0..0.. 0..0..0.000........0....0.0.. 0.0.00.... 0...0.0 0..,..000 0. 0. 0. 0. 0.0 0. 0.0 0.0 0. 0. 0. 0.0 0.0 0.00 0.00 0.0 0.0 0.0 0.0 0.00 0.00 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.00 0. 0. 0. 0. 0. 0. 0.00 0.00 0.0 0.0 0.0 0.00 0.0 0.00 0.00 0.0 0.0 0.0 0.0 0.00 0.00 0.0 0.0 0.0 0.0 0.00 0.00 0.00 0.000 0. 0....0....00...0..0..0...0...0..0 0..0..0.

ENGINEERING ECONOMICS Factor Table - =.00% 0 0 0 0 0 0 00 0. 0. 0. 0.0 0.0 0.0 0. 0.0 0.00 0. 0. 0. 0. 0.0 0. 0. 0.0 0.0 0. 0. 0. 0. 0.0 0. 0.0 0.0 0.00 0.0 0.00 0.000 0.......0...0.0..0......0. 0.0 0.00 0. 0. 0...... 0..0.0. 0..0.0.0. 0...0...0. 0..0.0.0. 0...0 0..0..000.0.000...0....0.0........000.0..0.0.... 0.0..0 0.,..000..0... 0........ 0..0.0..0 0.. 0...0..0.0,.,..000 0.0 0.0 0.0 0.0 0. 0. 0.0 0.0 0.0 0.0 0. 0. 0. 0. 0.0 0.0 0.0 0.0 0.0 0.0 0.00 0.0 0.00 0.0 0.0 0.0 0.0 0.00 0.000 0.0 0.00 0. 0.0 0. 0. 0.00 0.00 0.00 0.00 0.0 0.0 0.0 0.0 0.00 0.0 0.0 0.0 0.0 0.0 0.00 0.0 0.00 0.0 0.00 0.00 0.00 0.000 0.0 0..00....0.0....0...0.0.0..0.0...00.. 0..0.0. Factor Table - = 0.00% 0 0 0 0 0 0 00 0.0 0. 0. 0.0 0.0 0. 0. 0. 0. 0. 0.0 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.0 0.0 0.0 0.0 0.00 0.00 0.000 0.0....0....0....0..0..0.0.......00..... 0.......0....0..00 0.0.....0.0 0.....0...00.0.000.00.0..0...........0.0....00.0.. 0....0 0.,0..000.00.0.0.........0.. 0....0.00.0.0...0.,.0,0.,..000 0. 0.0 0. 0. 0. 0.0 0. 0. 0. 0.0 0. 0.0 0. 0. 0. 0. 0. 0. 0. 0. 0.0 0. 0. 0.0 0.0 0.0 0.00 0.00 0.000 0. 0.0 0. 0. 0. 0.0 0.0 0.0 0.0 0.00 0.0 0.00 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.00 0.0 0.0 0.00 0.00 0.00 0.000 0.000 0. 0...0...00...0......0.0..0...0..0..0.0.0.

ENGINEERING ECONOMICS Factor Table - =.00% 0 0 0 0 0 0 00 0. 0. 0. 0. 0. 0.0 0. 0.0 0.0 0.0 0. 0. 0. 0.0 0. 0. 0. 0.00 0. 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.00 0.00 0.00 0..0.0.0.0.....0.....0.0.....0.....0..0.0. 0..0..0.0... 0....0..0.0. 0.00.... 0...0....00..00..0....0.0..0..0....0.0.00.. 0.0.00...000..00.00.,..00.... 0.00... 0...0.......0..0 0.0....0,00.0,.,00..00 0. 0. 0. 0. 0. 0. 0.0 0. 0.0 0. 0. 0. 0.0 0. 0. 0.0 0. 0. 0. 0. 0.0 0. 0. 0. 0. 0. 0.0 0.0 0.00 0. 0. 0.0 0. 0. 0.0 0.0 0.0 0.00 0.0 0.0 0.0 0.00 0.0 0.0 0.00 0.0 0.0 0.0 0.0 0.00 0.00 0.00 0.00 0.00 0.00 0.000 0.000 0. 0....0.........0.....00...00.0.0..... Factor Table - =.00% 0 0 0 0 0 0 00 0. 0. 0.0 0. 0. 0.0 0. 0.0 0. 0. 0. 0. 0. 0.0 0.0 0.00 0.000 0.00 0.0 0.0 0.00 0.0 0.0 0.0 0.0 0.000 0.00 0.000 0.000 0....0....0.00..0..0.00.0.......0..0...... 0.....0.0 0...... 0........000.0.... 0. 0. 0. 0..00..0.......... 0...0....0...00.00..0 0.,. 0,.00,,..00......0.0.... 0.0 0..0.00 0.0..0.00 0....0 0.0,.0,.0,.,,..00 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.0 0.0 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.0 0.00 0.00 0.00 0. 0. 0. 0. 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.000 0. 0.0...0.....0.0..00...0..00....0.00.0..0...

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