ngineering Economics Chapter 9DEPRECIATION & INCOME TAX. Depreciation -- concepts & methods. Capital cost allowance (CCA). Tax concept. After tax comparisons of projects & economic feasibility_____________________________________________________________Depreciation:a decrease in worth of an asset; recognized by tax regulations as an expenseof operating a business for tax purposes.Causes of Declining Value-- physical, technological, etc.Depreciation Methods:. Straight Line (constant depreciation) Method. Declining Balance Method. Other methods___________________________________________________________CHEER/SHEER Software: Use Depreciation Methods & After Tax Cash Flow Modules (Canadian & U.S. regulations).___________________________________________________________Straight Line Method of DepreciationP= purchase price S=Salvage value at the end of useful life N= useful life (yrs)n= years from time of purchaseAnnual depreciation charge DC=(P-S)/NBook value at the end of year n = BV(n)=P-n[(P-S)/N]Example: P = $7000 S=$1000 N=5 yearsDC (Constant/Yr.)= (7000-1000)/5= 1,200Accumulated depreciation (depreciation reserve) at the end of Yr.3 = BV(3) = Book value at the beginning of Yr.4 = 7000-3[(7000-1000)/5]= 3,400Or it could be found as:= Purchase price - Sum(of depreciation charges) = 7000-3(1200)= $3,400Note: This method is used for company asset valuation, etc. Revenue Canada requires another method (described later).________________________________________________________________Capital Cost Allowance (CCA)Under the Canadian Tax Regulations, businesses can claim allowances on property, equipment, etc. used to earn income.The depreciation deduction is referred to as a Capital Cost Allowance (CCA). Under the CCA system, depreciable property or assets are grouped into specific classes. Property and assets within each class have the same method and rate of depreciation. See Tables 9.2 (CCA Declining Balance Classes and Rates) and Table 9.3 (CCA, Straight Line Classes)._________________________________________________________Methods used to determine CCA:.Declining Balance Method: CCA rate is applied to the Undepreciated Capital Cost Allowance (UCC), also called Book Value..Straight Line Method: CCA rate is applied to the purchase price._______________________________________________________________Note: Depreciation is the same as Capital Cost Allowance.For Straight Line Depreciation, S may not specified. See Table 9.3 (of text book). A percentage of purchase price (e.g., 50%) can be specified._________________________________________________________________Capital Cost Allowance, Straight Line Classes (Table 9.3)ExamplesClass 12 .. computer software(except system software) . CCA rate =100%For example, if $10,000 is the purchase price, the CCA allowance is $10,000 in yr.1Class 27 air pollution control equipment .. CCA rate = 50%For example, if P=10,000, the CCA allowance is: 5000 for yr.1 and 5000 for year 2._____________________________________________________________________________Half-Year RuleDuring year 1, for specified assets, one-half of the normally allowable depreciation can be claimed.Example: Class 8: 20% CCA => 10% for yr.1 is allowed._____________________________________________________________________________Capital Cost Allowance: Straight Line ClassesClass 29: CCA rate = 50%Half-yr exempt.Purchase price = $10,000 in 2001CCA in 2001= 10,000x0.5= $5000CCA in 2002= $5000Sum of depreciation = $10,000Now assume that for this class, half-year rule is applicable; CCA = 50%CCA in 2001 = ($10,000)(0.5)(1/2) = $2,500CCA in 2002 = ($10,000)(0.5) = $5,000CCA in 2003 = ($10,000-($2500+$5000))= $2,500Sum of depreciation = $10,000______________________________________________________________________________Declining Balance MethodIt is a means of amortizing an asset at an accelerated rate early in its life.For "Half-Year Rule" Exempt Assets:BV(n) = P(1-depreciation rate)nDC(n) = BV(n-1)(depreciation rate)WhereP = purchase pricen= year from time of purchaseBV(n) = Book value at the end of year n (also called undepreciated capital cost UCC)BV(n-1)= Book value at the end of year n-1DC(n)= Depreciation charge for year nFor Assets with "Half-Year Rule" Applicable:BV(n) = (P/2)(1-depreciation rate)n-1+(P/2)(1-depreciation rate)nDC(n) = BV(n-1)(depreciation rate)Half-Year Rule & Declining Balance MethodExample: Purchase price of equipment = $700Million. CCA = 20%. Half-Yr. rule is applicable.Year 1 Depreciation = $700x20% CCA ratex0.5 = $140/2=$70Yr.2 Depreciation = ($700-70)x20% rate = $126Note: ($700/2)(0.2) + [($700/2)-$70](0.2) = $126Yr.3 Depreciation = ($700-$196 total of yrs.1 and 2 depreciation)(0.2) = $101Undepreciated Capital Cost (UCC) or Book value at the end of year 3= [Undepreciated balance at the beginning of yr.3 of $504]-[Yr.3 depreciation of $101]= $403Another Approach:UCC @ the end of yr.3 = (Purchase price/2)(1-CCA rate)3+ (Purchase price/2)(1-CCA rate)2= ($700/2)(1-0.2)3+ ($700/2)(1-0.2)2= $179.20 + $224.00 = $403.20______________________________________________________________________________Capital Cost Allowance: Declining Balance MethodExample: Purchase price of equipment = $700M. CCA = 20%. Half-yr. rule is not applicable. Find depreciation for years 1,2,and 3 and book value at the end of year 3.Solution: (drop M)Yr.1: CCA=(700)(0.2)=140Yr.2: UCC=700-140=560CCA=560x0.2= $112Yr.3: UCC=560-112=448CCA=448x0.2= 89.6Book Value at the end of Yr.3 = UCC= 448-89.6=358.4YearUCC @ beginning of yearUCC @ end of yearCCA

0$700

1$700$560$140

2560448112

3448358.489.6

Income Tax ConsiderationsTypes of Taxes: Governments (i.e. federal, provincial, and municipal) charge various types of taxes. Some of these are: property taxes, excise taxes (on production of certain products), income taxes.Corporate Income Taxes. Taxable income = (gross income - expenses - interest on debt - capital cost allowance). Corporate income tax = (taxable income)x(effective tax rate). After tax cash flow (ATCF) = gross income - expenses - debt payment - income taxEffective tax rates: See text bookTypes of corporations & income/gains: a number of types. See text book.Capital Gain, CCA Recapture, Tax Shield AdjustmentCapital Gain: If sale price (i.e., salvage or disposition) > original purchase price, apply capital gain tax at 1/2(tax rate t) or any other capital gain tax rate specified.Sale price - Purchase price = Capital gainIf sale price = purchase price, no capital gain.CCA Recapture: If sale price is higher than UCC or book value, CCA recapture applies.CCA Recapture = (Sale price - UCC)(tax rate)Note: Here, sale price < purchase price. On the other hand, if sale price > purchase price, both capital gain tax and CCA recapture applyTax Shield Adjustment:If (sale price - UCC) = 0, no CCA recapture or tax shield adjustment applies.If (UCC-sale price) > 0, tax shield adjustment could be required.Capital Gain & CCA Recapture: ExamplePurchase price = $50,000 five years ago.Sale price = $60,000Effective tax rate = 46%Class 8=> CCA rate = 20% Declining Balance class (half-yr. rule)Capital Gain:Capital Gain = 60,000-50,000 = 10,000Assumed tax rate for capital gain = (1/2)(effective income tax rate)Capital gain tax = (1/2)(0.46)(10,000) = $2,300CCA Recapture:UCC or book value after 5 yrs of use (half yr. rule) = (50,000/2)(1-CCA rate of 0.2)4+ (50,000/2)(1-CCA rate of 0.2)5= $18,429CCA recapture = (purchase price - UCC)(tax rate) = (50,000-18,429)(0.46) = $14,522.66Total tax on asset disposal = $2,300 + $14,522.66 = $16,822.66______________________________________________________________________________After-Tax Cash Flow AnalysisExample: For a 3 year project, the following estimates are provided. Find the Net Present Worth (after-tax). Purchase price=$700M. Resale=$450M. Income/yr=$500M. Expenses=$350M/yr. CCA=20% (half yr. rule applicable). Loan = $550M, to be repaid in 3 years @ 8% interest rate. Tax rate = 40% and MARR (after tax) = 9%.Solution: Drop M.Yr.IncomeExpensesCCALoanPrincipalLoanInterestTaxable IncomeTaxAfter Tax Cash Flow

0700550-150

150035070169.4244.0036.0014.40-77.82

2500350126182.9730.45-6.45-2.58-60.84

3500350100.8197.6115.8133.3913.36-76.78

3Salvage450.00

3CCA recapture-18.72

NPW= (-700+550)-77.82(P/F,9%,1)-60.84(P/F,9,2)+(-76.78+450.00-18.72)(P/F,9%,3)= $1.14M (Feasible)Calculations:CCA for Yr.1=700(1/2)(0.2)= 70CCA for Yr. 2 =(700-70)(0.2)=126CCA for Yr.3=(700-70-126)(0.2)=100.80UCC (at the end of Yr.3)=700- Sum of (70+126+100.80)=403.20 UCC, CCA recapture applies.CCA recapture=[450-403.20](tax rate of 0.4)= 18.72 ( a tax, a negative cash flow item).Loan: principal = 550 Interest = 8%Equal annual payment A = 550(A/P,8%,3)=213.42Yr.1: Interest= 550x0.08= 44.00; Principal = 213.42-44.00=169.42Yr.2: Balance of principal= 550-169.42=380.58; Interest=380.58x0.08=30.45; Principal=213.42-30.45=182.97Etc.Taxable Income = income-expenses-CCA-interestYr.1: 500-350-70-44=36.00Yr.2: 500-350-126-30.45=-6.45Etc.Tax @ 40% = (Taxable Income)(0.40)Yr. 1: 36x0.4=14.40Yr.2: -6.45x0.4 = -2.58Etc.After Tax Cash Flow (ATCF) = Income-Expenses-Loan repayment-TaxYr.1: 500-350-213.42-14.40 = -77.82Etc.______________________________________________________________________________CCA Tax Shield (Tax Deductions/Savings)Assumed investment of $1CCA rate (depreciation) = d (declining balance)Tax rate = tYr.1 capital cost allowance = $1(d)Yr.1 tax saving due to CCA = $1(d)(t)Yr.2 capital cost allowance = (1-d)(d)Yr.2 tax savings due to CCA=(1-d)(d)(t)Yr.3 capital cost allowance=[(1-d)-(1-d)(d)]dYr.3 tax savings=(1-d)2(d)(t)..Yr.N tax savings=(1-d)N-1(d)(t)Sum of tax savings in PW= (P/F,i,1)[(dt)]+ (P/F,i,2)(1-d)(dt)]+ (P/F,i,3)[(1-d)2(dt)]+..+..=CCA Tax Shield = [td/(i+d)]Capital Cost Tax Factor (i.e. actual cost to investor): CCTF=1-Tax Shield= 1-[td/(i+d)]Note: P/F,i,N = 1/(1+i)NTax Shield & Capital Cost Tax FactorFull-Yr. Rule:PW of CCA Tax Shield = td/(i+d)CCTF=1-Tax Shield= 1-[td/(i+d)]Out of $1, the amount of capital cost for after-tax calculations -- the actual cost to the investorExample: If CCTF=0.7, you pay $0.70, not $1. You save$0.30 due to CCA allowance.Half Yr.-Rule:PW of CCA tax shield= 0.5[td/(i+d)]+ 0.5[td/(i+d)][1 /(1+i)]______________________________________________________________________________Note: If (UCC-Sale price or salvage) = 0, no tax shield and no CCA recapture.If (UCC-Sale price)>0, tax shield adjustment can be claimed.If salvage(sale price)>UCC, CCA recapture applies.If sale price>purchase price, capital gain and CCA recapture apply.______________________________________________________________________________After-Tax Cash Flow AnalysisExample: For a 3 yr. project, find the After Tax Cash Flow (ATCF) and Present Worth of ATCF.Purchase price=700M. Resale (salvage) =300M. Income/Yr.=500M. Expenses=$200M/Yr.Asset is declining balance type, with CCA rate=20%, half-yr. rule exempt. Tax rate=40%. MARR (after tax)= 7.5%Solution: (Drop M)Yr.IncomeExpensesCCATaxable IncomeTaxATCF

0700-700

1500200140.00160.0064.00236.00

2500200112.00188.0075.20224.80

350020089.60210.4084.16215.84

3Salvage300.00

3Tax shield adjustment16.99

NPW= - 700+236.00(P/F,7.5%,1)+224.80(P/F,7.5%,2)+(215.84+300.00+16.99)(P/F,7.5%,3)= $142.97 (Feasible).Calculations:CCA for Yr.1=(700)(0.2)= 140CCA for Yr.2=(700-140)(0.2)=112.00CCA for Yr.3=(700-140-112)(0.2)=89.60UCC=700-Sum of (140+112+89.60)=358.40>300 salvageTax shield adjustment applies.For t=0.4, d=0.2, i=0.075Tax shield adjustment = [(358.40)-(300)]x[td/(i+d)]=$16.99Taxable income:Yr.1: Income -expenses-CCA = (500-200-140)=160Yr.2: (500-200-112) = 188Yr.3: (500-200-89.60)= 210.40Tax @ 40%Yr.1: (Taxable income)x0.4=160x0.4=64Etc.After Tax Cash FlowYr.1: (Taxable income - expenses - tax) = (500-200-64) = 236Etc.CCTF Method:If half-yr. rule is applicable, apply CCTF (half-yr rule) to investment & CCTF full-yr. rule to salvage. In this case, half-yr. rule does not apply. So apply CCTF full-year to both investment and salvage.NPW = - (Investment)(CCTF) + PW of Net Income (after tax) + (Salvage)(CCTF)x(P/F,7.5%,3)Yr.Income-ExpensesTaxable IncomeTaxATCF

1500-200=300300120180

2500-200=300300120180

3500-200=300300120180

PW of after tax net income = $180(P/A,7.5%,3) = $468.09CCTF=1-tax shield =1-[td/(i+d)]=0.709NPW = -700(CCTF 0.709) + 468.09 + 300(CCTF 0.709)(P/F,7.5%,3)= $143.00M (feasible)______________________________________________________________________________Engineering Economics Chapter 10EFFECTS OF INFLATIONInflation:A general increase in the price level. A decline in the buying power of the dollar.Causes of Inflation:"Too much money chasing too few goods". Cost-push inflation Demand-pull inflation Impact of international forces on prices and markets (e.g. energy prices) Unresponsive prices that seldom decline, regardless of market conditions -- when wages are set by unions and prices are set by large firms Inflation psychology "buy ahead" and repay loan with cheaper dollars.Consequences of Inflation & Control of Inflation: See text book.Measures of Inflation.Consumer Price Index (CPI) :An index of general inflation -- for retail price change..Wholesale Price Index (WPI):for both consumer and industrial goods at the wholesale level,but not services..Construction Price Index.Transportation Price Index. Etc.Rate of Inflation (CanadaYear19911992199319941995

CPI98.5100101.8102.0104.2

Year19961997199819992000

CPI105.9107.6108.6110.5113.5

Using an annual compound rate of inflation of f, average rate of inflation during 1996-2000 period:104.2(1+f)5= 113.5f = 1.7%Average rate of inflation during 1992-2000 period:98.5(1+f)9= 113.5f = 1.58%Inflation rate in 2000 = [(113.5-110.5)/110.5]x100 = 2.7%______________________________________________________________________________Current or Actual dollars (i.e. inflated dollars) vs. Constant or Real dollars (i.e. inflation removed)199819992000

CPIRevenue of ABC Co. in current $(M)108.6$20110.5$20.35113.520.90

Revenue in constant $ of 1998*202020

Revenue in constant $ of 2000**20.920.920.9

Revenue in constant $ of 199920.3520.3520.35

Calculations:* 1998 revenue is already in 1998$. No change.1999 revenue: 20.35(108.6/110.5)= 202000 revenue: 20.9(108.6/113.5)=20** 2000 revenue is already in 2000$. No change.1998 revenue; 20(113.5/108.6)=20.91999 revenue: 20.35(113.5/110.5)=20.9______________________________________________________________________________Treatment of Inflation in Economic EvaluationsEstimate costs & revenues in current or actual dollars or convert to constant or real dollars.Inflation, Cost of Capital & MARR. Cost of capital is generally higher than (experienced & expected) rate of inflation.. Investors who obtain funds by borrowing -- they assign MARR higher than cost of capital.______________________________________________________________________________Note:MARR could be specified in actual dollars (i.e. inflation included) or in real dollars (i.e. constant dollars -- inflation removed). Unless otherwise stated, consider MARR to be in actual $ terms.______________________________________________________________________________Example: For a project in country X, proposed initial cost in 2001$ = $2000. Net income/yr for 3 years = $850/yr (in yr. 2001$ -- i.e. in the constant dollar of 2001). Expected inflation = 5%/yr (average). MARR = 15% (in actual dollars) (includes inflation). Feasible?Solution:Since MARR is in actual dollars, use actual dollar calculations (i.e. convert constant dollars into actual dollars).NPW = - $2,000+ $850(F/P,5%,1yr)(P/F,15%,1) + $850(F/P,5%,2)(P/F,15%,2)+ $850(F/P,5%,3)(P/F,15%,3) = $132 (Feasible)______________________________________________________________________________Combined Interest-Inflation RateAn interest rate (discount rate) can be found that represents both (a) the minimum required rate-of-return (ireal) in constant dollars, and (b) the inflation factor or rate (f).if= interest rate in actual dollars = (1+ ireal)(1+f) - 1______________________________________________________________________________Example: In country ABC, XYZ Co.ireal= 12% (in constant $s), f=6%if= interest rate in actual dollars = (1+ 0.12)(1+0.06)-1 = 0.1872 => 18.72%Revenue in real or constant dollars of year 0ProposalCost @ end of Yr.0RevenueYr.1RevenueYr.2RevenueYr.3RevenueYr.4

A$10,000$4,000$4,000$4,000$4,000

B14,0005,5005,5005,5005,500

DifferenceA=>B4,0001,5001,5001,5001,500

Calculations in real $ terms @ ireal= 12%:NPW A=>B = -$4000 + $1500(P/F,12%,1) + $1500(P/F,12%,2) + $1500(P/F,12%,3)+$1500(P/F,12%,4) = $556 (feasible)Calculation in actual $ terms @ if= 18.72%, f = 6%:NPW A=>B = -$4000 + $1500(F/P,6%,1)(P/F,18.72%,1) + $1500(F/P,6%,2)(P/F,18.72%,2) + $1500(F/P,6%,3)(P/F,18.72%,3)+ $1500(F/P,6%,4)(P/F,18.72%,4) = $556 (feasible)______________________________________________________________________________Example: Investment = $100,000; Salvage = $5,000; N= 3 years; CCA=20% declining balance & Half-yr. rule exempt. ireal= 8%. General inflation f = 4%. Tax rate = 40%.Two cost categories: cost category 1 inflation = 3%. Cost category 2 inflation = 4%Yr.Cost Item 1 (Actual $)Cost Item 2 (Actual $)Total

1$30,000$40,000$70,000

230,90041,60072,500

331,82743,26475,091

Example calculations:Item 1:For yr.2: $30,000(F/P,3%,1) = $30,900For yr.3: $30,000(F/P,3%,2)=$31,827Item 2:For yr.2: $40,000(F/P,4%,1) = $41,600For yr.3: $40,000(F/P,4%,2) = $43,264Sales :1000 units in year 1, growth in sales = 5%/yr.Yr. 2 sales = 1000(F/P,5%,1) = 1050 itemsYr. 3 sales = 1000(F/P,5%,2) = 1103 itemsPrice in yr. 1= $100/unit, price inflation = 4%Price in yr.2 =$100(F/P,4%,1) = $104.00Price in yr. 3 = $100(F/P,4%,2) = $108.16Revenue in actual dollars:Yr.1: $100/unitx1000 units = $100,000.00Yr.2: $104/unitx1050 units = $109,200.00Yr.3: $108.16/unitx1103units = $119,300.48CCAYr.1: 0.2($100,000) = $20,000Yr.2: 0.2($100,000-20,000) = $16,000Yr.3: 0.2($100,000 - $20,000 - $16,000) = $12,800UCC @ end of yr.3 = $100,000 - Sum(CCA) = $51,200Since UCC>Salvage, tax shield adjustment applies.Tax shield adjustment = (UCC-Salvage)x[td/(i+d)]Here t = 0.4, d=0.2, i=0.1232 (see below)Tax shield adjustment = $11,435.64After-Tax Analysis (Actual$)if= interest rate in actual dollars = (1+ ireal)(1+f) - 1 = = (1+ 0.08)(1+0.04) - 1 => 12.32%YrRevenueInvestment & ExpensesCCATaxable IncomeTaxATCF

0$100,000-$100,000

1$100,00070,00020,00010,0004,00026,000

2109,20072,50016,00020,7008,28028,420

3119,30075,09112,80031,40912,563.6048,081.04

3Salvage5,000

3Tax shield adjustment11,435.64

NPW= - $100,000 +$26,000(P/F,12.32%,1) + $28,420(P/F,12.32%,2)+ ($48,081.04+$5,000+$11,435.64)(P/F,12.32%,3)= - $20,393.05 (Not feasible)______________________________________________________________________________Engineering Economics Chapter 11SENSITIVITY ANALYSISIt involves repeated computations with different values of variables involved & answer is checked.Examples: Change demand, cash flow (costs, revenues), N, i, etc. and see change in answer.Example:{Demand levels}=>{Corresponding network design or plant size, or organization size}=>{Forecast of cost, revenues}=>{NPWs}______________________________________________________________________________Example:For the following cash flow, find NPW @ 15% interest. Next vary interest and revenue by 10%, 20%,-10% and -20%.PeriodCapital InvestmentGross RevenueO&M ExpensesSalvage

0$10.0M

1$5M$1M

2$5M$1M

3$5M$1M$4.17M

Solution:Base Case:NPW = - $10M + $5.0M(P/A,15%,3) - $1M(P/A,15%,3) + $4.17M(P/F,15%,3) = $1.87MChange i by +10%: i=15%(1.1)=16.5%NPW @ i =16.5% = $1.55MChange revenue by 10%: new revenue/yr = $5M(1.1) = $5.5M/yrNPW @ 15% with $5.5M/yr revenue = $3.02MResults (in $M): sensitivity of proposal's NPW to changes in i values & revenue/yr.% DeviationRevenueInterest Rate

-20%- 0.41M2.58M

-10%0.73M2.22M

0% (Base Case)1.87M1.87M

+10%3.02M1.55M

+20%4.16M1.24M

These results can be plotted for visual observation.______________________________________________________________________________Engineering Economics Chapter 12BREAKEVEN ANALYSIS. To define conditions when revenues = costs or benefits=costs. To establish- selling price- no. of items to produce- etc.. To define regions of feasibilityCosts & Pricesa. Selling price/unit = (Fixed cost + Variable cost)/unit + Profit/unitb. Examples of fixed costs:These do not vary with units produced: rent, insurance, infrastructure ownership cost, property taxes, executive salaries, research & development, etc.c. Examples of variable costs: direct labour & supervision, direct supplies & raw material, packaging, sales commission, royalties, etc.Breakeven AnalysisAt breakeven point(s):TC=TR or Z=TR -TC=0WhereTC is total cost = FC + VCFC is fixed costVC is variable costZ is profitTR is total revenue = (price/unit)x(no. of units sold)Notes:. Average Total Cost (ATC) = TC/n. Average Revenue = TR/n. Marginal Cost (Marginal total cost) = d(TC)/dn(i.e., it is the slope of the total cost function). Marginal Revenue = d(TR)/dn______________________________________________________________________________From basic principles, it can be shown that:. Maximum profit occurs @ the point when marginal revenue = marginal cost. At the point of minimum average total cost, average total cost = marginal cost______________________________________________________________________________Example: Minimum Unit Cost Level of ProductionTotal cost TC = 0.005n2+ 4n + 200,000Average total cost ATC = TC/n = 0.005n + 4 + (200,000/n)To find n for min. ATC: d(ATC)/dn =0= 0.005-(200,000/n2)n = 6,325ATC @ n of 6,325 units = $67.25Marginal total cost(MTC) = d(TC)/dn = 2x0.005xn +4At n=6,325, MTC= $67.25Note: At the point of minimum ATC, MTC=ATC______________________________________________________________________________Costs, Revenues, Profit, Production LevelsExample: Total cost TC = 10,000 + 2n2x10-4Where n = number of units produced/yr.Total revenue TR = 100n - 0.01n2Find :(a) Min. unit cost & n for min. unit cost. (b) Production for max. profit. (c) Breakeven level of production.Solution:(a) ATC= TC/n= [10,000 + 2n2x10-4]/n = 10,000/n + 2n x10-4To find Min. ATC: d(ATC)/dn=0= - 10,000/n2+ 2x10-4n = 7,071 units/yr. ATC min = 2.83(b) Total revenue = (price/unit) x (units sold)Given TR = 100n - 0.01n2Marginal revenue MR = d(TR)/dn = 100-0.02n (1)Marginal cost MC = d(TC)/dn = d(10,000 + 2n2x10-4)/dn= 4n x10-4. (2)Since Max. Profit occurs @ Marginal Revenue = Marginal Cost, set (1) = (2) and solve for nn = 4,902 units for max. profitd. Break-even point(s) (BEP):At BEP, total cost = total revenue10,000 + 2n2x10-4=100n - 0.01n2n = 100 or 9,700 units______________________________________________________________________________Example: Given TC=$63,000+$30n and TR= $120n. Find (a) breakeven point (BEP), (b) Average total cost, (c) Marginal total cost, (d) Average revenue, (e) Average revenue, (f) Production level for min. unit cost, (g) Production level for max. profit.Solution:. BEP @ TC=TR$63,000+$30n = $120n, solve for nn = 700 units. ATC = TC/n = ($63,000+$30n)/n. Avg. Revenue = TR/n = 120n/n = $120. Marginal Revenue = dTR)/dn = $120. Marginal total cost = MTC = d(TC)/dn = $30. BEP @ avg. revenue = avg. total costAns. 700 units. Production level for min. ATC @ n=> infinity. Production level for max. profit @ MTC=MR.Ans: n => infinity______________________________________________________________________________Breakeven Analysis: Further information on RelationshipsTotal revenue = TR=n.SPWhere n is units sold and SP is sale priceTotal cost = TC = nVC+FCWhere VC is variable cost per unit and FC is fixed costGross Profit = Z = TR-TC = nSP-(nVC+FC) = n(SP-VC) - FC(SP-VC) is called contribution.It is a measure of the portion of the selling price that contributes to paying the fixed cost.If SP=VC, contribution = 0At BEP: Z=0=n(SP-VC)-FCFC=n(SP-VC)n = FC/(SP-VC)______________________________________________________________________________Example:Given: Fixed Cost FC = $63,000Selling Price SP = $120Contribution (SP-VC) = 75% of SP = $90Full capacity @ n = 1000 unitsTax rate = 40%Find: (a) Net profit at full capacity. (b) Break-even level of production.Solution:a. SP-VC = $90VC = $120-$90 = $30Z = TR-TC = [n(SP-VC) - FC] = [1000($120-$30) - $63,000] = $27,000Net profit after tax = (1- Tax rate)(Profit) = (1-0.4)($27,000) = $16,200(b) BEP @ n = FC/(SP-VC) = 63,000/90 = 700 units______________________________________________________________________________Engineering Economics Chapter 13RISK ANALYSIS & UNCERTAINTYDecisions are made under the following conditions:Certainty assumption. All outcomes are known. Single "State of Nature" is assumed (e.g., a single demand level).Risk. Chances of loss or unfavourable impacts. Cash flows or other outcomes may not be known with certainty, but probabilities can be assigned (probabilities known/estimated).Uncertainty. Probabilities of chance events are not known but can be assigned subjectively or other decision criteria have to be used.Decision Making under Risk. Expected value calculations (decision theory). Expected values & study of variances (standard deviations). Simulation of events -- Monte Carlo Simulation Technique______________________________________________________________________________Statistical and probability concepts and methodsare used in risk analysis. Some of these are noted here.Sigma = standard deviationSigma square = variance -- a measure of dispersionVariance=[Sum for i=1 to N(Xi- Avg. value of X)2]/NWhere Xi is an estimate ( a data point)N = no. of data points (for whole population).Probability concepts: see Glossary 5 (Pages A-19 to A-20) of the Text Book.Expected ValueEV(X)= Sum for i = 1 to n[P(X= Xi). Xi]Wheren is number of possible outcomes of variable XP(X= Xi) is the probability that X= Xiand Sum of P(X= Xi) for i equal to 1 to n = 1.0Measures of Variatione.g. Variance (NPW)Variance & St. DeviationV(X) = Sum from i to n [Xi - EV(X)]2P(X= Xi)This formula reduces to :V(X) = Sum from i to n P(X= Xi) Xi2- [EV(X)]2or V(X) = EV(X2) - [EV(X)]2St. deviation Sigma = Sq. root of V(X)Also, Coefficient of Variation = [St. deviation/EV(X)]Risk in Financial AnalysisExpected ValueInvestment of $10,000 in a machine. Service duration is N years. Salvage = L. Maintenance cost for Yr.1 = $1000. For following years, an increase of $200/yr. MARR = 10%. Given the following information, find Expected Equivalent Annual Cost.NSalvage LP(N)

63,0000.2

82,0000.4

101,0000.4

Solution:EAC(N=6 yrs) = -10,000[A/P,10%,6]-1,000-200(A/G,10%,6) + 3,000(A/F,10%,6) = -$3,3351.95EAC(N=8 yrs) = -$3,300.46EAC(N=10 yrs) = -$3,309.81E(EAC) = (0.2)(-$3,3351.95) +(0.4)(-$3,300.46) + (0.4)(-$3,309.81) = -$3,314.47______________________________________________________________________________Expected Values and VariancesExample: An asset has a first cost of $50,000. Salvage value depends upon how long it remains in service.Estimates of salvage value: for 4 yrs of service: $20,000, 5 years of service: 15,000, 6 years of service: 12,000 and 7 years of service: 10,000.Given that all service periods are equally likely, find the Mean and Standard Deviation of the asset's present worth. i=15%Solution:First find PW of salvage = Salvage(P/F,15%,N)N= 4 yrsN=5 yrsN=6 yrsN=7 yrs

$11,4357,4585,1883,759

Expected value of PW of salvage = E(PW of salvage)= (0.25)($11,435) + (0.25)(7,458) + (0.25)(5,188) +(0.25)(3,759) = $6,960Note: P(4 yrs) = P(5 yrs) = P(6 yrs) = P(7 yrs) = 1/4=0.25Now find E(NPW) = -$50,000+$6,960 = -$43,040Variance of NPW: Use formula or V(NPW) = EV(NPW2) - [EV(NPW)]2Since there is no variability in first cost,V(NPW) = V(PW of salvage) = [(0.25)($11,435)2+ (0.25)(7,458)2+ (0.25)(5,188)2+(0.25)(3,759)2] - (6,960)2= $8,415,003.5St deviation of NPW = Sq. root of Variance = $2,900.85Another approach to finding V(NPW) and St deviation of NPWPW call it XP(PW)(Xi- Avg. value of X)2P(PW)

- 38,565*0.255,006,406**

- 42,5420.2562,001

- 44,8120.25748,996

- 46,2410.252,561,600

Avg. X=-$43,040Sum=1.0V(PW)=$8,415,003.25

V(PW)=$8,415,003.25St. Deviation = Sq. Root of V(PW) = $2,900.86Sample calculations:* PW= - 50,000 + $20,000(P/F,15%,4yrs) = -50,000 + 11,435 = - 38,565** (Xi- Avg. value of X)2P(PW) = [- 38,565 - (-43,040)]2(0.25) = 5,006,406______________________________________________________________________________Expected Values and VariancesExample: Proposals A & B have EV(A)=EV(B) = $1000V(A) = $4000 V(B) = 144,000.Choice?Solution: Find St. deviations (sigma) and then find Sigma/EV= Coefficient of variation.The lower the coefficient of variation, the better. Choice is A.______________________________________________________________________________Decision Theory. Payoff matrix -- dollars are revenue or profit or benefits.. States of Nature -- their occurrence is probabilistic.. Actions of the decision maker.Actions of decision makerState of Nature S1P(S1) = 0.4State of Nature S2P(S2) = 0.6

A1$x=$100M$y=$125M

A2$m=$110M$n=$120M

Note: P(S1)+P(S2) = 1.0Expected value calculations:EV(A1) = P(S1)($x) + P(S2)($y)= (0.4)(100)+(0.6)(125) = $115EV(A2) = P(S1)($m) + P(S2)($n)= (0.4)(110)+(0.6)(120) = $116 (Choice)______________________________________________________________________________Risk Analysis: Use of Normal Probability Density FunctionAssume that an outcome (e.g. NPW) is normally distributed. What is the probability that the outcome is less than a selected value x?That is:P(Outcome < x) = P(z < (x-Mew)/Sigma)Where z is the standard normal deviateMew is mean valueSigma is the standard deviationExample:Outcome is NPW of a cash flowx = $875Mew = $1000Sigma = $100P(NPW0) = P(z>1.12) = 0.5-0.3684 = 0.1316 or 13.16%______________________________________________________________________________Risk Analysis: Most Probable Future, Aspiration LevelProbability of returns from three equal size, equal-life investments are provided.AlternativesNPW-$1000NPW$0NPW$1000NPW$2000NPW$3000NPW$4000Sum ofProb.

A00.110.260.220.020.391.00

B0.290.180.07000.461.00

C0.140.100.110.370.2801.00

Note: the numbers in the table are probabilities.Most probable future:Alt. A: P=0.39 & PW=$4000Alt. B: P=0.46 & PW=$4000 (Choice)Alt. C: P=0.37 & PW=$2000For Aspiration Level of $2000 or higher, probability of $2000 or overAlt A: 0.22+0.02++0.39 = 0.63Alt. B: 0.46Alt. C: 0.37+0.28 = 0.65 (Choice)______________________________________________________________________________Decision Making Under UncertaintyCriteria (Rules, Principles, Methods):. Extremely optimistic criterion (Maximax). Extremely pessimistic criterion (Maximin). Expected Value Criterion: Subjective probabilities used Subjective probabilities modified as a result of "new information" -- Baye's Theorem used(Bayesian approach is not covered in this course).. Laplace criterion -- equal likelihood criterion. Hurwicz criterion -- blending of optimism & pessimism. Regret criterion (minimax regret)______________________________________________________________________________Example: Payoff matrix is shown below. Which alternative is the best? Use the following criteria:a. Maximax (b) Maximin (c) Hurwicz (alpha = 3/8) (d) Minimax regret (e) Laplace______________________________________________________________________________Payoff Matrix ($M of NPW); States of Nature are S1 to S4.AlternativesS1S2S3S4

A2222

B1510

C1411

D1314

E3430

Solution:a. Maximax-- for each alternative, find the max. payoff & then select the best (to maximize the max. value).AlternativeABCDE

Payoff25*444

Answer=> Select Bb. Maximin-- for each alternative, find the minimum payoff & then select the best.AlternativeABCDE

Payoff2*0110

Answer=> Select Ac. Hurwicz Criterion(Alpha = 3/8)Use of an index of optimism, alpha, applied to Maximax payoff and (1-alpha) applied to Maximin payoff.AlternativeABCDE

Payoff(3/8)(2)+(1-3/8)(2)= 2(3/8)(5)+(1-3/8)(0)= 15/8(3/8)(4)+(1-3/8)(1)= 17/8*(3/8)(4)+(1-3/8)(1)= 17/8*(3/8)(4)+(1-3/8)(0)= 12/8

Answer=> Select C or Dd. Minimax Regret Criterion (Rule):to minimize the maximum regret.Steps: (1) For each state S, find max. payoff. (2) Find (max. payoff -payoff given) -- Rij Regret Matrix.Alternative i , Sate jAlternativeS1S2S3S4

A3-2 = 15-2 = 3*3-2 = 14-2 = 2

B3-1 = 25-5 = 03-1 = 24-0 = 4*

C3-1 = 25-4 = 13-1 = 24-1 = 3*

D3-1 = 2*5-3 = 2*3-1 = 2*4-4 = 0

E3-3 = 05-4 = 13-3 = 04-0 = 4*

Step (3): Find max. Rij for each alternative. See above.Step (4): Find the alternative with min[max Rij]. Ans: Alt. D.e. Equal Likelihood Criterion: Laplace RuleAssume that all states have the same probability.Alt.Expected Value

ABCDE(1/4)(2) + (1/4)(2) + (1/4)(2) + (1/4)(2) = 2.0= 1.75= 1.75= 2.25= 2.5*

Ans: Alt. ESummary:Maximax: Alt BMaximin: Alt. AHurwicz (@ alpha = 3/8): Alt. C or DMinimax Regret: Alt. DLaplace (Equal likelihood): Alt. EEngineering economics, previously known asengineering economy, is a subset ofeconomicsfor application to engineering projects.Engineersseek solutions to problems, and the economic viability of each potential solution is normally considered along with the technical aspects.It is science as well as an art.Considering thetime value of moneyis central to most engineering economic analyses.Cash flowsarediscountedusing aninterest rate, i, except in the most basic economic studies.For each problem, there are usually many possiblealternatives. One option that must be considered in each analysis, and is often thechoice, is thedo nothing alternative. Theopportunity costof making one choice over another must also be considered. There are also non-economic factors to be considered, like color, style, public image, etc.; such factors are termedattributes.[1]Costsas well asrevenuesare considered, for each alternative, for ananalysis periodthat is either a fixed number of years or the estimated life of the project. Thesalvage valueis often forgotten, but is important, and is either the net cost or revenue for decommissioning the project.Some other topics that may be addressed in engineering economics areinflation,uncertainty, replacements,depreciation, resourcedepletion,taxes,tax credits,accounting, cost estimations, orcapital financing. All these topics are primary skills and knowledge areas in the field ofcost engineering.Since engineering is an important part of themanufacturingsector of theeconomy, engineering industrial economics is an important part of industrial or business economics. Major topics in engineering industrial economics are: the economics of the management, operation, and growth and profitability of engineering firms; macro-level engineering economic trends and issues; engineering product markets and demand influences; and the development, marketing, and financing of new engineering technologies and products.[2][1] economic environment

Definition The totality ofeconomic factors, such asemployment,income,inflation,interest rates,productivity, andwealth, thatinfluencethebuying behaviorofconsumersandinstitutions.

DEFINITION OF 'TIME VALUE OF MONEY - TVM'The idea that money available at the present time is worth more than the same amount in the future due to its potential earning capacity. This core principle of finance holds that, provided money can earn interest, any amount of money is worth more the sooner it is received.

Also referred to as "present discounted value".Everyone knows that money deposited in a savings account will earn interest. Because of this universal fact, we would prefer to receive money today rather than the same amount in the future.

For example, assuming a 5% interest rate, $100 invested today will be worth $105 in one year ($100 multiplied by 1.05). Conversely, $100 received one year from now is only worth $95.24 today ($100 divided by 1.05), assuming a 5% interest rate.Concept of EquivalenceTo compare alternatives that provide the same service over extended periods of time when interest is involved, we must reduce them to an equivalent basis that is dependent on: ---If two alternatives are economically equivalent, then they are equallydesirable.Equivalence factors are needed in engineering economy to make cash flows (CF) at different points in time comparable. For example, a cash payment that has to be made today cannot be compared directly to a cash flow that must be made in 5 years.Since the time value of money changes according to:1.The interest rate,2.The amount of money involved,3.The timing of receipt or payment,4. The manner in which interest is compounded,We need a way to reduce CF's at different times to an equivalent basis. Equivalence factors allow us to do so.Principles of Equivalence Equivalent cash flows have the same economic value at the same point in time. Cash flows that are equivalent at one point in time are equivalent at any point in time. Conversion of a cash flow to its equivalent, at another point in time must reflect the interest rate(s) in effect for eachperiod between the equivalent cash flows. Equivalence between receipts and disbursements: the interest rate that sets the receipts equivalent to the disbursements isthe actual interest rate (IRR). Economic equivalence is established, in general, when we are indifferent between a future payment, or series of payments, and a present sum of money.Notation and Cash Flow Diagrams (CFDs)The following notation is utilized in formulas for compound interest calculations:I = effective interest rate per interest periodN = number of compounding periodsP = present sum of money; the equivalent value of one or more cash flows at a reference point in time called presentF= future sum of money; the equivalent value of one or more cash flows at a reference point in time called futureA = end-of-period cash flows (or equivalent end-of-period values) in a uniform series continuing for a specified number of periods, starting at the end of the first period and continuing through the last period1. The Horizontal line is a time scale, with progression of time moving from left to right. The period (e.g., year, quarter, month) labels can be applied to intervals of time rather than to points on the time scale.2. The arrows signify cash flows and are placed at the end of the period. If a distinction needs to be made, downward arrows represent expenses (negative cash flows or cash outflows) and upward arrows represent receipts (positive cash flows or cash inflows).3. The cash flow diagram is dependent on the point of view. The situations shown in the figure were based on the cash flows as seen by the lender. If the directions of all arrows had been reversed, the problem will have to be diagrammed from borrower's viewpoint.

Cash Flow DiagramDEFINITION OF 'PRESENT VALUE - PV'The current worth of a future sum of money or stream of cash flows given a specified rate of return. Future cash flows are discounted at the discount rate, and the higher the discount rate, the lower the present value of the future cash flows. Determining the appropriate discount rate is the key to properly valuing future cash flows, whether they be earnings or obligations.

Also referred to as "discounted value".Future valueis thevalueof anassetat a specific date.[1]It measures the nominal future sum of money that a given sum of money is "worth" at a specified time in the future assuming a certaininterest rate, or more generally,rate of return; it is thepresent valuemultiplied by theaccumulation function.[2]The value does not include corrections for inflation or other factors that affect the true value of money in the future.RELATION SHIP BETWEEN PV AND FV Thefuture value(FV) measures the nominal future sum of money that a given sum of money is "worth" at a specified time in the future assuming a certaininterestrate, or more generally, rate ofreturn. The FV is calculated by multiplying thepresent valueby the accumulation function. PV and FV vary jointly: when one increases, the other increases, assuming that theinterest rateand number ofperiodsremain constant. the interest rate (discountrate) and number of periods increase, FV increases or PV decree.

DEFINITION OF 'DISCOUNTED CASH FLOW - DCF'A valuation method used to estimate the attractiveness of an investment opportunity. Discounted cash flow (DCF) analysis uses future free cash flow projections and discounts them (most often using the weighted average cost of capital) to arrive at a present value, which is used to evaluate the potential for investment. If the value arrived at through DCF analysis is higher than the current cost of the investment, the opportunity may be a good one.Calculated as:

Also known as the Discounted Cash Flows Model.There are many variations when it comes to what you can use for your cash flows and discount rate in a DCF analysis. Despite the complexity of the calculations involved, the purpose of DCF analysis is just to estimate the money you'd receive from an investment and to adjust for the time value of money.Discounted cash flow models are powerful, but they do have shortcomings. DCF is merely a mechanical valuation tool, which makes it subject to the axiom "garbage in, garbage out". Small changes in inputs can result in large changes in the value of a company. Instead of trying to project the cash flows to infinity, terminal value techniques are often used. A simple annuity is used to estimate the terminal value past 10 years, for example. This is done because it is harder to come to a realistic estimate of the cash flows as time goes on.

obsolescenceDefinition Significantdecline in thecompetitiveness, usefulness, orvalueof anarticleorproperty. Obsolescence occurs generallydueto theavailabilityof alternatives that perform better or arecheaperor both, or due tochangesinuserpreferences,requirements, orstyles. It is distinct from fall in value (depreciation) due tophysical deteriorationor normalwear and tear. Obsolescence is a majorfactorinoperating risk, and may requirewrite offof the value of theobsoleteitem againstearningsto comply with theaccountingprincipleof showinginventoryatlower of cost or market value.Insurance companiestake obsolescence intoaccountto reduce theamountofclaimto be paid on damaged or destroyed property.costingDefinition.Systemofcomputingcost of productionor of running abusiness, by allocatingexpenditureto variousstagesofproductionor to differentoperationsof a firm.

cost factorsThe cost of training requires two separate estimates. One estimate for start up costs and one for ongoing costs or, in other words, the cost of each class held.Start up costsare normally expended just once to develop the class lesson plan and to obtain reusable tools and materials required to hold the classes. Tools and materials might include the one time purchase of equipment such as overhead projectors, white boards, televisions, and video cassette recorders. It may also include the cost of specialized equipment associated specifically with the training to be held.Development of the class includes the time for a training consultant to prepare a lesson plan and handouts. This can be the one largest expenditure to develop a class but is also the one place where money is well spent. The training will not be effective if the class is not thoroughly planned, fun and interesting for students. A good lesson plan that outlines almost minute by minute how class time is spent, the learning goals to be achieved, and how those goals will be accomplished is essential to the training success.Finally, start up cost may include the preparation of displays, lab boards and lab areas where students will practice their new skills. This cost can vary from zero to very considerable depending on the subject of the training.Ongoing costswill include consumable materials, replacement tools, lunch and sodas, room rentals, and teachers fees. These costs will require a detailed estimate that takes into consideration the unique aspects of the particular training being developed.Definition:To establish a selling price for a productNo matter what type of product you sell, the price you charge your customers or clients will have a direct effect on the success of your business. Though pricing strategies can be complex, the basic rules of pricing are straightforward: All prices must cover costs and profits. The most effective way to lower prices is to lower costs. Review prices frequently to assure that they reflect the dynamics of cost, market demand, response to the competition, and profit objectives. Prices must be established to assure sales.Before setting a price for your product, you have to know the costs of running your business. If the price for your product or service doesn't cover costs, your cash flow will be cumulatively negative, you'll exhaust your financial resources, and your business will ultimately fail.To determine how much it costs to run your business, include property and/or equipment leases, loan repayments, inventory, utilities, financing costs, and salaries/wages/commissions. Don't forget to add the costs of markdowns, shortages, damaged merchandise, employee discounts, cost of goods sold, and desired profits to your list of operating expenses.Most important is to add profit in your calculation of costs. Treat profit as a fixed cost, like a loan payment or payroll, since none of us is in business to break even.Because pricing decisions require time and market research, the strategy of many business owners is to set prices once and "hope for the best." However, such a policy risks profits that are elusive or not as high as they could be.When is the right time to review your prices? Do so if: You introduce a new product or product line; Your costs change; You decide to enter a new market; Your competitors change their prices; The economy experiences either inflation or recession; Your sales strategy changes; or Your customers are making more money because of your product or service.Prices are generally established in one of four ways:Cost-Plus PricingMany manufacturers use cost-plus pricing. The key to being successful with this method is making sure that the "plus" figure not only covers all overhead but generates the percentage of profit you require as well. If your overhead figure is not accurate, you risk profits that are too low. The following sample calculation should help you grasp the concept of cost-plus pricing:Cost of materials$50.00

+ Cost of labor30.00

+ Overhead40.00

= Total cost$120.00

+ Desired profit (20% on sales)30.00

= Required sale price$150.00

Demand PriceDemand pricing is determined by the optimum combination of volume and profit. Products usually sold through different sources at different prices--retailers, discount chains, wholesalers, or direct mail marketers--are examples of goods whose price is determined by demand. A wholesaler might buy greater quantities than a retailer, which results in purchasing at a lower unit price. The wholesaler profits from a greater volume of sales of a product priced lower than that of the retailer. The retailer typically pays more per unit because he or she are unable to purchase, stock, and sell as great a quantity of product as a wholesaler does. This is why retailers charge higher prices to customers. Demand pricing is difficult to master because you must correctly calculate beforehand what price will generate the optimum relation of profit to volume.Competitive PricingCompetitive pricing is generally used when there's an established market price for a particular product or service. If all your competitors are charging $100 for a replacement windshield, for example, that's what you should charge. Competitive pricing is used most often within markets with commodity products, those that are difficult to differentiate from another. If there's a major market player, commonly referred to as the market leader, that company will often set the price that other, smaller companies within that same market will be compelled to follow.To use competitive pricing effectively, know the prices each competitor has established. Then figure out your optimum price and decide, based on direct comparison, whether you can defend the prices you've set. Should you wish to charge more than your competitors, be able to make a case for a higher price, such as providing a superior customer service or warranty policy. Before making a final commitment to your prices, make sure you know the level of price awareness within the market.If you use competitive pricing to set the fees for a service business, be aware that unlike a situation in which several companies are selling essentially the same products, services vary widely from one firm to another. As a result, you can charge a higher fee for a superior service and still be considered competitive within your market.Markup PricingUsed by manufacturers, wholesalers, and retailers, a markup is calculated by adding a set amount to the cost of a product, which results in the price charged to the customer. For example, if the cost of the product is $100 and your selling price is $140, the markup would be $40. To find the percentage of markup on cost, divide the dollar amount of markup by the dollar amount of product cost:$40 ? $100 = 40%This pricing method often generates confusion--not to mention lost profits--among many first-time small-business owners because markup (expressed as a percentage of cost) is often confused with gross margin (expressed as a percentage of selling price). The next section discusses the difference in markup and margin in greater depth.Pricing BasicsTo price products, you need to get familiar with pricing structures, especially the difference between margin and markup. As mentioned, every product must be priced to cover its production or wholesale cost, freight charges, a proportionate share of overhead (fixed and variable operating expenses), and a reasonable profit. Factors such as high overhead (particularly when renting in prime mall or shopping center locations), unpredictable insurance rates, shrinkage (shoplifting, employee or other theft, shippers' mistakes), seasonality, shifts in wholesale or raw material, increases in product costs and freight expenses, and sales or discounts will all affect the final pricing.Overhead Expenses.Overhead refers to all nonlabor expenses required to operate your business. These expenses are either fixed or variable: Fixed expenses.No matter what the volume of sales is, these costs must be met every month. Fixed expenses include rent or mortgage payments, depreciation on fixed assets (such as cars and office equipment), salaries and associated payroll costs, liability and other insurance, utilities, membership dues and subscriptions (which can sometimes be affected by sales volume), and legal and accounting costs. These expenses do not change, regardless of whether a company's revenue goes up or down. Variable expenses.Most so-called variable expenses are really semivariable expenses that fluctuate from month to month in relation to sales and other factors, such as promotional efforts, change of season, and variations in the prices of supplies and services. Fitting into this category are expenses for telephone, office supplies (the more business, the greater the use of these items), printing, packaging, mailing, advertising, and promotion. When estimating variable expenses, use an average figure based on an estimate of the yearly total.Cost of Goods Sold.Cost of goods sold, also known as cost of sales, refers to your cost to purchase products for resale or to your cost to manufacture products. Freight and delivery charges are customarily included in this figure. Accountants segregate cost of goods on an operating statement because it provides a measure of gross-profit margin when compared with sales, an important yardstick for measuring the business' profitability. Expressed as a percentage of total sales, cost of goods varies from one type of business to another.Normally, the cost of goods sold bears a close relationship to sales. It will fluctuate, however, if increases in the prices paid for merchandise cannot be offset by increases in sales prices, or if special bargain purchases increase profit margins. These situations seldom make a large percentage change in the relationship between cost of goods sold and sales, making cost of goods sold a semivariable expense.Determining Margin.Margin, or gross margin, is the difference between total sales and the cost of those sales. For example: If total sales equals $1,000 and cost of sales equals $300, then the margin equals $700.Gross-profit margin can be expressed in dollars or as a percentage. As a percentage, the gross-profit margin is always stated as a percentage of net sales. The equation: (Total sales ? Cost of sales)/Net sales = Gross-profit marginUsing the preceding example, the margin would be 70 percent.($1,000 ? $300)/$1,000 = 70%When all operating expenses (rent, salaries, utilities, insurance, advertising, and so on) and other expenses are deducted from the gross-profit margin, the remainder is net profit before taxes. If the gross-profit margin is not sufficiently large, there will be little or no net profit from sales.Some businesses require a higher gross-profit margin than others to be profitable because the costs of operating different kinds of businesses vary greatly. If operating expenses for one type of business are comparatively low, then a lower gross-profit margin can still yield the owners an acceptable profit.The following comparison illustrates this point. Keep in mind that operating expenses and net profit are shown as the two components of gross-profit margin, that is, their combined percentages (of net sales) equal the gross-profit margin:Business ABusiness B

Net sales100%100%

Cost of sales4065

Gross-profit margin6035

Operating expenses4319

Net profit1716

Markup and (gross-profit) margin on a single product, or group of products, are often confused. The reason for this is that when expressed as a percentage, margin is always figured as a percentage of the selling price, while markup is traditionally figured as a percentage of the seller's cost. The equation is:(Total sales ? Cost of sales)/Cost of sales = MarkupUsing the numbers from the preceding example, if you purchase goods for $300 and price them for sale at $1,000, your markup is $700. As a percentage, this markup comes to 233 percent:$1,000 ? $300 ? $300 = 233%In other words, if your business requires a 70 percent margin to show a profit, your average markup will have to be 233 percent.You can now see from the example that although markup and margin may be the same in dollars ($700), they represent two different concepts as percentages (233% versus 70%). More than a few new businesses have failed to make their expected profits because the owner assumed that if his markup is X percent, his or her margin will also be X percent. This is not the case.PROJECT CASH FLOWSWhen beginning capital-budgeting analysis, it is important to determine a project's cash flows. These cash flows can be segmented as follows:

1. Initial Investment OutlayThese are the costs that are needed to start the project, such as new equipment, installation, etc.

2. Operating Cash Flowover a Project's LifeThis is the additional cash flow a new project generates.

3. Terminal-Year Cash FlowThis is the final cash flow, both the inflows and outflows, at the end of the project's life; for example, potential salvage value at the end of a machine's life. Example: Expansion ProjectNewco wants to add to its production capacity and is looking closely at investing in Machine B. Machine B has a cost of $2,000, with shipping and installation expenses of $500 and a $300 cost in net working capital. Newco expects the machine to last for five years, at which point Machine B will have a book value (BV) of $1,000 ($2,000 minus five years of $200 annual depreciation) and a potential market value of $800.

With respect to cash flows, Newco expects the new machine to generate an additional $1,500 in revenues and costs of $200. We will assume Newco has a tax rate of 40%. The maximum payback period that the company has established is five years.

Let's calculate the project's initial investment outlay, operating cash flow over the project's life and the terminal-year cash flow for the expansion project.

Initial Investment Outlay:Machine cost + shipping and installation expenses + change in net working capital = $2,000 + $500 + $300 = $2,800

Operating Cash Flow:CFt= (revenues - costs)*(1 - tax rate)CF1= ($1,500 - $200)*(1 - 40%) = $780CF2= ($1,500 - $200)*(1 - 40%) = $780CF3= ($1,500 - $200)*(1 - 40%) = $780CF4= ($1,500 - $200)*(1 - 40%) = $780CF5= ($1,500 - $200)*(1 - 40%) = $780

Terminal Cash Flow:Tips and TricksThe key metrics for determining the terminal cash flow are salvage value of the asset, net working capital and tax benefit/loss from the asset.

The terminal cash flow can be calculated as illustrated:

Return of net working capital +$300Salvage value of the machine +$800Tax reduction from loss (salvage < BV)+$80Net terminal cash flow $1,180Operating CF5+$780Total year-five cash flow $1,960

For determining the tax benefit or loss, a benefit is received if the book value of the asset is more than the salvage value, and a tax loss is recorded if the book value of the asset is less than the salvage value.DEFINITION OF 'ABSORPTION COSTING'A managerial accounting cost method of expensing all costs associated with manufacturing a particular product. Absorption costing uses the total direct costs and overhead costs associated with manufacturing a product as the cost base. Generally accepted accounting principles (GAAP) require absorption costing for external reporting.

Absorption costing is also known as "full absorption costing".Some of the direct costs associated with manufacturing a product include wages for workers physically manufacturing a product, the raw materials used in producing a product, and all of the overhead costs, such as all utility costs, used in producing a good.

Absorption costing includes anything that is a direct cost in producing a good as the cost base. This is contrasted with variable costing, in which fixed manufacturing costs are not absorbed by the product. Advocates promote absorption costing because fixed manufacturing costs provide future benefits.Debt FinancingTheactofabusinessraisingoperating capitalorothercapitalbyborrowing.Mostoften,thisreferstotheissuanceofabond,debenture,orotherdebt security.Inexchangeforlendingthe money,bond holdersandothersbecomecreditorsofthebusinessandareentitledtothepaymentofinterestandtohavetheirloanredeemedattheendofagivenperiod.Debtfinancingcanbelong-termorshort-term.Long-termdebtfinancingusuallyinvolvesabusiness'needtobuythebasicnecessitiesforitsbusiness,suchasfacilitiesandmajorassets,whileshort-termdebtfinancingincludesdebtsecuritieswithshorterredemptionperiodsandisusedtoprovideday-to-daynecessitiessuchasinventoryand/orpayroll.

DEFINITION OF 'EQUITY FINANCING'The process of raising capital through the sale of shares in an enterprise. Equity financing essentially refers to the sale of an ownership interest to raise funds for business purposes. Equity financing spans a wide range of activities in scale and scope, from a few thousand dollars raised by an entrepreneur from friends and family, to giant initial public offerings (IPOs) running into the billions by household names such as Google and Facebook. While the term is generally associated with financings by public companies listed on an exchange, it includes financings by private companies as well. Equity financing is distinct from debt financing, which refers to funds borrowed by a business.Equity financing involves not just the sale of common equity, but also the sale of other equity or quasi-equity instruments such as preferred stock, convertible preferred stock and equity units that include common shares and warrants.A startup that grows into a successful company will have several rounds of equity financing as it evolves. Since a startup typically attracts different types of investors at various stages of its evolution, it may use different equity instruments for its financing needs.For example, angel investors and venture capitalists who are generally the first investors in a startup are inclined to favor convertible preferred shares rather than common equity in exchange for funding new companies, since the former have greater upside potential and some downside protection. Once the company has grown large enough to consider going public, it may consider selling common equity to institutional and retail investors. Later on, if it needs additional capital, the company may go in for secondary equity financings such as a rights offering or an offering of equity units that includes warrants as a sweetener.The equity-financing process is governed by regulation imposed by a local or national securities authority in most jurisdictions. Such regulation is primarily designed to protect the investing public from unscrupulous operators who may raise funds from unsuspecting investors and disappear with the financing proceeds. An equity financing is therefore generally accompanied by an offering memorandum or prospectus, which contains a great deal of information that should help the investor make an informed decision about the merits of the financing. Such information includes the company's activities, details on its officers and directors, use of financing proceeds, risk factors, financial statements and so on.Investor appetite for equity financings depends significantly on the state of financial markets in general and equity markets in particular. While a steady pace of equity financings is seen as a sign of investor confidence, a torrent of financings may indicate excessive optimism and a looming market top. For example, IPOs by dot-coms and technology companies reached record levels in the late 1990s, before the tech wreck that engulfed the Nasdaq from 2000 to 2002. The pace of equity financings typically drops off sharply after a sustained market correction due to investor risk-aversion during this period.

DEFINITION OF 'LEASE 'A legal document outlining the terms under which one party agrees to rent property from another party. A lease guarantees the lessee (the renter) use of an asset and guarantees the lessor (the property owner) regular payments from the lessee for a specified number of months or years. Both the lessee and the lessor must uphold the terms of the contract for the lease to remain valid.Leases are the contracts that lay out the details of rental agreements in the real estate market. For example, if you want to rent an apartment, the lease will describe how much the monthly rent is, when it is due, what will happen if you don't pay, how much of a security deposit is required, the duration of the lease, whether you are allowed to have pets, how many occupants may live in the unit and any other essential information. The landlord will require you to sign the lease before you can occupy the property as a tenant.DEFINITION OF 'CAPITAL ALLOCATION'A process of how businesses divide their financial resources and other sources of capital to different processes, people and projects. Overall, it is management's goal to optimize capital allocation so that it generates as much wealth as possible for its shareholders.The process behind making a capital allocation decision is complex, as management virtually has an unlimited number of options to consider.

For example, if a company ends up with a larger than expected windfall at the end of the year, management needs to decide whether to use the extra funds to buy back stock, issue a special dividend, purchase new equipment or increase the research and development budget. In one way or another, each one of these actions will likely benefit the shareholder, but the difficult part is in determining how much money should be allocated to each action in order to yield the most benefit.