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Chapter #: 04, 05Chapter #: 04, 05

Engineering EconomicsEngineering Economics

Shaz_353@yahoo.comShaz_353@yahoo.com

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RevenueRevenue

The amount ofThe amount of moneymoney that a companythat a company

actually receivesactually receives during a specific period,during a specific period,

including discounts and deductionsincluding discounts and deductionsforfor returned merchandise.returned merchandise.

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CostCost

ValuationValuation inin termsterms ofofmoneymoney ofof

(1) effort,(1) effort,

(2)(2) materialmaterial,,

(3)(3) resourcesresources,,(4) time and(4) time and utilitiesutilities consumed,consumed,

(5)(5) risksrisks incurred, andincurred, and

(6)(6) opportunityopportunity forgone inforgone in productionproduction andand deliverydelivery of a good orof a good orserviceservice. All. All expensesexpenses areare costscosts, but not all costs (such as, but not all costs (such asthose incurred inthose incurred in acquisitionacquisition of an incomeof an income--generatinggenerating assetasset))are expenses.are expenses.

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Salvage value:Salvage value:

The estimatedThe estimated valuevalue of anof an assetasset at the end ofat the end ofitsits useful lifeuseful life..

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Present worth method ofPresent worth method of

comparison.comparison.In this method of comparison , the cash flowsIn this method of comparison , the cash flows

of each alternative will beof each alternative will be

reduced/discounted to time zero( i.e presentreduced/discounted to time zero( i.e presentworth) at specific interest rateworth) at specific interest rate i .i .

There could be two types decisions in thisThere could be two types decisions in this

type of comparison.type of comparison.

(a)(a) Revenue dominated cash flow diagramRevenue dominated cash flow diagram

(b)(b) CCash dominated cash flow diagramash dominated cash flow diagram

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Revenue dominated cash flowRevenue dominated cash flow

diagramdiagramIn this type of cash flow diagram, the profit,In this type of cash flow diagram, the profit,

revenue, salvage value (all inflows to anrevenue, salvage value (all inflows to an

organization) will be assigned with positiveorganization) will be assigned with positive

sign, the cost (outflows) will be assigned withsign, the cost (outflows) will be assigned with

negative sign.negative sign.

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Formula for this will be:Formula for this will be:

Pw(i) =Pw(i) = --P+R1[1/(1+i)^1]+R2[1/(1+i)^2]+.P+R1[1/(1+i)^1]+R2[1/(1+i)^2]+.

.+ Rn[1/(1+i)^n]+S[1/(1+i)^n].+ Rn[1/(1+i)^n]+S[1/(1+i)^n]OrOr

Pw(i) =Pw(i) = --P+R1(P/R,i,1)+R2(P/R,i,2)P+R1(P/R,i,1)+R2(P/R,i,2)

+Rn(P/R,i,n) +S(P/S,i,n)+Rn(P/R,i,n) +S(P/S,i,n)

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with this formula, the present worth of otherwith this formula, the present worth of other

alternatives are computed and then compared.alternatives are computed and then compared.

The alternative with the maximum presentThe alternative with the maximum present

worth amount should be selected as the bestworth amount should be selected as the best

alternative.alternative.

Example 4.1Example 4.1

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Cost dominated cash flow diagramCost dominated cash flow diagram

In a cost dominated cash flow diagram, theIn a cost dominated cash flow diagram, the

costs (outflows) will be assigned positive signcosts (outflows) will be assigned positive sign

and the profit , revenue, salvage value (alland the profit , revenue, salvage value (all

inflows) will be assigned negative sign.inflows) will be assigned negative sign.

For selecting an alternative with minimumFor selecting an alternative with minimum

costs the alternative with the least presentcosts the alternative with the least present

worth amount will be selecetd.worth amount will be selecetd.

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formula for this is:formula for this is:

Pw(i) = P+C1[1/(1+i)^1]+C2[1/(1+i)^2]+.Pw(i) = P+C1[1/(1+i)^1]+C2[1/(1+i)^2]+..+ Cn[1/(1+i)^n].+ Cn[1/(1+i)^n]--S[1/(1+i)^n]S[1/(1+i)^n]

OrOr

Pw(i) = P+ C1(P/C,i,1)+ C2 (P/C,i,2).Pw(i) = P+ C1(P/C,i,1)+ C2 (P/C,i,2).

+Cn(P/C,i,n) +Cn(P/C,i,n) -- S(P/C,i,n)S(P/C,i,n)

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The alternative with minimum present worthThe alternative with minimum present worth

amount should be selected as the bestamount should be selected as the best

alternative.alternative.

Example 4.2Example 4.2

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Future Worth Method.Future Worth Method.

In future worth method of comparison , the futureIn future worth method of comparison , the future

worth of different alternatives is compared with thisworth of different alternatives is compared with this

method .method .

The alternative with maximum future worth of netThe alternative with maximum future worth of net

revenue dominated cash flow or with minimum futurerevenue dominated cash flow or with minimum future

worth of net cost dominated cash flow will beworth of net cost dominated cash flow will beselected, as best alternative for implememntation.selected, as best alternative for implememntation.

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RevenueRevenue--Dominated cash flowDominated cash flow

diagramdiagramFormula for this is:Formula for this is:

FW(i) =FW(i) = --P(1+i)^n+R1(1+i)^nP(1+i)^n+R1(1+i)^n--1+ R2(1+i)^n1+ R2(1+i)^n--22.+Rn+S.+Rn+S

example 5.1example 5.1

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Cost Dominated cash flow diagram:Cost Dominated cash flow diagram:

Future worth cost formula isFuture worth cost formula is

Fw(i) = P(1+i)^n+ C1(1+i)^nFw(i) = P(1+i)^n+ C1(1+i)^n--1.+1.++Cn+Cn--SS

the alternative with minimum futureworththe alternative with minimum futureworth

amount should be selected as the bestamount should be selected as the bestalternative.alternative.

Examples from bookExamples from book