Nfv and Aev-irr Bme Ee-lec8

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Net Future Value (NFV)y The NPV measures the surplus in an investment

project at time '0'. Sometimes we might need to

find the equivalent worth or value of a project atthe end of the investment period. Hence, the NetFuture Value (NFV) measures the surplus at theend of the investment period.

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Net Future Value (NFV)NFV Criterion

NFV = A0(1+i)n + A1(1+i)n-1 + A2/(1+i) n-2 + ..+An

NFV =sum of An(F/A, i,N-n)

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Net Future Value (NFV)y If NFV >0, accept the project

y If NFV = 0, remain indifferent

y If NFV


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Capitalized Equivalent Method

iANiAPAiPV

iiiiNiAPNN

NN

/),,/()(

/1])1(/)1)1[((lim),,/(lim

!g!

!!gg

C

CC

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Capitalized Equivalent Methody The process of calculating PV cost for infinite period is

called capitalization of project cost. The cost is known

as th

e Capitalized cost i.e. th

e amount of money to beinvested now to get a certain return 'A' at the end ofeach and every year forever.

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APV

i!


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Types of Projectsy Mutually Exclusive Projects

y Mutually exclusive means that any one of severalalternatives will fulfill the same need and that selectingone alternative means that others will be excluded.

y Revenue Projects and Service Projectsy Revenue projects are those projects hose revenues

depend on the choice of the alternative.

y Service projects are those projects whose revenues donot depend on the choice of the project.

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Annual Equivalent Value AnalysisThe annual equivalent value (AE) criterion is a basis for

measuring investment value by determining equalpayments on an annual basis.

First, we have to find the NPV of the project and thenconvert it to equal annual payments.

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Annual Equivalent Value (AEV)AE(i) =PV(i)(A/P,i,n)

If AE>0, accept the projectIf AE =0, remain indifferent

If AE


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Benefits ofAE analysisy 1. Consistency of report format. Financial and

engineering managers may prefer to work onyearly costs rather than overall costs.

y 2. Need for unit costs. In many situations,project must be broken down into unit costs forcomparison and ease.

y

3. Unequal project lives. Comparing projectswith unequal service lives is complicated incalculations, but using AE analysis, this problemcan be easily solved.

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Operating Costs and Capital Costsy Operating costs are incurred by the operations of the

plant or factory.

y

Capital costs are incurred only one time in th

e projectlife, where operating costs incur annually. The annualequivalent of the capital cost is capital recovery cost'CR'.

CR = P(A/P,i,n) - S(A/F,i,n)

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Operating Costs and Capital Costsy (A/F, i, n)=(A/P, i, N) I

y CR(i) =(i-S)(A/P,i, N) +iS

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Life Cycle Cost (LCC)y If a project investment cost is P with the service life of

n period.

yThe annual operating cost is Ai.

y The life cycle cost (LCC) is

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LCC = Capital cost + operating cost

1

( / , , )n

i

n

LCC P A P A r n

!

!


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Annualized Life Cycle Cost (ALCC)y Sometime in the big investment project, we have to

spread the capital cost for the entire service period, in

order to minimize th

e th

e lumpy financial burden,then we have to calculate ALCC.

ALCC = annual capital cost + annualoperating cost

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ALCC = annual capital cost + annual operating cost


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Annualized Life Cycle Cost (ALCC)

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ALCC =LCC (A/P, I,n)


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Internal Rate of Return (IRR)IRR is the interest rate earned on the unrecovered

project balance of investment such that, when theproject terminates, the unrecovered project balance

will be zero.

NPV = A0/(1+i*)0 + A1/(1+i

*)1 + A2/(1+i*)2 .+ An/(1+i

*)n

=0

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Internal Rate of Return (IRR)Simple Investments

A simple investment is defined as that investment, when

th

e sign ch

ange in th

e project cash

flow occurs onlyonce.

A non-simple investment is that investment where thesign change occurs more than once.

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Investment ClassificationInvestment type

0 period 1 2 3 4 5

Simple -

Simple - - 0

Non-simple

_ _ _

Non-simple

_ - 0

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Internal Rate of Return (IRR)Methods of project Evaluation byIRR

y IfIRR>MARR, accept the project

yIfIRR = MARR, remain indifferent

y IfIRR < MARR, reject the project

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Cash Flow Rule of SignsNet Cash flow rule of sign

y The number of real i* that are greater than -100% for aproject with 'n' periods is never greater than the numberof sign changes in the sequence of the Anvalues.

y Accumulated Cash flow rule of sign

y If the net cash flow sign test shows multiple values of i*,then we should proceed to this sign test.

y If the series of cumulative cash flows start negativelyand changes the sign only once, then there exists aunique positive i*.

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Direct Solution Methodn Project 1 Project 2

1 -$1,000 _$2,0002 0 1,300

3 0 1,500

4 0

5 1,500

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Direct Solution Method

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Project 1

* *

* * 4

* 4

1* 4

*

( ) $1,000( / , , 4) $1, 500 0

$1,500 $1,000( / , , 4) $1,000(1 )

1.5 (1 )

1.5 1

0.1067 10.67%

FV i F P i

F P i i

i

i

i or

! !

! !

!

!

!


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Direct Solution Method

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Project 22

2

2

$1, 300 $1, 500$2, 000 0

(1 ) (1 )

1(1 )

$2, 000 $1, 300 $1, 500 0

1,300 1,300 4(1,500)( 2, 000)

2(1, 500)

1, 300 3, 7003, 000

0.8 1.667

10.8

1

25%

NPVi i

Let

xi

NPV x x

x

x

x or

i

i

! !

!

! !

s !

s!

!

!

!


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Incremental investment Analysisy Under NPV and AEV analysis, the mutually

exclusive project with the highest value is selectedand this method is known as Total Investment

Approach. NPV, NFV, and AEV methods ofproject evaluation are absolute measures, whereasthe IRR method is a relative (percentage) measure,and it ignores the scale of investment. But for

comparison of mutually exclusive projects byIRRmethod, we have to do Incremental Investment

Analysis.

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Incremental investment Analysis

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,

,

,

B A

B A

B A

IRR MARR SelectB IRR MARR Beindifferent

IRR MARR SelectA

"

If


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Assignment

10/04/07 31

Please read and study carefully the design economics8.4 sub-chapter

Page 3838.1, 8.2, 8.4, 8.6, 8.8, 8.9, 8.10, 8.13, 8.14, 8.15, 8.19, 8.208.22, 8.24, 8.30, 8.34, 8.36, 8.38, and 8.41Page 4369.4, 9.5,9.7,9.10,9.13,9.16,9.18,9.21,9.22,9.25,9.30,9.33 and 9.34

Page 848A.1 to A.5, A.8, A.10

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