Lecture

5

Engineering Economics ENGR 3300

Department of Mechanical EngineeringInter American University of Puerto Rico

Bayamon CampusDr. Omar E. Meza Castillo

omeza@bayamon.inter.eduhttp://www.facultad/bayamon.inter.edu/omeza

Lecture

5 Present Worth Analysis

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Bank Loan vs. Investment Project

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Project Cash Flow

Representation of project’s future earnings, along with the capital expenditures and annual expenses (such as wages, raw materials, operating costs, maintenance costs and income taxes) at different time periods is called a Project Cash Flow.

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Identifying Project Cash Flows

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Initial Project Screening Methods

One of the primary concerns of most businesspeople is whether and when the money invested in a project can be recovered. The payback method screens projects on the basis of how long it takes for net receipts to equal investment outlays.

This calculation can take one of two forms: either ignore time-value-of-money considerations or include then. The former case is usually designated the conventional payback method, the latter case the discounted payback method.

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Payback Period

Principle:How fast can I recover my initial investment?

Method:Based on cumulative cash flow (or accounting profit)

Screening Guideline:If the payback period is less than or equal to some specified payback period, the project would be considered for further analysis.

Weakness:Does not consider the time value of money

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takes to Pay Back Principle:

How fast can I recover my initial investment?

Method:Based on cumulative cash flow (or accounting profit)

Screening Guideline:If the payback period is less than or equal to some specified payback period, the project would be considered for further analysis.

Weakness:Does not consider the time value of money

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Convectional Payback Period Consider the cash flows given in the

example of Computer Process Control System. Determine the payback period.

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Convectional Payback Period with Salvage Value Example

5.3

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-50,000

0

50,000

100,000

150,000

0 1 2 3 4 5 6

Years (n)

3.2 years Payback period

$85,000

$15,000$25,000

$35,000$45,000 $45,00

0 $35,000

0

1 2 3 4 5 6YearsA

nnual ca

sh fl

ow

Cum

ula

tive c

ash

flow

($

)

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Comments If the cash flow occur continuously

throughout the year, the payback period calculation needs adjustment.

A negative balance of $10,000 remains at t he start of year 4. If $45,000 is expected to be received as a more or less continuous flow during year 4, the total investment will be recovered two tenths ($10,000/$45,000) of the way through the four year. Thus, in this situation, the payback period is 3.2 years.

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Benefits and Flaws of Payback Screening

Investment Cash Flows for Two Competing Projects

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Is the number of years required to recover the investment from discounted cash flows.

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Present-Worth Analysis

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Present-Worth Analysis

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Present-Worth Analysis

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Present-Worth Analysis

Principle: Compute the equivalent net surplus at n = 0 for a given interest rate of i.

Decision Rule: Accept the project if the net surplus is positive.

2 3 4 50 1

Inflow

Outflow

0

PW(i)inflow

PW(i)outflow

Net surplus

PW(i) > 0

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Net Present Worth: Uniform Flows

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Net Present Worth: Uniform Flows

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Net Present Worth: Uneven Flows

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Net Present Worth: Uneven Flows

PW P F P F

P F

PW

PW

( $24, ( / , ) $27, ( / , )

$55, ( / , )

$78,

( $75,

( $78, $75,

$3, ,

15%) 400 15%,1 340 15%,2

760 15%,3

553

15%) 000

15%) 553 000

553 0

inflow

outflow

Accept

$75,000

$24,400 $27,340$55,760

01 2 3

outflow

inflow

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Varying Interest Rates

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Future-Worth Analysis Net present worth measures the surplus in

an investment project at time 0. Net future worth (NFW) measures this surplus at a time other than 0.

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Net Future Worth: At the End of the Project

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Net Future Worth: At the End of the Project

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Net Future Worth: At the End of the Project

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Project Balance Concept

N 0 1 2 3

BeginningBalance

Interest

Payment

Project Balance

-$75,000

-$75,000

-$75,000

-$11,250

+$24,400

-$61,850

-$61,850

-$9,278

+$27,340

-$43,788

-$43,788

-$6,568

+$55,760

+$5,404

Net future worth, FW(15%)

PW(15%) = $5,404 (P/F, 15%, 3) = $3,553

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Project Balance Diagram

60,000

40,000

20,000

0

-20,000

-40,000

-60,000

-80,000

-100,000

-120,000

0 1 2 3

-$75,000-$61,850

-$43,788

$5,404

Year(n)

Terminal project balance(net future worth, or

project surplus)

Discounted payback period

Pro

ject

bala

nce

($

)

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Capitalized-Equivalent Worth

Principle: PW for a project with an annual receipt of A over infinite service life

Equation: CE(i) = A(P/A, i, ) = A/i

P = CE(i)

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Capitalized-Equivalent Worth

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Capitalized-Equivalent Worth

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Homework 3 www.bc.inter.edu/facultad/omeza