Flash back before we compare mutually exclusive alternatives.

Flash back before we compare mutually exclusive alternatives

Bank Loan vs. Investment Project

Bank Customer

Loan

Repayment

Company Project

Investment

Return

� Bank Loan

� Investment Project

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

-100,000

-50,000

0

50,000

100,000

150,000

0 1 2 3 4 5 6Years (n)

3.2 years Payback period

$85,000

$15,000

$25,000

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

$35,000

0

1 2 3 4 5 6

Years

Ann

ual c

ash

flow

Cum

ulat

ive

cash

flo

w (

$)

Discounted Payback Period Principle:

How fast can I recover my initial investment plus interest?

Method: Based on cumulative discounted cash flow

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

Weakness: Cash flows occurring after DPP are ignored

Example 5.2 Discounted Payback Period CalculationPeriod Cash Flow Cost of Funds

(15%)*

Cumulative

Cash Flow

0 -$85,000 0 -$85,000

1 15,000 -$85,000(0.15) = -$12,750 -82,750

2 25,000 -$82,750(0.15) = -12,413 -70,163

3 35,000 -$70,163(0.15) = -10,524 -45,687

4 45,000 -$45,687(0.15) =-6,853 -7,540

5 45,000 -$7,540(0.15) = -1,131 36,329

6 35,000 $36,329(0.15) = 5,449 76,778

* Cost of funds = (Unrecovered beginning balance) X (interest rate)

Net Present Worth Measure 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 5

0 1Inflow

Outflow

0

PW(i)inflow

PW(i)outflow

Net surplus

PW(i) > 0

Future Worth Criterion

Given: Cash flows and MARR (i)

Find: The net equivalent worth at the end of project life

$75,000

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

01 2 3

Project life

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

A

0

P = CE(i)

Project Balance Concept

NN 00 11 22 33

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

Guideline for Selecting a MARR

Real Return 2%

Inflation 4%

Risk premium 0%

Total expected return

6%

Real Return 2%

Inflation 4%

Risk premium 20%

Total expected return

26%

Risk-free real return

InflationRisk

premium

U.S. Treasury Bills

Amazon.com

Very safe

Very risky

Chapter 5Present-Worth Analysis Loan versus Project

Cash Flows Initial Project Screening

Methods Present-Worth Analysis Methods to Compare

Mutually Exclusive Alternatives

Comparing Mutually Exclusive Alternatives

Lecture No.16Professor C. S. ParkFundamentals of Engineering EconomicsCopyright © 2005

Comparing Mutually Exclusive Projects

Mutually Exclusive Projects

Alternative vs. Project

Do-Nothing Alternative

Revenue Projects

Projects whose revenues depend on the choice of alternatives

Service Projects

Projects whose revenues do not depend on the choice of alternative

Analysis PeriodThe time span over which the economic effects of an investment will be evaluated (study period or planning horizon).

Required Service PeriodThe time span over which the service of an equipment (or investment) will be needed.

Comparing Mutually Exclusive Projects

PrinciplePrinciple: Projects must be : Projects must be compared over an compared over an equal timeequal time span. span.

Rule of ThumbRule of Thumb: If the required : If the required service period is given, the analysis service period is given, the analysis period should be the same as the period should be the same as the required service period.required service period.

Case 1: Analysis Period Equals Project Lives

Compute the PW for each project over its life

$450$600

$500 $1,400

$2,075$2,110

0

$1,000 $4,000A B

PW (10%) = $283PW (10%) = $579

A

B

$1,000

$450$600

$500

Project A

$1,000

$600

$500$450

$3,000

3,993

$4,000

$1,400

$2,075

$2,110

Project BModifiedProject A

Comparing projects requiring different levels of investment – Assume that theunused funds will be invested at MARR.

PW(10%)A = $283PW(10%)B = $579

This portionof investmentwill earn 10%return on investment.

Case 2: Analysis Period Shorter than Project Lives

Estimate the salvage value at the end of the required service period.

Compute the PW for each project over the required service period.

Example 5.6 - Comparison of unequal-lived service projects when the required service period is shorter than the individual project life

Required Service Period = 2 years

PW(15%)B = -$364,000PW(15%)A = -$362,000

Case 3: Analysis Period Longer than Project Lives

Come up with replacement projects that match or exceed the required

service period.

Compute the PW for each project over the required service period.

Example 5.7 - Comparison for Service Projects with Unequal Lives when the required service period is longer than the individual project life

Required ServicePeriod= 5 years

Model A

Model B

$15,000

$12,500

$4,000 $4,500 $5,000$5,500

$1,500

$5,000 $5,500 $6,000

$2,000

4 5

5

0

0

1 23

1 2 34

Lease Model A to serve the remaining service life

PW(15%)A = -$35.929

PW(15%)B = -$33,173

Summary Present worth is an equivalence method of analysis in which

a project’s cash flows are discounted to a lump sum amount at present time.

The MARR or minimum attractive rate of return is the interest rate at which a firm can always earn or borrow money.

MARR is generally dictated by management and is the rate at which NPW analysis should be conducted.

Two measures of investment, the net future worth and the capitalized equivalent worth, are variations to the NPW criterion.

The term mutually exclusive means that, when one of several alternatives that meet the same need is selected, the others will be rejected.

Revenue projects are those for which the income generated depends on the choice of project.

Service projects are those for which income remains the same, regardless of which project is selected.

The analysis period (study period) is the time span over which the economic effects of an investment will be evaluated.

The required service period is the time span over which the service of an equipment (or investment) will be needed.

The analysis period should be chosen to cover the required service period.

When not specified by management or company policy, the analysis period to use in a comparison of mutually exclusive projects may be chosen by an individual analyst.