Contemporary Engineering Economics, 4 th edition, © 2007 Internal Rate of Return Criterion Lecture...

Contemporary Engineering Economics, 4th edition, © 2007

Internal Rate of Return Criterion

Lecture No. 27Chapter 7Contemporary Engineering EconomicsCopyright © 2006


Decision Rule for Pure Investment Decision Criterion for a Single Project:

If IRR > MARR, accept the project. If IRR = MARR, remain indifferent. If IRR < MARR, reject the project.

Decision Criterion for Mutually Exclusive Projects: Use the incremental analysis (See Lecture No.

28)


Example 7.7 Investment Decision for a Pure Investment


Solution:

*

= $1,250,000 + $731,500 , , 15

$80,000( / , ,15)

=0

58.71%

Since * > MARR(18%), accept the investment.

PW i P A i

P F i

i

i


Decision Rule for Mixed Investments Need for an external interest rate for mixed

investments. We will use the MARR as established external interest rate—the rate earned by money invested outside of the project.

Calculate a rate of return on the portion of capital that remains invested internally—commonly known as the return on invested capital (RIC)

Select the investment if RIC > MARR.


Procedure to Calculate the RIC Step 1: Identify the MARR (or external interest rate). Step 2: Calculate PB(i, MARR)n (or simply PBn) according to the rule

Step 3: Determine the value of i by solving the terminal project balance equation

That interest rate i is the RIC (or IRR) for the mixed investment.

0)1(

0)1(

11

11

00

nnn

nnnn PBAMARRPB

PBAiPBPB

APB

0NPB


Computational Logic for RIC


Example 7.8 RIC for a Mixed Investment

n An

0

1

2

-$1,000,000

2,300,000

-1,320,000

MARR = 15%


Solution: PB(i,15%)0 = -$1,000 PB(i,15%)1 = -$1,000(1 + i) + $2,300 = 1,000(1.3 – i)

Case 1: i < 1.3 → PB(i,15%)1 > 0 PB(i,15%)2 = 1,000(1.3 –i)(1.15) – 1,320 = 175 – 1,150i = 0 RIC = IRR = i = 15.22% > 15%

Case 2: i >1.3 → PB(i,15%)1 < 0 There is no solution.


Calculation of the IRR


Finding the RIC for Mixed Investments with Cash Flow Analyzer

Return on invested capital15.21% at MARR of 15%

MARR of 15%

Nonsimple Investment Cash Flows

0 -$1,0001 2,3002 -1,320


Example 7.9 RIC for a Mixed Investment by Trial and Error

n An

0

1

2

3

-$1,000

3,900

-5,030

2,145

External interest rate = MARR = 6%Find the RIC for the project.


Solution: RIC =6.13% > MARR, Select the investment Guess i = RIC at 8%:

Guess i = RIC at 6.13%:

The net investmentis negative at theend of the project,indicating that ourtrial i =8% is in error.We lower the guessvalue and try again.

06.59$2145$)08.01(80.2040$%)6%,8(

80.2040$5030$)06.01(2820$%)6%,8(

2820$3900$)08.01(1000$%)6%,8(

1000$%)6%,8(

3

2

1

0

PB

PB

PB

PB

02145$)0613.01(02.2021$%)6%,13.6(

02.2021$5030$)06.01(66.2838$%)6%,13.6(

66.2838$3900$)0613.01(1000$%)6%,13.6(

1000$%)6%,13.6(

3

2

1

0

PB

PB

PB

PB


Summary of IRR Criterion

Contemporary Engineering Economics, 4 th edition, © 2007 Internal Rate of Return Criterion Lecture...

Documents

Transcript of Contemporary Engineering Economics, 4 th edition, © 2007 Internal Rate of Return Criterion Lecture...