Contemporary Engineering Economics, 4 th edition, © 2007 Multiple Rates of Return Problem Lecture No. 26 Chapter 7 Contemporary Engineering Economics Copyright

Contemporary Engineering Economics, 4th edition, © 2007

Multiple Rates of Return Problem

Lecture No. 26Chapter 7Contemporary Engineering EconomicsCopyright © 2006


Net Investment Test

What it is: A process to determine whether or not a firm borrows money from a project during the investment period.

How to test: A project is said to be a net investment when the project balances computed at the project’s i* values, PB(i*)n, are either less than or equal to zero throughout the life of the investment.

Meaning: The investment is net in the sense that the firm does not overdraw on its return any point and hence is not indebted to the project


Pure Investment

Definition: An investment in which a firm never borrows money from the project.

How to Determine: If the project passes the net investment test, it is a pure investment.

Relationship: A simple investment is always a pure investment.


Mixed Investment

Definition: An investment in which a firm borrows money from the project during the investment period

How to determine: If a project fails the net investment test, it is a mixed investment.

Relationship: If a project is a mixed investment, it is a nonsimple investment. (However, we can’t say that a nonsimple investment is also a mixed investment.)


Example 7.6 Pure versus Mixed Investments

n

Project Cash Flows

A B C D

0

1

2

3

-$1,000

1,000

2,000

1,500

-$1,000

1,600

-300

-200

-$1,000

500

-500

2,000

-$1,000

3,900

-5,030

2,145

i* 33.64% 21.95% 29.95% (10%,30%,50%)


Sample Calculation – Net Investment Test (Project B)

(-, +, +, 0) Mixed investment

Use 21.95% as an interest rate to find the project balances

0200$)2195.01(02.164$%)95.21(

02.164$300$)2195.01(5.380$%)95.21(

5.380$1600$)2195.01(1000$%)95.21(

1000$%)95.21(

3

2

1

0

PB

PB

PB

PB


Net investment test (Example 7.6)


Multiple Rates of Return Problem

• Find the rate(s) of return:

2

$2,300 $1,320( ) $1,000

1 (1 )

0

PW ii i

$1,000

$2,300

$1,320


Let Then,

Solving for yields,

or

Solving for yields

or 20%

xi

PW ii i

x x

x

x x

i

i

1

1

000300

1

320

1

000 300 320

0

10 11 10 12

10%

2

2

.

( ) $1,$2,

( )

$1,

( )

$1, $2, $1,

/ /

Analytical Solution:


PW Plot for a Nonsimple Investment with Multiple Rates of Return


n = 0 n = 1 n = 2

Beg. Balance

Interest Charged

Payment -$1,000

-$1,000

-$200

+$2,300

+$1,100

+$220

-$1,320

Ending Balance -$1,000 +$1,100 $0

Use either i* =20% or 10%

Cash borrowed (released) from the project is assumed toearn the same interest rate through external investmentas money that remains internally invested a mixed investment

Fail the Net Investment Test


Can the firm be able to invest the money released from the project at 20% externally in Period 1?

• If the firm’s MARR is exactly 20%, the answer is “yes”, because it represents the rate at which the firm can always invest the money in its investment pool. Then, the 20% is also true IRR for the project..• Suppose the firm’s MARR is 15% instead of 20%. The assumption used in calculating i* is no longer valid. In order to calculate i*, we assumed that all cash released from the project can be invested at the i* instead of MARR.

• Conclusion: Neither 10% nor 20% is a true IRR.

Conceptual Issue:


If NPW criterion is used at MARR = 15%

PW(15%) = -$1,000 + $2,300 (P/F, 15%, 1)

- $1,320 (P/F, 15%, 2 )

= $1.89 > 0

Accept the investment

• If you encounter multiple rates of return, abandon the IRR analysis and use the PW criterion.

• If you want to find the true rate of return (or return on invested capital) to the project, follow the procedure outlined in Section 7.3.4.

How to Proceed:

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Contemporary Engineering Economics, 4 th edition, © 2007 Multiple Rates of Return Problem Lecture No. 26 Chapter 7 Contemporary Engineering Economics Copyright