Lecture no25 internal rate of return criterion

Internal Rate of Return Criterion Lecture No... Net Investment Test• What it is: Whether or not a firm borrows money from a project during the investment period • How to test: Passes a

Internal Rate of Return

Criterion

Lecture No 25 Chapter 7 Contemporary Engineering Economics

Copyright © 2016

Net Investment Test

• What it is: Whether or not a firm borrows money from

a project during the investment period

• How to test: Passes a net investment test 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 firm does not overdraw on its return in any point and hence is not indebted to the project.

Pure versus Mixed Investment

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

Example 7.6: Pure versus Mixed Investments

 

 01  

PB 21.95% = $1,000.

PB 21.95% = $1,000 1+0.2195 +$1,600=$380.50.





PB 21.95% =+$380.50 1+0.2195 $300=$164.02.

PB 21.95% =+$164.02 1+0.2195 $200=0.





(−, +, +, 0)  Mixed investment

Sample Calculation for Project B:

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

Decision Rules for Pure Investment

Decision Rules

• 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 incremental analysis

(see Lecture No 26).

Example

*

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

$80,000( / , ,15)

=0 58.71%

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

P F i

i i







Decision Rule for Mixed Investments

• We need an external interest rate for mixed investments

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

• We calculate a rate of return on the portion of capital that

remains invested internally—commonly known as the

return on invested capital (RIC)

• Then select the investment if RIC > MARR

Procedure to Calculate the RIC

Computational Logic for RIC

Lending

to project

Borrowing from project

Example 7.8: RIC for a Mixed Investment

2

$260 $168

(1 *) (1 *) 20% and 40%

i i

NPW plot for a nonsimple investment with multiple rates of return

A mixed investment

• Case 1: i < 1.6

PB(i,25%)1 > 0

• Case 2: i > 1.6

PB(i,25%)1 < 0

 Step 1 :

External

interest rate =

MARR = 25%

 Step 2 :

Calculate

PB(i,25%) n

2

125 32 0

25.60% 25%

i

i IRR



2

2

PB( ,25%) (160 100 )(1 ) 168

8 60 100 0

0.20 or 0.40 1.6 (not valid)

i

   

   



0 1

2

PB( ,25%) 100 0

PB( ,25%) 100(1 ) 260

160 100 PB( ,25%) ?

i

i i

  

   

 



RIC = 25.60% > 25%, Accept

Finding RIC Using

Cash Flow Analyzer

Example 7.8

RIC at 25%

External interest rate

Input cash flows

Example 7.9

 Given : RIC for a Mixed Investment by Trial and Error Approach

External interest rate = 6%

• Guess i = RIC at 8%:

• Guess i = RIC at 6.13%:

PB(8%,6%)3 < 0, indicating that our guess I =

8% is in error

We need to lower the guess value and try again.

Summary of IRR Criteria

Modified Internal Rate of Return (MIRR)

up with a single ROR for nonsimple investment?

inflows) are invested at the firm’s MARR, and (2) negative cash flows (cash outflows) are financed at the firm’s cost of capital.

MIRR > MARR

Example 7.10: Calculation of MIRR

MIRR (6.026%) > 6%, accept the investment.