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 ID: 626065
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Slide1
Internal Rate of Return Criterion
Lecture No.
25
Chapter 7
Contemporary Engineering Economics
Copyright ©
2016Slide2
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.Slide3
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. Slide4
Example
7.6:
Pure
versus
Mixed Investments
(−,
+, +, 0)
Mixed
investment
Sample Calculation for Project B:
Use
21.95% as an interest rate to find the project
balances.Slide5
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).
ExampleSlide6
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
.Slide7
Procedure to Calculate the RICSlide8
Computational Logic for RIC
Lending
to project
Borrowing
from projectSlide9
Example
7.8:
RIC for a Mixed Investment
NPW plot for a
nonsimple
investment
with multiple rates of return
A mixed investmentSlide10
Solution
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
RIC = 25.60% > 25%, AcceptSlide11
Finding RIC Using Cash Flow Analyzer
Example 7.8
RIC at 25%
External interest rate
Input cash flowsSlide12
Example 7.9
Given
:
RIC for a Mixed Investment by Trial and Error Approach
External interest rate = 6%
Find
: RICSlide13
Solution
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.Slide14
Summary of IRR
CriteriaSlide15
Modified Internal Rate of Return (MIRR)
Idea
: Can we avoid a multiple ROR problem? Is there a way to come up with a single ROR for
nonsimple
investment?
Procedure
: Use two interest rates: (1) positive cash flows (cash inflows) are invested at the firm’s MARR, and (2) negative cash flows (cash outflows) are financed at the firm’s cost of capital.
Decision Rule: Accept the investment if: MIRR > MARRSlide16
Example 7.10: Calculation of MIRR
Given
: MARR (
i
) = cost of capital (
k
) = 6%
Find: MIRRSlide17
Solution
MIRR (6.026%) > 6%, accept the investment.