Selection of a
Minimum Attractive Rate of
Return
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EGR 403 Capital Allocation Theory
Dr. Phillip R. Rosenkrantz
Industrial & Manufacturing Engineering Department
Cal Poly Pomona
EGR 403 - The Big Picture
• Framework: Accounting & Breakeven Analysis
• “Time-value of money” concepts - Ch. 3, 4
• Analysis methods
–
–
–
–
Ch. 5 - Present Worth
Ch. 6 - Annual Worth
Ch. 7,7A,8 - Rate of Return (incremental analysis)
Ch. 9 - Benefit Cost Ratio & other methods
• Refining the analysis
– Ch. 10, 11 - Depreciation & Taxes
– Ch. 12 - Replacement Analysis
– Selection of the MARR
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Selecting a MARR
• MARR is generally the maximum of the:
– Cost of borrowed money
– Cost of capital
– Opportunity cost
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Sources of Capital
• Money generated from the operation of the firm
(retained profits and cash flow generated from
depreciation).
• External sources of funds:
– Short term borrowing - banks (generally unsecured).
– Long term borrowing - banks, insurance companies,
pension funds, bonds (secured).
– Permanent - sale of company stock.
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Cost of Funds
Cost of capital is the after tax weighted ROR of
borrowed funds from all sources.
Total capital invested (millions) $ 100.00
Bank loan
Mortgage bonds
Common stock and
retained earnings
Capital
Structure
%
20%
$ 20.00
20%
$ 20.00
60%
$ 60.00
Cost of capital
Tax rate
Interest
paid
ROR
40%
Taxes
AT
Interest
cost
$ 1.08
$ 0.84
9%
7%
$
$
1.80
1.40
$
$
0.72
0.56
11%
$
6.60
$
-
$
6.60
$
9.80
$
1.28
$
8.52
8.52%
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Investment Opportunities
• There are
many
investment
opportunities
in an active
firm and often
limited capital.
• Opportunity
cost is the
ROR of the
best
opportunity
foregone.
Capital available $ 1,200.00
Project
Number
2
4
3
5
1
6
8
9
7
11
10
12
Cost
$
50.00
$ 100.00
$
50.00
$ 200.00
$ 150.00
$ 100.00
$ 250.00
$ 300.00
$ 200.00
$ 400.00
$ 300.00
$ 1,200.00
Estimated
ROR
45%
40%
38%
35%
30%
28%
25%
20%
18%
15%
10%
8%
ROR of
Select
Capital to Rejected
Projects be Invested Projects
1
$
50.00
1
$ 100.00
1
$
50.00
1
$ 200.00
1
$ 150.00
1
$ 100.00
1
$ 250.00
1
$ 300.00
0
$
18%
0
$
15%
0
$
10%
0
$
8%
$ 1,200.00
Opportunity cost
18%
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Adjusting MARR to Account for
Risk and Uncertainty
• Increase MARR to avoid marginal projects.
• Assess the projects using techniques other than
economic analysis.
Additionally, MARR might be adjusted to reflect imminent
inflation.
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Selecting a MARR
• MARR is generally the maximum of the:
– Cost of borrowed money
– Cost of capital
– Opportunity cost
• If a project we are considering does not generate a
greater return than these would cost, then we
should put our money into these rather than the
project.
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Representative Values of MARR
Used in Industry
Group
Small project
Struggling
One year payback One year payback
= 60 % ROR
= 60 % ROR
Limited funds
Stable
Adequate funding
Payback with a
variable life
Large project
12 to 15%
After-tax
In addition to these two factors,many other factors
also affect interest rates: a public vs. a private
organization, debt/equity position, risk posture,
etc.
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