Matakuliah : D 0094 Ekonomi Teknik
Tahun : 2007
Pemilihan Investasi Terbaik
Pertemuan 19 dan 20
Pendahuluan
• Dalam mengevaluasi proyek, di pokok bahasan
yang lalu hanya satu metode ekonomi teknik
yang perlu digunakan karena metode berbeda
akan memberikan hasil yang sama.
• Bagaimana cara memilih metode yang digunakan
(bila tidak diberikan oleh soal/bila didunia kerja)
adalah dengan menggunakan tabel berikut ini:
Bina Nusantara
Comparing Mutually Exclusive Alternatives
Evaluation
Period
Type of
Alternatives
Recommended
Method
Series to
evaluate
Equal lives of
alternatives
Revenue or service
Public Sector
AW or PW
B/C based on AW or
PW
Cash Flow
Incremental Cash
Flow
Unequal lives of
alternatives
Revenue or service
Public Sector
AW
B/C based on AW
Cash Flow
Incremental Cash
Flow
Study period
Revenue or service
Public Sector
AW or PW
B/C based on AW or
PW
Updated Cash Flow
Updated
Incremental Cash
Flow
Long to infinite
Revenue or service
Public Sector
AW or PW
B/C based on AW
Cash Flow
Incremental Cash
Flow
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Memilih Proyek
• Setelah melakukan pemilihan metode,
selanjutnya dilakukan pemilihan Rate of Return,
atau interest rate berdasarkan metode evaluasi
(seperti dalam tabel berikut ini)
• Setelah itu dapat dipilih investasi terbaik.
• Disini kita akan kembali bertemu dengan MARR
(Minimum Attractive Rate of Return) sebagai
alternative Rate of Return yang digunakan.
• MARR sendiri disini kita anggap sebagai hurdle
rate, ambang batas, agar kita memperoleh
keuntungan.
Bina Nusantara
Evaluation
Method
Equivalence
Lives of
Alternatives
Time
Periods for
Analysis
Series to
Evaluate
Rate of
Return;
Interest
Rate
Decision
Guideline:
Select*
Present
Worth
PW
Equal
Lives
Cash flow
MARR
Numerically
largest PW
PW
Unequal
LCM
Cash flow
MARR
Numerically
largest PW
PW
Study
period
Study
period
Updated
cash flow
MARR
Numerically
largest PW
CC
Long to
infinite
Infinity
Cash flow
MARR
Numerically
largest CC
Future
Worth
FW
Same as present worth for equal lives, unequal
lives, and study period
Numerically
largest FW
Annual
Worth
AW
Equal
Or unequal
Lives
Cash flow
MARR
Numerically
largest AW
AW
Study
period
Study
period
Updated
cash flow
MARR
Numerically
largest AW
AW
Long to
infinite
Infinity
Cash flow
MARR
Numerically
largest AW
* Lowest
Relation
equivalent cost or largest equivalent income
Evaluation
Method
Equivalence
Rate of
Return
Benefit /
Cost
* Lowest
Lives of
Alternatives
Time
Periods for
Analysis
Series to
Evaluate
Rate of
Return;
Interest
Rate
Decision
Guideline:
Select*
PW or AW
Equal
Lives
Incremental
cash flow
Find Di*
Last Di*>
MARR
PW or AW
Unequal
LCM of
pair
Incremental
cash flow
Find Di*
Last Di*>
MARR
AW
Unequal
Lives
Cash flow
Find Di*
Last Di*>
MARR
PW or AW
Study
period
Study
period
Updated
Incremental
cash flow
Find Di*
Last Di*>
MARR
PW
Equal or
Unequal
LCM of
pair
Incremental
cash flow
Discount
rate
Last D B/C
> 1.0
AW
Equal or
Unequal
Lives
Incremental
cash flow
Discount
rate
Last D B/C
> 1.0
AW or PW
Long to
infinite
Infinity
Incremental
cash flow
Discount
rate
Last D B/C
> 1.0
Relation
equivalent cost or largest equivalent income
Choice of MARR
Or you can choose MARR based on:
• Choice of MARR when Project Financing is Known
• Choice of MARR when Project Financing is
Unknown
• Choice of MARR under Capital Rationing
Bina Nusantara
Choice of MARR when Project Financing is
Known
Explicit accounts
For debt flows
When you find the
Net present worth of
the project, use cost
of equity (ie) as the
discount rate.
Choice of MARR when Project Financing is
Unknown
Without explicitly treating
the debt flows, make a tax
adjustment to the discount
rate, using the weighted
cost of capital k.
Choice of MARR as a Function of Budget
Project
Borrowing rate
(k) = 10%
Lending rate
(r) = 6%
Bina Nusantara
AO
Cash Flow
A1
IRR
1
-$10,000
$12,000
20%
2
-10,000
11,500
15
3
-10,000
11,000
10
4
-10,000
10,800
8
5
-10,000
10,700
7
6
-10,000
10,400
4
Rate of return (%)
An Investment Opportunity Schedule
24
22
20
18
16
14
12
10
8
6
4
2
Project 1
Project 2
Project 3
Project 4
Project 5
20%
0
Bina Nusantara
15%
10%
8%
7%
$20,000
$40,000
Required capital budget
Project 6
4%
$60,000
Rate of return (%)
A Choice of MARR under Capital Rationing
24
22
20
18
16
14
12
10
8
6
4
2
Borrowing rate (k) = 10%
Lending rate (r) = 6%
Project 1
Project 2
k = 10%
Project 3
Project 5 Project 6
20%
0
Bina Nusantara
MARR
Project 4
15%
10%
8%
7%
$20,000
$40,000
Required capital budget
4%
$60,000
r = 6%
Capital Budgeting
• Evaluation of Multiple Investment Alternatives
– Independent projects
– Dependent projects
• Capital Budgeting Decisions with Limited Budgets
Bina Nusantara
Independent Projects
Alternative
Bina Nusantara
Description
Xa
Xb
1
Reject A,
Reject B
0
0
2
Accept A,
Reject B
1
0
3
Reject A,
Accept B
0
1
4
Accept A,
Accept B
1
1
Mutually Exclusive Projects
Bina Nusantara
Alternative
(XA1, XA2)
(XB1,XB2)
1
(0,0)
(0,0)
2
(1,0)
(0,0)
3
(0,1)
(0,0)
4
(0,0)
(1,0)
5
(0,0)
(0,1)
6
(1,0)
(1,0)
7
(0,1)
(1,0)
8
(1,0)
(0,1)
9
(0,1)
(0,1)
Contingent Projects
Alternative
XA
XB
XC
1
0
0
0
2
1
0
0
3
1
1
0
4
1
1
1
Bina Nusantara
Four Energy Saving Projects under Budget
Constraints (Budget Limit = $250,000)
Project
Bina Nusantara
Investment
Annual
O&M Cost
Annual
Savings
(Energy)
Annual
Savings
(Dollars)
IRR
1
$46,800
$1,200 151,000 kWh
$11,778
15.43%
2
104,850
1,050 513,077 kWh
40,020
33.48%
3
135,480
1,350 6,700,000 CF
32,493
15.95%
4
94,230
942 385,962 kWh
30,105
34.40%
Marginal Cost of Capital Schedule (MCC) and
Investment Opportunity Schedule (OSC)
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Optimal Capital Budget
Bina Nusantara
j
Best
Alt.
Alternative
Required
Budget
Combined Annual
Savings
1
0
0
0
2
A1
$(46,800
$10,578
3
A2
(104,850)
38,970
4
A3
(135,480)
31,143
5
A4
(94,230)
35,691
6
A4, A1
(141,030)
46,269
7
A2, A1
(151,650)
49,548
8
A3, A1
(182,280)
41,721
9
A4, A2
(199,080)
74,661
10
A4, A3
(229,710)
66,834
11
A2, A3
(240,330)
70,113
12
A4, A2, A1
(245,880)
85,239
13
A4, A3, A1
(276,510)
77,412
14
A2, A3, A1
(287,130)
80,691
15
A4, A2, A3
(334,560)
105,804
16
A4, A2, A3, A1
(381,360)
116,382
Infeasible
alternatives
Summary
• Methods of financing:
1. Equity financing uses retained earnings or funds
raised from an issuance of stock to finance a
capital.
2. Debt financing uses money raised through loans or
by an issuance of bonds to finance a capital
Investment.
• Companies do not simply borrow funds to finance projects. Wellmanaged firms usually establish a target capital structure and strive to
maintain the debt ratio when individual projects are financed.
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Summary (Cont)
• The selection of an appropriate MARR depends generally
upon the cost of capital—the rate the firm must pay to
various sources for the use of capital.
1. The cost of equity (ie) is used when debt-financing
methods and repayment schedules are known explicitly.
2. The cost of capital (k) is used when exact financing
methods are unknown, but a firm keeps it capital structure
on target. In this situation, a project’s after-tax cash flows
contain no debt cash flows such as principal and interest
payment
Bina Nusantara
• The cost of the capital formula is a composite index
reflecting the cost of funds raised from different
sources. The formula is
id Cd ie Ce
k

,
V
V
where V  Cd  Ce
• The marginal cost of capital is defined as the cost of
obtaining another dollar of new capital. The marginal
cost rises as more and more capital is raised during a
given period.
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• Under conditions of capital rationing, the selection of
MARR is more difficult, but generally the following
possibilities exist:
Conditions
A firm borrows some capital from lending
institutions at the borrowing rate, k, and some
from its investment pool at the lending rate, r.
Bina Nusantara
MARR
r <MARR< k
A firm borrows all capital from lending
institutions at the borrowing rate, k.
MARR = k
A firm borrows all capital from its investment
pool at the lending rate, r.
MARR = r
• The cost of capital used in the capital budgeting process
is determined at the intersection of the IOS and MCC
schedules.
• If the cost of capital at the intersection is used, then the
firm will make correct accept/reject decisions, and its
level of financing and investment will be optimal. This
view assumes that the firm can invest and borrow at the
rate where the two curves intersect.
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• If a strict budget is placed in a capital budgeting
problem and no projects can be taken in part, all
feasible investment decision scenarios need to be
enumerated. Depending upon each investment
scenario, the cost of capital will also likely change. Our
task is to find the best investment scenario in light of a
changing cost of capital environment. As the number of
projects to consider increases, we may eventually resort
to a more advanced technique, such as a mathematical
programming procedure.
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