?The McGraw-Hill Companies,Inc.,2001
6- 1
Irwin/McGraw-Hill
Chapter 6Fundamentals of Corporate FinanceThird Edition
Net Present
Value and
Other
Investment
Criteria
Brealey Myers Marcus
slides by Matthew Will
?The McGraw-Hill Companies,Inc.,2001
6- 2
Irwin/McGraw-Hill
Topics Covered
?Net Present Value
?Other Investment Criteria
?Project Interactions
?Capital Rationing
?The McGraw-Hill Companies,Inc.,2001
6- 3
Irwin/McGraw-Hill
Net Present Value
Opportunity Cost of Capital - Expected rate
of return given up by investing in a project,
Net Present Value - Present value of cash
flows minus initial investments.
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6- 4
Irwin/McGraw-Hill
Net Present Value
Example
Suppose we can invest $50 today and receive $60
in one year,What is our increase in value given a
10% expected return?
This is the definition of NPV
P r o f i t = - 5 0 + 60
1, 1 0
? $4, 55
Initial Investment
Added Value
$50
$4.55
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6- 5
Irwin/McGraw-Hill
Net Present Value
NPV = PV - required investment
N P V C C
r
t
t? ? ?0 1( )
N P V C C
r
C
r
C
r
t
t? ? ? ? ? ? ? ?0
1
1
2
21 1 1( ) ( ),,, ( )
?The McGraw-Hill Companies,Inc.,2001
6- 6
Irwin/McGraw-Hill
Net Present Value
Terminology
C = Cash Flow
t = time period of the investment
r =,opportunity cost of capital”
?The Cash Flow could be positive or negative at
any time period.
?The McGraw-Hill Companies,Inc.,2001
6- 7
Irwin/McGraw-Hill
Net Present Value
Net Present Value Rule
Managers increase shareholders’ wealth by
accepting all projects that are worth more
than they cost,
Therefore,they should accept all projects
with a positive net present value.
?The McGraw-Hill Companies,Inc.,2001
6- 8
Irwin/McGraw-Hill
Net Present Value
Example
You have the opportunity to
purchase an office building,You
have a tenant lined up that will
generate $16,000 per year in cash
flows for three years,At the end
of three years you anticipate
selling the building for $450,000,
How much would you be willing
to pay for the building?
?The McGraw-Hill Companies,Inc.,2001
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Irwin/McGraw-Hill
Net Present Value
0 1 2 3
$16,000$16,000$16,000
$450,000
$466,000
Present Value
14,953
14,953
380,395
$409,323
Example - continued
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Irwin/McGraw-Hill
Net Present Value
Example - continued
If the building is being
offered for sale at a price
of $350,000,would you
buy the building and what
is the added value
generated by your
purchase and management
of the building?
?The McGraw-Hill Companies,Inc.,2001
6- 11
Irwin/McGraw-Hill
Net Present Value
Example - continued
If the building is being offered for sale at a price of
$350,000,would you buy the building and what is the
added value generated by your purchase and management
of the building?N P V
N P V
? ? ? ? ?
?
350 000
16 000
1 07
16 000
1 07
466 000
1 07
323
1 2 3
,
,
(, )
,
(, )
,
(, )
$59,
?The McGraw-Hill Companies,Inc.,2001
6- 12
Irwin/McGraw-Hill
Other Investment Criteria
Internal Rate of Return (IRR) - Discount rate at
which NPV = 0.
Rate of Return Rule - Invest in any project offering
a rate of return that is higher than the opportunity
cost of capital.
R at e o f R e t u rn = C - i n v es t m en t
i n v es t m en t
1
?The McGraw-Hill Companies,Inc.,2001
6- 13
Irwin/McGraw-Hill
Internal Rate of Return
Example
You can purchase a building for $350,000,The investment will
generate $16,000 in cash flows (i.e,rent) during the first three years,
At the end of three years you will sell the building for $450,000,What
is the IRR on this investment?
0 350 000 16 0001 16 0001 466 00011 2 3? ? ? ? ? ? ? ?,,( ),( ),( )I R R I R R I R R
IRR = 12.96%
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Irwin/McGraw-Hill
Internal Rate of Return
-200
-150
-100
-50
0
50
100
150
200
0 5 10 15 20 25 30 35
D i s c o u n t r a te (% )
N
PV
(,
0
0
0
s
)
IRR=12.96%
?The McGraw-Hill Companies,Inc.,2001
6- 15
Irwin/McGraw-Hill
Payback Method
Payback Period - Time until cash flows recover the
initial investment of the project.
?The payback rule specifies that a project be
accepted if its payback period is less than the
specified cutoff period,The following example
will demonstrate the absurdity of this statement.
?The McGraw-Hill Companies,Inc.,2001
6- 16
Irwin/McGraw-Hill
Payback Method
Example
The three project below are available,The company accepts
all projects with a 2 year or less payback period,Show how
this decision will impact our decision.
Cash Flows
Prj,C0 C1 C2 C3 Payback NPV@10%
A -2000 +1000 +1000 +10000 2 +7,249
B -2000 +1000 +1000 0 2 - 264
C -2000 0 +2000 0 2 - 347
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6- 17
Irwin/McGraw-Hill
Book Rate of Return
Book Rate of Return - Average income divided by
average book value over project life,Also called
accounting rate of return.
Managers rarely use this measurement to make
decisions,The components reflect tax and
accounting figures,not market values or cash
flows,
B o o k r a t e o f r e t u r n = b o o k i n c o m e
b o o k a s s e t s
?The McGraw-Hill Companies,Inc.,2001
6- 18
Irwin/McGraw-Hill
Project Interactions
When you need to choose between mutually
exclusive projects,the decision rule is
simple,Calculate the NPV of each project,
and,from those options that have a positive
NPV,choose the one whose NPV is highest.
?The McGraw-Hill Companies,Inc.,2001
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Irwin/McGraw-Hill
Mutually Exclusive Projects
Example
Select one of the two following projects,based on
highest NPV,
Proj 0 1 2 3 4 NPV
A -15 5.5 5.5 5.5 5.5
B -20 9 9 9
assume 9% discount rate
?The McGraw-Hill Companies,Inc.,2001
6- 20
Irwin/McGraw-Hill
Mutually Exclusive Projects
Example
Select one of the two following projects,based on
highest NPV,
Proj 0 1 2 3 4 NPV
A -15 5.5 5.5 5.5 5.5 2.82
B -20 9 9 9 2.78
assume 9% discount rate
?The McGraw-Hill Companies,Inc.,2001
6- 21
Irwin/McGraw-Hill
Investment Timing
Sometimes you have the ability to defer an
investment and select a time that is more
ideal at which to make the investment
decision,A common example involves a
tree farm,You may defer the harvesting of
trees,By doing so,you defer the receipt of
the cash flow,yet increase the cash flow.
?The McGraw-Hill Companies,Inc.,2001
6- 22
Irwin/McGraw-Hill
Investment Timing
Example
You may purchase a computer anytime within the next five years,While
the computer will save your company money,the cost of computers
continues to decline,If your cost of capital is 10% and given the data
listed below,when should you purchase the computer?
Year Cost PV Savings NPV at Purchase NPV Today
0 50 70 20 20.0
1 45 70 25 22.7
2 40 70 30 24.8
3 36 70 34 Date to purchase 25.5
4 33 70 37 25.3
5 31 70 39 24.2
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6- 23
Irwin/McGraw-Hill
Equivalent Annual Cost
Equivalent Annual Cost - The cost per period
with the same present value as the cost of
buying and operating a machine.
E q u i v a l e n t a n n u a l c o st = p re s e n t v a l u e o f c o s ts
a n n u i t y fa c t o r
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6- 24
Irwin/McGraw-Hill
Equivalent Annual Cost
Example
Given the following costs of operating two machines
and a 6% cost of capital,select the lower cost
machine using equivalent annual cost method.
Year
Mach.1 2 3 4 PV@6% Ann,Cost
D -15 -4 -4 -4 -25.69 -9.61
E -10 -6 -6 -21.00 -11.45
?The McGraw-Hill Companies,Inc.,2001
6- 25
Irwin/McGraw-Hill
Equivalent Annual Cost
Example (with a twist)
Select one of the two following projects,based on
highest,equivalent annual annuity” (r=9%),
Proj 0 1 2 3 4 NPV Eq,Ann
A -15 5.5 5.5 5.5 5.5 2.82,87
B -20 9 9 9 2.78 1.10
?The McGraw-Hill Companies,Inc.,2001
6- 26
Irwin/McGraw-Hill
Internal Rate of Return
Example
You have two proposals to choice between,The initial proposal (H)
has a cash flow that is different than the revised proposal (I),Using
IRR,which do you prefer?
P r o j e c t C 0 C 1 C 2 C 3 I R R N P V @ 7 %
H - 3 5 0 400 1 4, 2 9 % 2 4,0 0 0$
I - 3 5 0 16 16 466 1 2, 9 6 % 5 9,0 0 0$
?The McGraw-Hill Companies,Inc.,2001
6- 27
Irwin/McGraw-Hill
Internal Rate of Return
Example
You have two proposals to choice between,The initial proposal (H)
has a cash flow that is different than the revised proposal (I),Using
IRR,which do you prefer?
%29.14
0
)1(
400
350
1
?
?
?
???
I R R
N P V
%96.12
0
)1(
466
)1(
16
)1(
16
350 321
?
?
?
?
?
?
?
???
I R RI R RI R R
N P V
?The McGraw-Hill Companies,Inc.,2001
6- 28
Irwin/McGraw-Hill
Internal Rate of Return
50
40
30
20
10
0
-10
-20
NPV
$,
1,
00
0s
Discount rate,%
8 10 12 14 16
Revised proposal
Initial proposal
?The McGraw-Hill Companies,Inc.,2001
6- 29
Irwin/McGraw-Hill
Internal Rate of Return
Pitfall 1 - Mutually Exclusive Projects
? IRR sometimes ignores the magnitude of the project.
? The following two projects illustrate that problem.
Pitfall 2 - Lending or Borrowing?
? With some cash flows (as noted below) the NPV of the project
increases s the discount rate increases,
? This is contrary to the normal relationship between NPV and
discount rates.
Pitfall 3 - Multiple Rates of Return
? Certain cash flows can generate NPV=0 at two different discount
rates.
? The following cash flow generates NPV=0 at both (-50%) and
15.2%.
?The McGraw-Hill Companies,Inc.,2001
6- 30
Irwin/McGraw-Hill
內部報酬率法
?內部報酬率 (Internal Rate of Return Md.;簡稱
IRR)法
?方法,
內部報酬率,使淨現值 (NPV)為 0之折現率
NPV= 或
?CFt,t 期淨現金流量 (即各期稅後現金入 )
?IRR,內部報酬率 (即投資人之報酬率 )
n
nI R RCFI R RCFI R RCFC )1(.,,,,,)1()1(
2
2
1
1 ???????? 0)1(
0
????
?
N P VRCFn
t t
t
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Irwin/McGraw-Hill
內部報酬率法 (續 )
?決策準則,
? 單一計劃, IRR> R; 互斥計劃, Max(IRR1,IRR2,…)> R
?優劣,
? 缺, (1)複雜 (2)某些狀況未符合價值最大化原則
(3)可能無解或 (4)有多重解 (5)再投資報酬率問題
? 優點, (1)考慮風險因素 （ 2）考慮整時間價值因素
(3）考慮投資人之機會成本
（ 4）考慮整個投資期間之現金流量
(5)考慮整個投資期末處分資產之現金流量
?The McGraw-Hill Companies,Inc.,2001
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Irwin/McGraw-Hill
修正內部報酬率法
?修正內部報酬率 (Modified Internal Rate of Return
Md.;簡稱 MIRR)法
?方法,
修正 內部報酬率,使各期淨現金流出現值之
和等於未來各期現金流入現值之和之折現率
PV cost = PV (terminal value)
n
n
t
tn
tn
t
t
t
M I R R
RCI F
R
CO F
)1(
)1(
)1(
0
0 ?
?
?
?
?
? ?
?
?
?The McGraw-Hill Companies,Inc.,2001
6- 33
Irwin/McGraw-Hill
修正內部報酬率法 (續 )
?決策準則,
? 單一計劃, MIRR> R; 互斥計劃, Max(MIRR1,MIRR2,…)>
R
?優劣,
? 缺, (1)複雜 (2)某些狀況未符合價值最大化原則
? 優點, (1)考慮風險因素 （ 2）考慮整時間價值因
素
(3）考慮投資人之機會成本
（ 4）考慮整個投資期間之現金流量
(5)考慮整個投資期末處分資產之現金流量
?The McGraw-Hill Companies,Inc.,2001
6- 34
Irwin/McGraw-Hill
Capital Rationing
Capital Rationing - Limit set on the amount of
funds available for investment.
Soft Rationing - Limits on available funds
imposed by management.
Hard Rationing - Limits on available funds
imposed by the unavailability of funds in
the capital market.
?The McGraw-Hill Companies,Inc.,2001
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Irwin/McGraw-Hill
Profitability Index
P r o f i t a b i l i t y
P r o j e c t PV I n v e s t m e n t N P V I n d e x
L 4 3 1 1 / 3 =, 3 3
M 6 5 1 1 / 5 =, 2 0
N 10 7 3 3 / 7 =, 4 3
O 8 6 2 2 / 6 =, 3 3
P 5 4 1 1 / 4 =, 2 5
6- 1
Irwin/McGraw-Hill
Chapter 6Fundamentals of Corporate FinanceThird Edition
Net Present
Value and
Other
Investment
Criteria
Brealey Myers Marcus
slides by Matthew Will
?The McGraw-Hill Companies,Inc.,2001
6- 2
Irwin/McGraw-Hill
Topics Covered
?Net Present Value
?Other Investment Criteria
?Project Interactions
?Capital Rationing
?The McGraw-Hill Companies,Inc.,2001
6- 3
Irwin/McGraw-Hill
Net Present Value
Opportunity Cost of Capital - Expected rate
of return given up by investing in a project,
Net Present Value - Present value of cash
flows minus initial investments.
?The McGraw-Hill Companies,Inc.,2001
6- 4
Irwin/McGraw-Hill
Net Present Value
Example
Suppose we can invest $50 today and receive $60
in one year,What is our increase in value given a
10% expected return?
This is the definition of NPV
P r o f i t = - 5 0 + 60
1, 1 0
? $4, 55
Initial Investment
Added Value
$50
$4.55
?The McGraw-Hill Companies,Inc.,2001
6- 5
Irwin/McGraw-Hill
Net Present Value
NPV = PV - required investment
N P V C C
r
t
t? ? ?0 1( )
N P V C C
r
C
r
C
r
t
t? ? ? ? ? ? ? ?0
1
1
2
21 1 1( ) ( ),,, ( )
?The McGraw-Hill Companies,Inc.,2001
6- 6
Irwin/McGraw-Hill
Net Present Value
Terminology
C = Cash Flow
t = time period of the investment
r =,opportunity cost of capital”
?The Cash Flow could be positive or negative at
any time period.
?The McGraw-Hill Companies,Inc.,2001
6- 7
Irwin/McGraw-Hill
Net Present Value
Net Present Value Rule
Managers increase shareholders’ wealth by
accepting all projects that are worth more
than they cost,
Therefore,they should accept all projects
with a positive net present value.
?The McGraw-Hill Companies,Inc.,2001
6- 8
Irwin/McGraw-Hill
Net Present Value
Example
You have the opportunity to
purchase an office building,You
have a tenant lined up that will
generate $16,000 per year in cash
flows for three years,At the end
of three years you anticipate
selling the building for $450,000,
How much would you be willing
to pay for the building?
?The McGraw-Hill Companies,Inc.,2001
6- 9
Irwin/McGraw-Hill
Net Present Value
0 1 2 3
$16,000$16,000$16,000
$450,000
$466,000
Present Value
14,953
14,953
380,395
$409,323
Example - continued
?The McGraw-Hill Companies,Inc.,2001
6- 10
Irwin/McGraw-Hill
Net Present Value
Example - continued
If the building is being
offered for sale at a price
of $350,000,would you
buy the building and what
is the added value
generated by your
purchase and management
of the building?
?The McGraw-Hill Companies,Inc.,2001
6- 11
Irwin/McGraw-Hill
Net Present Value
Example - continued
If the building is being offered for sale at a price of
$350,000,would you buy the building and what is the
added value generated by your purchase and management
of the building?N P V
N P V
? ? ? ? ?
?
350 000
16 000
1 07
16 000
1 07
466 000
1 07
323
1 2 3
,
,
(, )
,
(, )
,
(, )
$59,
?The McGraw-Hill Companies,Inc.,2001
6- 12
Irwin/McGraw-Hill
Other Investment Criteria
Internal Rate of Return (IRR) - Discount rate at
which NPV = 0.
Rate of Return Rule - Invest in any project offering
a rate of return that is higher than the opportunity
cost of capital.
R at e o f R e t u rn = C - i n v es t m en t
i n v es t m en t
1
?The McGraw-Hill Companies,Inc.,2001
6- 13
Irwin/McGraw-Hill
Internal Rate of Return
Example
You can purchase a building for $350,000,The investment will
generate $16,000 in cash flows (i.e,rent) during the first three years,
At the end of three years you will sell the building for $450,000,What
is the IRR on this investment?
0 350 000 16 0001 16 0001 466 00011 2 3? ? ? ? ? ? ? ?,,( ),( ),( )I R R I R R I R R
IRR = 12.96%
?The McGraw-Hill Companies,Inc.,2001
6- 14
Irwin/McGraw-Hill
Internal Rate of Return
-200
-150
-100
-50
0
50
100
150
200
0 5 10 15 20 25 30 35
D i s c o u n t r a te (% )
N
PV
(,
0
0
0
s
)
IRR=12.96%
?The McGraw-Hill Companies,Inc.,2001
6- 15
Irwin/McGraw-Hill
Payback Method
Payback Period - Time until cash flows recover the
initial investment of the project.
?The payback rule specifies that a project be
accepted if its payback period is less than the
specified cutoff period,The following example
will demonstrate the absurdity of this statement.
?The McGraw-Hill Companies,Inc.,2001
6- 16
Irwin/McGraw-Hill
Payback Method
Example
The three project below are available,The company accepts
all projects with a 2 year or less payback period,Show how
this decision will impact our decision.
Cash Flows
Prj,C0 C1 C2 C3 Payback NPV@10%
A -2000 +1000 +1000 +10000 2 +7,249
B -2000 +1000 +1000 0 2 - 264
C -2000 0 +2000 0 2 - 347
?The McGraw-Hill Companies,Inc.,2001
6- 17
Irwin/McGraw-Hill
Book Rate of Return
Book Rate of Return - Average income divided by
average book value over project life,Also called
accounting rate of return.
Managers rarely use this measurement to make
decisions,The components reflect tax and
accounting figures,not market values or cash
flows,
B o o k r a t e o f r e t u r n = b o o k i n c o m e
b o o k a s s e t s
?The McGraw-Hill Companies,Inc.,2001
6- 18
Irwin/McGraw-Hill
Project Interactions
When you need to choose between mutually
exclusive projects,the decision rule is
simple,Calculate the NPV of each project,
and,from those options that have a positive
NPV,choose the one whose NPV is highest.
?The McGraw-Hill Companies,Inc.,2001
6- 19
Irwin/McGraw-Hill
Mutually Exclusive Projects
Example
Select one of the two following projects,based on
highest NPV,
Proj 0 1 2 3 4 NPV
A -15 5.5 5.5 5.5 5.5
B -20 9 9 9
assume 9% discount rate
?The McGraw-Hill Companies,Inc.,2001
6- 20
Irwin/McGraw-Hill
Mutually Exclusive Projects
Example
Select one of the two following projects,based on
highest NPV,
Proj 0 1 2 3 4 NPV
A -15 5.5 5.5 5.5 5.5 2.82
B -20 9 9 9 2.78
assume 9% discount rate
?The McGraw-Hill Companies,Inc.,2001
6- 21
Irwin/McGraw-Hill
Investment Timing
Sometimes you have the ability to defer an
investment and select a time that is more
ideal at which to make the investment
decision,A common example involves a
tree farm,You may defer the harvesting of
trees,By doing so,you defer the receipt of
the cash flow,yet increase the cash flow.
?The McGraw-Hill Companies,Inc.,2001
6- 22
Irwin/McGraw-Hill
Investment Timing
Example
You may purchase a computer anytime within the next five years,While
the computer will save your company money,the cost of computers
continues to decline,If your cost of capital is 10% and given the data
listed below,when should you purchase the computer?
Year Cost PV Savings NPV at Purchase NPV Today
0 50 70 20 20.0
1 45 70 25 22.7
2 40 70 30 24.8
3 36 70 34 Date to purchase 25.5
4 33 70 37 25.3
5 31 70 39 24.2
?The McGraw-Hill Companies,Inc.,2001
6- 23
Irwin/McGraw-Hill
Equivalent Annual Cost
Equivalent Annual Cost - The cost per period
with the same present value as the cost of
buying and operating a machine.
E q u i v a l e n t a n n u a l c o st = p re s e n t v a l u e o f c o s ts
a n n u i t y fa c t o r
?The McGraw-Hill Companies,Inc.,2001
6- 24
Irwin/McGraw-Hill
Equivalent Annual Cost
Example
Given the following costs of operating two machines
and a 6% cost of capital,select the lower cost
machine using equivalent annual cost method.
Year
Mach.1 2 3 4 PV@6% Ann,Cost
D -15 -4 -4 -4 -25.69 -9.61
E -10 -6 -6 -21.00 -11.45
?The McGraw-Hill Companies,Inc.,2001
6- 25
Irwin/McGraw-Hill
Equivalent Annual Cost
Example (with a twist)
Select one of the two following projects,based on
highest,equivalent annual annuity” (r=9%),
Proj 0 1 2 3 4 NPV Eq,Ann
A -15 5.5 5.5 5.5 5.5 2.82,87
B -20 9 9 9 2.78 1.10
?The McGraw-Hill Companies,Inc.,2001
6- 26
Irwin/McGraw-Hill
Internal Rate of Return
Example
You have two proposals to choice between,The initial proposal (H)
has a cash flow that is different than the revised proposal (I),Using
IRR,which do you prefer?
P r o j e c t C 0 C 1 C 2 C 3 I R R N P V @ 7 %
H - 3 5 0 400 1 4, 2 9 % 2 4,0 0 0$
I - 3 5 0 16 16 466 1 2, 9 6 % 5 9,0 0 0$
?The McGraw-Hill Companies,Inc.,2001
6- 27
Irwin/McGraw-Hill
Internal Rate of Return
Example
You have two proposals to choice between,The initial proposal (H)
has a cash flow that is different than the revised proposal (I),Using
IRR,which do you prefer?
%29.14
0
)1(
400
350
1
?
?
?
???
I R R
N P V
%96.12
0
)1(
466
)1(
16
)1(
16
350 321
?
?
?
?
?
?
?
???
I R RI R RI R R
N P V
?The McGraw-Hill Companies,Inc.,2001
6- 28
Irwin/McGraw-Hill
Internal Rate of Return
50
40
30
20
10
0
-10
-20
NPV
$,
1,
00
0s
Discount rate,%
8 10 12 14 16
Revised proposal
Initial proposal
?The McGraw-Hill Companies,Inc.,2001
6- 29
Irwin/McGraw-Hill
Internal Rate of Return
Pitfall 1 - Mutually Exclusive Projects
? IRR sometimes ignores the magnitude of the project.
? The following two projects illustrate that problem.
Pitfall 2 - Lending or Borrowing?
? With some cash flows (as noted below) the NPV of the project
increases s the discount rate increases,
? This is contrary to the normal relationship between NPV and
discount rates.
Pitfall 3 - Multiple Rates of Return
? Certain cash flows can generate NPV=0 at two different discount
rates.
? The following cash flow generates NPV=0 at both (-50%) and
15.2%.
?The McGraw-Hill Companies,Inc.,2001
6- 30
Irwin/McGraw-Hill
內部報酬率法
?內部報酬率 (Internal Rate of Return Md.;簡稱
IRR)法
?方法,
內部報酬率,使淨現值 (NPV)為 0之折現率
NPV= 或
?CFt,t 期淨現金流量 (即各期稅後現金入 )
?IRR,內部報酬率 (即投資人之報酬率 )
n
nI R RCFI R RCFI R RCFC )1(.,,,,,)1()1(
2
2
1
1 ???????? 0)1(
0
????
?
N P VRCFn
t t
t
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內部報酬率法 (續 )
?決策準則,
? 單一計劃, IRR> R; 互斥計劃, Max(IRR1,IRR2,…)> R
?優劣,
? 缺, (1)複雜 (2)某些狀況未符合價值最大化原則
(3)可能無解或 (4)有多重解 (5)再投資報酬率問題
? 優點, (1)考慮風險因素 （ 2）考慮整時間價值因素
(3）考慮投資人之機會成本
（ 4）考慮整個投資期間之現金流量
(5)考慮整個投資期末處分資產之現金流量
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修正內部報酬率法
?修正內部報酬率 (Modified Internal Rate of Return
Md.;簡稱 MIRR)法
?方法,
修正 內部報酬率,使各期淨現金流出現值之
和等於未來各期現金流入現值之和之折現率
PV cost = PV (terminal value)
n
n
t
tn
tn
t
t
t
M I R R
RCI F
R
CO F
)1(
)1(
)1(
0
0 ?
?
?
?
?
? ?
?
?
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Irwin/McGraw-Hill
修正內部報酬率法 (續 )
?決策準則,
? 單一計劃, MIRR> R; 互斥計劃, Max(MIRR1,MIRR2,…)>
R
?優劣,
? 缺, (1)複雜 (2)某些狀況未符合價值最大化原則
? 優點, (1)考慮風險因素 （ 2）考慮整時間價值因
素
(3）考慮投資人之機會成本
（ 4）考慮整個投資期間之現金流量
(5)考慮整個投資期末處分資產之現金流量
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Capital Rationing
Capital Rationing - Limit set on the amount of
funds available for investment.
Soft Rationing - Limits on available funds
imposed by management.
Hard Rationing - Limits on available funds
imposed by the unavailability of funds in
the capital market.
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Profitability Index
P r o f i t a b i l i t y
P r o j e c t PV I n v e s t m e n t N P V I n d e x
L 4 3 1 1 / 3 =, 3 3
M 6 5 1 1 / 5 =, 2 0
N 10 7 3 3 / 7 =, 4 3
O 8 6 2 2 / 6 =, 3 3
P 5 4 1 1 / 4 =, 2 5
