? 2002,Prentice Hall,Inc,
Ch,9,Capital
Budgeting
Decision
Criteria
Capital Budgeting,the process of
planning for purchases of long-
term assets,
? example,
Suppose our firm must decide whether to
purchase a new plastic molding machine
for $125,000,How do we decide?
? Will the machine be profitable?
? Will our firm earn a high rate of return
on the investment?
Decision-making Criteria in
Capital Budgeting
How do we decide
if a capital
investment
project should
be accepted or
rejected?
? The Ideal Evaluation Method
should,
a) include all cash flows that occur
during the life of the project,
b) consider the time value of money,
c) incorporate the required rate of
return on the project,
Decision-making Criteria in
Capital Budgeting
Payback Period
? How long will it take for the project
to generate enough cash to pay for
itself?
Payback Period
? How long will it take for the project
to generate enough cash to pay for
itself?
0 1 2 3 4 5 8 6 7
(500) 150 150 150 150 150 150 150 150
Payback Period
? How long will it take for the project
to generate enough cash to pay for
itself?
0 1 2 3 4 5 8 6 7
(500) 150 150 150 150 150 150 150 150
Payback period = 3.33 years,
? Is a 3.33 year payback period good?
? Is it acceptable?
? Firms that use this method will compare
the payback calculation to some
standard set by the firm,
? If our senior management had set a cut-
off of 5 years for projects like ours,what
would be our decision?
? Accept the project,
Payback Period
Drawbacks of Payback Period
? Firm cutoffs are subjective,
? Does not consider time value of
money,
? Does not consider any required
rate of return,
? Does not consider all of the
project’s cash flows,
Drawbacks of Payback Period
? Does not consider all of the
project’s cash flows,
? Consider this cash flow stream!
0 1 2 3 4 5 8 6 7
(500) 150 150 150 150 150 (300) 0 0
Drawbacks of Payback Period
? Does not consider all of the
project’s cash flows,
? This project is clearly unprofitable,
but we would accept it based on a 4-
year payback criterion!
0 1 2 3 4 5 8 6 7
(500) 150 150 150 150 150 (300) 0 0
Discounted Payback
? Discounts the cash flows at the firm’s
required rate of return,
? Payback period is calculated using
these discounted net cash flows,
Problems,
? Cutoffs are still subjective,
? Still does not examine all cash flows,
Discounted Payback
0 1 2 3 4 5
(500) 250 250 250 250 250
Discounted
Year Cash Flow CF (14%)
0 -500 -500.00
1 250 219.30
Discounted Payback
0 1 2 3 4 5
(500) 250 250 250 250 250
Discounted
Year Cash Flow CF (14%)
0 -500 -500.00
1 250 219.30 1 year
280.70
Discounted Payback
0 1 2 3 4 5
(500) 250 250 250 250 250
Discounted
Year Cash Flow CF (14%)
0 -500 -500.00
1 250 219.30 1 year
280.70
2 250 192.37
Discounted Payback
0 1 2 3 4 5
(500) 250 250 250 250 250
Discounted
Year Cash Flow CF (14%)
0 -500 -500.00
1 250 219.30 1 year
280.70
2 250 192.37 2 years
88.33
Discounted Payback
0 1 2 3 4 5
(500) 250 250 250 250 250
Discounted
Year Cash Flow CF (14%)
0 -500 -500.00
1 250 219.30 1 year
280.70
2 250 192.37 2 years
88.33
3 250 168.74
Discounted Payback
0 1 2 3 4 5
(500) 250 250 250 250 250
Discounted
Year Cash Flow CF (14%)
0 -500 -500.00
1 250 219.30 1 year
280.70
2 250 192.37 2 years
88.33
3 250 168.74,52 years
Discounted Payback
0 1 2 3 4 5
(500) 250 250 250 250 250
Discounted
Year Cash Flow CF (14%)
0 -500 -500.00
1 250 219.30 1 year
280.70
2 250 192.37 2 years
88.33
3 250 168.74,52 years
The Discounted
Payback
is 2.52 years
Other Methods
1) Net Present Value (NPV)
2) Profitability Index (PI)
3) Internal Rate of Return (IRR)
Each of these decision-making criteria,
? Examines all net cash flows,
? Considers the time value of money,and
? Considers the required rate of return,
Net Present Value
? NPV = the total PV of the annual net
cash flows - the initial outlay,
NPV = - IO FCFt (1 + k) t
n
t=1
S
Net Present Value
?Decision Rule,
?If NPV is positive,accept,
?If NPV is negative,reject,
NPV Example
? Suppose we are considering a capital
investment that costs $250,000 and
provides annual net cash flows of
$100,000 for five years,The firm’s
required rate of return is 15%,
NPV Example
0 1 2 3 4 5
(250,000) 100,000 100,000 100,000 100,000 100,000
? Suppose we are considering a capital
investment that costs $250,000 and
provides annual net cash flows of
$100,000 for five years,The firm’s
required rate of return is 15%,
Net Present Value (NPV)
NPV is just the PV of the annual cash
flows minus the initial outflow,
Using TVM,
P/Y = 1 N = 5 I = 15
PMT = 100,000
PV of cash flows = $335,216
- Initial outflow,($250,000)
= Net PV $85,216
NPV with the HP10B,
? -250,000 CFj
? 100,000 CFj
? 5 shift Nj
? 15 I/YR
? shift NPV
? You should get NPV = 85,215.51,
NPV with the HP17BII,
? Select CFLO mode,
? FLOW(0)=? -250,000 INPUT
? FLOW(1)=? 100,000 INPUT
? #TIMES(1)=1 5 INPUT
EXIT
? CALC 15 I% NPV
? You should get NPV = 85,215.51
NPV with the TI BAII Plus,
? Select CF mode,
NPV with the TI BAII Plus,
? Select CF mode,
? CFo=? -250,000 ENTER
NPV with the TI BAII Plus,
? Select CF mode,
? CFo=? -250,000 ENTER
? C01=? 100,000 ENTER
NPV with the TI BAII Plus,
? Select CF mode,
? CFo=? -250,000 ENTER
? C01=? 100,000 ENTER
? F01= 1 5 ENTER
NPV with the TI BAII Plus,
? Select CF mode,
? CFo=? -250,000 ENTER
? C01=? 100,000 ENTER
? F01= 1 5 ENTER
? NPV I= 15 ENTER
NPV with the TI BAII Plus,
? Select CF mode,
? CFo=? -250,000 ENTER
? C01=? 100,000 ENTER
? F01= 1 5 ENTER
? NPV I= 15 ENTER
CPT
NPV with the TI BAII Plus,
? Select CF mode,
? CFo=? -250,000 ENTER
? C01=? 100,000 ENTER
? F01= 1 5 ENTER
? NPV I= 15 ENTER
CPT
? You should get NPV = 85,215.51
Profitability Index
Profitability Index
NPV = - IO FCFt (1 + k) t
n
t=1
S
Profitability Index
PI = IO FCFt (1 + k)
n
t=1
S t
NPV = - IO FCFt (1 + k) t
n
t=1
S
?Decision Rule,
?If PI is greater than or equal
to 1,accept,
?If PI is less than 1,reject,
Profitability Index
PI with the HP10B,
? -250,000 CFj
? 100,000 CFj
? 5 shift Nj
? 15 I/YR
? shift NPV
? Add back IO,+ 250,000
? Divide by IO,/ 250,000 =
? You should get PI = 1.34
Internal Rate of Return (IRR)
? IRR,the return on the firm’s
invested capital,IRR is simply the
rate of return that the firm earns on
its capital budgeting projects,
Internal Rate of Return (IRR)
Internal Rate of Return (IRR)
NPV = - IO FCFt (1 + k) t
n
t=1
S
Internal Rate of Return (IRR)
NPV = - IO FCFt (1 + k) t
n
t=1
S
n
t=1
S IRR,= IO FCFt (1 + IRR) t
Internal Rate of Return (IRR)
? IRR is the rate of return that makes the PV
of the cash flows equal to the initial outlay,
? This looks very similar to our Yield to
Maturity formula for bonds,In fact,YTM
is the IRR of a bond,
n
t=1
S IRR,= IO FCFt (1 + IRR) t
Calculating IRR
? Looking again at our problem,
? The IRR is the discount rate that
makes the PV of the projected cash
flows equal to the initial outlay,
0 1 2 3 4 5
(250,000) 100,000 100,000 100,000 100,000 100,000
IRR with your Calculator
? IRR is easy to find with your
financial calculator,
? Just enter the cash flows as you did
with the NPV problem and solve for
IRR,
? You should get IRR = 28.65%!
IRR
? Decision Rule,
? If IRR is greater than or equal to
the required rate of return,
accept,
? If IRR is less than the required
rate of return,reject,
? IRR is a good decision-making tool as
long as cash flows are conventional,
(- + + + + +)
? Problem,If there are multiple sign
changes in the cash flow stream,we
could get multiple IRRs,(- + + - + +)
? IRR is a good decision-making tool as
long as cash flows are conventional,
(- + + + + +)
? Problem,If there are multiple sign
changes in the cash flow stream,we
could get multiple IRRs,(- + + - + +)
0 1 2 3 4 5
(500) 200 100 (200) 400 300
? IRR is a good decision-making tool as
long as cash flows are conventional,
(- + + + + +)
? Problem,If there are multiple sign
changes in the cash flow stream,we
could get multiple IRRs,(- + + - + +)
0 1 2 3 4 5
(500) 200 100 (200) 400 300
1
? IRR is a good decision-making tool as
long as cash flows are conventional,
(- + + + + +)
? Problem,If there are multiple sign
changes in the cash flow stream,we
could get multiple IRRs,(- + + - + +)
0 1 2 3 4 5
(500) 200 100 (200) 400 300
1 2
? IRR is a good decision-making tool as
long as cash flows are conventional,
(- + + + + +)
? Problem,If there are multiple sign
changes in the cash flow stream,we
could get multiple IRRs,(- + + - + +)
0 1 2 3 4 5
(500) 200 100 (200) 400 300
1 2 3
Summary Problem
? Enter the cash flows only once,
? Find the IRR,
? Using a discount rate of 15%,find NPV,
? Add back IO and divide by IO to get PI,
0 1 2 3 4 5
(900) 300 400 400 500 600
Summary Problem
? IRR = 34.37%,
? Using a discount rate of 15%,
NPV = $510.52,
? PI = 1.57,
0 1 2 3 4 5
(900) 300 400 400 500 600
Modified Internal Rate of Return
(MIRR)
? IRR assumes that all cash flows are
reinvested at the IRR,
? MIRR provides a rate of return
measure that assumes cash flows are
reinvested at the required rate of return,
MIRR Steps,
? Calculate the PV of the cash outflows,
– Using the required rate of return,
? Calculate the FV of the cash inflows at
the last year of the project’s time line,
This is called the terminal value (TV),
– Using the required rate of return,
? MIRR,the discount rate that equates
the PV of the cash outflows with the PV
of the terminal value,ie,that makes,
? PVoutflows = PVinflows
MIRR
? Using our time line and a 15% rate,
? PV outflows = (900)
? FV inflows (at the end of year 5) = 2,837,
? MIRR,FV = 2837,PV = (900),N = 5
? solve,I = 25.81%,
0 1 2 3 4 5
(900) 300 400 400 500 600
MIRR
? Using our time line and a 15% rate,
? PV outflows = (900)
? FV inflows (at the end of year 5) = 2,837,
? MIRR,FV = 2837,PV = (900),N = 5
? solve,I = 25.81%,
? Conclusion,The project’s IRR of
34.37%,assumes that cash flows are
reinvested at 34.37%,
MIRR
? Using our time line and a 15% rate,
? PV outflows = (900)
? FV inflows (at the end of year 5) = 2,837,
? MIRR,FV = 2837,PV = (900),N = 5
? solve,I = 25.81%,
? Conclusion,The project’s IRR of
34.37%,assumes that cash flows are
reinvested at 34.37%,
? Assuming a reinvestment rate of 15%,
the project’s MIRR is 25.81%,
Ch,9,Capital
Budgeting
Decision
Criteria
Capital Budgeting,the process of
planning for purchases of long-
term assets,
? example,
Suppose our firm must decide whether to
purchase a new plastic molding machine
for $125,000,How do we decide?
? Will the machine be profitable?
? Will our firm earn a high rate of return
on the investment?
Decision-making Criteria in
Capital Budgeting
How do we decide
if a capital
investment
project should
be accepted or
rejected?
? The Ideal Evaluation Method
should,
a) include all cash flows that occur
during the life of the project,
b) consider the time value of money,
c) incorporate the required rate of
return on the project,
Decision-making Criteria in
Capital Budgeting
Payback Period
? How long will it take for the project
to generate enough cash to pay for
itself?
Payback Period
? How long will it take for the project
to generate enough cash to pay for
itself?
0 1 2 3 4 5 8 6 7
(500) 150 150 150 150 150 150 150 150
Payback Period
? How long will it take for the project
to generate enough cash to pay for
itself?
0 1 2 3 4 5 8 6 7
(500) 150 150 150 150 150 150 150 150
Payback period = 3.33 years,
? Is a 3.33 year payback period good?
? Is it acceptable?
? Firms that use this method will compare
the payback calculation to some
standard set by the firm,
? If our senior management had set a cut-
off of 5 years for projects like ours,what
would be our decision?
? Accept the project,
Payback Period
Drawbacks of Payback Period
? Firm cutoffs are subjective,
? Does not consider time value of
money,
? Does not consider any required
rate of return,
? Does not consider all of the
project’s cash flows,
Drawbacks of Payback Period
? Does not consider all of the
project’s cash flows,
? Consider this cash flow stream!
0 1 2 3 4 5 8 6 7
(500) 150 150 150 150 150 (300) 0 0
Drawbacks of Payback Period
? Does not consider all of the
project’s cash flows,
? This project is clearly unprofitable,
but we would accept it based on a 4-
year payback criterion!
0 1 2 3 4 5 8 6 7
(500) 150 150 150 150 150 (300) 0 0
Discounted Payback
? Discounts the cash flows at the firm’s
required rate of return,
? Payback period is calculated using
these discounted net cash flows,
Problems,
? Cutoffs are still subjective,
? Still does not examine all cash flows,
Discounted Payback
0 1 2 3 4 5
(500) 250 250 250 250 250
Discounted
Year Cash Flow CF (14%)
0 -500 -500.00
1 250 219.30
Discounted Payback
0 1 2 3 4 5
(500) 250 250 250 250 250
Discounted
Year Cash Flow CF (14%)
0 -500 -500.00
1 250 219.30 1 year
280.70
Discounted Payback
0 1 2 3 4 5
(500) 250 250 250 250 250
Discounted
Year Cash Flow CF (14%)
0 -500 -500.00
1 250 219.30 1 year
280.70
2 250 192.37
Discounted Payback
0 1 2 3 4 5
(500) 250 250 250 250 250
Discounted
Year Cash Flow CF (14%)
0 -500 -500.00
1 250 219.30 1 year
280.70
2 250 192.37 2 years
88.33
Discounted Payback
0 1 2 3 4 5
(500) 250 250 250 250 250
Discounted
Year Cash Flow CF (14%)
0 -500 -500.00
1 250 219.30 1 year
280.70
2 250 192.37 2 years
88.33
3 250 168.74
Discounted Payback
0 1 2 3 4 5
(500) 250 250 250 250 250
Discounted
Year Cash Flow CF (14%)
0 -500 -500.00
1 250 219.30 1 year
280.70
2 250 192.37 2 years
88.33
3 250 168.74,52 years
Discounted Payback
0 1 2 3 4 5
(500) 250 250 250 250 250
Discounted
Year Cash Flow CF (14%)
0 -500 -500.00
1 250 219.30 1 year
280.70
2 250 192.37 2 years
88.33
3 250 168.74,52 years
The Discounted
Payback
is 2.52 years
Other Methods
1) Net Present Value (NPV)
2) Profitability Index (PI)
3) Internal Rate of Return (IRR)
Each of these decision-making criteria,
? Examines all net cash flows,
? Considers the time value of money,and
? Considers the required rate of return,
Net Present Value
? NPV = the total PV of the annual net
cash flows - the initial outlay,
NPV = - IO FCFt (1 + k) t
n
t=1
S
Net Present Value
?Decision Rule,
?If NPV is positive,accept,
?If NPV is negative,reject,
NPV Example
? Suppose we are considering a capital
investment that costs $250,000 and
provides annual net cash flows of
$100,000 for five years,The firm’s
required rate of return is 15%,
NPV Example
0 1 2 3 4 5
(250,000) 100,000 100,000 100,000 100,000 100,000
? Suppose we are considering a capital
investment that costs $250,000 and
provides annual net cash flows of
$100,000 for five years,The firm’s
required rate of return is 15%,
Net Present Value (NPV)
NPV is just the PV of the annual cash
flows minus the initial outflow,
Using TVM,
P/Y = 1 N = 5 I = 15
PMT = 100,000
PV of cash flows = $335,216
- Initial outflow,($250,000)
= Net PV $85,216
NPV with the HP10B,
? -250,000 CFj
? 100,000 CFj
? 5 shift Nj
? 15 I/YR
? shift NPV
? You should get NPV = 85,215.51,
NPV with the HP17BII,
? Select CFLO mode,
? FLOW(0)=? -250,000 INPUT
? FLOW(1)=? 100,000 INPUT
? #TIMES(1)=1 5 INPUT
EXIT
? CALC 15 I% NPV
? You should get NPV = 85,215.51
NPV with the TI BAII Plus,
? Select CF mode,
NPV with the TI BAII Plus,
? Select CF mode,
? CFo=? -250,000 ENTER
NPV with the TI BAII Plus,
? Select CF mode,
? CFo=? -250,000 ENTER
? C01=? 100,000 ENTER
NPV with the TI BAII Plus,
? Select CF mode,
? CFo=? -250,000 ENTER
? C01=? 100,000 ENTER
? F01= 1 5 ENTER
NPV with the TI BAII Plus,
? Select CF mode,
? CFo=? -250,000 ENTER
? C01=? 100,000 ENTER
? F01= 1 5 ENTER
? NPV I= 15 ENTER
NPV with the TI BAII Plus,
? Select CF mode,
? CFo=? -250,000 ENTER
? C01=? 100,000 ENTER
? F01= 1 5 ENTER
? NPV I= 15 ENTER
CPT
NPV with the TI BAII Plus,
? Select CF mode,
? CFo=? -250,000 ENTER
? C01=? 100,000 ENTER
? F01= 1 5 ENTER
? NPV I= 15 ENTER
CPT
? You should get NPV = 85,215.51
Profitability Index
Profitability Index
NPV = - IO FCFt (1 + k) t
n
t=1
S
Profitability Index
PI = IO FCFt (1 + k)
n
t=1
S t
NPV = - IO FCFt (1 + k) t
n
t=1
S
?Decision Rule,
?If PI is greater than or equal
to 1,accept,
?If PI is less than 1,reject,
Profitability Index
PI with the HP10B,
? -250,000 CFj
? 100,000 CFj
? 5 shift Nj
? 15 I/YR
? shift NPV
? Add back IO,+ 250,000
? Divide by IO,/ 250,000 =
? You should get PI = 1.34
Internal Rate of Return (IRR)
? IRR,the return on the firm’s
invested capital,IRR is simply the
rate of return that the firm earns on
its capital budgeting projects,
Internal Rate of Return (IRR)
Internal Rate of Return (IRR)
NPV = - IO FCFt (1 + k) t
n
t=1
S
Internal Rate of Return (IRR)
NPV = - IO FCFt (1 + k) t
n
t=1
S
n
t=1
S IRR,= IO FCFt (1 + IRR) t
Internal Rate of Return (IRR)
? IRR is the rate of return that makes the PV
of the cash flows equal to the initial outlay,
? This looks very similar to our Yield to
Maturity formula for bonds,In fact,YTM
is the IRR of a bond,
n
t=1
S IRR,= IO FCFt (1 + IRR) t
Calculating IRR
? Looking again at our problem,
? The IRR is the discount rate that
makes the PV of the projected cash
flows equal to the initial outlay,
0 1 2 3 4 5
(250,000) 100,000 100,000 100,000 100,000 100,000
IRR with your Calculator
? IRR is easy to find with your
financial calculator,
? Just enter the cash flows as you did
with the NPV problem and solve for
IRR,
? You should get IRR = 28.65%!
IRR
? Decision Rule,
? If IRR is greater than or equal to
the required rate of return,
accept,
? If IRR is less than the required
rate of return,reject,
? IRR is a good decision-making tool as
long as cash flows are conventional,
(- + + + + +)
? Problem,If there are multiple sign
changes in the cash flow stream,we
could get multiple IRRs,(- + + - + +)
? IRR is a good decision-making tool as
long as cash flows are conventional,
(- + + + + +)
? Problem,If there are multiple sign
changes in the cash flow stream,we
could get multiple IRRs,(- + + - + +)
0 1 2 3 4 5
(500) 200 100 (200) 400 300
? IRR is a good decision-making tool as
long as cash flows are conventional,
(- + + + + +)
? Problem,If there are multiple sign
changes in the cash flow stream,we
could get multiple IRRs,(- + + - + +)
0 1 2 3 4 5
(500) 200 100 (200) 400 300
1
? IRR is a good decision-making tool as
long as cash flows are conventional,
(- + + + + +)
? Problem,If there are multiple sign
changes in the cash flow stream,we
could get multiple IRRs,(- + + - + +)
0 1 2 3 4 5
(500) 200 100 (200) 400 300
1 2
? IRR is a good decision-making tool as
long as cash flows are conventional,
(- + + + + +)
? Problem,If there are multiple sign
changes in the cash flow stream,we
could get multiple IRRs,(- + + - + +)
0 1 2 3 4 5
(500) 200 100 (200) 400 300
1 2 3
Summary Problem
? Enter the cash flows only once,
? Find the IRR,
? Using a discount rate of 15%,find NPV,
? Add back IO and divide by IO to get PI,
0 1 2 3 4 5
(900) 300 400 400 500 600
Summary Problem
? IRR = 34.37%,
? Using a discount rate of 15%,
NPV = $510.52,
? PI = 1.57,
0 1 2 3 4 5
(900) 300 400 400 500 600
Modified Internal Rate of Return
(MIRR)
? IRR assumes that all cash flows are
reinvested at the IRR,
? MIRR provides a rate of return
measure that assumes cash flows are
reinvested at the required rate of return,
MIRR Steps,
? Calculate the PV of the cash outflows,
– Using the required rate of return,
? Calculate the FV of the cash inflows at
the last year of the project’s time line,
This is called the terminal value (TV),
– Using the required rate of return,
? MIRR,the discount rate that equates
the PV of the cash outflows with the PV
of the terminal value,ie,that makes,
? PVoutflows = PVinflows
MIRR
? Using our time line and a 15% rate,
? PV outflows = (900)
? FV inflows (at the end of year 5) = 2,837,
? MIRR,FV = 2837,PV = (900),N = 5
? solve,I = 25.81%,
0 1 2 3 4 5
(900) 300 400 400 500 600
MIRR
? Using our time line and a 15% rate,
? PV outflows = (900)
? FV inflows (at the end of year 5) = 2,837,
? MIRR,FV = 2837,PV = (900),N = 5
? solve,I = 25.81%,
? Conclusion,The project’s IRR of
34.37%,assumes that cash flows are
reinvested at 34.37%,
MIRR
? Using our time line and a 15% rate,
? PV outflows = (900)
? FV inflows (at the end of year 5) = 2,837,
? MIRR,FV = 2837,PV = (900),N = 5
? solve,I = 25.81%,
? Conclusion,The project’s IRR of
34.37%,assumes that cash flows are
reinvested at 34.37%,
? Assuming a reinvestment rate of 15%,
the project’s MIRR is 25.81%,
