Capital Budgeting
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Capital Budgeting Decision Criteria
1999, Prentice Hall, Inc.
Capital Budgeting: the process of planning for purchases of longterm 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?
Decision-making Criteria in Capital Budgeting ■ 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.
Payback Period ■ The number of years needed to
recover the initial cash outlay. ■ 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? (500) 150 150 150 150 150 150 150
0
1
2
3
4
5
6
7
150
8
Payback Period ■ How long will it take for the project
to generate enough cash to pay for itself? (500) 150 150 150 150 150 150 150
0
1
2
3
4
5
6
7
Payback period = 3.33 years.
150
8
■ 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.
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. (500) 150 150 150 150 150 (300) 0
0
7
8
0
1
2
3
4
5
6
Consider this cash flow stream!
Drawbacks of Payback Period: ■ Does not consider all of the project’s
cash flows. (500) 150 150 150 150 150 (300) 0
0
7
8
0
1
2
3
4
5
6
This project is clearly unprofitable, but we would accept it based on a 4-year payback criterion!
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 (500)
250
0
1
250 250 250 250 2
3
4
Discounted
Year Cash Flow 0 1
-500 250
CF (14%) -500.00 219.30
5
Discounted Payback (500)
250
0
1
250 250 250 250 2
3
4
5
Discounted
Year Cash Flow 0 1
-500 250
CF (14%) -500.00 219.30 280.70
1 year
Discounted Payback (500)
250
0
1
250 250 250 250 2
3
4
5
Discounted
Year Cash Flow 0 1
-500 250
2
250
CF (14%) -500.00 219.30 280.70 192.38
1 year
Discounted Payback (500)
250
0
1
250 250 250 250 2
3
4
5
Discounted
Year Cash Flow 0 1
-500 250
2
250
CF (14%) -500.00 219.30 280.70 192.38 88.32
1 year 2 years
Discounted Payback (500)
250
0
1
250 250 250 250 2
3
4
5
Discounted
Year Cash Flow 0 1
-500 250
2
250
3
250
CF (14%) -500.00 219.30 280.70 192.38 88.32 168.75
1 year 2 years
Discounted Payback (500)
250
0
1
250 250 250 250 2
3
4
5
Discounted
Year Cash Flow 0 1
-500 250
2
250
3
250
CF (14%) -500.00 219.30 280.70 192.38 88.32 168.75
1 year 2 years .52 years
Discounted Payback (500)
250
0
1
250 250 250 250 2
3
4
5
Discounted
Year Cash Flow 0 1
CF (14%)
The Discounted -500 -500.00 Payback 250 219.30 is 2.52 years 280.70
2
250
3
250
280.70 192.38 88.32 168.75
1 year 2 years .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. n
NPV =
Σ t=1
ACFt (1 + k) t
- IO
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 $276,400 and provides annual net cash flows of $83,000 for four years and $116,000 at the end of the fifth year. The firm’s required rate of return is 15%.
NPV Example ■
Suppose we are considering a capital investment that costs $276,400 and provides annual net cash flows of $83,000 for four years and $116,000 at the end of the fifth year. The firm’s required rate of return is 15%.
83,000 (276,400)
0
1
83,000
2
83,000
3
83,000 116,000
4
5
NPV with the HP10B: ■ -276,400 ■ 83,000 ■4 ■ 116,000 ■ 15 ■ shift
CFj CFj shift Nj CFj I/YR
NPV ■ You should get NPV = 18,235.71.
NPV with the HP17BII: ■ Select CFLO mode. ■ FLOW(0)=?
-276,400 INPUT ■ FLOW(1)=? 83,000 INPUT ■ #TIMES(1)=1 4 INPUT ■ FLOW(2)=? 116,000 INPUT ■ #TIMES(2)=1 INPUT EXIT ■ CALC 15 I% NPV ■ You should get NPV = 18,235.71
NPV with the TI BAII Plus: ■ Select CF mode.
NPV with the TI BAII Plus: ■ Select CF mode. ■ CFo=?
-276,400
ENTER
NPV with the TI BAII Plus: ■ Select CF mode. ■ CFo=? ■ C01=?
-276,400 83,000
ENTER ENTER
NPV with the TI BAII Plus: ■ Select CF mode. ■ CFo=? ■ C01=? ■ F01=
1
-276,400 83,000 4
ENTER ENTER ENTER
NPV with the TI BAII Plus: ■ Select CF mode. ■ CFo=? ■ C01=? ■ F01=
1 ■ C02=?
-276,400 83,000 4 116,000
ENTER ENTER ENTER ENTER
NPV with the TI BAII Plus: ■ Select CF mode. ■ CFo=? ■ C01=? ■ F01=
1 ■ C02=? ■ F02= 1
-276,400 83,000 4 116,000
ENTER ENTER ENTER ENTER ENTER
NPV with the TI BAII Plus: ■ Select CF mode. ■ CFo=? ■ C01=? ■ F01=
-276,400 83,000 4 116,000
1 ■ C02=? ■ F02= 1 ■ NPV I= 15
ENTER ENTER ENTER ENTER ENTER ENTER
CPT
NPV with the TI BAII Plus: ■ Select CF mode. ■ CFo=?
-276,400 83,000 4 116,000
ENTER ■ C01=? ENTER ■ F01= 1 ENTER ■ C02=? ENTER ■ F02= 1 ENTER ■ NPV I= 15 ENTER ■ You should get NPV = 18,235.71
CPT
Profitability Index n
NPV =
Σ t=1
ACFt t (1 + k)
- IO
Profitability Index n
NPV =
Σ t=1
n
PI
=
Σ t=1
ACFt t (1 + k)
ACFt (1 + k) t
- IO
IO
Profitability Index •
Decision Rule:
If PI is greater than or equal to 1, ACCEPT. • If PI is less than 1, REJECT. •
■ -276,400 ■ 83,000 ■4 ■ 116,000 ■ 15 ■ shift
CFj CFj shift Nj CFj I/YR
PI with the HP10B:
NPV ■ You should get NPV = 18,235.71. ■ Add back IO: + 276,400 ■ Divide by IO: / 276,400 = ■ You should get PI = 1.066
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) n
NPV =
Σ t=1
ACFt (1 + k) t
- IO
Internal Rate of Return (IRR) n
NPV =
Σ t=1
n
IRR:
Σ t=1
ACFt (1 + k) t
ACFt t (1 + IRR)
- IO
= IO
Internal Rate of Return (IRR) n
IRR:
Σ
ACFt t (1 + IRR)
= IO
t=1
■ 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
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. 83,000 (276,400)
0
1
83,000
2
83,000
3
83,000 116,000
4
5
83,000 83,000 83,000 83,000 116,000 (276,400)
0 1 2 3 4 ■ This is what we are actually doing:
5
83,000 (PVIFA 4, IRR) + 116,000 (PVIF 5, IRR) = 276,400
83,000 83,000 83,000 83,000 116,000 (276,400)
0
1
2
3
4
5
■ This is what we are actually doing:
83,000 (PVIFA 4, IRR) + 116,000 (PVIF 5, IRR) = 276,400 ■ This way, we have to solve for IRR by trial
and error.
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 = 17.63%!
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. (- + + - + +) (500) 0
200
100
(200)
400
300
1
2
3
4
5
■ 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. (- + + - + +) (500) 0
200
100
(200)
400
300
1
2
3
4
5
■ Problem:
If there are multiple sign changes in the cash flow stream, we could get multiple IRRs. (- + + - + +) ■ We could find 3 different IRRs! 1 (500) 0
2
3
200
100
(200)
400
300
1
2
3
4
5
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.
(900) 0
300
400
400
500
600
1
2
3
4
5
Summary Problem: ■ IRR = 34.37%. ■ Using a discount rate of 15%,
NPV = $510.52. ■ PI = 1.57. (900) 0
300
400
400
500
600
1
2
3
4
5
1999, Prentice Hall, Inc.
Capital Budgeting: the process of planning for purchases of longterm 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?
Decision-making Criteria in Capital Budgeting ■ 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.
Payback Period ■ The number of years needed to
recover the initial cash outlay. ■ 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? (500) 150 150 150 150 150 150 150
0
1
2
3
4
5
6
7
150
8
Payback Period ■ How long will it take for the project
to generate enough cash to pay for itself? (500) 150 150 150 150 150 150 150
0
1
2
3
4
5
6
7
Payback period = 3.33 years.
150
8
■ 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.
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. (500) 150 150 150 150 150 (300) 0
0
7
8
0
1
2
3
4
5
6
Consider this cash flow stream!
Drawbacks of Payback Period: ■ Does not consider all of the project’s
cash flows. (500) 150 150 150 150 150 (300) 0
0
7
8
0
1
2
3
4
5
6
This project is clearly unprofitable, but we would accept it based on a 4-year payback criterion!
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 (500)
250
0
1
250 250 250 250 2
3
4
Discounted
Year Cash Flow 0 1
-500 250
CF (14%) -500.00 219.30
5
Discounted Payback (500)
250
0
1
250 250 250 250 2
3
4
5
Discounted
Year Cash Flow 0 1
-500 250
CF (14%) -500.00 219.30 280.70
1 year
Discounted Payback (500)
250
0
1
250 250 250 250 2
3
4
5
Discounted
Year Cash Flow 0 1
-500 250
2
250
CF (14%) -500.00 219.30 280.70 192.38
1 year
Discounted Payback (500)
250
0
1
250 250 250 250 2
3
4
5
Discounted
Year Cash Flow 0 1
-500 250
2
250
CF (14%) -500.00 219.30 280.70 192.38 88.32
1 year 2 years
Discounted Payback (500)
250
0
1
250 250 250 250 2
3
4
5
Discounted
Year Cash Flow 0 1
-500 250
2
250
3
250
CF (14%) -500.00 219.30 280.70 192.38 88.32 168.75
1 year 2 years
Discounted Payback (500)
250
0
1
250 250 250 250 2
3
4
5
Discounted
Year Cash Flow 0 1
-500 250
2
250
3
250
CF (14%) -500.00 219.30 280.70 192.38 88.32 168.75
1 year 2 years .52 years
Discounted Payback (500)
250
0
1
250 250 250 250 2
3
4
5
Discounted
Year Cash Flow 0 1
CF (14%)
The Discounted -500 -500.00 Payback 250 219.30 is 2.52 years 280.70
2
250
3
250
280.70 192.38 88.32 168.75
1 year 2 years .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. n
NPV =
Σ t=1
ACFt (1 + k) t
- IO
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 $276,400 and provides annual net cash flows of $83,000 for four years and $116,000 at the end of the fifth year. The firm’s required rate of return is 15%.
NPV Example ■
Suppose we are considering a capital investment that costs $276,400 and provides annual net cash flows of $83,000 for four years and $116,000 at the end of the fifth year. The firm’s required rate of return is 15%.
83,000 (276,400)
0
1
83,000
2
83,000
3
83,000 116,000
4
5
NPV with the HP10B: ■ -276,400 ■ 83,000 ■4 ■ 116,000 ■ 15 ■ shift
CFj CFj shift Nj CFj I/YR
NPV ■ You should get NPV = 18,235.71.
NPV with the HP17BII: ■ Select CFLO mode. ■ FLOW(0)=?
-276,400 INPUT ■ FLOW(1)=? 83,000 INPUT ■ #TIMES(1)=1 4 INPUT ■ FLOW(2)=? 116,000 INPUT ■ #TIMES(2)=1 INPUT EXIT ■ CALC 15 I% NPV ■ You should get NPV = 18,235.71
NPV with the TI BAII Plus: ■ Select CF mode.
NPV with the TI BAII Plus: ■ Select CF mode. ■ CFo=?
-276,400
ENTER
NPV with the TI BAII Plus: ■ Select CF mode. ■ CFo=? ■ C01=?
-276,400 83,000
ENTER ENTER
NPV with the TI BAII Plus: ■ Select CF mode. ■ CFo=? ■ C01=? ■ F01=
1
-276,400 83,000 4
ENTER ENTER ENTER
NPV with the TI BAII Plus: ■ Select CF mode. ■ CFo=? ■ C01=? ■ F01=
1 ■ C02=?
-276,400 83,000 4 116,000
ENTER ENTER ENTER ENTER
NPV with the TI BAII Plus: ■ Select CF mode. ■ CFo=? ■ C01=? ■ F01=
1 ■ C02=? ■ F02= 1
-276,400 83,000 4 116,000
ENTER ENTER ENTER ENTER ENTER
NPV with the TI BAII Plus: ■ Select CF mode. ■ CFo=? ■ C01=? ■ F01=
-276,400 83,000 4 116,000
1 ■ C02=? ■ F02= 1 ■ NPV I= 15
ENTER ENTER ENTER ENTER ENTER ENTER
CPT
NPV with the TI BAII Plus: ■ Select CF mode. ■ CFo=?
-276,400 83,000 4 116,000
ENTER ■ C01=? ENTER ■ F01= 1 ENTER ■ C02=? ENTER ■ F02= 1 ENTER ■ NPV I= 15 ENTER ■ You should get NPV = 18,235.71
CPT
Profitability Index n
NPV =
Σ t=1
ACFt t (1 + k)
- IO
Profitability Index n
NPV =
Σ t=1
n
PI
=
Σ t=1
ACFt t (1 + k)
ACFt (1 + k) t
- IO
IO
Profitability Index •
Decision Rule:
If PI is greater than or equal to 1, ACCEPT. • If PI is less than 1, REJECT. •
■ -276,400 ■ 83,000 ■4 ■ 116,000 ■ 15 ■ shift
CFj CFj shift Nj CFj I/YR
PI with the HP10B:
NPV ■ You should get NPV = 18,235.71. ■ Add back IO: + 276,400 ■ Divide by IO: / 276,400 = ■ You should get PI = 1.066
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) n
NPV =
Σ t=1
ACFt (1 + k) t
- IO
Internal Rate of Return (IRR) n
NPV =
Σ t=1
n
IRR:
Σ t=1
ACFt (1 + k) t
ACFt t (1 + IRR)
- IO
= IO
Internal Rate of Return (IRR) n
IRR:
Σ
ACFt t (1 + IRR)
= IO
t=1
■ 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
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. 83,000 (276,400)
0
1
83,000
2
83,000
3
83,000 116,000
4
5
83,000 83,000 83,000 83,000 116,000 (276,400)
0 1 2 3 4 ■ This is what we are actually doing:
5
83,000 (PVIFA 4, IRR) + 116,000 (PVIF 5, IRR) = 276,400
83,000 83,000 83,000 83,000 116,000 (276,400)
0
1
2
3
4
5
■ This is what we are actually doing:
83,000 (PVIFA 4, IRR) + 116,000 (PVIF 5, IRR) = 276,400 ■ This way, we have to solve for IRR by trial
and error.
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 = 17.63%!
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. (- + + - + +) (500) 0
200
100
(200)
400
300
1
2
3
4
5
■ 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. (- + + - + +) (500) 0
200
100
(200)
400
300
1
2
3
4
5
■ Problem:
If there are multiple sign changes in the cash flow stream, we could get multiple IRRs. (- + + - + +) ■ We could find 3 different IRRs! 1 (500) 0
2
3
200
100
(200)
400
300
1
2
3
4
5
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.
(900) 0
300
400
400
500
600
1
2
3
4
5
Summary Problem: ■ IRR = 34.37%. ■ Using a discount rate of 15%,
NPV = $510.52. ■ PI = 1.57. (900) 0
300
400
400
500
600
1
2
3
4
5
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