Capital Budgeting Capital Budgeting Techniques Techniques
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Chapter 13 Capital Capital Budgeting Budgeting Techniques Techniques © Pearson Education Limited 2004 Fundamentals of Financial Management, 12/e Created by: Gregory A. Kuhlemeyer, Ph.D. Carroll College, Waukesha, WI
Proposed Proposed Project Project Data Data Julie Miller is evaluating a new project for her firm, Basket Wonders (BW). She has determined that the after-tax cash flows for the project will be Tk10,000; Tk12,000; Tk15,000; Tk10,000; and Tk7,000, respectively, for each of the Years 1 through 5. The initial cash outlay will be Tk40,000. • •
For this project, assume that it is independent of any other potential projects that Basket Wonders may undertake. Independent -- A project whose acceptance (or rejection) does not prevent the acceptance of other projects under consideration.
1. 1. Project Project Evaluation: Evaluation: Alternative Alternative Methods Methods – – – –
Payback Period (PBP) Internal Rate of Return (IRR) Net Present Value (NPV) Profitability Index (PI)
Payback Payback Period Period (PBP) (PBP) 0
1
2
-40 K -b
10 K 10 K
12 K 22 K
(a)
3
4
15 K 37 K (c)
5
10 K (d) 7 K 47 K 54 K
Cumulative Inflows PBP is the period of time required for the cumulative expected cash flows from an investment project to equal the initial cash outflow. a – minimum whole year for recovery b – initial cash outflow
PBP = a + ( b - c ) / d = 3 + (40 - 37) / 10
c – maximum amount not crossing b
= 3 + (3) / 10
d – portion of payment necessary for payback
= 3.3 Years
PBP PBP Acceptance Acceptance Criterion Criterion The management of Basket Wonders has set a maximum PBP of 3.5 years for projects of this type.
Should this project be accepted?
Yes! The firm will receive back the initial cash outlay in less than 3.5 years. [3.3 Years < 3.5 Year Max.]
If maximum PBP is set for 3 years? No! The firm will receive back the initial cash outlay in more than 3 years. [3.3 Years > 3 Year Max.]
PBP PBP Strengths Strengths and and Weaknesses Weaknesses Strengths:
Weaknesses:
Easy to use and understand – Does not account for TVM (time value of money) – Can be used as a – Does not consider cash flows beyond the PBP measure of liquidity – Cutoff period is subjective – Easier to forecast ST than LT flows –
Internal Internal Rate Rate of of Return Return (IRR) (IRR) IRR is the discount rate that equates the present value of the future net cash flows from an investment project with the project’s initial cash outflow. CF1 ICO =
(1+IRR)
1
Tk10,000 Tk40,000 = + (1+IRR)
1
+
CF2 +
CFn
+...+
(1+IRR)2
(1+IRR)n
Tk12,000Tk15,000 (1+IRR)
2
+
(1+IRR)
3
+
Tk10,000 (1+IRR)
+
4
Tk7,000
(1+IRR)5
Find the interest rate (IRR) that causes the discounted cash flows to equal Tk40,000.
IRR IRR Solution Solution (Try (Try 10% 10% and and 15%) 15%) Tk40,000 = Tk10,000(PVIF10%,1) + Tk12,000(PVIF10%,2) +Tk15,000(PVIF10%,3) + Tk10,000(PVIF10%,4) + Tk 7,000(PVIF10%,5) Tk40,000 = Tk10,000(.909) + Tk12,000(.826) + Tk15,000(.751) + Tk10,000(.683) + Tk 7,000(.621) Tk40,000 = Tk9,090 + Tk9,912 + Tk11,265 + Tk6,830 + Tk4,347 = Tk 41,444 [Rate is too low!!]
Tk40,000 = Tk10,000(PVIF15% ,1 ) + Tk12,000(PVIF15% ,2 ) + Tk15,000(PVIF15% ,3 ) + Tk10,000(PVIF15% ,4 ) + Tk 7,000(PVIF15% ,5 ) Tk40,000 = Tk10,000(.870) + Tk12,000(.756) + Tk15,000(.658) + Tk10,000(.572) + Tk 7,000(.497) Tk40,000 = =
Tk8,700 + Tk9,072 + Tk9,870 + Tk5,720 + Tk3,479 Tk 36,841 [Rate is too high!!]
IRR IRR Solution Solution (Interpolate) (Interpolate) .05
X
X .05
=
.10 IRR .15
Tk41,444 Tk40,000 Tk36,841
Tk1,444 Tk4,603
Tk1,444 Tk4,603
IRR IRR Solution Solution (Interpolate (Interpolate [Trial [Trial and and Error]) Error]) .05
X
X .05
=
.10 IRR .15
Tk41,444 Tk40,000 Tk36,841
Tk1,444 Tk4,603
Tk1,444 Tk4,603
IRR IRR Solution Solution (Interpolate) (Interpolate) .05
X
.10 IRR .15
Tk41,444 Tk40,000 Tk36,841
Tk1,444 Tk4,603
(Tk1,444)(0.05)
X=
X = .0157 Tk4,603
IRR = .10 + .0157 = .1157 or 11.57%
IRR IRR Acceptance Acceptance Criterion Criterion The management of Basket Wonders has determined that the Hurdle (cutoff) rate is 13% for projects of this type.
Should this project be accepted?
No! The firm will receive 11.57% for each dollar invested in this project at a cost of 13%. [ IRR < Hurdle Rate ]
IRR IRR Strengths Strengths and and Weaknesses Weaknesses Strengths: – Accounts for TVM – Considers all cash flows – Less subjectivity
Weaknesses: – Assumes all cash flows reinvested at – Difficulties with project rankings and IRRs
the IRR
Multiple
Net Net Present Present Value Value (NPV) (NPV) NPV is the present value of an investment project’s net cash flows minus the project’s initial cash outflow.
CF1 CF2 + NPV = (1+k)1 (1+k)2
CFn ICO +...+ (1+k)n
NPV NPV Solution Solution Basket Wonders has determined that the appropriate discount rate (k) for this project is 13%.
Tk15,000 NPV = Tk10,000+ Tk12,000 + + (1.13)1 (1.13)2 (1.13)3 Tk10,000 Tk7,000 4 + 5 - Tk40,000 (1.13) (1.13)
NPV NPV Solution Solution NPV = Tk10,000(PVIF13%,1) + Tk12,000(PVIF13%,2) + Tk15,000(PVIF13%,3) + Tk10,000(PVIF13%,4) + Tk 7,000(PVIF13%,5) - Tk40,000 NPV = Tk10,000(.885) + Tk12,000(.783) + Tk15,000(.693) + Tk10,000(.613) + 7,000(.543) - Tk40,000 NPV = Tk8,850 + Tk9,396 + Tk10,395 + Tk6,130 + Tk3,801 - Tk40,000 = - Tk1,428
Tk
NPV NPV Acceptance Acceptance Criterion Criterion The management of Basket Wonders has determined that the required rate is 13% for projects of this type. Should this project be accepted?
No! The NPV is negative. This means that the project is reducing shareholder wealth. [Reject as NPV < 0 ]
NPV NPV Strengths Strengths and and Weaknesses Weaknesses Strengths: – Cash flows assumed to be reinvested at the hurdle rate. – Accounts for TVM. – Considers all cash flows.
Weaknesses: – May not include managerial options embedded in the project. See Chapter 14.
Profitability Profitability Index Index (PI) (PI) PI is the ratio of the present value of a project’s future net cash flows to the project’s initial cash outflow. Method #1:
PI =
CF1 CF2 + (1+k)1 (1+k)2
+...+
CFn (1+k)n
<< OR >> Method #2:
PI = 1 + [ NPV / ICO ]
ICO
PI PI Acceptance Acceptance Criterion Criterion PI
= Tk38,572 / Tk40,000 = .9643 (Method #1, 13-34)
Should this project be accepted?
No! The PI is less than 1.00. This means that the project is not profitable. [Reject as PI < 1.00 ]
PI PI Strengths Strengths and and Weaknesses Weaknesses Strengths: – Same as NPV – Allows comparison of different scale projects
Weaknesses: – Same as NPV – Provides only profitability – Potential Ranking Problems
relative
Evaluation Summary Basket Wonders Independent Project
Method Project Comparison Decision PBP
3.3
3.5
Accept
IRR
11.47%
13%
Reject
NPV
-$1,424
$0
Reject
PI
.96
1.00
Reject
Other Project Relationships ◆
Dependent -- A project whose acceptance depends on the acceptance of one or more other projects.
• Mutually Exclusive -- A project whose acceptance precludes the acceptance of one or more alternative projects.
Potential Potential Problems Problems Under Under Mutual Mutual Exclusivity Exclusivity Ranking of project proposals may create contradictory results. A. B. C.
Scale of Investment Cash-flow Pattern Project Life
A. A. Scale Scale Differences Differences Compare a small (S) and a large (L) project.
END OF YEAR 0
NET CASH FLOWS Project S Project L -Tk100
1
0
2
Tk400
-Tk100,000 0 Tk156,250
Scale Scale Differences Differences Calculate the PBP, IRR, NPV@10%, and PI@10%. Which project is preferred? Why? Project
S L
IRR
100% 25%
NPV
Tk 231 Tk29,132
PI
3.31 1.29
B. B. Cash Cash Flow Flow Pattern Pattern Let us compare a decreasing cash-flow (D) project and an increasing cash-flow (I) project.
END OF YEAR 0 1 2 3
NET CASH FLOWS Project D Project I -Tk1,200 -Tk1,200 1,000 100 500 600 100 1,080
Cash Cash Flow Flow Pattern Pattern Calculate the IRR, NPV@10%, and PI@10%. Which project is preferred? Project D I
IRR 23% 17%
NPV Tk198 Tk198
PI 1.17 1.17
600
Plot NPV for each project at various discount rates.
400
Project I
200
NPV@10% IRR Project D
0 -200
Net Present Value (Tk)
Examine Examine NPV NPV Profiles Profiles
0
5
10 15 20 Discount Rate (%)
25
Net Present Value (Tk) -200 0 200 400 600
Fisher’s Fisher’s Rate Rate of of Intersection Intersection
0
At k<10%, I is best!
Fisher’s Rate of Intersection At k>10%, D is best!
5
10 15 20 Discount Rate (Tk)
25
C. C. Project Project Life Life Differences Differences Let us compare a long life (X) project project.
END OF YEAR 0 1 2 3
and a short life (Y)
NET CASH FLOWS Project X Project Y -Tk1,000 -Tk1,000 0 2,000 0 0 3,375 0
Project Project Life Life Differences Differences Calculate the PBP, IRR, NPV@10%, and PI@10%. Which project is preferred? Why? Project X Y
IRR 50% 100%
NPV Tk1,536 Tk 818
PI 2.54 1.82
Proposed Proposed Project Project Data Data Julie Miller is evaluating a new project for her firm, Basket Wonders (BW). She has determined that the after-tax cash flows for the project will be Tk10,000; Tk12,000; Tk15,000; Tk10,000; and Tk7,000, respectively, for each of the Years 1 through 5. The initial cash outlay will be Tk40,000. • •
For this project, assume that it is independent of any other potential projects that Basket Wonders may undertake. Independent -- A project whose acceptance (or rejection) does not prevent the acceptance of other projects under consideration.
1. 1. Project Project Evaluation: Evaluation: Alternative Alternative Methods Methods – – – –
Payback Period (PBP) Internal Rate of Return (IRR) Net Present Value (NPV) Profitability Index (PI)
Payback Payback Period Period (PBP) (PBP) 0
1
2
-40 K -b
10 K 10 K
12 K 22 K
(a)
3
4
15 K 37 K (c)
5
10 K (d) 7 K 47 K 54 K
Cumulative Inflows PBP is the period of time required for the cumulative expected cash flows from an investment project to equal the initial cash outflow. a – minimum whole year for recovery b – initial cash outflow
PBP = a + ( b - c ) / d = 3 + (40 - 37) / 10
c – maximum amount not crossing b
= 3 + (3) / 10
d – portion of payment necessary for payback
= 3.3 Years
PBP PBP Acceptance Acceptance Criterion Criterion The management of Basket Wonders has set a maximum PBP of 3.5 years for projects of this type.
Should this project be accepted?
Yes! The firm will receive back the initial cash outlay in less than 3.5 years. [3.3 Years < 3.5 Year Max.]
If maximum PBP is set for 3 years? No! The firm will receive back the initial cash outlay in more than 3 years. [3.3 Years > 3 Year Max.]
PBP PBP Strengths Strengths and and Weaknesses Weaknesses Strengths:
Weaknesses:
Easy to use and understand – Does not account for TVM (time value of money) – Can be used as a – Does not consider cash flows beyond the PBP measure of liquidity – Cutoff period is subjective – Easier to forecast ST than LT flows –
Internal Internal Rate Rate of of Return Return (IRR) (IRR) IRR is the discount rate that equates the present value of the future net cash flows from an investment project with the project’s initial cash outflow. CF1 ICO =
(1+IRR)
1
Tk10,000 Tk40,000 = + (1+IRR)
1
+
CF2 +
CFn
+...+
(1+IRR)2
(1+IRR)n
Tk12,000Tk15,000 (1+IRR)
2
+
(1+IRR)
3
+
Tk10,000 (1+IRR)
+
4
Tk7,000
(1+IRR)5
Find the interest rate (IRR) that causes the discounted cash flows to equal Tk40,000.
IRR IRR Solution Solution (Try (Try 10% 10% and and 15%) 15%) Tk40,000 = Tk10,000(PVIF10%,1) + Tk12,000(PVIF10%,2) +Tk15,000(PVIF10%,3) + Tk10,000(PVIF10%,4) + Tk 7,000(PVIF10%,5) Tk40,000 = Tk10,000(.909) + Tk12,000(.826) + Tk15,000(.751) + Tk10,000(.683) + Tk 7,000(.621) Tk40,000 = Tk9,090 + Tk9,912 + Tk11,265 + Tk6,830 + Tk4,347 = Tk 41,444 [Rate is too low!!]
Tk40,000 = Tk10,000(PVIF15% ,1 ) + Tk12,000(PVIF15% ,2 ) + Tk15,000(PVIF15% ,3 ) + Tk10,000(PVIF15% ,4 ) + Tk 7,000(PVIF15% ,5 ) Tk40,000 = Tk10,000(.870) + Tk12,000(.756) + Tk15,000(.658) + Tk10,000(.572) + Tk 7,000(.497) Tk40,000 = =
Tk8,700 + Tk9,072 + Tk9,870 + Tk5,720 + Tk3,479 Tk 36,841 [Rate is too high!!]
IRR IRR Solution Solution (Interpolate) (Interpolate) .05
X
X .05
=
.10 IRR .15
Tk41,444 Tk40,000 Tk36,841
Tk1,444 Tk4,603
Tk1,444 Tk4,603
IRR IRR Solution Solution (Interpolate (Interpolate [Trial [Trial and and Error]) Error]) .05
X
X .05
=
.10 IRR .15
Tk41,444 Tk40,000 Tk36,841
Tk1,444 Tk4,603
Tk1,444 Tk4,603
IRR IRR Solution Solution (Interpolate) (Interpolate) .05
X
.10 IRR .15
Tk41,444 Tk40,000 Tk36,841
Tk1,444 Tk4,603
(Tk1,444)(0.05)
X=
X = .0157 Tk4,603
IRR = .10 + .0157 = .1157 or 11.57%
IRR IRR Acceptance Acceptance Criterion Criterion The management of Basket Wonders has determined that the Hurdle (cutoff) rate is 13% for projects of this type.
Should this project be accepted?
No! The firm will receive 11.57% for each dollar invested in this project at a cost of 13%. [ IRR < Hurdle Rate ]
IRR IRR Strengths Strengths and and Weaknesses Weaknesses Strengths: – Accounts for TVM – Considers all cash flows – Less subjectivity
Weaknesses: – Assumes all cash flows reinvested at – Difficulties with project rankings and IRRs
the IRR
Multiple
Net Net Present Present Value Value (NPV) (NPV) NPV is the present value of an investment project’s net cash flows minus the project’s initial cash outflow.
CF1 CF2 + NPV = (1+k)1 (1+k)2
CFn ICO +...+ (1+k)n
NPV NPV Solution Solution Basket Wonders has determined that the appropriate discount rate (k) for this project is 13%.
Tk15,000 NPV = Tk10,000+ Tk12,000 + + (1.13)1 (1.13)2 (1.13)3 Tk10,000 Tk7,000 4 + 5 - Tk40,000 (1.13) (1.13)
NPV NPV Solution Solution NPV = Tk10,000(PVIF13%,1) + Tk12,000(PVIF13%,2) + Tk15,000(PVIF13%,3) + Tk10,000(PVIF13%,4) + Tk 7,000(PVIF13%,5) - Tk40,000 NPV = Tk10,000(.885) + Tk12,000(.783) + Tk15,000(.693) + Tk10,000(.613) + 7,000(.543) - Tk40,000 NPV = Tk8,850 + Tk9,396 + Tk10,395 + Tk6,130 + Tk3,801 - Tk40,000 = - Tk1,428
Tk
NPV NPV Acceptance Acceptance Criterion Criterion The management of Basket Wonders has determined that the required rate is 13% for projects of this type. Should this project be accepted?
No! The NPV is negative. This means that the project is reducing shareholder wealth. [Reject as NPV < 0 ]
NPV NPV Strengths Strengths and and Weaknesses Weaknesses Strengths: – Cash flows assumed to be reinvested at the hurdle rate. – Accounts for TVM. – Considers all cash flows.
Weaknesses: – May not include managerial options embedded in the project. See Chapter 14.
Profitability Profitability Index Index (PI) (PI) PI is the ratio of the present value of a project’s future net cash flows to the project’s initial cash outflow. Method #1:
PI =
CF1 CF2 + (1+k)1 (1+k)2
+...+
CFn (1+k)n
<< OR >> Method #2:
PI = 1 + [ NPV / ICO ]
ICO
PI PI Acceptance Acceptance Criterion Criterion PI
= Tk38,572 / Tk40,000 = .9643 (Method #1, 13-34)
Should this project be accepted?
No! The PI is less than 1.00. This means that the project is not profitable. [Reject as PI < 1.00 ]
PI PI Strengths Strengths and and Weaknesses Weaknesses Strengths: – Same as NPV – Allows comparison of different scale projects
Weaknesses: – Same as NPV – Provides only profitability – Potential Ranking Problems
relative
Evaluation Summary Basket Wonders Independent Project
Method Project Comparison Decision PBP
3.3
3.5
Accept
IRR
11.47%
13%
Reject
NPV
-$1,424
$0
Reject
PI
.96
1.00
Reject
Other Project Relationships ◆
Dependent -- A project whose acceptance depends on the acceptance of one or more other projects.
• Mutually Exclusive -- A project whose acceptance precludes the acceptance of one or more alternative projects.
Potential Potential Problems Problems Under Under Mutual Mutual Exclusivity Exclusivity Ranking of project proposals may create contradictory results. A. B. C.
Scale of Investment Cash-flow Pattern Project Life
A. A. Scale Scale Differences Differences Compare a small (S) and a large (L) project.
END OF YEAR 0
NET CASH FLOWS Project S Project L -Tk100
1
0
2
Tk400
-Tk100,000 0 Tk156,250
Scale Scale Differences Differences Calculate the PBP, IRR, NPV@10%, and PI@10%. Which project is preferred? Why? Project
S L
IRR
100% 25%
NPV
Tk 231 Tk29,132
PI
3.31 1.29
B. B. Cash Cash Flow Flow Pattern Pattern Let us compare a decreasing cash-flow (D) project and an increasing cash-flow (I) project.
END OF YEAR 0 1 2 3
NET CASH FLOWS Project D Project I -Tk1,200 -Tk1,200 1,000 100 500 600 100 1,080
Cash Cash Flow Flow Pattern Pattern Calculate the IRR, NPV@10%, and PI@10%. Which project is preferred? Project D I
IRR 23% 17%
NPV Tk198 Tk198
PI 1.17 1.17
600
Plot NPV for each project at various discount rates.
400
Project I
200
NPV@10% IRR Project D
0 -200
Net Present Value (Tk)
Examine Examine NPV NPV Profiles Profiles
0
5
10 15 20 Discount Rate (%)
25
Net Present Value (Tk) -200 0 200 400 600
Fisher’s Fisher’s Rate Rate of of Intersection Intersection
0
At k<10%, I is best!
Fisher’s Rate of Intersection At k>10%, D is best!
5
10 15 20 Discount Rate (Tk)
25
C. C. Project Project Life Life Differences Differences Let us compare a long life (X) project project.
END OF YEAR 0 1 2 3
and a short life (Y)
NET CASH FLOWS Project X Project Y -Tk1,000 -Tk1,000 0 2,000 0 0 3,375 0
Project Project Life Life Differences Differences Calculate the PBP, IRR, NPV@10%, and PI@10%. Which project is preferred? Why? Project X Y
IRR 50% 100%
NPV Tk1,536 Tk 818
PI 2.54 1.82
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