Capital Budgeting
Syed Mohammed Shamsul Arifeen Financial Theory & Practices, MBA Spring 2013, IBA, DUTuesday, June 18, 2013
Capital Budgeting
The process of evaluating and selecting long-term
investments that are consistent with the firm’s goal of
maximizing owners’ wealth.
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Motives for Capital Expenditure
Capital Expenditure Vs Operating
Expenditure
An outlay of funds resulting in benefits received within 1 year
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Motives for Capital Expenditure
An outlay of funds that is expected to produce benefits over a period of time greater than 1 year
Capital Expenditure Vs Operating
Expenditure
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Motives for Capital Expenditure
Expansion
Replacement
Renewal Others
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Steps in the Process
Proposal generation
Review and analysis
Decision making
Implementation
Follow-up
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Basic Terminology
Projects whose cash flows are unrelated or independent of one another; the acceptance of one does not eliminate the others from further consideration.
Projects that compete with one another, so that the acceptance of one eliminates from further consideration all other projects that serve a similar function.
Independent Projects
Mutually Exclusive Projects
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Basic Terminology
Capital RationingUnlimited Fund
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Basic Terminology
The financial situation in which a firm is able to accept all independent projects that provide an acceptable return.
The financial situation in which a firm has only a fixed amount available for capital expenditures, and numerous projects compete for this resource.
Unlimited Funds
Capital Rationing
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Basic Terminology
Accept-RejectApproach
RankingApproach
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Basic Terminology
The evaluation of capital expenditure proposals to determine whether they meet the firm’s minimum acceptance criterion.
The ranking of capital expenditure projects on the basis of some predetermined measure, such as the rate of return.
Accept-Reject Approach
Ranking Approach
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Basic Terminology
0
1 2 3 4 5
An initial outlay followed only by a series of inflows
ConventionalCash Flow Pattern
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Basic Terminology
0
1 2
3
4 5
NonconventionalCash Flow Pattern
An initial outlay followed by a series of inflows and outflows
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Basic Terminology
Cash outlays that have already been made and therefore have no effect on the cash flows relevant to a current decision.
Cash flows that could be realized from the best alternative use of an owned asset.
Sunk Costs
Opportunity Costs
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Capital Budgeting Techniques
• Accounting Rate of Return (ARR)
• Payback Period
• Discounted Payback Period
• Net Present Value (NPV)
• Internal Rate of Return (IRR)
• Modified Internal Rate of Return (MIRR)
• Profitability Index (PI)
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Accounting Rate of Return (ARR)
Focuses on a project’s net income rather than its cash flows
Average annual incomeAverage investment
=
Average annual income = Average cash flow − Average annual depreciation
Average investment = (Cost + Salvage value) ÷ 2
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Accounting Rate of Return (ARR)
• If the ARR is greater than the minimum acceptable rate of return, ACCEPT the project.
• If the payback period is less than the minimum acceptable rate of return, REJECT the project.
• If the projects are mutually exclusive, accept the project with the highest ARR.
The Decision Criteria
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Accounting Rate of Return (ARR)
RevenueExpenses
433,333200,000
450,000150,000
266,667100,000
200,000100,000
133,333100,000
Before-tax cash flowDepreciation
233,333100,000
300,000100,000
166,667100,000
100,000100,000
33,333100,000
EBTTaxes (TC = 25%)
133,33333,333
200,00050,000
66,66716,667
00
-66,667-16,667
Net income 100,000 150,000 50,000 0 -50,000
Average annual income = (100,000+150,000+50,000+0−50,000)/5 = 50,000Average investment = (500,000+0)/2 = 250,000ARR = 50,000/250,000 = 20%
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Accounting Rate of Return (ARR)
• Considers accounting profit and not cash flows
• Does not consider time value of money
• Does not consider risk
• Minimum acceptable ARR is determined subjectively
Disadvantages
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Payback Period
Year Cash Flow
0 -1,000
1 500
2 400
3 300
4 100
The expected number of years required to recover the initial investment
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Payback Period
Year Cash Flow Cumulative Cash Flow
0 -1,000 -1,000
1 500 -500
2 400 -100
3 300 200
4 100 300
Year before complete recovery
Unrecovered investment
Cash flow during the yearin which complete recovery occurs
+=
= 2 + (100/300) = 2⅓ years
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Payback Period
• If the payback period is less than the maximum acceptable payback period, ACCEPT the project.
• If the payback period is greater than the maximum acceptable payback period, REJECT the project.
• If the projects are mutually exclusive, accept the project with the lowest payback period.
The Decision Criteria
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Payback Period
• Easy to compute and intuitive
• Considers cash flows rather than accounting profits
• Measure of project’s riskiness
• Measure of liquidity
Advantages
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Payback Period
• Ignores time value of money
• Ignores all cash flows after the payback period
• The maximum acceptable payback period is set subjectively
• Does not indicate whether or not an investment increases the company’s value
Disadvantages
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Discounted Payback Period
Year Cash Flow Discounted Cash Flow (@10%)
0 -1,000 -1,000
1 500 455
2 400 331
3 300 225
4 100 68
The expected number of years required to recover the investment from discounted net cash flows
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Discounted Payback Period
= 2 + (214/225) = 2.95 years
Year CF DCF (@10%) CDCF
0 -1,000 -1,000 -1,000
1 500 455 -545
2 400 331 -214
3 300 225 11
4 100 68 79
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Discounted Payback Period
• Considers cash flows rather than accounting profits
• Considers time value of money
• Is a measure of project’s riskiness
• Is a measure of liquidity
Advantages
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Discounted Payback Period
• Ignores all cash flows after the payback period
• The maximum acceptable discounted payback period is set subjectively
• Does not indicate whether or not an investment increases the company’s value
Disadvantages
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Net Present Value (NPV)
The difference between the present value of the cash inflows and the present value of the cash outflows of a project discounted at a rate equal to the firm’s cost of capital.
= PV of Cash Inflows − PV of Cash Outflows
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Net Present Value (NPV)
• If the NPV is positive, ACCEPT the project.
• If the NPV is negative, REJECT the project.
• If the projects are mutually exclusive, accept the project with the highest NPV.
The Decision Criteria
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Net Present Value (NPV)Calculation
=78.82
0 1 2 3 4
-1,000 500 400 300 100
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NPV Profile
A graph which relates a project’s NPV to the
discount rate used to calculate the NPV
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NPV Profile
-150.00
0
150.00
300.00
0 0.05 0.10 0.15 0.20
Cost of capital (%)
Net Present Value (Tk)
IRR = 14.5%
Net Present Value Profile
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• Tells whether or not an investment increases firm value
• Considers all cash flows of the project
• Considers time value of money
• Considers risk of future cash flows
Advantages
Net Present Value (NPV)
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• Requires an estimate of the firm’s cost of capital
• Expressed in terms of dollars, not as a percentage
Disadvantages
Net Present Value (NPV)
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Internal Rate of Return(IRR)
The discount rate which equates the NPV of an investment opportunity with zero.
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Internal Rate of Return (IRR)
• If the IRR is greater than the cost of capital, ACCEPT the project.
• If the IRR is less than the cost of capital, REJECT the project.
• If the projects are mutually exclusive, accept the project with the highest IRR.
The Decision Criteria
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Internal Rate of Return (IRR)Calculation
Trial & Error Method
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Calculation
0 1 2 3 4
-1,000 500 400 300 100
Internal Rate of Return (IRR)
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Calculation
Internal Rate of Return (IRR)
= 0.1243
=12.43%
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Improper Decision
Year 0 1 IRR
CFL -100,000 120,000 20%
CFB 83,333 -100000 20%
-20000
-15000
-10000
-5000
0
5000
10000
15000
20000
0 12.5 25.0 37.5 50.0-20000
-15000
-10000
-5000
0
5000
10000
15000
20000
0 12.5 25.0 37.5 50.0
k (%)
NPV (Tk)
Investment or Financing?
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No IRR
Year 0 1 2
CF 1.0 -2.0 1.5
0
0.10
0.20
0.30
0.40
0.50
0.60
0% 24% 48% 72% 96% 120% k (%)
NPV (Tk)
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Multiple IRR
Year 0 1 2
CF -1.5 10 -10
-1.50
-1.25
-1.00
-0.75
-0.50
-0.25
0
0.25
0.50
0.75
1.00
1.25
1.50
0% 100% 200% 300% 400% 500%
k (%)
NPV
(T
k)IRR2
IRR1
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• Tells whether or not an investment increases firm value
• Considers all cash flows of the project
• Considers time value of money
• Considers risk of future cash flows
Advantages
Internal Rate of Return (IRR)
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• Requires an estimate of the firm’s cost of capital
• May not give the value-maximizing decision when used to compare mutually exclusive projects
• May not give the value-maximizing decision when there is capital rationing
• Cannot be used with projects with non-conventional cash flow pattern
Disadvantages
Internal Rate of Return (IRR)
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• For independent projects: there is no conflict
• For mutually exclusive projects
Conflict between NPV & IRR
- Scale difference
- Timing difference
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Scale DifferenceYear 0 1 2 3 4 5
Project L -20 6 6 6 6 6
Project S -6 2 2 2 2 2
Project ∆ -14 4 4 4 4 4
NPVL = Tk 2.74 NPVS = Tk 1.58 NPV∆ = Tk 1.16
IRRL = 15.2% IRRS = 19.9% IRR∆ = 13.2%
k = 10%
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Timing DifferenceYear 0 1 2 3 4 5
Project L -10 0 2 3 5 9
Project S -10 4 4 3 3 2
Project ∆ 0 -4 -2 0 2 7
NPVL = Tk 2.91 NPVS = Tk 2.49 NPV∆ = Tk 0.42
IRRL = 17.3% IRRS = 20.5% IRR∆ = 12.5%
k = 10%
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Cause of Conflict
The use of NPV method implicitly assumes that the opportunity cost rate at which cash flows can be reinvested is the cost of capital.
The IRR method assumes that the firm has the opportunity to reinvest at the IRR.
Reinvestment Rate Assumption
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Cause of Conflict
The correct reinvestment rate assumption is the
cost of capital, which is implicit in the NPV method.
Reinvestment Rate Assumption
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NPV Profiles
-200
-100
0
100
200
300
400
500
0% 5.00% 10.00% 15.00% 20.00%-200
-100
0
100
200
300
400
500
0% 5.00% 10.00% 15.00% 20.00%
Cost of capital (%)
Net Present Value (Tk)
IRRS = 14.5%
IRRL = 11.8%
Fisher’s Rate of Intersectionor
Crossover Rate = 7.2%
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Modified IRR (MIRR)
The discount rate which forces the present value of the cash outflows to equate the present value of the project’s terminal value.
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Modified IRR (MIRR)
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Modified IRR (MIRR)
• If the MIRR is greater than the cost of capital, ACCEPT the project.
• If the MIRR is less than the cost of capital, REJECT the project.
• If the projects are mutually exclusive, accept the project with the highest MIRR.
The Decision Criteria
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Modified IRR (MIRR)
0 1 2 3 4
-10,000 7,000 -5,000 8,000 5,000
= 1.1309 − 1 = 0.1309 = 13.09%
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• Tells whether or not an investment increases firm value
• Considers all cash flows of the project
• Considers time value of money
• Considers risk of future cash flows
Advantages
Modified IRR (MIRR)
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• Requires an estimate of the firm’s cost of capital
• May not give the value-maximizing decision when used to compare mutually exclusive projects
• May not give the value-maximizing decision when there is capital rationing
Disadvantages
Modified IRR (MIRR)
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Profitability Index (PI)
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Profitability Index (PI)
• If the PI > 1.0, ACCEPT the project.
• If the PI < 1.0, REJECT the project.
• If the projects are mutually exclusive, accept the project with the highest PI.
The Decision Criteria
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Profitability Index (PI)
PV of cash inflows = 1,078.82
PV of cash outflows = 1,000
PI = 1,078.82÷1,000 = 1.08
Year Cash Flow
0 -1,000
1 500
2 400
3 300
4 100
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• Tells whether or not an investment increases firm value
• Considers all cash flows of the project
• Considers time value of money
• Considers risk of future cash flows
• Useful in ranking and selecting projects when capital is rationed
Advantages
Profitability Index (PI)
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• Requires an estimate of the firm’s cost of capital
• May not give the value-maximizing decision when used to compare mutually exclusive projects
Disadvantages
Profitability Index (PI)
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Beximco Limited is considering an investment proposal to install new equipment costing Tk. 60,000. The facility has life expectancy of five years and has no salvage value. Assume that the company uses straight line depreciation. The tax rate is 35 percent. The cash flows before depreciation and tax (CFBDT) from the investments are as follows:
Year CFBDT
1 Tk. 12,000
2 12,000
3 15,000
4 20,000
5 25,000
Requirements:(i)Payback period(ii)ARR(iii)IRR(iv)NPV @ 12% discount rate
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CFBDT(-) DepreciationEBT(-) Tax @ 35%EAT/NI(+) DeprecationCFAT
Year 1
Tk. 12,00012,000
000
12,00012,000
Year 2
Tk. 12,00012,000
000
12,00012,000
Year 3
Tk. 15,00012,000
3,0001,0501,950
12,00013,950
Year 4
Tk. 20,00012,0008,0002,8005,200
12,00017,200
Year 5
Tk. 25,00012,00013,0004,5508,450
12,00020,450
CCF -48,000 -36,000 -22,050 -4,850 15,600
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NPV at 5% discount rate
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Phoenix Company is considering two mutually exclusive investments, Project P and Project Q. The expected cash flows of these projects are as follows:
Year Project P Project Q
0 Tk -1,000 Tk -1,600
1 -1,200 200
2 -600 400
3 -250 600
4 2,000 800
5 4,000 100
Requirements:(i) What is the IRR of each project?(ii) Which project would you choose if the cost of capital is 10 percent?(iii)What is each project’s MIRR if the cost of capital is 12 percent?(iv)Construct the NPV profiles for projects P and Q.
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Adam Smith is considering automating his pen factory with the purchase
of a $475,000 machine. Shipping and installation would cost $5,000. Smith
has calculated that automation would result in savings of $45,000 a year
due to reduced scrap and $65,000 a year due to reduced labor costs. The
machine has a useful life of 4 years for depreciation purposes. The
estimated salvage of the machine at the end of four years is $120,000.
The old machine is fully depreciated, but has a salvage value today of
$100,000. The firm’s marginal tax rate is 34 percent.
What is the initial cash inflow at time period 0?
What would be the relevant incremental cash inflows over the machine’s
useful life?
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Basket Wonders (BW) is considering the purchase of a new basket
weaving machine. The machine will cost $50,000 plus $20,000 for
shipping and installation and will be depreciated over 4 years. NWC will
rise by $5,000. Lisa Miller forecasts that revenues will increase by
$110,000 for each of the next 4 years. The machine will then be sold
(scrapped) for $10,000 at the end of the fourth year, when the project
ends. Operating costs will rise by $70,000 for each of the next four
years. BW is in the 40 percent tax bracket.
What is the initial cash outflow?
What are the interim incremental net cash flows for each year?
What is the terminal year cash flow?
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BugBusters of Antarctica, Inc. is considering replacing a machine that has
a four-year life. The purchase of this new machine has a cost of
$700,000, shipping cost of $80,000, and a installation charge of $20,000.
This machine will not require any additional working capital. The old
machine can be salvaged for $75,000 currently. The old machine has four
years useful life remaining with a depreciation expense of $200,000. The
new machine will not generate additional revenues, but will decrease
operating expenses by $90,000 for each of the four-year project. The
equipment has four years of operable life. The company is subject to a
marginal tax rate of 40%. The salvage value at the end of the fourth year
for the new machine is expected to be $50,000.
What is the initial cash outflow?
What are the interim incremental net cash flows for each year?
What is the terminal year cash flow?
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