chapter 10 - capital budgeting. capital budgeting a major part of the financial management of the...
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Capital BudgetingA major part of the financial management of the firm
Kinds Of Spending In BusinessShort term - to support day to day operations
Long term - to support long lived equipment and projects
Long term money and the things acquired with it are both called capital
Capital BudgetingPlanning and Justifying How Capital Dollars Are Spent On Long
Term ProjectsProvides methods for evaluating whether projects make financial sense and for choosing among them
Capital Budgeting
Capital budgeting involves planning and justifying large expenditures on long-term projects– Projects can be classified as:
Replacement – low risk
Expansion – moderate risk
New venture – high risk
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Characteristics of Business Projects
Project Types and Risk– Capital projects have increasing risk according to
whether they are replacements, expansions or new ventures
Stand-Alone and Mutually Exclusive Projects– Stand-alone project has no competing alternatives– Mutually exclusive projects involve selecting one
project from among two or more alternatives
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Characteristics of Business Projects
Project Cash Flows– Reduce projects to a series of cash flows:
C0 $(50,000)
C1 (10,000)
C2 15,000
C3 15,000
C4 15,000
C5 5,000
– Business projects: early cash outflows and later inflows
– C0 is the Initial Outlay and usually required to get started
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Characteristics of Business Projects
The Cost of Capital– The average rate a firm pays investors for
use of its long term moneyFirms raise money from two sources: debt and equity
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Capital Budgeting Techniques
Payback Period– How many years to recover initial cost
Net Present Value – Present value of inflows less outflows
Internal Rate of Return – Project’s return on investment
Profitability Index – Ratio of present value of inflows to outflows
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Capital Budgeting TechniquesPayback
Payback period is the time it takes to recover early cash outflows– Shorter paybacks are better
Payback Decision Rules– Stand-alone projects– Mutually Exclusive Projects
Weaknesses of the Payback Method– Ignores time value of money– Ignores cash flows after payback period
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Concept Connection Example 10-1 Payback Period
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Payback period is easily visualized by the cumulative cash flows
Example 10-2: Weakness of the Payback Technique
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Use the payback period technique to choose between mutually exclusive projects A and B.
Project A’s payback is 3 years as its initial outlay is fully recovered in that time. Project B doesn’t fully recover until sometime in the 4th year. Thus, according to the payback method, Project A is better than B. But project B is clearly better because of the large inflows in the last two years
NET PRESENT VALUE (NPV)The present value of future cash flows is what counts
when making decisions based on value.
The Net Present Value of all of a project's cash flows is its expected contribution
to the firm's value and shareholder wealth
PVs are taken at k, the cost of capital
Calculate NPV usingNPV = C0 + C1[PVFk,1] + C2[PVFk,2] + · · · + Cn[PVFk,n]
Outflows are Ci with negative values and tend to occur first
NPV: Difference between the present values of positives and negativesProjects with positive NPVs increase the firm’s value
Projects with negative NPVs decrease the firm’s value
nn
221
)k1(
C...
)k1(
C
)k1(
C
0C =NPV
Net Present Value (NPV)
NPV and Shareholder Wealth– A project’s NPV is the net effect that it is
expected to have on the firm’s value
– To maximize shareholder wealth, select the capital spending program with the highest NPV
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Net Present Value (NPV)
Decision Rules
– Stand-alone ProjectsNPV > 0 accept
NPV < 0 reject
– Mutually Exclusive ProjectsNPVA > NPVB choose Project A over B
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Concept Connection Example 10-3 Net Present Value (NPV)
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Project Alpha has the following cash flows. If the firm considering Alpha has a cost of capital of 12%, should the project be undertaken?
Concept Connection Example 10-3 Net Present Value (NPV)
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The NPV is found by summing the present value of the cash flows when discounted at the firm’s cost of capital.
Since Alpha’s NPV<0, it should
not be undertaken.
)30.377($
70.622,4$000,5$
40.2135$40.594,1$90.829$000,5$
)7118(.000,3$)7972(.000,2$)8929(.000,1$000,5$
000,5312.1
000,3212.1
000,2)12.1(
000,1
1
AlphaNPV
Internal Rate of Return (IRR)
A project’s IRR is the return it generates on the investment of its cash outflows– For example, if a project has the following cash flows
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The IRR is the interest rate at which the present value of the three inflows just equals the $5,000 outflow
The “price” of receiving the inflows
Defining IRR Through the NPV Equation
At the IRR the PVs of project inflows and
outflows are equal, so NPV = 0
Set NPV=0 and substitute IRR for k
0 = C0 + C1[PVFIRR,1] + C2[PVFIRR,2] + · · + Cn[PVFIRR,n]
IRR is the solution to this equation for a given set of Ci
Requires an iterative approach if the Ci are irregular
0 = C0
C
IRR
C
IRR
C
IRR
nn
1 221 1 1( ) ( )
...( )
nn
221
)k1(
C...
)k1(
C
)k1(
C
0C =NPV
Internal Rate of Return (IRR)
Decision Rules
– Stand-alone ProjectsIf IRR > cost of capital (k) accept
If IRR < cost of capital (k) reject
– Mutually Exclusive ProjectsIRRA > IRRB choose Project A over Project B
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Internal Rate of Return (IRR)
Calculating IRRs– Finding IRRs usually requires an iterative,
trial-and-error techniqueGuess at the project’s IRR
Calculate the project’s NPV using this interest rate
– If NPV = zero, guessed interest rate is the project’s IRR
– If NPV > 0, try a higher interest rate– If NPV < 0, try a lower interest rate
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Concept Connection Example 10-5IRR – Iterative Procedure
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Find the IRR for the following series of cash flows:
If the firm’s cost of capital is 8%, is the project a good idea? What if the cost of capital is 10%?
Example 10-5 IRR – Iterative Procedure
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Start by guessing IRR = 12% and calculate NPV.
NPV = C0 + C1[PVFk,1] + C2[PVFk,2] + · · · + Cn[PVFk,n] NPV = -5,000 + 1,000[PVF12,1] + 2,000[PVF12,2] + 3,000[PVF12,3] NPV = -5,000 + 1,000[.8929] + 2,000[.7972] + 3,000[.7118] NPV = -5,000 + 892.90 + 1,594.4 + 2,135.40 NPV = -$377.30
Since NPV<0, the project’s IRR must be < 12%.
Figure 10-1 NPV Profile
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A project’s NPV profile is a graph of its NPV vs. the cost of capital. It crosses the horizontal axis at the IRR.
Concept Connection Example 10-5 IRR – Iterative Procedure
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We’ll try a different, lower interest rate, say 10%. At 10%, the project’s NPV is ($184). Since the NPV is still less than zero, we need to try a still lower interest rate, say 9%. The following table lists the project’s NPV at different interest rates.
Since NPV becomes positive somewhere between 8% and 9%, the project’s IRR must be between 8% and 9%. If the
firm’s cost of capital is 8%, the project is marginal. If the
firm’s cost of capital is 10%, the project is not a good idea.
$1307
$228
($83)9
($184)10
($377)12%
Calculated NPV
Interest Rate Guess
Techniques: Internal Rate of Return (IRR)
Technical Problems with IRR– Multiple Solutions
Unusual projects can have more than one IRR
The number of positive IRRs to a project depends on the number of sign reversals to the project’s cash flows
– The Reinvestment AssumptionIRR method implicitly assumes cash inflows will be reinvested at the project’s IRR
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Comparing IRR and NPV
NPV and IRR do not always select the same project in mutually exclusive decisions
A conflict can arise if NPV profiles cross in the first quadrant
In the event of a conflict The selection of the NPV method is preferred
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Figure 10-2 Projects for Which IRR and NPV Can Give Different Solutions
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At a cost of capital of k1, Project A is better than Project B, while at k2 the opposite is
true.
PROJECTS WITH A SINGLE OUTFLOW AND REGULAR INFLOWS
Many projects are characterized by an initial outflow and a series of equal, regular inflows:
PV of annuity formula makes the pattern easy to work with
NPV: NPV = C0 + C [PVFAk,n]
IRR: 0 = C0 + C [PVFAIRR,n]
Example 10-6 – Regular Cash InflowsFind the NPV and IRR for the following project if the cost of capital is
12%.
C0 C1 C2 C3
($5,000) $2,000 $2,000 $2,000
Solution: For NPVNPV = C0 + C[PVFAk,n]
= -$5,000 + $2,000[PVFA12,3] = -$5,000 + $2,000(2.4018) = -$196.40
For IRR
0 = C0 + C[PVFAIRR,n]
= -$5,000 + $2,000[PVFAIRR,3]
PVFAIRR,3 = $5,000 / $2,000 = 2.5000
From which IRR is between 9% and 10%
Profitability Index (PI)
Is a variation on the NPV method
A ratio of the present value of a project’s inflows to the present value of a project’s outflows
Projects are acceptable if PI>1
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Profitability Index (PI)
Also known as the benefit/cost ratio– Positive future cash flows are the benefit– Negative initial outlay is the cost
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1 2 n
1 2 n
0
C C C
1+k 1+k 1+kPI
C
or
present value of inflowsPI
present value of outflows
Profitability Index (PI)
Decision Rules– Stand-alone Projects
If PI > 1.0 accept
If PI < 1.0 reject
– Mutually Exclusive ProjectsPIA > PIB choose Project A over Project B
Comparison with NPV– With mutually exclusive projects the two
methods may not lead to the same choices
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Comparing Projects with Unequal Lives
If a significant difference exists between mutually exclusive projects’ lives, a direct comparison is meaningless
The problem arises due to the NPV method– Longer lived projects almost always have
higher NPVs
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Comparing Projects with Unequal Lives
Two solutions exist– Replacement Chain Method
Extends projects until a common time horizon is reached
– Equivalent Annual Annuity (EAA) MethodReplaces each project with an equivalent perpetuity that equates to the project’s original NPV
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Concept Connection Example 10-8 Replacement Chain
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Thus, choosing the Long-Lived Project is a better decision than choosing the Short-Lived Project twice.
The IRR method argues for undertaking the Short-Lived Project while the NPV method argues for the Long-Lived Project. We’ll correct for the unequal life problem by using both the Replacement Chain Method and the EAA Method. Both methods will lead to the same decision.
Concept Connection Example 10-8 Replacement Chain
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Which of the two following mutually exclusive projects should a firm purchase?
Concept Connection Example 10-9 Equivalent Annual Annuity (EAA)
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The EAA Method equates each project’s original NPV to an equivalent annual annuity. For the Short-Lived Project the EAA is $167.95 (the equivalent of receiving $432.82 spread out over 3 years at 8%); while the Long-Lived Project has an EAA of $187.58 (the equivalent of receiving $867.16 spread out over 6 years at 8%).
Concept Connection Example 10-9 Equivalent Annual Annuity (EAA)
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Because the Long-Lived Project has the higher EAA, it should be chosen. This is the same decision reached by the Replacement Chain Method.
Capital Rationing
Used when capital funds for new projects are limited
Generally rank projects in descending order of IRR and cut off at the cost of capital
However this doesn’t always make the best use of capital so a complex mathematical process called constrained maximization can be used
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