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**Chapter 10 - Capital Budgeting**

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**A major part of the financial management of the firm**

Capital Budgeting A major part of the financial management of the firm Kinds Of Spending In Business Short 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 Budgeting Planning and Justifying How Capital Dollars Are Spent On Long Term Projects Provides methods for evaluating whether projects make financial sense and for choosing among them

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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) C ,000 C ,000 C ,000 C ,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 money Firms 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 Techniques Payback**

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**

Payback period is easily visualized by the cumulative cash flows

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**Example 10-2: Weakness of the Payback Technique**

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

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**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 using NPV = 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 negatives Projects with positive NPVs increase the firm’s value Projects with negative NPVs decrease the firm’s value

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**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 Projects NPV > 0 accept NPV < 0 reject Mutually Exclusive Projects NPVA > NPVB choose Project A over B

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**Concept Connection Example 10-3 Net Present Value (NPV)**

Project Alpha has the following cash flows. If the firm considering Alpha has a cost of capital of 12%, should the project be undertaken?

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**Concept Connection Example 10-3 Net Present Value (NPV)**

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.

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**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 The “price” of receiving the inflows The IRR is the interest rate at which the present value of the three inflows just equals the $5,000 outflow

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**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

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**Internal Rate of Return (IRR)**

Decision Rules Stand-alone Projects If IRR > cost of capital (k) accept If IRR < cost of capital (k) reject Mutually Exclusive Projects IRRA > 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 technique Guess 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 10-5 IRR – Iterative Procedure**

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%?

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**Example 10-5 IRR – Iterative Procedure**

Start by guessing IRR = 12% and calculate NPV. NPV = C0 + C1[PVFk,1] + C2[PVFk,2] + · · · + Cn[PVFk,n] NPV = -5, ,000[PVF12,1] + 2,000[PVF12,2] + 3,000[PVF12,3] NPV = -5, ,000[.8929] + 2,000[.7972] + 3,000[.7118] NPV = -5, , ,135.40 NPV = -$377.30 Since NPV<0, the project’s IRR must be < 12%.

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Figure 10-1 NPV Profile A project’s NPV profile is a graph of its NPV vs. the cost of capital. It crosses the horizontal axis at the IRR.

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**Concept Connection Example 10-5 IRR – Iterative Procedure**

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. Interest Rate Guess Calculated NPV 12% ($377) 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. 10 ($184) 9 ($83) 8 $22 7 $130

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**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 Assumption IRR 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**

At a cost of capital of k1, Project A is better than Project B, while at k2 the opposite is true.

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**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: = C0 + C [PVFAIRR,n]

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**Example 10-6 – Regular Cash Inflows**

Find the NPV and IRR for the following project if the cost of capital is 12%. C C C C3 ($5,000) $2, $2, $2,000 Solution: For NPV NPV = 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 = From which IRR is between 9% and 10%

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**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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**Profitability Index (PI)**

Decision Rules Stand-alone Projects If PI > 1.0 accept If PI < 1.0 reject Mutually Exclusive Projects PIA > 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) Method Replaces 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**

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. Thus, choosing the Long-Lived Project is a better decision than choosing the Short-Lived Project twice.

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**Concept Connection Example 10-8 Replacement Chain**

Which of the two following mutually exclusive projects should a firm purchase?

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**Concept Connection Example 10-9 Equivalent Annual Annuity (EAA)**

The EAA Method equates each project’s original NPV to an equivalent annual annuity. For the Short-Lived Project the EAA is $ (the equivalent of receiving $ spread out over 3 years at 8%); while the Long-Lived Project has an EAA of $ (the equivalent of receiving $ spread out over 6 years at 8%).

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**Concept Connection Example 10-9 Equivalent Annual Annuity (EAA)**

Because the Long-Lived Project has the higher EAA, it should be chosen. This is the same decision reached by the Replacement Chain Method.

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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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**Figure 10-6 Capital Rationing**

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