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**12 Capital Budgeting Chapter Terry Fegarty Seneca College**

Slides Developed by: Terry Fegarty Seneca College

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**Chapter 12 – Outline (1) Capital Budgeting**

Characteristics of Business Projects Capital Budgeting Techniques Capital Budgeting Techniques—Payback Capital Budgeting Techniques—Net Present Value (NPV) Capital Budgeting Techniques—Internal Rate of Return (IRR) NPV Profile Conflicting Results Between IRR and NPV NPV and IRR Solutions Using Spreadsheets © 2006 by Nelson, a division of Thomson Canada Limited

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Chapter 12 – Outline (2) Projects with a Single Outflow and Regular Inflows Profitability Index (PI) Comparing Projects with Unequal Lives Capital Rationing © 2006 by Nelson, a division of Thomson Canada Limited

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Capital Budgeting Capital budgeting involves planning and justifying large expenditures on long-term projects Projects can be classified as: Replacements Expansions New business ventures © 2006 by Nelson, a division of Thomson Canada Limited

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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 A stand-alone project has no competing alternatives The project is judged on its own viability Mutually exclusive projects—when selecting one project excludes selecting the other © 2006 by Nelson, a division of Thomson Canada Limited

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**Characteristics of Business Projects**

Project Cash Flows First and usually most difficult step in capital budgeting is reducing projects to series of cash flows Business projects involve early cash outflows and later inflows Initial outlay is required to get started Annual net inflows, after tax, generated by project Terminal value from sale or salvage of project © 2006 by Nelson, a division of Thomson Canada Limited

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**Characteristics of Business Projects**

Cost of Capital Firm’s cost of capital is average rate it pays its investors for use of their money In general, firm can raise money from two sources: debt and equity If potential project is expected to generate return greater than cost of money to finance it, it is a good investment © 2006 by Nelson, a division of Thomson Canada Limited

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**Capital Budgeting Techniques**

Four techniques for determining a project’s financial viability: Payback—how many years to recover project’s initial cost Net Present Value—how much the present value of project’s inflows exceeds present value of its outflows Internal Rate of Return—return on investment in the project Profitability Index—ratio of project’s inflows vs. outflows—in present value terms) © 2006 by Nelson, a division of Thomson Canada Limited

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**Capital Budgeting Techniques—Payback**

Payback period—time to recover early cash outflows Shorter paybacks are better Payback Decision Rules Stand-alone projects If payback period < (>) policy maximum accept (reject) Mutually Exclusive Projects If PaybackA < PaybackB choose Project A Weaknesses of the Payback Method Ignores time value of money Ignores cash flows after the payback period © 2006 by Nelson, a division of Thomson Canada Limited

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**Capital Budgeting Techniques—Payback—Example**

Consider the following cash flows Example Year 1 2 3 4 Cash flow (Cn) ($200,000) $60,000 Payback period is easy to see by the cumulative cash flows Year 1 2 3 4 Cash flow (Cn) ($200,000) $60,000 Cumulative cash flows ($140,000) ($80,000) ($20,000) $40,000 Payback period occurs at 3.33 years © 2006 by Nelson, a division of Thomson Canada Limited

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**Example 12.1: Capital Budgeting Techniques—Payback**

Q: Use the payback period technique to choose between mutually exclusive projects A and B. Example 800 200 C5 C4 350 400 C3 C2 C1 ($1,200) C0 Project B Project A A: 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. Example © 2006 by Nelson, a division of Thomson Canada Limited

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**Capital Budgeting Techniques—Payback**

Why Use the Payback Method? Quick and easy to apply Serves as rough screening device The Present Value Payback Method Involves finding present value of project’s cash flows, then calculating project’s payback © 2006 by Nelson, a division of Thomson Canada Limited

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**Capital Budgeting Techniques—Net Present Value (NPV)**

NPV—sum of present values of project’s cash flows, discounted at cost of capital PVoutflows PVinflows If PVinflows > PVoutflows, NPV > 0 © 2006 by Nelson, a division of Thomson Canada Limited

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**Capital Budgeting Techniques—Net Present Value (NPV)**

NPV and Shareholder Wealth Project’s NPV is net effect that undertaking project is expected to have on firm’s value A project with NPV > (<) 0 should increase (decrease) firm value Since firm desires to maximize shareholder wealth, it should select capital spending program with highest total NPV © 2006 by Nelson, a division of Thomson Canada Limited

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**Capital Budgeting Techniques—Net Present Value (NPV)**

NPV Decision Rules Stand-alone Projects NPV > 0 accept NPV < 0 reject Mutually Exclusive Projects NPVA > NPVB choose Project A over B © 2006 by Nelson, a division of Thomson Canada Limited

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**Example 12.2: Capital Budgeting Techniques—Net Present Value**

Q: Project Alpha has the following cash flows. If the firm considering Alpha has a cost of capital of 12%, should the project be undertaken? Example $3,000 C3 $2,000 C2 $1,000 C1 ($5,000) C0 A: 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 © 2006 by Nelson, a division of Thomson Canada Limited

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**Example 12.2: Capital Budgeting Techniques—Net Present Value**

1 2 3 -$5,000 $1,000 $2,000 $3,000 $892.90 $1,594.40 $2,135.40 -$377.30 Solution is calculated by discount each of the cash flows back to time period zero using a discount rate of 12%. © 2006 by Nelson, a division of Thomson Canada Limited

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**Capital Budgeting Techniques—Internal Rate of Return (IRR)**

Project’s IRR is return it generates on investment of its cash outflows For example, if a project has the following cash flows 1 2 3 -5,000 1,000 2,000 3,000 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 © 2006 by Nelson, a division of Thomson Canada Limited

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**Capital Budgeting Techniques—Internal Rate of Return (IRR)**

Defining IRR Through the NPV Equation The IRR is the interest rate that makes a project’s NPV zero — © 2006 by Nelson, a division of Thomson Canada Limited

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**Techniques—Internal Rate of Return**

IRR Decision Rules Stand-alone Projects If IRR > cost of capital (or k) accept If IRR < cost of capital (or k) reject Mutually Exclusive Projects IRRA > IRRB choose Project A over Project B If NPV > 0, IRR > k If NPV < 0, IRR < k © 2006 by Nelson, a division of Thomson Canada Limited

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**Techniques—Internal Rate of Return**

Calculating IRRs Finding IRRs usually requires an iterative, trial-and-error technique Guess at project’s IRR Calculate project’s NPV using this interest rate If NPV is zero, the guessed interest rate is the project’s IRR If NPV > (<) 0, try a new, higher (lower) interest rate © 2006 by Nelson, a division of Thomson Canada Limited

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**Example 12.3: Capital Budgeting Techniques—Internal Rate of Return**

Q: 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 $1,000 C1 ($5,000) C0 $2,000 C2 $3,000 C3 A: We’ll start by guessing an IRR of 12%. We’ll calculate the project’s NPV at this interest rate. Since NPV<0, the project’s IRR must be < 12%. © 2006 by Nelson, a division of Thomson Canada Limited

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**Example 12.3: Capital Budgeting Techniques—Internal Rate of Return**

A: 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. Example 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 9%, the project is not a good idea. $130 7 $22 8 ($83) 9 ($184) 10 ($377) 12% Calculated NPV Interest Rate Guess The exact IRR can be calculated using a financial calculator or spreadsheet © 2006 by Nelson, a division of Thomson Canada Limited

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NPV Profile Project’s NPV Profile—graph of its NPV vs. the cost of capital It crosses the horizontal axis at the IRR © 2006 by Nelson, a division of Thomson Canada Limited

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Figure 12.1: NPV Profile © 2006 by Nelson, a division of Thomson Canada Limited

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**Techniques—Internal Rate of Return (IRR)**

Technical Problems with IRR Multiple Solutions If some future cash flows are negative, project can have more than one IRR solution Normal pattern involves negative initial outlay and positive future cash flows Rarely presents practical difficulties The Reinvestment Assumption IRR method assumes cash inflows will be reinvested at project’s IRR For projects with extremely high IRRs, this is unlikely © 2006 by Nelson, a division of Thomson Canada Limited

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**Conflicting Results Between IRR and NPV**

NPV and IRR do not always provide the same decision for a project’s acceptance Occasionally give conflicting results in mutually exclusive decisions If two projects’ NPV profiles cross: one project is accepted below a certain cost of capital the other project is accepted above that cost of capital The NPV profiles have to cross in the first quadrant of the graph, where interest rates are practical NPV method is the preferred over IRR method because the reinvestment interest rate assumption is more practical © 2006 by Nelson, a division of Thomson Canada Limited

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**Figure 12.2: 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. © 2006 by Nelson, a division of Thomson Canada Limited

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**NPV and IRR Solutions Using Spreadsheets**

NPV function in Microsoft® Excel® =Cash Flow0 + NPV(interest rate, Cash Flow1:Cash Flown) Every cash flow within the parentheses is discounted at the interest rate IRR function in Excel® =IRR (interest rate, Cash Flow0:Cash Flown) © 2006 by Nelson, a division of Thomson Canada Limited

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**Example 12.3: Spreadsheet Solution**

Formula in B6: =B2 + NPV(C4,C2:E2) Formula in B8: =IRR(B2:E2,C4) © 2006 by Nelson, a division of Thomson Canada Limited

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**Projects with a Single Outflow and Regular Inflows**

Many projects have one outflow at time 0 and inflows representing an annuity stream For example, consider the following cash flows C0 C1 C2 C3 ($5,000) $2,000 In this case, the NPV formula can be rewritten as NPV = -C0 + C[PVFAk, n] The IRR formula can be rewritten as 0 = C0 + C[PVFAIRR, n] © 2006 by Nelson, a division of Thomson Canada Limited

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**Example 12.5: Projects with a Single Outflow and Regular Inflows**

Q: Find the NPV and IRR for the following series of cash flows: Example A: Substituting the cash flows into the NPV equation with annuity inflows we have: NPV = -$5,000 + $2,000[PVFA12, 3] NPV = -$5,000 + $2,000[2.4018] = -$196.40 Substituting the cash flows into the IRR equation with annuity inflows we have: 0 = -$5,000 + $2,000[PVFAIRR, 3] Solving for the factor gives us: $5,000 $2,000 = [PVFAIRR, 3] The interest factor is 2.5 which equates to an interest rate between 9% and 10%. $2,000 C1 ($5,000) C0 C2 C3 © 2006 by Nelson, a division of Thomson Canada Limited

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**Example 12.5: Spreadsheet Solution**

Formula in B6: =B2 + NPV(C4,C2:E2) Formula in B8: =IRR(B2:E2,C4) © 2006 by Nelson, a division of Thomson Canada Limited

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**Profitability Index (PI)**

Profitability Index—ratio of the present value of a project’s inflows to the present value of a project’s outflows a variation on the NPV method Projects are acceptable if PI>1 Larger PIs are preferred © 2006 by Nelson, a division of Thomson Canada Limited

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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 © 2006 by Nelson, a division of Thomson Canada Limited

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**Profitability Index (PI)**

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, two methods may not lead to same choice © 2006 by Nelson, a division of Thomson Canada Limited

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**Comparing Projects with Unequal Lives**

If significant difference exists between lives of mutually exclusive projects, direct comparison of the projects is meaningless Problem arises due to the NPV method Longer lived projects almost always have higher NPVs © 2006 by Nelson, a division of Thomson Canada Limited

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**Figure 12.3: Comparing Projects with Unequal Lives**

Example © 2006 by Nelson, a division of Thomson Canada Limited

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**Comparing Projects with Unequal Lives—Example**

Q: Which of the two following mutually exclusive projects should a firm purchase? Example Short-Lived Project (NPV = $ at an 8% discount rate; IRR = 23.4%) $750 ($2,600) - C5 C4 C3 Long-Lived Project (NPV = $ at an 8% discount rate; IRR = 18.3%) C1 ($1,500) C0 C2 C6 A: The IRR method favours the Short-Lived Project while the NPV method favours the Long-Lived Project. We’ll correct for the unequal life problem by using the EAA Method. © 2006 by Nelson, a division of Thomson Canada Limited

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**Comparing Projects with Unequal Lives**

Equivalent Annual Annuity (EAA) Method Replaces each project with an equivalent perpetuity that equates to the project’s original NPV © 2006 by Nelson, a division of Thomson Canada Limited

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**Comparing Projects with Unequal Lives—Example**

A: 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%). The Long-Lived Project has an EAA of $ (the equivalent of receiving $ spread out over 6 years at 8%). Since the Long-Lived Project has the higher EAA, it should be chosen. Example © 2006 by Nelson, a division of Thomson Canada Limited

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**Figure 12.4: Comparing Projects with Unequal Lives**

Example © 2006 by Nelson, a division of Thomson Canada Limited

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Capital Rationing Capital rationing— exists when there is limit (maximum) to amount of funds available for new projects Thus, there may be some projects with +NPVs, IRRs > discount rate or PIs >1 that will be rejected, because not enough money available How do you choose the set of projects in which to invest? Use complex mathematical process called constrained maximization Use intuition and judgment © 2006 by Nelson, a division of Thomson Canada Limited

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**Figure 12.5: Capital Rationing**

© 2006 by Nelson, a division of Thomson Canada Limited

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