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Capital Budgeting For 9.220

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**Outline Introduction Net Present Value (NPV) Payback Period Rule (PP)**

Discounted Payback Period Rule Average Accounting Return (AAR) Internal Rate of Return Rule (IRR) Profitability Index Rule (PI) Special Situations Mutually Exclusive, Differing Scales Capital Rationing Summary and Conclusions

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**Returns from Investment Returns to Security Holders**

Recall the Flows of funds and decisions important to the financial manager Investment Decision Financing Decision Reinvestment Refinancing Financial Manager Financial Markets Real Assets Returns from Investment Returns to Security Holders Capital Budgeting is used to make the Investment Decision

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Introduction Capital Budgeting is the process of determining which real investment projects should be accepted and given an allocation of funds from the firm. To evaluate capital budgeting processes, their consistency with the goal of shareholder wealth maximization is of utmost importance.

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**Capital Budgeting Mutually Exclusive versus Independent Project**

Mutually Exclusive Projects: only ONE of several potential projects can be chosen, e.g. acquiring an accounting system. RANK all alternatives and select the best one. Independent Projects: accepting or rejecting one project does not affect the decision of the other projects. Must exceed a MINIMUM acceptance criteria.

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**The Net Present Value (NPV) Rule**

Total PV of future CF’s - Initial Investment Estimating NPV: 1. Estimate future cash flows: how much? and when? 2. Estimate discount rate 3. Estimate initial costs Minimum Acceptance Criteria: Accept if: NPV > 0 Ranking Criteria: Choose the highest NPV

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**NPV - An Example Assume you have the following information on**

Project X: Initial outlay -$1,100 Required return = 10% Annual cash revenues and expenses are as follows: Year Revenues Expenses $1, $500 , ,300 , ,700 , ,400 Draw a time line and compute the NPV of project X.

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**The Time Line & NPV of Project X**

1 2 3 4 Initial outlay ($1,100) Revenues $1,000 Expenses 500 Cash flow $500 Revenues $2,000 Expenses 1,300 Cash flow $700 Revenues $2,200 Expenses 2,700 Cash flow (500) Revenues $2,600 Expenses 1,400 Cash flow $1,200 – $1,100.00 +$377.02 1 $500 x 1.10 1 $700 x 1.10 2 1 - $500 x 1.10 3 1 $1,200 x 1.10 4 NPV NPV = -C0 + PV0(Future CFs) = -C0 + C1/(1+r) + C2/(1+r)2 + C3/(1+r)3 + C4/(1+r)4 = ______ + ______ + ______ + _______ + _______ = $ > 0

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**NPV in your HP 10B Calculator**

First, clear previous data, and check that your calculator is set to 1 P/YR: CLEAR ALL The display should show: 1 P_Yr Input data (based on above NPV example) Yellow INPUT Display should show: CF 0 Key in CF0 1,100 +/- CFj Display should show: CF 1 Key in CF1 500 CFj Display should show: CF 2 Key in CF2 700 CFj Display should show: CF 3 Key in CF3 500 +/- CFj Display should show: CF 4 Key in CF4 1,200 CFj Key in r 10 I/YR NPV Display should show: Compute NPV Yellow PRC

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**NPV: Strengths and Weaknesses**

Resulting number is easy to interpret: shows how wealth will change if the project is accepted. Acceptance criteria is consistent with shareholder wealth maximization. Relatively straightforward to calculate Weaknesses An improper NPV analysis may lead to the wrong choices of projects when the firm has capital rationing – this will be discussed later.

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**The Payback Period Rule**

How long does it take the project to “pay back” its initial investment? Payback Period = # of years to recover costs of project Minimum Acceptance Criteria: set by management Ranking Criteria: set by management

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**Discounted Payback - An Example**

Initial outlay -$1,000 r = 10% PV of Year Cash flow Cash flow 1 $ $ 182 Accumulated Year discounted cash flow 1 $ 182 2 513 3 1,039 4 1,244 Discounted payback period is just under 3 years

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**Average Accounting Return (AAR)**

Also known as Accounting Rate of Return (ARR) Method: using accounting data on profits and book value of the investment AAR = Average Net Income / Average Book Value If AAR > some target book rate of return, then accept the project

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**Average Accounting Return (AAR)**

You want to invest in a machine that produces squash balls. The machine costs $90,000. The machine will ‘die’ after 3 years (assume straight line depreciation, the annual depreciation is $30,000). You estimate for the life of the project: Year 1 Year 2 Year 3 Sales Expenses EBD

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**Calculating Projected NI**

Year 1 Year 2 Year 3 Sales Expenses E.B.D. Depreciation E.B.T. Taxes (40%) NI:

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We calculate: (i) Average NI = (ii) Average book value (BV) of the investment (machine): time-0 time-1 time-2 time-3 BV of investment: => Average BV = (divide by 4 - not 3) (iii) The Average Accounting Return: AAR = = 44.44% Conclusion: If target AAR < 44.44% => accept If target AAR > 44.44% => reject

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**The Internal Rate of Return (IRR) Rule**

IRR: the discount rate that sets the NPV to zero Minimum Acceptance Criteria: Accept if: IRR > required return Ranking Criteria: Select alternative with the highest IRR Reinvestment assumption: the IRR calculation assumes that all future cash flows are reinvested at the IRR

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**Internal Rate of Return - An Example**

Initial outlay = -$2,200 Year Cash flow 1 800 2 900 3 500 4 1,600 Find the IRR such that NPV = 0 ______ _______ ______ _______ 0 = (1+IRR)1 (1+IRR) (1+IRR) (1+IRR)4 ,600 2,200 =

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**IRR in your HP 10B Calculator**

First, clear previous data, and check that your calculator is set to 1 P/YR: CLEAR ALL The display should show: 1 P_Yr Input data (based on above NPV example) Yellow INPUT Display should show: CF 0 Key in CF0 2,200 +/- CFj Display should show: CF 1 Key in CF1 800 CFj Display should show: CF 2 Key in CF2 900 CFj Display should show: CF 3 Key in CF3 500 CFj Key in CF4 1,600 CFj Display should show: CF 4 IRR/YR Display should show: % Compute IRR Yellow CST

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**Internal Rate of Return and the NPV Profile**

Discount rates NPV 0% $1,600.00 5% 1,126.47 10% 15% 20% 25% IRR is between 20% and 25% -- about 23.30% If required rate of return (r) is lower than IRR => accept the project (e.g. r = 15%) If required rate of return (r) is higher than IRR => reject the project (e.g. r = 25%)

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**The Net Present Value Profile**

Year Cash flow 0 – $2,200 1 800 2 900 3 500 4 1,600 1,600.00 1,126.47 739.55 419.74 159.62 Discount rate – 72.64 2% 6% 10% 14% 18% 22% IRR=23.30%

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**IRR: Strengths and Weaknesses**

IRR number is easy to interpret: shows the return the project generates. Acceptance criteria is generally consistent with shareholder wealth maximization. Weaknesses Does not distinguish between investing and financing scenarios IRR may not exist or there may be multiple IRR Problems with mutually exclusive investments

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**IRR for Investment and Financing Projects**

Initial outlay = $4,000 Year Cash flow 1 -1,200 2 -800 3 -3,500 Find the IRR such that NPV = 0 _______ _______ _______ 0 = (1+IRR)1 (1+IRR) (1+IRR)3 -1, ,500 - 4,000 =

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**Internal Rate of Return and the NPV Profile for a Financing Project**

The NPV Profile of a Financing Project: Discount rates NPV 0% -$1,500.00 5% 10% 15% 50.2 20% IRR is between 10% and 15% -- about 14.37% For a Financing Project, the required rate of return is the cost of financing, thus If required rate of return (r) is lower than IRR => reject the project (e.g. r = 10%) If required rate of return (r) is higher than IRR => accept the project (e.g. r = 15%)

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**The NPV Profile for a Financing Project**

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**Multiple Internal Rates of Return**

Example 1 Assume you are considering a project for which the cash flows are as follows: Year Cash flows $900 ,200 ,300 ,200

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**Multiple IRRs and the NPV Profile - Example 1**

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**INPUT Multiple IRRs in your HP 10B Calculator**

First, clear previous data, and check that your calculator is set to 1 P/YR: CLEAR ALL The display should show: 1 P_Yr Input data (based on above NPV example) Yellow INPUT Display should show: CF 0 Key in CF0 900 +/- CFj Display should show: CF 1 Key in CF1 1,200 CFj Display should show: CF 2 Key in CF2 1,300 CFj Display should show: CF 3 Key in CF3 1,200 +/- CFj IRR/YR Display should show: % Compute 1st IRR Yellow CST STO IRR/YR Compute 2nd IRR by guessing it first 30 +/- Yellow RCL Yellow CST Display should show: %

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**No or Multiple IRR Problem – What to do?**

IRR cannot be used in this circumstance, the only solution is to revert to another method of analysis. NPV can handle these problems. How to recognize when this IRR problem can occur When changes in the signs of cash flows happen more than once the problem may occur (depending on the relative sizes of the individual cash flows). Examples: +-+ ; -+- ; -+++-; +---+

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**Multiple Internal Rates of Return**

Example 2 Assume you are considering a project for which the cash flows are as follows: Year Cash flows $260

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**Multiple IRRs and the NPV Profile - Example 2**

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**Multiple Internal Rates of Return**

Example 3 Assume you are considering a project for which the cash flows are as follows: Year Cash flows $660

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**Multiple IRRs and the NPV Profile - Example 3**

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**The Profitability Index (PI) Rule**

Total Present Value of future CF’s / Initial Investment Minimum Acceptance Criteria: Accept if PI > 1 Ranking Criteria: Select alternative with highest PI

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**Profitability Index - An Example**

Consider the following information on Project Y: Initial outlay -$1,100 Required return = 10% Annual cash benefits: Year Cash flows 1 $ 500 ,000 What’s the NPV? What’s the Profitability Index (PI)?

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**The NPV of Project Y is equal to:**

= $1, ,100 = $ PI = PV Cashflows/Initial Investment = This is a good project according to the PI rule.

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**The Profitability Index (PI) Rule**

Disadvantages: Problems with mutually exclusive investments (to be discussed later) Advantages: May be useful when available investment funds are limited (to be discussed later). Easy to understand and communicate Correct decision when evaluating independent projects

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Special situations When projects are independent and the firm has few constraints on capital, then we check to ensure that projects at least meet a minimum criteria – if they do, they are accepted. NPV≥0; IRR≥hurdle rate; PI≥1 Sometimes a firm will have plenty of funds to invest, but it must choose between projects that are mutually exclusive. This means that the acceptance of one project precludes the acceptance of any others. In this case, we seek to choose the one highest ranked of the acceptable projects. If the firm has capital rationing, then its funds are limited and not all independent projects may be accepted. In this case, we seek to choose those projects that best use the firm’s available funds. PI is especially useful here.

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**Using IRR and PI correctly when projects are mutually exclusive and are of differing scales**

Year Cash flows of Project A Cash flows of Project B -$100,000 -$50 1 +$150,000 +$100 Consider the following two mutually exclusive projects. Assume the opportunity cost of capital is 12%

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**Incremental Cash Flows: Solving the Problem with IRR and PI**

As you can see, individual IRRs and PIs are not good for comparing between two mutually exclusive projects. However, we know IRR and PI are good for evaluating whether one project is acceptable. Therefore, consider “one project” that involves switching from the smaller project to the larger project. If IRR or PI indicate that this is worthwhile, then we will know which of the two projects is better. Incremental cash flow analysis looks at how the cash flows change by taking a particular project instead of another project.

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**Incremental Cash flows of A instead of B (i.e., A-B)**

Using IRR and PI correctly when projects are mutually exclusive and are of differing scales Year Cash flows of Project A Cash flows of Project B Incremental Cash flows of A instead of B (i.e., A-B) -$100,000 -$50 -$99,950 1 +$150,000 +$100 +$149,900

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**Using IRR and PI correctly when projects are mutually exclusive and are of differing scales**

IRR and PI analysis of incremental cash flows tells us which of two projects are better. Beware, before accepting the better project, you should always check to see that the better project is good on its own (i.e., is it better than “do nothing”).

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**IRR, NPV, and Mutually Exclusive Projects**

Year Project A: – $ Project B: – $

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**IRR, NPV, and the Incremental Project**

Year Project A: – $ Project B: – $ (A-B): The Crossover Rate = IRRA-B = 8.07%

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Capital Rationing Recall: If the firm has capital rationing, then its funds are limited and not all independent projects may be accepted. In this case, we seek to choose those projects that best use the firm’s available funds. PI is especially useful here. Note: capital rationing is a different problem than mutually exclusive investments because if the capital constraint is removed, then all projects can be accepted together. Analyze the projects on the next page with NPV, IRR, and PI assuming the opportunity cost of capital is 10% and the firm is constrained to only invest $50,000 now (and no constraint is expected in future years).

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**Capital Rationing – Example (All $ numbers are in thousands)**

Year Proj. A Proj. B Proj. C Proj. D Proj. E -$50 -$20 -$10 1 $60 $24.2 $25 $12.6 2 $0 $37.862 NPV $4.545 $2.0 $2.2 $2.727 $1.4545 IRR 20% 21% 14.84% 25% 26% PI 1.0909 1.1 1.11 1.136 1.145

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**Capital Rationing Example: Comparison of Rankings**

NPV rankings (best to worst) A, D, C, B, E A uses up the available capital Overall NPV = $4,545.45 IRR rankings (best to worst) E, D, B, A, C E, D, B use up the available capital Overall NPV = NPVE+D+B=$6,181.82 PI rankings (best to worst) E, D, C, B, A E, D, C use up the available capital Overall NPV = NPVE+D+C=$6,381.82 The PI rankings produce the best set of investments to accept given the capital rationing constraint.

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**Capital Rationing Conclusions**

PI is best for initial ranking of independent projects under capital rationing. Comparing NPV’s of feasible combinations of projects would also work. IRR may be useful if the capital rationing constraint extends over multiple periods (see project C).

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**Summary and Conclusions**

Discounted Cash Flow (DCF) techniques are the best of the methods we have presented. In some cases, the DCF techniques need to be modified in order to obtain a correct decision. It is important to completely understand these cases and have an appreciation of which technique is best given the situation.

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