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Managerial Finance Finance 6335 Lecture 5 Chapter 6 & 7 Alternative Decision Rules Fundamentals of Capital Budgeting Ronald F. Singer

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**6.1 NPV and Stand-Alone Projects**

Consider a take-it-or-leave-it investment decision involving a single, stand-alone project for Fredrick Feed and Farm (FFF). The project costs $250 million and is expected to generate cash flows of $35 million per year, starting at the end of the first year and lasting forever.

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**NPV Rule The NPV of the project is calculated as:**

The NPV depends on the discount rate, r The Internal Rate of Return (IRR) is that discount rate that makes the NPV = 0

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**Alternative Rules Versus the NPV Rule**

Sometimes alternative investment rules may give the same answer as the NPV rule, but at other times they may disagree. When the rules conflict, the NPV decision rule should be followed.

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**6.2 Alternative Decision Rules**

The Payback Rule The payback period is amount of time it takes to recover or pay back the initial investment. If the payback period is less than a pre-specified length of time, you accept the project. Otherwise, you reject the project. The payback rule is used by many companies because of its simplicity. However, the payback rule does not always give a reliable decision since it ignores the time value of money.

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**NPV Rule The NPV of the project is calculated as:**

Therefore the Internal Rate of Return (IRR) is 14%

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**Figure 6.1 NPV of FFF’s New Project**

If FFF’s cost of capital is 10%, the NPV is $100 million and they should undertake the investment.

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**Measuring Sensitivity with IRR**

For FFF, if their cost of capital estimate is more than 14%, the NPV will be negative, as illustrated on the previous slide. In general, the difference between the cost of capital and the IRR is the maximum amount of estimation error in the cost of capital estimate that can exist without altering the original decision.

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When does IRR work? You can take all or no project (stand alone project) “Normal Project” Negative Cash flows first, followed by positive cash flows In other cases, the IRR rule may disagree with the NPV Rule. If that is the case always go with the NPV Rule

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**See excel File IRR, NPV versus Payback**

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**Practical Problems in Capital Budgeting**

We have stated that we want the firm to take all projects that generate positive NPV and reject all projects that have a negative NPV. Capital budgeting complications arise when you cannot, either physically or financial undertake all positive NPV projects. Then we have to devise methods of choosing between alternative positive NPV projects.

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**Mutually Exclusive Projects**

IF,AMONG A NUMBER OF PROJECTS, THE FIRM CAN ONLY CHOOSE ONE, THEN THE PROJECTS ARE SAID TO BE MUTUALLY EXCLUSIVE. For example: Suppose you have the choice of modifying an existing machine, or replacing it with a brand new one. You could not do both and produce the desired amount of output. Thus, these projects are mutually exclusive. Given the cash flows below, which of these projects do you choose?

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**Mutually Exclusive Projects**

Time Modify Replace Difference , , ,000 , , ,000 , , ,500 IRR Suppose the cost of capital is 10%

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**Mutually Exclusive Projects**

Time Modify Replace Difference , , ,000 , , ,000 , , ,500 IRR 10%) , , ,700 Notice the conflict that can exist between NPV and IRR.

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**CAPITAL BUDGETING COMPLICATIONS**

Capital Budgeting Complications occur when you cannot take all positive NPV PROJECTS. Thus, the firm is faced with the choice of two possibilities. Remember: Goal is still Max NPV of all possibilities

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Differences in Scale If a project’s size is doubled, its NPV will double. This is not the case with IRR. Thus, the IRR rule cannot be used to compare projects of different scales.

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**Differences in Scale (cont'd)**

Identical Scale Consider two projects: Girlfriend’s Business Laundromat Initial Investment $1,000 Cash FlowYear 1 $1,100 $400 Annual Growth Rate -10% -20% Cost of Capital 12%

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**Differences in Scale (cont'd)**

Identical Scale Girlfriend’s Business

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**Differences in Scale (cont'd)**

Identical Scale Laundromat IRR = 20% Both the NPV rule and the IRR rule indicate the girlfriend’s business is the better alternative.

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**Figure 6.5 NPV of Investment Opportunities**

The NPV of the girlfriend’s business is always larger than the NPV of the single machine laundromat. The IRR of the girlfriend’s business is 100%, while the IRR for the laundromat is 20%.

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**Differences in Scale (cont'd)**

Changes in Scale What if the laundromat project was 20 times larger? The NPV would be 20 times larger, but the IRR remains the same at 20%. Give an discount rate of 12%, the NPV rule indicates you should choose the 20-machine laundromat (NPV = $5,000) over the girlfriend’s business (NPV = $4,000).

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**Figure 6.6 NPV of Investment Opportunities with the 20-Machine Laundromat**

The NPV of the 20-machine laundromat is larger than the NPV of the girlfriend’s business only for discount rates less than 13.9%.

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**Differences in Scale (cont'd)**

Percentage Return Versus Impact on Value The girlfriend’s business has an IRR of 100%, while the 20-machine laundromat has an IRR of 20%, so why not choose the girlfriend’s business? Because the 20-machine laundromat makes more money It has a higher NPV.

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**Differences in Scale (cont'd)**

Percentage Return Versus Impact on Value Would you prefer a 200% return on $1 dollar or a 10% return on $1 million? The former investment makes only $2, while the latter opportunity makes $100,000. The IRR is a measure of the average return, but NPV is a measure of the total dollar impact on value, and thus stockholders’ wealth.

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Timing of Cash Flows Another problem with the IRR is that it can be affected by changing the timing of the cash flows, even when that change in timing does not affect the NPV. It is possible to alter the ranking of projects’ IRRs without changing their ranking in terms of NPV. Hence you cannot use the IRR to choose between mutually exclusive investments.

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**Timing of Cash Flows (cont'd)**

Assume you are offered a maintenance contract on the laundromat machines which would cost $250 per year per machine. With this contract, you would not have to pay for maintenance and so the cash flows from the machines would not decline. The expected cash flows would then be: $400 – $250 = $150 per year per machine

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**Timing of Cash Flows (cont'd)**

The time line would now be: The NPV of the project remains $5,000 but the IRR falls to 15%.

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**Figure 6.7 NPV With and Without the Maintenance Contract**

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**Timing of Cash Flows (cont'd)**

The NPV without the maintenance contract exceeds the NPV with the contract for discount rates that are greater than 12%. The IRR without the maintenance contract (20%) is larger than the IRR with the maintenance contract (15%). The correct decision is to agree to the contract if the cost of capital is less than 12% and to decline the contract if the cost of capital exceeds 12%. With a 12% cost of capital, you are indifferent.

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Capital Rationing In this situation, the decision maker is faced with a limited capital budget (or limitations on some other input). As a result, it may not be possible to take all positive net present value projects. Under this scenario, the problem is to find that combination of projects (within the capital budgeting constraint) that leads to the highest Net Present Value. The problem here is that the number of possibilities become very large with a relatively small number of projects. Thus, in order to make the problem "manageable", we can systematize the search.

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Capital Rationing Since we have a constraint, what we want to do is invest in those projects which gives us the highest BENEFIT per dollar invested. (The highest bang per buck). What is the benefit?, it is the Present Value of the Cash Flows. So that we would want to choose that set of projects within the capital budgeting constraint that gives the highest: Net Present Value INVESTMENT This ratio is called the profitability Index.

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Capital Rationing For example, suppose we have a $13 million capital budgeting constraint, with 7 alternative capital budgeting projects with the following projections. Project NPV Investment A B C D E F G

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**Project Profitability Index Investment Total**

Capital Rationing Rank by Profitability Index {(NPV/INV} Project Profitability Index Investment Total E C G F D B A COMBINATION WITH HIGHEST PROFITABILITY INDEX WITHIN THE CAPITAL BUDGET (E,C,G,F) has a NPV of $20.5 million, and a cost of $13 million.

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See Spreadsheet

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Capital Rationing However, if the budget were 15 million rather than 13 million we would have a problem. Adding D would go over the budget and be infeasible, but the combination CDEF has a higher NPV ($22 million) than the chosen combination of ECGF. This is because the amount spent was only 13 million leaving 2 million in unspent funds. In this case, we are better off choosing a combination which spends all the funds. THE ONLY WAY TO DO THIS RIGHT IS TO DO A FULL BLOWN LINEAR PROGRAMING PROBLEM WITH CONSTRAINTS.

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Capital Budgeting We are now ready to consider the capital budgeting decision. As we said repeatedly, the idea is to invest in such a way that you maximize the Net Present Value of your decision. What we mean by the NPV is the Present Value of the Cash Flow from Operations generated by the project less the initial Cash Investment

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**Cougar Enterprises Pro-Forma Income Statement**

(Year ending December 31, 2006) ($ thousand) Sales $5,000 Less: Operating Expenses (COGS) ,000 Depreciation & Amortization Allocated G & A Costs Operating Income (EBIT) $2,200 Less: Interest Expense Earnings Before Tax(taxable income) ,430 Less Tax 40%) Net Income (Earnings after Tax) $858 Earnings per Share (EPS) = Net Income/Shares = $0.858

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**Cougar Enterprises Pro-Forma Cash Flow Statement**

(Year ending December 31, 2006) ($ thousand) Earnings Before Interest and Taxes $2,200 Less: Tax on Operations 40%) (Note: not $572) Operating Income after Tax (EBIT(1-t) ) ,320 Plus: Non-Cash Expenses (Depreciation & Amortization) Less: Change in Working Capital (Change a/c receivable Change in Inventory Change other ST Assets Less: Change in a/c payable Change in ST Liabil (50) Change in Working Capital Free Cash Flow from Operations $1,520 Plus Interest Tax Shield (707 times 0.40) CASH FLOW $1828 Less: Net New Investment (net of capital gains tax) Less: Cash Flow to Bondholders (Interest, principal, Bond Repurchase, Call) Less: Cash Flow to Preferred stockholders Free Cash Flow to Common Stockholders EBITDA ,700

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**Capital Budgeting Decisions Check List**

1. Net Present Value is the "Discounted value of incremental cash flow” 2. Cash flow is: CASH MONEY IN - CASH MONEY OUT

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**Capital Budgeting Decisions Check List**

3. Consider only if it is an incremental cash flow, and consider all incremental cash flows: (a) not historical, or averages; (b) consider only cash flows that appear as a result of the project (c) consider the impact of the project on cash flows from other projects (d) exclude fixed or sunk costs (e) exclude allocated overhead unless it will change as a result of the project.

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**Capital Budgeting Decisions Check List**

4. Treat inflation consistently: Make sure that you have considered the impact of inflation on Cash Flows 5. All Cash Flow should be on an After-Tax basis. Use actual tax changes when paid! Don't forget to allow for the tax on capital gains Use future marginal tax rates applied to future taxable income

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**Capital Budgeting Decisions Check List**

6. Include the opportunity cost of the project, even if there is no explicit cash flow realized Account for assets sold and not sold as a result of adoption of a project. 7. Account for changes in working capital and only changes in working capital. Recognize that working capital will in general be re-cooped at the end of the project. 8. Ignore financing including the tax shield on interest

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**Capital Budgeting Decisions Check List**

9. Include Asset's Entire Life 10. Include the depreciation tax shield, but not depreciation itself.

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**Capital Budgeting Decisions Check List**

No matter how complicated the decision: What is important? MAXIMIZE NPV PLAN TO TAKE ALL PROJECTS WITH A POSITIVE NET PRESENT VALUE AND REJECT ALL PROJECTS WITH A NEGATIVE NET PRESENT VALUE

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**Application of the NPV Rule and Capital Budgeting**

For now we are going to assume that the appropriate discount rate is known. The problem we want to tackle is to forecast the relevant cash flows.

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**Only Cash Flows Affect Wealth.**

What is and is not Cash Flow -Expenses are cash flow regardless of whether the accountant capitalizes and depreciates them or expenses them. -Capital expenditures are cash outflows regardless of the fact that accountants depreciate them over a period.

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**Only Incremental cash flows are relevant**

Not historical cash flows, not averages, not sunk costs! Example 1: Consider a firm having made an investment one year in the past. The project required an initial investment of $10,000- with the expectation of $14,000 to be generated within two years. At a discount rate of 10% should the firm have made the investment?

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**Only Incremental cash flows are relevant**

14,000 10,000 Of course it should have. The NPV was: NPV = 1,564

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**Only Incremental cash flows are relevant**

NOW THINGS CHANGE. A NEW DEVICE INTRODUCED BY A COMPETITOR MAKES THE PRODUCT OBSOLETE. THUS EXPECTED CASH FLOWS DECLINE TO $7,000. THAT IS THE INVESTMENT, DID NOT PAY OFF AS EXPECTED AND THE PROJECT IS NOW A LOSER. SUPPOSE THAT FOR AN ADDITIONAL INVESTMENT OF $5,000, YOU CAN REGAIN YOUR COMPETITIVE POSITION, SO THAT EXPECTED CASH FLOW INCREASES TO THE ORIGINAL $14,000. SHOULD YOU MAKE THE NEW INVESTMENT?

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**Only Incremental cash flows are relevant**

14,000 -10, ,000 Note that the project, looked at as a whole is still a loser: NPV(-1) = -10, , ,000 (1.1) (1.1)2 = - 2,975 BUT the additional investment should be made. Determine the incremental cash flows. Determine Net Present Value of the incremental cash flows Incremental Cash Flow: -5, ,000/(1.1) = 1,363.65

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**Only Incremental cash flows are relevant**

Example 2: Assume that the original cash flow estimates were accurate. But, that you can, by making an additional investment of 1,000 generate total second period cash flow of 15,050. Should the additional investment be made? (Still Assume r= 10%)

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**Only Incremental cash flows are relevant**

14,000 initial -10, ,000 1,050 Incremental -1,000 NPV (of Additional Investment) = = 1.1 Even though, the original project is a winner, do not make the additional investment Y0u must Ignore Sunk Costs, and consider only incremental cash flows.

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**Treat inflation consistently**

MAKE SURE THAT INFLATION IS ACCOUNTED FOR IN A CONSISTENT MANNER. EITHER: Revenues and Expenses are not necessarily effected uniformly by inflation Depreciation expense is not effected by inflation

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**Tying up assets uses a valuable resource and must be accounted for.**

Example: A firm is considering installing a brick manufacturing kiln. The initial investment will require $300,000 in building and equipment. The kiln will be located on a vacant lot having an estimated market value of $1,000,000. The project is expected to generate net cash flow of $50,000 per year for 20 years. After 20 years, the kiln will be worthless. It is anticipated that the lot could be sold for $2,653,000 at the end of 20 years. At a 10% discount rate, is this a good investment? (Ignore taxes)

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**Tying up assets uses a valuable resource and must be accounted for.**

ALTERNATIVE ONE Ignoring the opportunity cost of the (tied-up) land. NET PRESENT VALUE CALCULATION: NPV=-300,000 + PMT(50,000, 10%, 20) =-300, , = 125,693.05 ACCEPT PROJECT The problem with this is that you ignore the fact that you lose the use of $1,000,000 that you could have had if you had not adopted the project and sold the land (or used it in an alternative project).

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**Tying up assets uses a valuable resource and must be accounted for.**

ALTERNATIVE TWO Explicitly consider the land as part of the inputs: You estimate that the land will be worth $2,653,000 in 20 years. PRESENT VALUE CALCULATION: NPV = -1,000, ,000 + PMT(50,000, 10%, 20) + PV($2,653,000, 10%,20) = - 1,300, , ,352 = - 479,970 REJECT PROJECT NOTICE HOW THE TIED UP LAND IS TREATED!

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**Rule 4: Tying up assets uses a valuable resource and must be accounted for.**

Other Incremental Costs Are Increases in overhead costs as a result of project. Increases in working capital as a result of project. Notice the reduction in working capital would be a cash inflow at that time. Do not use allocated overhead, or allocated working capital.

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**Changes in Working Capital Should be accounted for**

Example: Suppose, due to the adoption of the project, the firm is required to increase working capital from $100,000 to $110,000 per annum for the life of the project. How do you account for the working capital? So you see that this is simply a timing problem

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**Remember taxes 1. Calculate all cash flows after taxes**

2. Include non-cash expenses (depreciation) for its effect on taxes, but not as a cash flow itself. HOW TO HANDLE THE DEPRECIATION TAX SHIELD We want the project's AFTER TAX CASH FLOW Equals: Before Tax Cash Flow Less Corporate Taxes Taxes = tc [Cash revenue - Cash Expenses - Depreciation] Therefore, for each year: After Tax Cash Flow =(Cash Revue - Cash Expenses)(1 - tc)+ tc Depr Where: tc x Depr is the Depreciation Tax Shield)

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**Remember taxes on Capital Gains**

3. Tax on gains/losses from sale of assets is an additional negative/positive cash flow Tax on Gains/Losses = tc x (Market Value - Book Value) On sale If Market Value > Book Value, then tax on gain is cash outflow. If Market Value < Book Value, then we have a loss on sale, tax is negative, and there is a cash inflow.

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**Remember taxes on Capital Gains**

Example: XYZ Corp. has a project which is going to last 5 years. P & E for this project of $1,000,000 can assume a scrap value of 300,000 at the end of 5 years. On a straight line basis, that means the firm depreciates the $140,000 per year, leaving 300,000 when the project ends.

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**Remember taxes and the effect of selling assets**

However, you expect that you can sell the asset for $500,000 at the end of 5 years. Thus there is a taxable capital gain of: (MV-BV) = $200,000. At a 35% Corporate Capital Gain Tax rate, that means that after tax cash flow from the disposal of P&E is 0.35 * $200,000 = $70,000 Thus the Cash flow from selling the asset is: $500, ,000 = $430,000 (Remember to add back Book Value)

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**Ignore the means of financing both as a direct cash flow and as its effect on taxes.**

Interest payment is not a cash flow. Discounting already takes the value of time into account. To deduct interest would be double counting. Example: Suppose that you borrow $500, and put in $500 of your money into the following project. (Bank charges 8% on loan) Cash Flow Interest Net To say that we reject the project since NPV (of net cash flow) is negative at 10% (NPV = -13) is double counting. We penalize the project twice, one by deducting interest, second by discounting. The NPV of this project is:- 1,000 + (1,125) X (0.909) = 23

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**STEPS IN PROJECT ANALYSIS**

1. MAKE INITIAL PROJECTIONS Made by operations manager Generally in form of income statement Clarify assumptions 2. ADJUST FOR INFLATION IF APPROPRIATE 3. REARRANGE IN CASH FLOW FORM 4. PERFORM NET PRESENT VALUE CALCULATIONS 5. PERFORM "WHAT IF" CALCULATIONS

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