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**Chapter 10 Making Capital Investment Decisions**

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**I. Discounted cash flow criteria**

Chapter 9 REVIEW I. Discounted cash flow criteria A. Net present value (NPV). The NPV of an investment is the difference between its market value and its cost. The NPV rule is to take a project if its NPV is positive. NPV has no serious flaws; it is the preferred decision criterion. B. Internal rate of return (IRR). The IRR is the discount rate that makes the estimated NPV of an investment equal to zero. The IRR rule is to take a project when its IRR exceeds the required return. When project cash flows are not conventional, there may be no IRR or there may be more than one. C. Profitability index (PI). The PI, also called the benefit-cost ratio, is the ratio of present value to cost. The profitability index rule is to take an investment if the index exceeds 1.0. The PI measures the present value per dollar invested.

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**III. Accounting criterion**

II. Payback criteria A. Payback period. The payback period is the length of time until the sum of an investment’s cash flows equals its cost. The payback period rule is to take a project if its payback period is less than some pre-specified cutoff. B. Discounted payback period. The discounted payback period is the length of time until the sum of an investment’s discounted cash flows equals its cost. The discounted payback period rule is to take an investment if the discounted payback is less than some pre-specified cutoff. III. Accounting criterion A. Average accounting return (AAR). The AAR is a measure of accounting profit relative to book value. The AAR rule is to take an investment if its AAR exceeds a benchmark.

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**Chapter 10 Making Capital Investment Decisions**

Chapter Organization Incremental Cash Flows Terminology Cash Flows vs. Accounting Income Pro Forma Financial Statements and Project Cash Flows More on Project Cash Flows Alternative Definitions of Operating Cash Flow Some Special Cases of Discounted Cash Flow Analysis Summary and Conclusions

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**Fundamental Principles of Project Evaluation: **

Project evaluation - the application of one or more capital budgeting decision rules to estimated relevant project cash flows in order to make the investment decision. Relevant cash flows - the incremental cash flows associated with the decision to invest in a project. The incremental cash flows for project evaluation consist of any and all changes in the firm’s future cash flows that are a direct consequence of taking the project. Stand-alone principle- evaluation of a project based on the project’s incremental cash flows.

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**Incremental Cash Flows**

= cash flow with project - cash flow without project IMPORTANT Ask yourself this question Would the cash flow still exist if the project does not exist? If yes, do not include it in your analysis. If no, include it.

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Terminology A. Sunk costs B. Opportunity costs C. Side effects D. Net working capital E. Financing costs F. Other issues

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A. Sunk costs Suppose $100,000 had been spent last year to improve the production line site. Should this cost be included in the analysis? NO. This is a sunk cost, already spent and irretrievable, so “forget it”, “water under the bridge”, SUNK. Focus on incremental investment and operating cash flows.

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B. Opportunity costs Suppose the plant space could be leased out for $25,000 a year. Would this affect the analysis? Yes. Accepting the project means we will not receive the $25,000. This is an opportunity cost and it should be charged to the project.

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**Net CF loss per year on other lines would be a cost to this project. **

C. Side effects If the new product line would decrease sales of the firm’s other products by $50,000 per year, would this affect the analysis? Yes. The effects on the other projects’ CFs are “externalities” or “spillover effects”. Net CF loss per year on other lines would be a cost to this project. Externalities will be positive if new projects are complements to existing assets, negative if substitutes.

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**NWC = - CA CL D. Net working capital**

= CA CL Usually the LT Investment will also require an increase in Net Working Capital to support the endeavor. For example, there may be an increase in inventories and/or accounts receivable (to cover credit sales). It is also true that these will wind out when the project does. For this reason these cash flows to the project are treated as “loans” to the project. CA - Current Assets CL - Current Liabilities

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**1. Fixed asset spending is zero. **

In estimating cash flows we must account for the fact that some of the incremental sales associated with a project will be on credit, and that some costs won’t be paid at the time of investment. How? Answer: Estimate changes in NWC. Assume: 1. Fixed asset spending is zero. 2. The change in net working capital spending is $200: 0 1 Change A/R $100 $ INV - A/P NWC $150 $ Change in NWC = $200 A/R - Accounts Receivable INV - Inventory A/P - Accounts Payable

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**Should CFs include interest expense? Dividends?**

E. Financing costs Should CFs include interest expense? Dividends? NO. The costs of capital are already incorporated in the analysis since we use them in discounting. If we included them as cash flows, we would be double counting them.

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**Depreciable Basis = Cost + Shipping + Installation**

F. Other issues Depreciation Basics Depreciable Basis = Cost + Shipping + Installation Depreciation is a non-cash deduction, so its cash flow consequences show up in taxes. Tax law governs the method of depreciation. The Tax Reform Act of 1986 involves a modification of the 1981 accelerated cost recovery system (ACRS). The 1986 version is called MACRS or the modified accelerated cost recovery system (MACRS.)

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**T10.7 Modified ACRS Property Classes (Table 10.6)**

Class Examples 3-year Equipment used in research 5-year Autos, computers 7-year Most industrial equipment Under MACRS: First, we classify the asset into an asset class. Then we apply the depreciation allowance in the MACRS to the asset.

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**T10.8 Modified ACRS Depreciation Allowances (Table 10.7)**

Property Class Year Year Year Year % 20.00% % 1986 MACRS Depreciation Schedule

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**Cash flow estimation bias**

CFs are estimated for many future periods. If company has many projects and errors are random and unbiased, errors will cancel out (aggregate NPV estimate will be OK). Studies show that forecasts often are biased upward (overly optimistic revenues, underestimated costs). Agency Problems?

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**What steps can management take to eliminate the incentives for cash flow estimation bias?**

Routinely compare CF estimates with those actually realized and reward managers who are forecasting well, penalize those who are not. When evidence of bias exists, the project’s CF estimates should be lowered or the cost of capital raised to offset the bias.

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Option value Investment in a project may lead to other valuable opportunities. Investment now may extinguish opportunity to undertake same project in the future. True project NPV = NPV + Value of options.

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**Cash Flow -VS- Accounting Income**

Discount actual cash flows Using accounting income, rather than cash flow, could lead to erroneous decisions.

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**Cash Flow -VS- Accounting Income**

Example A project costs $2,000 and is expected to last 2 years, producing cash income of $1,500 and $500 respectively. The cost of the project can be depreciated at $1,000 per year. Given a 10% required return, compare the NPV using cash flow to the NPV using accounting income. | | | -$ $ $500 Depreciate at $1000/year Required Return = 10%

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**Cash Flow -VS- Accounting Income**

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**Cash Flow -VS- Accounting Income**

Accounting NPV = =

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**Cash Flow -VS- Accounting Income**

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**Cash Flow -VS- Accounting Income**

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**Pro Forma Financial Statements and Project Cash Flows**

Suppose we want to prepare a set of pro forma financial statements for a project for Norma Desmond Enterprises. In order to do so, we must have some background information. In this case, assume: 1. Sales of 10,000 $5/unit. 2. Variable cost per unit is $3. Fixed costs are $5,000 per year. The project has no salvage value. Project life is 3 years. 3. Project cost is $21,000. Depreciation is $7,000/year. 4. Additional net working capital is $10,000. 5. The firm’s required return is 20%. The tax rate is 34%. Standardized format for evaluating a project or investment is called a Pro Forma Financial Statement. Once the Pro Forma Financial Statement is in place we can apply the tools of last chapter to do the analysis.

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**Pro Forma Financial Statements Projected Income Statements **

Sales $______ Var. costs ______ $20,000 Fixed costs 5,000 Depreciation 7,000 EBIT $______ Taxes (34%) 2,720 Net income $______ Total Revenues or Total Sales = 10,000 units X $5/unit = $50,000 Total Variable Costs = 10,000 units X $3/unit = $30,000 EBIT = $20,000 - $5,000 - $7000 = $8,000 Net Income = EBIT - ((EBIT)(Tax Rate)) = $8,000 - $2,720 = $5,280

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**Pro Forma Financial Statements**

Projected Income Statements Sales $50,000 Var. costs 30,000 $20,000 Fixed costs 5,000 Depreciation 7,000 EBIT $ 8,000 Taxes (34%) 2,720 Net income $ 5,280

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**Projected Balance Sheets 0 1 2 3 NWC $______ $10,000 $10,000 $10,000 **

NWC $______ $10,000 $10,000 $10,000 NFA 21,000 ______ ______ 0 Total Invest $31,000 $24,000 $17,000 $10,000 Remember that Net Working Capital plus Net Fixed Assets = Total Investment So easy to fill in the blanks here.

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**Projected Balance Sheets**

NWC $10,000 $10,000 $10,000 $10,000 NFA 21, ,000 7,000 0 Total $31,000 $24,000 $17,000 $10,000

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**Project operating cash flow (OCF): EBIT $8,000 Depreciation +7,000 **

Now let’s use the information from the previous example to do a capital budgeting analysis. Project operating cash flow (OCF): EBIT $8,000 Depreciation +7,000 Taxes -2,720 OCF $12,280 P Project Operating Cash Flow OCF = EBIT + Depreciation - Taxes

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**Total ______ $12,280 $12,280 $______**

Project Cash Flows OCF $12,280 $12,280 $12,280 Chg. NWC ______ ______ Cap. Sp. -21,000 Total ______ $12,280 $12,280 $______ Chg. NWC = - $10,000 from “0” so “$10k” from the get go. So total in period “0” is -$31,000. Chg. NWC = + $10,000 from “2” so the “$10k” is recovered at the end of project. So total in period “2” is + $22,280. See Next Slide!

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Project Cash Flows OCF $12,280 $12,280 $12,280 Chg. NWC -10, ,000 Cap. Sp. -21,000 Total -31,000 $12,280 $12,280 $22,280

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**Capital Budgeting Evaluation:**

NPV = -$31,000 + $12,280/ $12,280/ $22,280/ = $655 IRR = 21% PBP = 2.3 years AAR = $5280/{(31, , , ,000)/4} = 25.76% Should the firm invest in this project? Why or why not? Yes -- the NPV > 0, and the IRR > required return

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Proposed Project Cost: $200,000 + $10,000 shipping +$30,000 installation. Depreciable cost $240,000. Inventories will rise by $25,000 and payables will rise by $5,000. Economic life = 4 years. Salvage value = $25,000. MACRS 3-year class.

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**Incremental gross sales = $250,000.**

Incremental cash operating costs = $125,000. Tax rate = 40%. Cost of capital = WACC = 10%

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**Set up without numbers a time line for the project CFs.**

1 2 3 4 Initial Outlay OCF1 OCF2 OCF3 OCF4 + Terminal CF Economic Life is 4 years. So, intial outlay and four years of cash flows and the terminal cash flow. NCF0 NCF1 NCF2 NCF3 NCF4

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**What is the annual depreciation?**

Year Rate x Basis Depreciation $240 $ 79 $240 Due to half-year convention, a 3-year asset is depreciated over 4 years. Using MACRS for a 3 year class. Rates are in table above. Half-year convention “meaning that all assets are assumed to be placed in service midway through the tax year” p. 290 footnote #11

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**Operating cash flows ($000): 1 2 3 4 Sales $250 $250 $250 $250 **

Sales $250 $250 $250 $250 Cash costs Depreciation EBIT $ 46 $ 17 $ 89 $108 Taxes (40%) Net Income Add: Depreciation Operating Cash flow $107 $118 $ 89 $ 82 Sales come from incremental gross sales $250,000 Cash Costs from incremental cash operating costs $125,000 DATA ON SLIDE 36 Depreciation calculated from the MACRS 3-year class table DATA FROM SLIDE 38 EBIT = TR-TC-Depreciation DEFINITION Tax Rate given as 40% Net Income = EBIT - Taxes Operating Cash Flow = EBIT + Depreciation - Taxes DEFINITION AND DATA ON SLIDE 36

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**Net Investment Outlay At t=0**

Equipment Ship + Install Change in NWC Net CF0 ($200,000) (40,000) (20,000) ($260,000) Change in NWC is the increase in inventories held ($25,000) [“dollars out”] offset by the rise in payables or accounts receivable ($5000) [“dollars in”] DATA ON SLIDE 35 NWC = $25,000 - $5,000

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**Net Terminal Cash Flow At t = 4**

Salvage value Tax on SV Recovery on NWC Net Termination CF $25,000 (10,000) 20,000 $35,000 Salvage Value is listed in the information as $25,000 DATA ON SLIDE 35 Pull out 40% for taxes on the Salvage Value (God Bless the IRS!) Recover your NWC as you always do and the Net CF upon Termination is calculated as $35,000

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**Project net CFs on a time line:**

(260) Enter CFs in CFLO register and I = 10. NPV = $81,573 IRR = 23.8%

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**What is the project’s MIRR?**

(260) 97.9 142.8 142.4 500.1 1) Find PV of all cash outflows at the firm’s required return (cost of capital). Often the only cash outflow is the initial investment. If other compute them as well. 2) Find the FV of all cash inflows at the firm’s required return (cost of capital). All positive CFs are compounded to the point in time at which the last CF is received. This is called the “terminal value” or TV 3) Compute the yield that sets the PV of the inflows equal to the PV of the outflows. This yield is the MIRR. TV= [$107(1.1)^3 + $118(1.1)^2 + $89(1.1) + $117] = $ = $500.10 Now compute the I-rate that will set the intial -$260 cash outflow (initial investment) equal to the terminal value of $500.10 2nd {CLR TVM} CE/C -260 PV FV 4 N 0 PMT CPT I/Y 17.77 The MIRR solves the reinvestment rate assumption problem by compounding at the cost of capital. It also solves the multiple rates or return problem with IRR. It cannot be used to rank projects due to its inability to distinguish between large and small scale projects (same as IRR). USE NPV. (260) MIRR = ?

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**What is the project’s payback?**

(260) (260) = (153) (153) = (35) 35/89 = 0.4 Payback = 2.4 years Cumulative: (260) (153) (35) Payback = /89 = 2.4 years

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**If this were a replacement rather than a new project, **

would the analysis change? Yes. The old equipment would be sold and the incremental CFs would be the changes from the old to the new situation.

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**The relevant depreciation would be the change with the new equipment.**

Also, if the firm sold the old machine now, it would not receive the salvage value at the end of the machine’s life.

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**T10.15 Alternative Definitions of OCF (concluded)**

The Tax-Shield Approach OCF = (S - C - D) + D - (S - C - D) T = (S - C) (1 - T) + (D T) = (S - C) (1 - T) + Depreciation x T The Bottom-Up Approach OCF = (S - C - D) + D - (S - C - D) T = (S - C - D) (1 - T) + D = Net income + Depreciation The Top-Down Approach = (S - C) - (S - C - D) T = Sales - Costs - Taxes

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**T10.16 Chapter 10 Quick Quiz -- Part 1 of 3**

Now let’s put our new-found knowledge to work. Assume we have the following background information for a project being considered by Gillis, Inc. See if we can calculate the project’s NPV and payback period. Assume: Required NWC investment = $40; project cost = $60; 3 year life Annual sales = $100; annual costs = $50; straight line depreciation to $0 Tax rate = 34%, required return = 12% Step 1: Calculate the project’s OCF OCF = (S - C)(1 - T) + Dep T OCF = (___ - __)( ) + (____)(.34) = $_____

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**T10.16 Chapter 10 Quick Quiz -- Part 1 of 3 (concluded)**

Project cash flows are thus: OCF $39.8 $39.8 $39.8 Chg. in NWC Cap. Sp. -60 -$100 $39.8 $39.8 $79.8 Payback period = ___________ NPV = ____________

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**T10.17 Example: A Cost-Cutting Proposal**

Consider a $10,000 machine that will reduce pretax operating costs by $3,000 per year over a 5-year period. Assume no changes in net working capital and a scrap (i.e., market) value of $1,000 after five years. For simplicity, assume straight-line depreciation. The marginal tax rate is 34% and the appropriate discount rate is 10%. Using the tax-shield approach to find OCF: OCF = (S - C)(1 - T) + (Dep T) = [$0 - (-3,000)](.66) + (2,000 .34) = $1,980 + $680 = $2,660 The after-tax salvage value is: market value - (increased tax liability) = market value - (market value - book) T = $1,000 - ($1, )(.34) = $660

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**T10.17 Example: A Cost-Cutting Proposal (concluded)**

The cash flows are Year OCF Capital spending Total 0 $ $10,000 -$10,000 1 2, ,660 2 2, ,660 3 2, ,660 4 2, ,660 5 2, ,320

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**T10.18 Chapter 10 Quick Quiz -- Part 2 of 3**

Evaluating Cost Cutting Proposals Cost = $900,000 Depreciation = $180,000 per year Life = 5 years Salvage = $330,000 Cost savings = $500,000 per year, before taxes Tax rate = 34 percent Add. to NWC = –$220,000 (note the minus sign) 1. After-tax cost saving: $500K (______) = $______ per year. 2. Depreciation tax shield: $180K ______ = $______ per year. 3. After-tax salvage value: $330K - ($330K - 0)(.34) = $______

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**T10.18 Chapter 10 Quick Quiz -- Part 2 of 3 (concluded)**

AT saving $330.0K $330.0K $330.0K $330.0K $330.0K Tax shield 61.2K 61.2K 61.2K 61.2K 61.2K OCF _____ _____ $391.2K $391.2K $391.2K Chg. in NWC ____ _____ Cap. Sp. -900K K - ____ $391.2K $391.2K $391.2K $391.2K _____

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**T10.19 Example: Setting the Bid Price**

The Army is seeking bids on Multiple Use Digitizing Devices (MUDDs). The contract calls for 4 units per year for 3 years. Labor and material costs are estimated at $10,000 per MUDD. Production space can be leased for $12,000 per year. The project will require $50,000 in new equipment which is expected to have a salvage value of $10,000 after 3 years. Making MUDDs will require a $10,000 increase in net working capital. Assume a 34% tax rate and a required return of 15%. Use straight-line depreciation to zero. Operating Increases Capital Total Year cash flow in NWC spending = cash flow 0 $ – $10,000 – $50,000 – $60,000 1 OCF 0 0 OCF 2 OCF 0 0 OCF 3 OCF 10, ,600 OCF + 16,600

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**T10.19 Example: Setting the Bid Price (continued)**

Taking the present value of $16,600 in year 3 ( = $10,915 at 15%) and netting against the initial outlay of – $60,000 gives Total Year cash flow 0 – $49,085 1 OCF 2 OCF 3 OCF The result is a three-year annuity with an unknown cash flow equal to “OCF.”

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**T10.19 Example: Setting the Bid Price (continued)**

The PV annuity factor for 3 years at 15% is Setting NPV = $0, NPV = $0 = – $49,085 + (OCF 2.283), thus OCF = $49,085/2.283 = $21,500 Using the bottom-up approach to calculate OCF, OCF = Net income + Depreciation $21,500 = Net income + $50,000/3 = Net income + $16,667 Net income = $4,833 Next, since annual costs are $40,000 + $12,000 = $52,000 Net income = (S - C - D) (1 - T) $4,833 = (S .66) - (52,000 .66) - (16,667 .66) S = $50,153/.66 = $75, Hence, sales need to be at least $76,000 per year (or $19,000 per MUDD)!

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**T10.19 Example: Setting the Bid Price (continued)**

Background: Suppose we also have the following information. 1. The bid calls for 20 MUDDs per year for 3 years. 2. Our costs are $35,000 per unit. 3. Capital spending required is $250,000; and depreciation = $250,000/5 = $50,000 per year 4. We can sell the equipment in 3 years for half its original cost: $125,000. 5. The after-tax salvage value equals the cash in from the sale of the equipment, less the cash out due to the increase in our tax liability associated with the sale of the equipment for more than its book value: Book value at end of 3 years = $250, ,000(3) = $100,000 Book gain from sale = $125, ,000 = $25,000 Net cash flow = $125, ,000(.39) = $115,250 6. The project requires investment in net working capital of $60,000. 7. Required return = 16%; tax rate = 39%

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**T10.19 Example: Setting the Bid Price (continued)**

The cash flows ($000) are: OCF $OCF $OCF $OCF Chg. in NWC - $ Capital Spending ______ ______ - $310 $OCF $OCF $OCF + 175.25 Find the OCF such that the NPV is zero at 16%: +$310, ,250/1.163 = OCF (1 - 1/1.163)/.16 $197, = OCF OCF = $88,038.50/year

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**T10.19 Example: Setting the Bid Price (concluded)**

If the required OCF is $88,038.50, what price must we bid? Sales $_________ Costs 700,000.00 Depreciation 50,000.00 EBIT $_________ Tax 24,319.70 Net income $ 38,038.50 Sales = $62, , ,000 = $812, per year, and the bid price should be $812,358.20/___ = ________ per unit.

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**T10.20 Example: Equivalent Annual Cost Analysis**

Two types of batteries are being considered for use in electric golf carts at City Country Club. Burnout brand batteries cost $36, have a useful life of 3 years, will cost $100 per year to keep charged, and have a salvage value of $5. Longlasting brand batteries cost $60 each, have a life of 5 years, will cost $88 per year to keep charged, and have a salvage value of $5.

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**T10.20 Example: Equivalent Annual Cost Analysis (continued)**

Using the tax shield approach, cash flows for Burnout are: OCF = (Sales - Costs)(1 - T) + Depreciation(T) = ( )(.66) + 12(.34) = -$ = -$62 Operating Capital Total Year cash flow - spending = cash flow 0 $ 0 -$ 36 -$36

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**T10.20 Example: Equivalent Annual Cost Analysis (continued)**

Again using the tax shield approach, OCFs for Longlasting are: OCF = (Sales - Costs)(1 - T) + Depreciation(T) = (0 - 88)(.66) + 12(.34) = -$ = -$54 Operating Capital Total Year OCF spending = cash flow 0 $ 0 -$ $60

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**T10.20 Example: Equivalent Annual Cost Analysis (continued)**

Using a 15% required return, calculate the cost per year for the two batteries. Calculate the PV of the cash flows: The present value of total cash flows for Burnout is -$175.40 The present value of total cash flows for Longlasting is -$239.40

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**T10.20 Example: Equivalent Annual Cost Analysis (concluded)**

What 3 year annuity has the same PV as Burnout? The PV annuity factor for 3 years at 15% is 2.283: -$ = EAC EAC = -$175.40/2.283 = -$76.83 What 5 year annuity has the same PV as Longlasting? The PV annuity factor for 5 years at 15% is 3.352: -$ = EAC 3.352 EAC = -$239.40/3.352 = -$71.42

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**T10.21 Chapter 10 Quick Quiz -- Part 3 of 3**

Here’s one more problem to test your skills. Von Stroheim Manufacturing is considering investing in a lathe that is expected to reduce costs by $70,000 annually. The equipment costs $200,000, has a four-year life (but will be depreciated as a 3-year MACRS asset), requires no additional investment in net working capital, and has a salvage value of $50,000. The firm’s tax rate is 39% and the required return on investments in this risk class is 10%. What is the NPV of the project? What is its IRR?

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**T10.21 Chapter 10 Quick Quiz -- Part 3 of 3 (continued)**

Depreciation: Year Dep (%) Dep ($) % $_______ % 88,880 % 29,640 4 7.41% 14,820 100% $200,000 The after-tax salvage is $50,000 - ($50, ) _____= $30,500

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**T10.21 Chapter 10 Quick Quiz -- Part 3 of 3 (concluded)**

The cash flows are thus: AT saving $42,700.0 $42,700.0 $42, $42,700.0 Tax shield 25, , , ,779.8 OCF $68,697.4 $77,363.2 $54,259.6 $48,479.8 Cap. Sp. -200, _______ -$200,000 $68,697.4 $77,363.2 $54, $_______ NPV = $_________ IRR = ________%

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