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**Capital Budgeting - Decision Criteria**

C1 Outline Capital Budgeting - Decision Criteria Net Present Value The Payback Rule The Discounted Payback The Average Accounting Return The Internal Rate of Return The Profitability Index The Practice of Capital Budgeting

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C2 Outline (continued) Project Cash Flows: A First Look Incremental Cash Flows 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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**Assume you have the following information on Project X: **

C3 NPV Illustrated 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 , ,000 Draw a time line and compute the NPV of project X.

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**C4 NPV Illustrated (concluded)**

1 2 Initial outlay ($1,100) Revenues $1,000 Expenses 500 Cash flow $500 Revenues $2,000 Expenses 1,000 Cash flow $1,000 – $1,100.00 +$181.00 1 $500 x 1.10 1 $1,000 x 1.10 2 NPV

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**C5 Underpinnings of the NPV Rule**

Why does the NPV rule work? And what does “work” mean? Look at it this way: A “firm” is created when securityholders supply the funds to acquire assets that will be used to produce and sell a good or a service; The market value of the firm is based on the present value of the cash flows it is expected to generate; Additional investments are “good” if the present value of the incremental expected cash flows exceeds their cost; Thus, “good” projects are those which increase firm value - or, put another way, good projects are those projects that have positive NPVs! Moral of the story: Invest only in projects with positive NPVs.

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**C6 Payback Rule Illustrated**

Initial outlay -$1,000 Year Cash flow 1 $200 2 400 3 600 Accumulated 2 600 3 1,200 Payback period = 2 2/3 years

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**C7 Discounted Payback Illustrated**

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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**C8 Ordinary and Discounted Payback**

Cash Flow Accumulated Cash Flow Year Undiscounted Discounted Undiscounted Discounted 1 $100 $89 $100 $89

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**C9 Average Accounting Return Illustrated**

Average net income: Year Sales $440 $240 $160 Costs Gross profit Depreciation Earnings before taxes Taxes (25%) Net income $105 $30 $0 Average net income = ($ )/3 = $45

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**C10 Average Accounting Return Illustrated (concluded)**

Average book value: Initial investment = $240 Average investment = ($ )/2 = $120 Average accounting return (AAR): Average net income $45 AAR = = = 37.5% Average book value $120

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**C11 Internal Rate of Return Illustrated**

Initial outlay = -$200 Year Cash flow 1 $ 50 2 100 3 150 Find the IRR such that NPV = 0 0 = (1+IRR) (1+IRR) (1+IRR)3 200 = (1+IRR) (1+IRR) (1+IRR)3

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**C12 Internal Rate of Return Illustrated (concluded)**

Trial and Error Discount rates NPV 0% $100 5% 68 10% 41 15% 18 20% -2 IRR is just under 20% -- about 19.44%

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**C13 Net Present Value Profile**

120 Year Cash flow 0 – $275 1 100 2 100 3 100 4 100 100 80 60 40 20 – 20 – 40 Discount rate 2% 6% 10% 14% 18% 22% IRR

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**C14 Multiple Rates of Return**

Assume you are considering a project for which the cash flows are as follows: Year Cash flows $252 ,431 ,035 ,850 ,000

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**C15 Multiple Rates of Return (continued)**

What’s the IRR? Find the rate at which the computed NPV = 0: at 25.00%: NPV = _______ at 33.33%: NPV = _______ at 42.86%: NPV = _______ at 66.67%: NPV = _______

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**C16 Multiple Rates of Return (continued)**

What’s the IRR? Find the rate at which the computed NPV = 0: at 25.00%: NPV = at 33.33%: NPV = at 42.86%: NPV = at 66.67%: NPV = Two questions: 1. What’s going on here? 2. How many IRRs can there be?

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**C17 Multiple Rates of Return (concluded)**

NPV $0.06 $0.04 IRR = 1/4 $0.02 $0.00 ($0.02) IRR = 1/3 IRR = 2/3 IRR = 3/7 ($0.04) ($0.06) ($0.08) 0.2 0.28 0.36 0.44 0.52 0.6 0.68 Discount rate

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**C18 IRR, NPV, and Mutually Exclusive Projects**

Net present value Year Project A: – $ Project B: – $ 160 140 120 100 80 60 40 Crossover Point 20 – 20 – 40 – 60 – 80 – 100 Discount rate 2% 6% 10% 14% 18% 22% 26% IRR A IRR B

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**C19 Profitability Index Illustrated**

Now let’s go back to the initial example - we assumed the following information on Project X: Initial outlay -$1,100 Required return = 10% Annual cash benefits: Year Cash flows 1 $ 500 ,000 What’s the Profitability Index (PI)?

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**C20 Profitability Index Illustrated (concluded)**

Previously we found that the NPV of Project X is equal to: ($ ) - 1,100 = $1, ,100 = $ The PI = PV inflows/PV outlay = $1,281.00/1,100 = This is a good project according to the PI rule. Can you explain why? It’s a good project because the present value of the inflows exceeds the outlay.

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**C21 Summary of Investment Criteria**

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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**C22 Summary of Investment Criteria (concluded)**

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 prespecified 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 prespecified 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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C23 A Quick Quiz 1. Which of the capital budgeting techniques do account for both the time value of money and risk? 2. The change in firm value associated with investment in a project is measured by the project’s _____________ . a. Payback period b. Discounted payback period c. Net present value d. Internal rate of return 3. Why might one use several evaluation techniques to assess a given project?

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C24 A Quick Quiz 1. Which of the capital budgeting techniques do account for both the time value of money and risk? Discounted payback period, NPV, IRR, and PI 2. The change in firm value associated with investment in a project is measured by the project’s Net present value. 3. Why might one use several evaluation techniques to assess a given project? To measure different aspects of the project; e.g., the payback period measures liquidity, the NPV measures the change in firm value, and the IRR measures the rate of return on the initial outlay.

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**Year Cash Flows A Cash Flows B 0 -$30,000 -$45,000 1 15,000 5,000 **

C25 Problem Offshore Drilling Products, Inc. imposes a payback cutoff of 3 years for its international investment projects. If the company has the following two projects available, should they accept either of them? Year Cash Flows A Cash Flows B 0 -$30,000 -$45,000 , ,000 , ,000 , ,000 , ,000

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**C26 Solution to Problem (concluded)**

Project A: Payback period = ($30, ,000)/10,000 = 2.50 years Project B: Payback period = ($45, ,000)/$250,000 = years Project A’s payback period is 2.50 years and project B’s payback period is 3.04 years. Since the maximum acceptable payback period is 3 years, the firm should accept project A and reject project B.

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C27 Another Problem A firm evaluates all of its projects by applying the IRR rule. If the required return is 18 percent, should the firm accept the following project? Year Cash Flow 0 -$30,000 ,000 2 0 ,000

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**C28 Another Problem (continued)**

To find the IRR, set the NPV equal to 0 and solve for the discount rate: NPV = 0 = -$30, $25,000/(1 + IRR)1 + $0/(1 + IRR) $15,000/(1 + IRR)3 At 18 percent, the computed NPV is ____. So the IRR must be (greater/less) than 18 percent. How did you know?

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**C29 Another Problem (concluded)**

To find the IRR, set the NPV equal to 0 and solve for the discount rate: NPV = 0 = -$30, $25,000/(1 + IRR)1 + $0/(1 + IRR) $15,000/(1 + IRR)3 At 18 percent, the computed NPV is $316. So the IRR must be greater than 18 percent. We know this because the computed NPV is positive. By trial-and-error, we find that the IRR is percent.

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**T30 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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**T31 Incremental Cash Flows**

Key issues: When is a cash flow incremental? Terminology A. Sunk costs B. Opportunity costs C. Side effects D. Net working capital E. Financing costs F. Other issues

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**T32 Example: Preparing Pro Forma Statements**

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%.

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**T33 Example: Preparing Pro Forma Statements (continued)**

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 $______

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**T34 Example: Preparing Pro Forma Statements (continued)**

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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**T35 Example: Preparing Pro Forma Statements (concluded)**

Projected Balance Sheets NWC $______ $10,000 $10,000 $10,000 NFA 21,000 ______ ______ 0 Total $31,000 $24,000 $17,000 $10,000

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**T36 Example: Preparing Pro Forma Statements (concluded)**

Projected Balance Sheets NWC $10,000 $10,000 $10,000 $10,000 NFA 21,000 14,000 7,000 0 Total $31,000 $24,000 $17,000 $10,000

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**T37 Example: Using Pro Formas for Project Evaluation**

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

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**T38 Example: Using Pro Formas for Project Evaluation (continued)**

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

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**T39 Example: Using Pro Formas for Project Evaluation (continued)**

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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**T40 Example: Using Pro Formas for Project Evaluation (concluded)**

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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**T41 Example: Estimating Changes in Net Working Capital**

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 S/U A/R $100 $ ___ INV ___ -A/P (50) ___ NWC $100 $ Chg. NWC = $_____

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**T42 Example: Estimating Changes in Net Working Capital**

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 S/U A/R $100 $ U INV U -A/P (50) U NWC $100 $ Chg. NWC = $200

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**T43 Example: Estimating Changes in Net Working Capital (continued)**

Now, estimate operating and total cash flow: Sales $300 Costs 200 Depreciation 0 EBIT $100 Tax 0 Net Income $100 OCF = EBIT + Dep. Taxes = $100 Total Cash flow = OCF Change in NWC Capital Spending = $100 ______ ______ = ______

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**T44 Example: Estimating Changes in Net Working Capital (continued)**

Now, estimate operating and total cash flow: Sales $300 Costs 200 Depreciation 0 EBIT $100 Tax 0 Net Income $100 OCF = EBIT + Dep. Taxes = $100 Total Cash flow = OCF Change in NWC Capital Spending = $100 = $100

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**T45 Example: Estimating Changes in Net Working Capital (concluded)**

Where did the - $100 in total cash flow come from? What really happened: Cash sales = $300 - ____ = $200 (collections) Cash costs = $200 + ____ + ____ = $300 (disbursements)

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**T46 Example: Estimating Changes in Net Working Capital (concluded)**

Where did the - $100 in total cash flow come from? What really happened: Cash sales = $ = $200 (collections) Cash costs = $ = $300 (disbursements) Cash flow = $ = - $100 (= cash in cash out)

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**T47 Modified ACRS Property Classes**

Class Examples 3-year Equipment used in research 5-year Autos, computers 7-year Most industrial equipment

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**T48 Modified ACRS Depreciation Allowances**

Property Class Year Year Year Year % 20.00% 14.29%

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**T49 MACRS Depreciation: An Example**

Calculate the depreciation deductions on an asset which costs $30,000 and is in the 5-year property class: Year MACRS % Depreciation 1 20% $_____ 2 32% _____ % 5,760 % 3,456 % 3,456 6 5.76% 1,728 100% $ _____

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**T50 MACRS Depreciation: An Example**

Calculate the depreciation deductions on an asset which costs $30,000 and is in the 5-year property class: Year MACRS % Depreciation 1 20% $6,000 2 32% 9,600 % 5,760 % 3,456 % 3,456 6 5.76% 1,728 100% $30,000

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**T51 Example: Fairways Equipment and Operating Costs**

Two golfing buddies are considering opening a new driving range, the “Fairways Driving Range” (motto: “We always treat you fairly at Fairways”). Because of the growing popularity of golf, they estimate the range will generate rentals of 20,000 buckets of balls at $3 a bucket the first year, and that rentals will grow by 750 buckets a year thereafter. The price will remain $3 per bucket. Capital spending requirements include: Ball dispensing machine $ 2,000 Ball pick-up vehicle ,000 Tractor and accessories ,000 $18,000 All the equipment is 5-year ACRS property, and is expected to have a salvage value of 10% of cost after 6 years. Anticipated operating expenses are as follows:

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**T52 Example: Fairways Equipment and Operating Costs (concluded)**

Operating Costs (annual) Land lease $ 12,000 Water 1,500 Electricity 3,000 Labor 30,000 Seed & fertilizer 2,000 Gasoline 1,500 Maintenance 1,000 Insurance 1,000 Misc. Expenses 1,000 $53,000 Working Capital Initial requirement = $3,000 Working capital requirements are expected to grow at 5% per year for the life of the project

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**T53 Example: Fairways Revenues, Depreciation, and Other Costs**

Projected Revenues Year Buckets Revenues 1 20,000 $60,000 2 20,750 62,250 3 21,500 64,500 4 22,250 66,750 5 23,000 69,000 6 23,750 71,250

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**Cost of balls and buckets Year Cost 1 $3,000 2 3,150 3 3,308 4 3,473 **

T54 Example: Fairways Revenues, Depreciation, and Other Costs (continued) Cost of balls and buckets Year Cost 1 $3,000 2 3,150 3 3,308 4 3,473 5 3,647 6 3,829

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**Depreciation on $18,000 of 5-year equipment **

T55 Example: Fairways Revenues, Depreciation, and Other Costs (concluded) Depreciation on $18,000 of 5-year equipment Year ACRS % Depreciation Book value $3,600 $14,400 ,760 8,640 ,456 5,184 ,074 3,110 ,074 1,036 ,036 0

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**T56 Example: Fairways Pro Forma Income Statement**

Year Revenues $60,000 $62,250 $64,500 $66,750 $69,000 $71,250 Variable costs 3,000 3,150 3,308 3,473 3,647 3,829 Fixed costs 53,000 53,000 53,000 53,000 53,000 53,000 Depreciation 3,600 5,760 3,456 2,074 2,074 1,036 EBIT $ $ $ 4,736 $ 8,203 $10,279 $13,385 Taxes ,230 1,542 2,008 Net income $ $ $ 4,026 $ 6,973 $ 8,737 $11,377

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**T57 Example: Fairways Projected Changes in NWC**

Projected increases in net working capital Year Net working capital Change in NWC 0 $ 3,000 $ 3,000 1 3, 2 3, 3 3, 4 3, 5 3, 6 4, ,829

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**T58 Example: Fairways Cash Flows**

Operating cash flows: Operating Year EBIT + Depreciation – Taxes = cash flow 0 $ $ $ $ , ,940 , ,049 3 4,736 3, ,482 4 8,203 2,074 1,230 9,047 5 10,279 2,074 1,542 10,811 6 13,385 1,036 2,008 12,413

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**T59 Example: Fairways Cash Flows (concluded)**

Total cash flow from assets: Year OCF – Chg. in NWC – Cap. Sp. = Cash flow 0 $ $ 3,000 $18,000 – $21,000 1 3, ,790 2 6, ,891 3 7, ,317 4 9, ,873 5 10, ,629 6 12,413 – 3,829 – 1,530 17,772

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**T60 Alternative Definitions of OCF**

Let: OCF = operating cash flow S = sales C = operating costs D = depreciation T = corporate tax rate

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**T61 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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**Step 1: Calculate the project’s OCF OCF = (S - C)(1 - T) + Dep T **

T62 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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**Step 1: Calculate the project’s OCF OCF = (S - C)(1 - T) + Dep T **

T63 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 = ( )( ) + (60/3)(.34) = $39.80

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**T64 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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**T65 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 = (100 – 79.6)/79.8 = 2.26 years NPV = $39.8/(1.12) + $39.8/(1.12) /(1.12) = $24.06

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