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FIN 468: Intermediate Corporate Finance Topic 3–Capital Budgeting Larry Schrenk, Instructor 1 (of 22) Topics Review of Decision Rules Incremental Cash Flow Analysis Model to Value the Net Cash Flows Investments of Unequal Lives Decision Rules Decision Rules Payback Period Discounted Payback Period Net Present Value (NPV) Internal Rate of Return (IRR) Modified Internal Rate of Return (MIRR) Criteria for Decision Rules Recognize the time value of money Incorporate all relevant free cash flows Minimize arbitrary assumptions Minimize need for uncertain data Minimize excessive calculation complexity Minimize problems Data For simplicity, we shall use the following cash flows for many of our examples (r = 10%): 0 -1,000 1 300 2 200 3 400 4 700 Payback Period EXAMPLE: 0 -1,000 2 200 3 400 4 700 3 Year Payback Period Calculation 1 300 300 + 200 + 400 = 900 < 1,000 Result: $900.00 < $1,000.00 Bad Project Discounted Payback Period EXAMPLE (r = 10%): 0 -1,000 1 300 2 200 3 400 4 700 3 Year Discounted Payback Period Calculation: 300.00 200.00 400.00 $738.54 $1,000.00 2 3 1.1 1.1 1.1 Result: $738.54 < $1,000.00 Bad Project Net Present Value (NPV) EXAMPLE (r = 10%): 0 -1,000 1 300 2 200 3 400 4 700 NPV Calculation: 300.00 200.00 400.00 700.00 1,000 $216.65 0 2 3 4 1.1 1.1 1.1 1.1 Result: $216.65 > 0 Good Project Internal Rate of Return (IRR) EXAMPLE (r = 10%): 0 -1,000 1 300 2 200 3 400 4 700 IRR Calculation: 300.00 200.00 400.00 700.00 1,000 0 2 3 4 1 IRR 1 IRR 1 IRR 1 IRR iff IRR = 18.1% 18.1% > 10% Result: 18.1% > 10% Good Project Modified Internal Rate of Return EXAMPLE (r = 10%): 0 -1,000 1 300 2 200 3 400 4 700 Find the MIRR that makes the present value of all cash outflows equal to the present value of the terminal value. $1,781.30 MIRR s.t 1,000 (1 MIRR )4 MIRR 15.53% Result: 15.53% > 10% Good Project Summary of the Five Rules Ineffective Rules: Payback Period: Payback period cash flow > investment Discounted Payback Period: Discounted payback period cash flow > investment Effective Rules NPV: NPV > 0 IRR: IRR > r MIRR: MIRR > r Some Additional Issues Some Additional Issues Comparing NPV, IRR, PI and MIRR Using Decision Rules to Compare or Select among Projects Sign Changes in the Cash Flows and Multiple IRR’s Capital Budgeting 15 (of 22) Topics Two General Principles Factors in Cash Flow Analysis Fixed versus Variable Costs Depreciation Working Capital Taxes Interest Payments and Financing Costs Sunk Costs Opportunity Costs Externalities Two General Principles Principle One: Use Increments. The Incremental Approach to Cash Flow Analysis Principle Two: Use Real Cash Flows. Real versus Accounting Cash Flows The Incremental Approach The Incremental Approach to Cash Flow Analysis Incremental: How real cash flows change Alternate: Averages Comparison Example New Project Costs Cost Before Furniture $10,000 Software $9,000 Insurance $4,000 After $12,000 $9,000 $6,000 Average Increment Comparison Example Average Approach Cost Before Furniture $10,000 Software $9,000 Insurance $4,000 After $12,000 $9,000 $6,000 Average $4,000 $3,000 $2,000 Increment Comparison Example Incremental Approach Cost change in costs, i.e., the increment, associated with the new project: Before Furniture $10,000 Software $9,000 Insurance $4,000 After $12,000 $9,000 $6,000 Average $4,000 $3,000 $2,000 Increment $2,000 $0 $2,000 Comparison Example Conclusion: Use the increment Cost Before Furniture $10,000 Software $9,000 Insurance $4,000 After $12,000 $9,000 $6,000 Average $4,000 $3,000 $2,000 Increment $2,000 $0 $2,000 Real versus Accounting Values Real: Actual transfers of value at this time; Market values Money, assets, etc. Accrual Accounting May not be market values Goodwill, depreciation May not be current ‘accrued’, ‘payable’ NOTE: Possible ambiguity… Real versus Accounting Real versus Nominal Real versus Accounting Example Payment of $6,000 for insurance over the next three years. Accounting Real Real versus Accounting Example Accrual Accounting Cash Flow ‘Matching’ Profit Accounting $2,000 $2,000 $2,000 Real Real versus Accounting Example Real Cash Flow Accounting Real $2,000 $6,000 $2,000 $0 $2,000 $0 Real versus Accounting Cash Flows A Complication Non-real cash flow has an effect on a real cash flow. Incorporate the effect, but not non-real cash flow itself. Depreciation Factors in Cash Flow Analysis Factors in Cash Flow Analysis Depreciation Working Capital Taxes Interest Payments and Financing Costs Sunk Costs Opportunity Costs Externalities Depreciation Depreciation Depreciation not real cash flow! Effects on real cash flow, i.e., taxes If a firm had no taxable income, then we could ignore depreciation. Incorporate the tax effect of depreciation not the depreciation itself. Classes of Expenditures Costs: ‘expensed’ In theory, the value is exhausted during that one period E.g. Stationary, production materials, etc. Deductible Investments: Over time. In theory, the value is exhausted over multiple periods. E.g. Factory equipment, computers, etc. Non-Deductible Investments: Never In theory, the value is never exhausted E.g. Land Depreciation Different methods (‘schedules’) and over different lengths of time. MARCS Example Schedule 1 2 3 4 20% 32% 19.2% 11.52% 11.52% 5.76% Capital investment $1,000,000 Yearly depreciation is: 1 2 3 4 5 5 6 6 $200,000 $320,000 $192,000 $115,200 $115,200 $57,600 For More Depreciation Details… If you actually want to know more… To dip in your toe: http://www.irs.gov/businesses/small/article/0,,id=137026,00.html Not for the faint of heart: Publication 946 (2005), How To Depreciate Property http://www.irs.gov/publications/p946/index.html Depreciation Calculation 1. 2. 3. 4. Begin with gross income/EBDIT. Subtract the depreciation to get taxable income/EBIT. Subtract the taxes based on this taxable income to get net income. Add depreciation back to net income to get operating cash flow. Depreciation Example▪ Gross Income/EBDIT $200,000 Less: Depreciation $50,000 Taxable Income/EBIT $150,000 Less: Taxes (tC = 35%) $52,500 Net Income $97,500 Plus: Depreciation $50,000 Real Cash Flow $147,500 ▪ Working Capital Working Capital Metaphorically, the grease that keeps the machine of business going! Production takes place over time. Materials paid for long before product sold Money must be available for suppliers, employees, etc. This investment is ‘working capital’. Working Capital All working capital eventually returned Working capital as a ‘loan’ to the project But ‘cost’ to tying up value in working capital Calculations Increase in working capital → negative CF Decrease in working capital → positive CF Working Capital Example Initial working capital required $10,000 Working capital must be10% of sales: Period 0 1 2 3 4 Sales $0 $130,000 $150,000 $90,000 $50,000 WC $10,000 $13,000 $15,000 $9,000 $5,000 D WC ($10,000) ($3,000) ($2,000) $6,000 $9,000* * Remember that at the end of the project all remaining working capital is recovered―$9,000 = $4,000 released plus $5,000 remaining. Taxes, Interest Payments, Sink Costs, etc. Taxes The corporate tax rate is tC. Marginal Tax Rate Negative Earnings Issue Interest/Financing Payments Not included in cash flows Accounted for in the discount rate ‘Double counting’ Contrast income statement Sunk Costs Past expenditures Irrelevant to project the. No value to project No value as salvage Ignore sunk costs Psychological Problem Behavioral finance Opportunity Costs What you give up Technically: next most valuable use for the asset The value from selling or renting, The value for another project, Nothing, Etc. Opportunity Costs Using Unoccupied Factory Space Could be rented out for $10,000/year. Otherwise unused. Opportunity cost = $10,000/year. Opportunity cost = $0/year. Include all opportunity costs. Externalities Project not independent of the firm. Externalities Possible interactions with other parts of firm Positive: Synergies Negative: Cannibalization Incremental principle Externality costs must be applied to the new project, Steps in Estimating Cash Flows▪ Get input parameters. Determine investment. Determine operating cash flow. Determine working capital needs. Incorporate after tax salvage value Find annual, net project cash flows. Apply decision criteria. ▪ Example: Data Production Units/year 1 50,000 100,000 3 4 5 80,000 60,000 20,000 Costs 2 Fixed = $50,000 (real) Variable = $150.00/unit (nominal) Revenue Initial Price = $300.00/unit (nominal) Increase in Price = 2%/year Example: Data Capital Spending Opportunity Cost Investment = $20,000,000 (nominal) Set Up Costs = $500,000 (nominal, non-depreciable) Factory Capacity = $5,000,000 (nominal) Project Feasibility Study = $2,000,000 (nominal) Salvage Value = $2,000,000 (nominal) Example: Data Nominal Discount Rate = 15% Inflation Rate = 5% Working Capital Initial = $250,000 (Nominal) Thereafter = 8% (of sales) Corporate Tax Rate = 38% Example: 1-Input Parameters 1) Parameters Tax Rate 38% Fixed Cost $50,000 Variable Cost $150 Initial Price $300 Price Growth 2% Salvage Value $2,000,000 Working Capital Rate 12% Inflation Rate 5% Nominal Discount Rate Year 15% 0 1 2 3 4 5 Units sold 50,000 100,000 80,000 60,000 20,000 MACRS Depreciation 20.00% 32.00% 19.20% 11.52% 11.52% 6 5.76% Example: 2-Capital Spending 2) Investment 0 1 2 3 4 5 Investment ($20,000,000) Set Up Costs ($500,000) Factory (Opportunity Cost) ($5,000,000) $5,000,000 Equals: Capital Spending ($25,500,000) $5,000,000 Total Investment = $25,500,000 Set-up and opportunity costs are not depreciable. Opportunity cost is ‘returned’ at project end. Example: 3-Operating CF Year 1 3) Operating Cash Flow Calculation 1 Sales revenue = units x price = 50,000 x $300 = $15,000,000 Less: variable costs = units x variable cost = 50,000 x $150 = ($7,500,000) Less: fixed costs Equals: EBDIT = fixed cost = = revenue – variable cost – fixed cost = Less: depreciation = investment x MARCS = $20,000,000 x 20% = ($50,000) $7,450,000 ($4,000,000) Equals: EBIT = EBDIT – depreciation = $3,450,000 Minus: taxes = tax rate x EBIT = 38% x $3,450,000 = ($1,311,000) Equals: net income = EBIT – Taxes = $2,139,000 Plus: depreciation ” $4,000,000 Equals: operating cash flow = net income + depreciation = $6,139,000 Example: 3-Operating CF Year 2-5 Changes in Sales Revenue Production changes Price increases at 2% per year 1 2 3 4 5 $300 $306 $312 $318 $325 Changes in Depreciation Follows MARCS Example: 3-Operating CF Year 2-5 Changes in Variable Costs Production changes Changes in Fixed Cost Fixed cost are stated in real terms, so inflation needs to be taken into account: 1 2 50,000 50,000(1.05) ($50,000) ($52,500) 3 4 5 50,000(1.05)2 50,000(1.05)3 50,000(1.05)4 ($55,125) ($57,881) ($60,775) Example: 3-Operating CF Year 2-5 3) Operating Cash Flow 0 1 2 3 4 5 Sales revenue $15,000,000 $30,600,000 $24,969,600 $19,101,744 $6,494,593 Less: variable costs ($7,500,000) ($15,000,000) ($12,000,000) ($9,000,000) ($3,000,000) Less: fixed costs ($50,000) ($52,500) ($55,125) ($57,881) ($60,775) Equals: EBDIT $7,450,000 $15,547,500 $12,914,475 $10,043,863 $3,433,818 Less: depreciation ($4,000,000) ($6,400,000) ($3,840,000) ($2,304,000) ($2,304,000) Equals: EBIT $3,450,000 $9,147,500 $9,074,475 $7,739,863 $1,129,818 Minus: taxes ($1,311,000) ($3,476,050) ($3,448,301) ($2,941,148) ($429,331) Equals: net income $2,139,000 $5,671,450 $5,626,175 $4,798,715 $700,487 Plus: depreciation $4,000,000 $6,400,000 $3,840,000 $2,304,000 $2,304,000 Equals: operating cash flow $6,139,000 $12,071,450 $9,466,175 $7,102,715 $3,004,487 Example: 4-Working Capital 4) Working Capital NWC requirement 0 $250,000 1 $1,200,000 2 $2,448,000 3 $1,997,568 4 $1,528,140 Liquidation of WC Change in WC $1,528,140 ($250,000) ($950,000) ($1,248,000) $450,432 Initial Working Capital = ($250,000) Change in Working Capital = 5 -(New WC Requirement – Old WC Requirement) Year 1: -($1,200,000 - $250,000) = ($950,000) Year 3: -($1,997,568 - $2,448,000) = $450,532 In final year all working capital is returned. $469,428 $1,528,140 Example: 5-Salvage Value Salvage value $2,000,000 Minus: tax on salvage value ($322,240) Equals: after tax salvage value $1,677,760 Remaining Book Value Undepreciated Salvage Value $2,000,000 - $1,152,000 = $848,000 Tax on Undepreciated Salvage Value $20,000,000 x 5.76% = $1,152,000 $848,000 x 38% = $322,240 After Tax Salvage Value $2,000,000 - $322,240 = $1,677,760 Example: 6-Net Project Cash Flows 6) Net Project Cash Flows 0 1 2 3 4 5 Operating cash flow $0 $6,139,000 $12,071,450 $9,466,175 $7,102,715 $3,004,487 change in NWC ($250,000) ($950,000) ($1,248,000) $450,432 $469,428 $1,528,140 after tax salvage value $0 $0 $0 $0 $0 $1,677,760 change capital spend ($25,500,000) $0 $0 $0 $0 $5,000,000 Project Cash Flows: ($25,750,000) $5,189,000 $10,823,450 $9,916,607 $7,572,143 $11,210,386 Annual, net project cash flows are sum of operating cash flows, changes in working capital, salvage value and change in capital spending. Example: 7-Decision Criteria 7) Decision Criteria Net Present Value $3,369,528 Internal Rate of Return 19.98% Complete Example You cannot read this–but you can paste it into a word document and expand it! 1) Parameters Tax_Rate Fixed_Cost Variable_Cost Initial_Price Price_Growth Salvage_Value Working_Capital_Rate Inflation_Rate Nominal_Discount_Rate Year Units sold MACRS Depreciation 38% $50,000 $150 $300 2% $2,000,000 12% 5% 15% 0 1 50,000 20.00% 2 100,000 32.00% 3 80,000 19.20% 4 60,000 11.52% 5 20,000 11.52% 2) Investment Investment ($20,000,000) Set Up Costs ($500,000) Factory (Opportunity Cost) ($5,000,000) Equals: Capital Spending ($25,500,000) $5,000,000 $5,000,000 3) Operating Cash Flow Sales revenue Less: variable costs Less: fixed costs Equals: EBDIT Less: depreciation Equals: EBIT Minus: taxes Equals: net income Plus: depreciation Equals: operating cash flow 4) Working Capital Net working capital requirement Liquidation of working capital Change in working capital $250,000 ($250,000) $15,000,000 ($7,500,000) ($50,000) $7,450,000 ($4,000,000) $3,450,000 ($1,311,000) $2,139,000 $4,000,000 $6,139,000 $30,600,000 ($15,000,000) ($52,500) $15,547,500 ($6,400,000) $9,147,500 ($3,476,050) $5,671,450 $6,400,000 $12,071,450 $24,969,600 ($12,000,000) ($55,125) $12,914,475 ($3,840,000) $9,074,475 ($3,448,301) $5,626,175 $3,840,000 $9,466,175 $1,200,000 $2,448,000 $1,997,568 $1,528,140 $450,432 $469,428 ($950,000) ($1,248,000) $19,101,744 $6,494,593 ($9,000,000) ($3,000,000) ($57,881) ($60,775) $10,043,863 $3,433,818 ($2,304,000) ($2,304,000) $7,739,863 $1,129,818 ($2,941,148) ($429,331) $4,798,715 $700,487 $2,304,000 $2,304,000 $7,102,715 $3,004,487 $1,528,140 $1,528,140 5) Salvage Value Salvage value Minus: tax on salvage value Equals: after tax salvage value $2,000,000 ($322,240) $1,677,760 6) Net Project Cash Flows Operating cash flow $0 Minus: change in net working capital ($250,000) Plus: after tax salvage value $0 Minus: change capital spend ($25,500,000) Project Cash Flows: ($25,750,000) 7) Decision Criteria Net Present Value Internal Rate of Return Profitability Index $3,369,528 19.98% 1.13 $6,139,000 $12,071,450 ($950,000) ($1,248,000) $0 $0 $0 $0 $5,189,000 $10,823,450 $9,466,175 $450,432 $0 $0 $9,916,607 $7,102,715 $469,428 $0 $0 $7,572,143 $3,004,487 $1,528,140 $1,677,760 $5,000,000 $11,210,386 6 5.76% Other Methods for Computing OCF Bottom-Up Approach Top-Down Approach Works only when there is no interest expense OCF = NI + depreciation OCF = Sales – Costs – Taxes Don’t subtract non-cash deductions Tax Shield Approach OCF = (Sales – Costs)(1 – T) + (Depreciation * T) NOTE: Cautions about ‘Formulae’ Approach Investments of Unequal Lives Investments of Unequal Lives Air cleaner is mandated by law. Two choices: Model Cadillac Cleaner Cheapskate Cleaner Price $4,000 $1,000 Annual Cost $100 $500 Life 10 years 5 years Assuming a 10% discount rate, which one should we choose? Investments of Unequal Lives Replacement Chain Repeat projects until they begin and end at the same time. Compute NPV for the “repeated projects.” The Equivalent Annual Cost Method Replacement Chain Approach The Cadillac cleaner time line of cash flows: -$4,000 –100 -100 0 1 2 -100 -100 -100 3 4 5 -100 -100 6 7 -100 8 -100 -100 9 10 The Cheapskate cleaner time line of cash flows over ten years: -$1,000 –500 -500 0 1 2 -500 -500 -1,500 3 4 5 -500 -500 6 7 -500 8 -500 -500 9 10 Equivalent Annual Cost (EAC) Greater Applicability The EAC is the value of the level payment annuity that has the same PV as our original set of cash flows. EAC like Average Annual Cost to Operate Equivalent Annual Cost (EAC) Cadillac Air Cleaner 1) Find PV of Annual Cost P/Y = 1; N = 10; I/Y = 10; PMT = -100; FV = 0 → PV = $614.47 2) Add Price $4,000.00 + 614.47 = $4,614.47 3) Find EAC P/Y = 1; N = 10; I/Y = 10; PMT = - 4,614.47; FV = 0 → PMT = $750.98 = EAC Problem: Cheapskate Air Cleaner flows.