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Corporate Finance 180.366 Spring 2011 Prof. Duffee VI. Investment decision rules 180.366, Spring 2011 2 Subjects in this chapter • Introduce concept “opportunity cost of capital” • Review some alternative rules for deciding whether to take on a project • Modify NPV rule for projects other than stand-alone projects 180.366, Spring 2011 3 PVs and discount rates • PV of a project’s risk-free cash flow is price of a risk- free bond with same future payoff (no-arbitrage) – How much do you have to spend today on Treasury securities to replicate a fixed payoff of $7MM in six months? • Equivalent: discount cash flow by rate inferred from bond – $7MM/(1.0016)1/2 = $6.994MM – Identical calculation, because source of 1.0016 is square root of ($1/price of Treasury bond paying $1 in six months) 180.366, Spring 2011 4 Discount rates for uncertain cash flows • PV price-based rule is same for uncertain cash flows… – What is price of instrument today that pays off in one year expected $15MM, standard deviation $4MM, perfectly correlated with return to aggregate stock market? • … but harder to apply in practice – Cannot easily find expected prices of financial instruments • Easier to use discount rates directly, calculated from a mathematical model 180.366, Spring 2011 5 Opportunity cost of capital • Model we use is outlined after first exam (and is focus of Investments course) • Intuition for now: discount rate = opportunity cost of capital – Highest expected return available in financial marketplace for investment with economically equivalent cash flow – Shorthand: “cost of capital,” “opportunity cost” • Logic – could commit resources (capital) to project, or to an alternative investment 180.366, Spring 2011 6 Review: Stand-alone projects • Definition: taking on project does not preclude taking on others • NPV rule: Take on project if NPV>0 – Use expected cash flows – Use discount rate appropriate for cash-flow characteristics (risk) • Later we will infer discount rates from the Capital Asset Pricing Model • Logic: Taking on project equivalent to putting NPV in pocket – Can sell off all cash flows today at their PVs; NPV is left over 180.366, Spring 2011 7 Example 1 • (Done in previous class) • Annual expected cash flows are C0=-100, C1=50, C2=55, C3=10, all others zero • Assume discount rate for all expected cash flows is 5% 180.366, Spring 2011 8 Alternative measures of value • Real-life firms commonly use other methods to evaluate projects – Some alternatives have benefit of simple computations – Other alternatives have intuitive appeal of return-on-revenue (ROR) • When results of alternative methods differ from NPV: – This may mean that project go/no-go result is different, or that – Priority ranking of projects is different. • Any method producing results that differ from NPV is WRONG (does not maximize wealth). Use such methods with great care 180.366, Spring 2011 9 Internal rate of return • IRR is the most popular alternative method, since it is intuitive and usually gives the right result. • A project’s IRR is defined as the interest rate that sets the NPV of expected cash flows equal to zero. The r that solves C1 C2 C3 0 C0 ... 1 r 1 r 1 r 2 3 • IRR rule: Go ahead with project if IRR > opportunity cost of capital for the project 180.366, Spring 2011 10 Example 1 again • Calculate IRR (cut and paste from Excel) 0 1 2 3 -100 50 55 10 Internal rate of return (IRR) function 8.923%(=irr(a2:d2)) 180.366, Spring 2011 11 Example 1 again • IRR rule: Take on project if opportunity cost of capital < 8.92% 180.366, Spring 2011 12 NPV vs. IRR Calculation Investment Decision Taking discount rate as Accept project if NPV given (r), calculate NPV NPV > hurdle (zero) Taking NPV as given (zero), Accept project if IRR calculate IRR. IRR > hurdle (r) Most of the time, these rules are equivalent Always when negative expected cash flows occur prior to any positive expected cash flows But … 180.366, Spring 2011 13 IRR pitfall 1: lending or borrowing • Change sign of all expected cash flows in example 1. – What is new NPV? – What is new IRR? 180.366, Spring 2011 14 Example 2 • Example 2. Expected cash flows C0 = 100, C1 = 360, C2 = 431, C3 = 171.6 • For 5% discount rate, what is NPV? – NVP=0.162 • For 25% discount rate, what is NPV? – NPV = 0.0192 • Calculate IRR -100 360 -431 171.6 10.000%(=irr(a8:d8,0%)) 30.000%(=irr(a8:d8,40%)) 180.366, Spring 2011 15 IRR pitfall 2: multiple IRR values 180.366, Spring 2011 16 IRR pitfall 3: time-varying discount rates • Example 3. Expected cash flows of Example 1 (-100, 50, 55, 10), but discount rates for expected cash flows in years 1-3 are 8%, 8.5%,11% respectively. What is NPV? 180.366, Spring 2011 17 IRR pitfall 3: time-varying discount rates • Example 3. Expected cash flows of Example 1, but discount rates for expected cash flows in years 1-3 are 8%, 8.5%,11% respectively. What is NPV? – 0.3283 • What is IRR? – Same as in Example 1, 8.92 • What does the IRR decision rule say? – Go ahead with project if IRR > weighted average cost of capital, but weights are complex to compute (depend on cash flows) • Easier to just compute NPV 180.366, Spring 2011 18 IRR pitfall 4: no IRR • Example 4. Expected cashflows are 4, -8, 15. • Try to calculate IRR 4 -8 15 #NUM! (=irr(a14:c14)) 180.366, Spring 2011 19 Another alternative: payback period • Some firms require investment “payback period” (e.g., adopt all projects that pay back within two years) • Example 5 Date Project A Project B Project C 0 -2000 -2000 -2000 1 500 500 1800 2 500 1800 500 3 5000 0 0 Payback 3 years 2 years 2 years NPV (10%) $2,624 ($58) $50 180.366, Spring 2011 20 Mutually exclusive projects • Projects that, if adopted, preclude adoption of other projects • NPV rule: Take on highest NPV project • Note that IRR rule is useless here; want to rank by generated wealth, not highest % return on investment 180.366, Spring 2011 21 Resource constraints • Definition: projects use a resource (say, managerial oversight) that cannot be adjusted by the firm before the resource is needed • Implication: firms must consider best use of resource • Rule: choose set of projects that maximize sum of NPV subject to resource constraint 180.366, Spring 2011 22 Example 6 • Project A requires all of a home builder’s available land; Projects B and C each require half of the available land Date Cash Flows $ Millions Project A Project B Project C 0 -10 -5 -5 1 30 5 5 2 5 20 15 NPV (10%) $21 $16 $12 • Aside from very simple cases, programming techniques are required to solve for max(NPV) subject to constraints 180.366, Spring 2011 23 VII. Fundamentals of capital budgeting 180.366, Spring 2011 24 Project (e)valuation – the cash flow side • We take a closer look at project analysis, taking the choice of discount rate(s) as given • Remaining question: What are the cash flows to discount? • The standard accounting framework is used to answer this question 180.366, Spring 2011 25 Step 1. Incremental effect of project on accounting earnings Sales Cost of goods sold (COGS) ---------------- Gross profit Selling, general, and administrative expenses (S,G&A) Research and development (R&D) Depreciation Other ----------------- Earnings before interest and taxes (EBIT) 180.366, Spring 2011 26 Step 1, continued EBIT Taxes Interest expense ---------------------- Net unlevered income 180.366, Spring 2011 27 Why unlevered income? • Method evaluates project as if owners of firm put new cash into firm for incremental investment, take out cash flows as they arrive – Initial cash flow (payment to owners) negative • Alternate method assumes borrowing, then paying interest – By law of one price, NPV is unchanged (conclusion modified later in semester) 180.366, Spring 2011 28 More about taxes Corporate Federal Income Tax Rates—2009 Taxable income Rate $0 to $ 50K 15% $50K to $ 75K 25% $75K to $100K 34% $100K to $335K 39% Selected state corporate income tax rates $335K to $10MM 34% $10MM to $15MM 35% California flat 8.84% $15MM to $18.3MM 38% DC flat 9.975% $18.3M and up 35% Hawaii Below $25K 4.40% $25K -- $100K 5.40% $100K + 6.40% Maryland flat 8.30% Pennsylvania flat 9.99% Wyoming flat 0% 180.366, Spring 2011 29 Refining incremental earnings • Opportunity costs or sunk costs? – If a project at Cisco uses a large amount of a firm’s unused bandwidth, is that an incremental expense for the project? – If a project at Honeywell employs 20 mid-career Honeywell engineers that were previously used on another project that the firm has decided to close, are their salaries and benefits an incremental expense? – If a project at Midwest Federal (a commercial bank) uses floor space in retail bank branches, is that an incremental expense? – If a research lab at 3M produces many new ideas for potential projects each year, should the projects’ incremental earnings include the expense of running the lab? 180.366, Spring 2011 30 • Principles of evaluating opportunity/sunk costs – Are there competing projects that could use the resources, either now or during the project’s life? – Could the resources be sold or leased out if not used in the project? – Does the use of the resources lower the profitability of other revenue streams? 180.366, Spring 2011 31 Refining incremental earnings • Synergies and cannibalism – Dr Pepper (1885) – Diet Dr Pepper, Cherry Vanilla Dr Pepper, Diet Cherry Vanilla Dr Pepper, Caffeine Free Dr Pepper, Caffeine Free Diet Dr Pepper, Dr Pepper Berries & Cream, Diet Dr Pepper Berries & Cream – Are new products cannibalizing old ones and/or helping to establish a brand? – Synergies/cannibalism refers not only to existing products, but potential future products! 180.366, Spring 2011 32 From incremental earnings to incremental cash flows • A reminder – Calculation of incremental earnings is difficult, and finance has nothing helpful to say about the calculation – it is an input • Incremental cash flows Start with EBIT x (1 – tax rate) Add back depreciation Subtract any capital expenditures Subtract any change in net working capital (e.g., inventories) ----------------------------------------- Result is incremental free cash flow 180.366, Spring 2011 33 More about depreciation • Methods – Straight-line • Depreciation each year is cost/(tax life) – Accelerated • Greatest acceleration is Modified Accelerated Cost Recovery System (MACRS) • Depreciation each year is cost x rate from schedule (Ch 7 appendix) 180.366, Spring 2011 34 Depreciation and taxes • Free cash flow formula free cash flow EBIT 1 tax rate CapEx - NWC depreciati on • Isolate depreciation component of EBIT free cash flow revenues - costs excluding depreciation - depreciation 1 tax rate CapEx NWC depreciation • Combine terms involving depreciation (next slide) 180.366, Spring 2011 35 Depreciation and taxes • Free cash flow formula free cash flow revenues - costs excluding depreciation 1 tax rate CapEx NWC depreciation tax rate • Final term is “depreciation tax shield” – The faster a firm is allowed to depreciate its assets, the more after-tax cash flow it generates 180.366, Spring 2011 36 More about taxes • Formula implicitly says that gross losses reduce taxes • Does this make sense for all projects? – Yes, for projects within profitable companies – Yes, for projects within companies that made profits during the previous two years • Tax loss “carrybacks” – IRS lets you offset past profits with current losses – they send the company a check for past taxes collected – Yes, for projects within companies that will make profits during the next 20 years • Tax loss “carryforwards” – IRS lets you offset future profits with current losses – but tax loss should also be carried forward to future year (and discounted) 180.366, Spring 2011 37 More about taxes • If a firm has substantial tax loss carryforwards from previous years, should new projects be evaluated using a zero tax rate? – Key issue: Would the carryforwards be used up if the project were not implemented? • When would they be used? • Think of this as opportunity cost of using carryforwards on this project 180.366, Spring 2011 38 Net working capital • Projects may require increased inventory • Revenues will be accounts receivable before cash flows • Expenses will be accounts payable before negative cash flows • Net effect is change in net working capital, which must be financed 180.366, Spring 2011 39 Example • Question 1 of distributed problems 2010 2011 2012 2013 2014 2015 2016 2017 Equipment -1 -3 Sales 9.000 11.700 12.051 12.413 12.785 0.000 180.366, Spring 2011 40 Initial investment $ 3.000 Initial sales 9.000 Sales growth rate from 1 to 2 30.00% Discount rate 11.00% Sales growth rate after year 2 3.00% COGS percentage 62.00% SG&A percentage 22.00% Depreciation rate 20.00% Year 0 1 2 3 4 5 Expected sales 9.000 11.700 12.051 12.413 12.785 COGS (5.580) (7.254) (7.472) (7.696) (7.927) SG&A (1.980) (2.574) (2.651) (2.731) (2.813) Other expenses (0.200) - - - - - Depreciation (0.600) (0.600) (0.600) (0.600) (0.600) Pretax profit (0.200) 0.840 1.272 1.328 1.386 1.446 After-tax profit (0.200) 0.840 1.272 1.328 1.386 1.446 Cash flow analysis Investment (3.000) Depreciation 0.600 0.600 0.600 0.600 0.600 Net cash flow (3.200) 1.440 1.872 1.928 1.986 2.046 PV (3.200) 1.297 1.519 1.410 1.308 1.214 NPV 3.549 IRR 46.55% 180.366, Spring 2011 41 Financing • What about Joe’s concern? – “If the firm uses $3MM of existing cash to make the initial investment, the true cost of the equipment purchase is $3MM plus the lost interest that would have been earned on $3MM.” 180.366, Spring 2011 42 Revised example • Question 1 of distributed problems • Add – Marginal tax rate of 40% – Implementation requires an increase in working capital of 25% of sales. Working capital is needed at the beginning of the year (i.e., end of previous year) 180.366, Spring 2011 43 Excel spreadsheet (top) Initial investment $ 3.000 Initial sales 9.000 Sales growth rate from 1 to 2 30.00% Discount rate 11.00% Sales growth rate after year 2 3.00% COGS percentage 62.00% SG&A percentage 22.00% Depreciation rate 20.00% Marginal tax rate 40.00% Working capital percentage 25.00% 180.366, Spring 2011 44 Excel spreadsheet Year 0 1 2 3 4 5 Expected sales 9.000 11.700 12.051 12.413 12.785 COGS (5.580) (7.254) (7.472) (7.696) (7.927) SG&A (1.980) (2.574) (2.651) (2.731) (2.813) Other expenses (0.200) - - - - - Depreciation (0.600) (0.600) (0.600) (0.600) (0.600) Pretax profit (0.200) 0.840 1.272 1.328 1.386 1.446 Taxes paid 0.080 (0.336) (0.509) (0.531) (0.554) (0.578) After-tax profit (0.120) 0.504 0.763 0.797 0.832 0.867 Cash flow analysis Investment (3.000) Depreciation 0.600 0.600 0.600 0.600 0.600 Working capital (2.250) (0.675) (0.088) (0.090) (0.093) 3.196 Net cash flow (5.370) 0.429 1.275 1.307 1.339 4.664 PV (5.370) 0.386 1.035 0.955 0.882 2.768 NPV 0.656 IRR 14.48% 180.366, Spring 2011 45 Break-even/sensitivity/scenario analyses • All alter inputs to evaluate their effect on project NPV – Break-even: Find values of particular inputs that set NPV to zero • Break-even sales growth after 2012 (perhaps not 30%)? • Break-even COGS percentage? – Sensitivity: how does NPV change when inputs are set to reasonable upper and lower bounds? – Scenario: vary multiple inputs at once to see how they interact 180.366, Spring 2011 46 Interpreting the analyses • What do we do with the results? • Important principle: cash flow uncertainty owing to future events is addressed in the choice of discount rates, not in direct adjustment of cash flows • Analyses should be used to determine which inputs are especially important to NPV, so that effort in calculating NPV can be concentrated on key inputs 180.366, Spring 2011 47

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