2Choosing the Right Discount Rate The numerators focus on project cash flows covered in Chapter 9.The denominators are the discount rates, the focus of chapter 10.The denominator should:Reflect opportunity costs to firm’s investorsReflect the project’s riskBe derived from market data
3The extent to which a firm finances operations by borrowing Cost of EquityBeta plays a central role in determining whether a firm’s cost of equity is high or low.What factors influence a firm’s beta?Operating leverageThe mix of fixed and variable costsFinancial LeverageThe extent to which a firm finances operations by borrowingThe fixed costs of repaying debt increase a firm’s beta in the same way that operating leverage does.
4A Simple CaseProject discount rate is easy to determine if we assume :Firm is financed with 100% equityProject is similar to the firm’s existing assetsIn this case, the appropriate discount rate equals the cost of equity.Cost of equity can be estimated using the CAPM
5Carbonlite Inc.: Cost of Equity Carbonlite Inc., an all-equity firm, is evaluating a proposal to build a new manufacturing facility.Firm manufactures bicycle frames.As a luxury good producer, firm is very sensitive to the economy (product demand is elastic).Carbonlite’s stock has a beta of 1.5.Managers note Rf = 5%, expect the market return will be 11%.E(Re ) = Rf + (E(Rm) - Rf) = 5% + 1.5(11%-5%) = 14% cost of equity
6Table 10.1 Financial Data for Carbonlite Inc. and Fiberspeed Corp.
7Figure 10.1 Operating Leverage for Carbonlite and Fiberspeed The higher operating leverage of Carbonlite is reflected in its steeper slope, demonstrating that its EBIT is more responsive to changes in sales than is the EBIT of Fiberspeed.
8Carbonlite Inc. vs. Fiberspeed Corp. The two firms are in the same industry.Carbonlite IncFiberspeed CorpSales volume10,000 sofasPrice$1,000Total Revenue$10,000,000Fixed costs per year$5,000,000$2,000,000Variable costs per frame$400$700Total cost$9,000,000EBIT$1,000,00011,000 frames$11,000,000$9,700,000$9,400,000$1,300,000$1,600,000What if sales volume increases by 10% ?Carbonlite’s EBIT increases faster because it has high operating leverage.
9The Effect of Financial Leverage on Shareholder Returns Firm 1Firm 2Assets$100 millionDebt (interest rate 8%)$0$50 millionEquityCase #1: Gross Return on Assets Equals 20 PercentEBIT$20 millionInterest$4 millionCash to equity$16 millionROE20 ÷ 100 = 20%16 ÷ 50 = 32%Case #2: Gross Return on Assets Equals 5 Percent$5 million$1 million5 ÷ 100 = 5%1 ÷ 50 = 2%Financial leverage makes Firm 2’s ROE more volatile, so its beta will be higher .
10Weighted Average Cost of Capital (WACC) Cost of equity applies to projects of an all-equity firm.But what if firm has both debt and equity?Problem is akin to finding expected return of portfolio.Use weighted average cost of capital (WACC) as discount rate.Lox-in-a-Box is a chain of fast food stores.Firm has $100 million equity (E), with cost of equity re = 15%;Also has bonds (D) worth $50 million, with rd = 9%.Assume that the investment considered will not change the cost structure or financial structure.
11Finding WACC For Firms with Complex Capital Structures How do we calculate WACC if firm has long-term (D) debt as well as preferred (P) and common stock (E)?An example....S.D. WilliamsTotal value = $50 million1 million common shares; $50/share; re = 15%.200,000 preferred shares, 8% coupon, $80/share, 10% rate of return, $16 million value.$47.1 million (par value) long term debt, fixed rate notes with 8% coupon rate, but 7% YTM.Notes sell at premium and worth $49 million.
12Rules for Finding the Right Discount Rate When an all-equity firm invests in an asset similar to its existing assets, the cost of equity is the appropriate discount rate.When a firm with both debt and equity invests in an asset similar to its existing assets, the WACC is the appropriate discount rate.When the investment is more risky than the firm’s average investment, a higher discount rate than the WACC is required, and vice versa.
13Accounting for Taxes in Finding WACC We have thus far assumed away taxes, which are often important in financing decisions.Tax deductibility of interest payments favors use of debt.The opportunity to deduct interest payments reduces the after-tax cost of debt and changes the WACC formula:Accounting for taxes doesn’t change the rules for selecting the discount rate.
14A Closer Look at Risk: Break-Even Analysis Managers often want to assess business’ value drivers.Finding the break-even point is often useful for assessing operating risk.Break-even point (BEP) is level of output where all operating costs (fixed and variable) are covered.
15Fig. 10-2a Break-Even Point for Carbonlite Costs &RevenuesTotal revenueTotal costsFixed costs$5,000,0008,333 unitsUnitsCarbonlite has high fixed costs and high contribution margin ($600/bike). High BEP, but once FC are covered, profits grow rapidly.
16Fig. 10-2b Break-Even Point for Fiberspeed Costs &RevenuesTotal revenueTotal costsFixed costs$2,000,0006,667 unitsUnitsFiberspeed has low fixed costs and low contribution margin ($300/bike). Low BEP, but profits grow slowly after FC are covered.
17Sensitivity AnalysisSensitivity analysis allows mangers to test the impact of each assumption underlying a forecast.Sensitivity analysis involves calculating the NPVs for various deviations from a “base case” set of assumptions.GTI has developed a new skateboard. Base case assumptions yield NPV = $236,000.The project’s life is five years.The project requires an up-front investment of $7 million.GTI will depreciate initial investment on straight line basis for five years.
18Sensitivity AnalysisGTI has developed a new skateboard. Base case assumptions yield NPV = $236,000.One year from now, the skateboard industry will sell 500,000 units.Total industry unit volume will increase by 5% per year.GTI expects to capture 5% of the market in the first year.GTI expects to increase its market share by one percentage point each year after year one.The selling price will be $200 in year one.Selling price will decline by 10% per year after year one.All production costs are variable and equal 60% of the selling price.GTI’s marginal tax rate is 30%.The appropriate discount rate is 14%.
19Table 10-4 Sensitivity Analysis of Skateboard Project Dollar values in thousands except priceNPVPessimisticAssumptionOptimistic-$558$8,000,0002. Initial investment$6,000,000$1,030-343450,000 units4. Market size in year 1550,000 units815-732% per year5. Growth in market size8% per year563-1,5123%6. Initial market share7%1,984-1,1890%7. Growth in market share1,661-488$1758. Initial selling price$225960-5462% of sales9. costs58% of sales526-873-20% per year10. Annual price change0% per year1,612-11516%12. Discount rate12%617
20Scenario AnalysisScenario analysis is a more complex form of sensitivity analysis.Rather than adjust one assumption up or down, analysts calculate the project NPV when a whole set of assumptions changes in a particular way.For example, if consumer interest in GTI’s new skateboard is low, the project may achieve a lower market share and a lower selling price than originally anticipated.
21Monte Carlo Simulation In a Monte Carlo simulation, analysts specify a range or a probability distribution of potential outcomes for each of the model’s assumptions.It is even possible to specify the degree of correlation between key variables.A simulation software package is then used to take random “draws” from these distributions, calculating the project’s cash flows (and NPV) over and over again.The simulation produces the probability distribution of project cash flows (and NPVs) as well as sensitivity figures for each of the model’s assumptions.
22Monte Carlo Simulation The use of Monte Carlo simulation has grown dramatically in the last decade because of steep declines in the costs of computer power and simulation software.The bottom line is that simulation is a powerful, effective tool when used properly.Simulation’s fundamental appeal is that it provides decision makers with a probability distribution of NPVs rather than a single point estimate of the expected NPV.
23Decision TreesA decision tree is a visual representation of the sequential choices that managers face over time with regard to a particular investment.The value of decision trees is that they force analysts to think through a series of “if-then” statements that describe how they will react as the future unfolds.
24Decision Trees for Odessa Investment Trinkle Foods Limited of Canada has invented a new salt substitute, branded Odessa.Trinkle is deciding whether to spend 5-million Canadian dollars (C$) to test-market a new line of potato chips flavored with Odessa in Vancouver.Depending on the outcome, Trinkle may spend an additional C$50 million 1 year later to launch a full line of snack foods across Canada.If consumer acceptance in Vancouver is high, the company predicts that its full product line will generate net cash inflows of C$12 million per year for 10 years.If consumers respond less favorably, cash inflows from a nationwide launch is expected to be just C$2 million per year for 10 years.Trinkle’s cost of capital equals 15 percent.
25Fig. 10-3 Decision Trees for Odessa Investment If the test market is successful, the NPV of launching the product is C$10.23 million; if the initial test results are negative, and it launches the product, it will have an NPV of – C$39.96 million.
26Decision Trees for Odessa Investment To work through a decision tree, begin at the end and then work backward to the initial decision.Suppose one year from now, Trinkle learns that the Vancouver market test was successful:If the initial test results are unfavorable and it launches the product:We then evaluate today’s decision about whether to spend the C$5 million. The expected NPV of conducting the market test is:Spending the money for market testing does not appear worthwhile.
27Real Options in Capital Budgeting Option pricing analysis is helpful in examining multi-stage projects.Embedded options arise naturally from investment.Called real options to distinguish from financial options.Value of a project equals value captured by NPV, plus option.Options can transform negative NPV projects into positive NPV!
28Follow-on investment options Types of Real OptionsExpansion optionsIf a product is a hit, expand production.Abandonment optionsFirm can abandon a project if not successful.Shareholders have valuable option to default on debt.Follow-on investment optionsSimilar to expansion options, but more complex (Ex: movie rights to sequel)Flexibility optionsAbility to use multiple production inputs (example: dual-fuel industrial boiler) or produce multiple outputs
29Strategy and Capital Budgeting Competition and NPVAdvocates of a positive NPV project should be able to articulate the project’s competitive advantage before running the numbersStrategic thinking and real optionsManagers must articulate their strategy for a given investment
30Risk and Capital Budgeting All-equity firms can discount their standard investment projects at cost of equity.Firms with debt and equity can discount their standard investment projects using WACC.A variety of tools exist to assist managers in understanding the sources of uncertainty of a project’s cash flows.