# Risk And Capital Budgeting Professor XXXXX Course Name / Number.

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Risk And Capital Budgeting Professor XXXXX Course Name / Number

2 Choosing the Right Discount Rate The numerator focuses on project cash flows covered in chapter 9. The denominator is the discount rate, the focus of chapter 10. The denominator should: Reflect opportunity costs to firms investors Reflect the projects risk Be derived from market data

3 A Simple Case Firm is financed with 100% equity Project is similar to the firms existing assets Project discount rate is easy to determine if we assume : In this case, the appropriate discount rate equals the cost of equity. Cost of equity estimated using the CAPM

4 Carbonlite Inc. Cost of Equity E(R e ) = R f + (E(R m ) - R f ) = 5% + 1.5(11%-5%) = 14% 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 economy (product demand is elastic). Carbonlites stock has a beta of 1.5 Managers note R f = 5%, expect the market return will be 11%.

5 Cost of Equity Beta plays a central role in determining whether a firms cost of equity is high or low. What factors influence a firms beta? Operating leverage The mix of fixed and variable costs Financial Leverage The extent to which a firm finances operations by borrowing The fixed costs of repaying debt increase a firms beta in the same way that operating leverage does.

6 Carbonlite IncFiberspeed Corp Sales volume10,000 sofas Price\$1,000 Total Revenue\$10,000,000 Fixed costs per year\$5,000,000\$2,000,000 Variable costs per frame\$400\$700 Total cost\$9,000,000 EBIT\$1,000,000 Carbonlite Inc. vs. Fiberspeed Corp. What if sales volume increases by 10% ? 11,000 frames \$11,000,000 \$9,700,000\$9,400,000\$1,300,000\$1,600,000 The two firms are in the same industry. Carbonlites EBIT increases faster because it has high operating leverage.

7 Operating Leverage for Carbonlite and Fiberspeed Fiberspeed Carbonlite EBIT Sales Other things equal, higher operating leverage means that Carbonlites beta will be higher than Fiberspeeds beta.

8 The Effect of Financial Leverage on Beta Firm 1Firm 2 Assets\$100 million Debt\$0\$50 million Equity\$100 million\$50 million Case #1: Gross Return on Assets Equals 20 Percent EBIT\$20 million Interest\$0\$4 million Cash to equity\$20 million\$16 million ROE20 ÷ 100 = 20%16 ÷ 50 = 32% Case #2: Gross Return on Assets Equals 5 Percent EBIT\$5 million Interest\$0\$4 million Cash to equity\$5 million\$1 million ROE5 ÷ 100 = 5%1 ÷ 50 = 2% Financial leverage makes Firm 2s ROE more volatile, so its beta will be higher.

9 The Weighted 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 r e = 15%; Also has bonds (D) worth \$50 million, with r d = 9%. Assume that the investment considered will not change the cost structure or financial structure.

10 Finding 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. Williams Total value = \$50 million Has 1,000,000 common shares; price = \$50/share; r e = 15%. Has 200,000 preferred shares, 8% coupon, price = \$80/share, 10% rate of return, \$16 million value. Has \$47.1 million long term debt, fixed rate notes with 8% coupon rate, but 7% YTM. Notes sell at premium and worth \$49 million.

11 Rules for Selecting an Appropriate Project Discount Rate Cost of equity is the appropriate discount rate for an all-equity firm. When a levered firm invests in a project similar to its existing projects, the WACC is the right discount rate. When a firm invests in a project different than its existing projects, using the WACC may lead to mistakes.

12 Accounting 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. Accounting for interest tax shields yields after- tax WACC. Accounting for taxes doesnt change the rules for selecting the discount rate.

13 A 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.

14 Break-Even Point for Carbonlite \$5,000,000 Total revenue Total costs Fixed costs Units 8,333 units Costs & Revenues Carbonlite has high fixed costs (\$5,000,000), but also high contribution margin (\$600/bike). High BEP, but once FC covered, profits grow rapidly.

15 Break-Even Point for Fiberspeed \$2,000,000 Total revenue Total costs Fixed costs Units 6,667 units Costs & Revenues Fiberspeed has low fixed costs (\$2,000,000), but also low contribution margin (\$300/bike). Low BEP, but profits grow slowly after FC covered.

16 Sensitivity Analysis Sensitivity analysis allows mangers to test importance of each assumption underlying a forecast. Test deviations from base case and associated NPV GTI has developed a new skateboard. Base case assumptions yield NPV = \$236,000. 1. The projects life is five years. 2. The project requires an up-front investment of \$7 million. 3. GTI will depreciate initial investment on straight line basis for five years.

17 Sensitivity Analysis 4. One year from now, the skateboard industry will sell 500,000 units. 5. Total industry unit volume will increase by 5% per year. 6. BEI expects to capture 5% of the market in the first year. 7. BEI expects to increase its market share one percentage point each year after year one. 8. The selling price will be \$200 in year one 9. Selling price will decline by 10% per year after year one. 10. Variable production costs will equal 60% of the selling price. 11. The appropriate discount rate is 14 percent.

18 Sensitivity Analysis of Skateboard Project NPVPessimisticAssumptionOptimisticNPV -\$558\$8,000Initial investment\$6,000,000\$1,030 -343450,000 unitsMarket size in year 1550,000 units815 -732% per yearGrowth in market size8% per year563 -1,5123%Initial market share7%1,984 -1,1890%Growth in market share2% per year1,661 -488\$175Initial selling price\$225960 -5462% of salesVariable costs58% of sales526 -873-20% per yearAnnual price change0% per year1,612 -11516%Discount rate12%617 Dollar values in thousands except price

19 Real Options in Capital Budgeting Embedded options arise naturally from investment Called real options to distinguish from financial options. Option pricing analysis is helpful in examining multi- stage projects. Can transform negative NPV projects into positive NPV! Value of a project equals value captured by NPV, plus option.

20 Real Options in Capital Budgeting Expansion options If a product is a hit, expand production. Abandonment options Firm can abandon a project if not successful. Shareholders have valuable option to default on debt. Follow-on investment options Similar to expansion options, but more complex (Ex: movie rights to sequel) Flexibility options Ability to use multiple production inputs (Ex: dual-fuel industrial boiler) or produce multiple outputs

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 projects cash flows. Risk And Capital Budgeting

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