# 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 8: The denominator is the discount rate, the focus of chapter 9. The denominator should: Reflect the opportunity costs of the 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 All Leathers Cost of Equity E(R e ) = R f + (E(R m ) - R f ) = 10.5% cost of equity All Leather Inc., an all-equity firm, is evaluating a proposal to build a new manufacturing facility. –Firm produces leather sofas. –As a luxury good producer, firm very sensitive to economy. –All Leathers stock has a beta of 1.3. Managers note R f = 4%, expect the market risk premium will be 5%.

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 All Leather Inc. and Microfiber Corp. All Leather IncMicrofiber Corp Sales volume40,000 sofas Price\$950 Total Revenue\$38,000,000 Fixed costs per year\$10,000,000\$2,000,000 Variable costs per sofa\$600\$800 Total cost\$34,000,000 EBIT\$4,000,000 What if sales volume increases by 10% ? 44,000 sofas \$41,800,000 \$37,200,000\$36,400,000\$4,600,000\$5,400,000 The two firms are in the same industry All Leathers EBIT increases faster because it has high operating leverage.

7 Operating Leverage for All Leather and Microfiber : Microfiber All Leather EBIT Sales Other things equal, higher operating leverage means that All Leathers beta will be higher than Microfibers beta.

8 The Effect of Leverage on Beta: Firm 1Firm 2 Assets\$250 million Debt\$0\$100 million Equity\$250 million\$150 million Case #1: Gross Return on Assets Equals 25 Percent. EBIT\$62.5 million Interest\$0\$8.5 million Cash to equity\$62.5 million\$54 million ROE62.5 ÷ 250 = 25%54 ÷ 150 = 36% Case #2: Gross Return on Assets Equals 5 Percent. EBIT\$12.5 million Interest\$0\$8.5 million Cash to equity\$12.5 million\$4 million ROE12.5 ÷ 250 = 5%4 ÷ 150 = 2.7% 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 akin to finding expected return of portfolio Use weighted average cost of capital (WACC) as discount rate: An example… –Comfy Inc builds houses. –Firm has \$150 million equity (E), with cost of equity r e = 12.5%. –Also has bonds (D) worth \$50 million, with r d = 6.5% –Assume initially that there are no corporate taxes.

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.... Sherwin Co. Total value = 211.5 million Has 10,000,000 common shares; price = \$15/share; r e = 15%. Has 500,000 preferred shares, 8% coupon, price = \$25/share, \$12.5 million value. Has \$40 million long term debt, fixed rate notes with 8% coupon rate, but 7% YTM. Notes sell at premium and worth \$49 million.

11 Connecting the WACC to the CAPM WACC consistent with CAPM Can use CAPM to compute WACC for levered firm. Calculate beta for bonds of a large corporation: –First find covariance between bonds and stock market. –Plug computed debt beta ( d ), R f and R m into CAPM to find r d. Debt beta typically quite low for healthy, low-debt firms –Debt beta rises with leverage. Any asset that generates a cash flow has a beta, and that beta determines its required return as per CAPM.

12 Calculating Asset Betas and Equity Betas An asset beta is the covariance of the cash flows generated by a firms assets with R M, return on market portfolio, divided by variance of markets return. –For all-equity firm, asset beta = equity beta. –For levered firm, asset beta will be less than equity beta (still assuming no taxes). If asset beta known, and debt beta is assumed to be 0, can compute equity beta directly from A : The CAPM establishes direct link between required return on debt and equity and betas of these securities.

13 Discount Rate for Unique Projects What if a company has diversified investments in many industries? In this case, using firms WACC to evaluate an individual project would be inappropriate. Use projects asset beta adjusted for desired leverage. An example… –Assume GE is evaluating an investment in oil and gas industry. –GE would examine existing firms that are pure plays (public firms operating only in oil and industry).

14 Data for Berry Petroleum and Forest Oil 0.550.56Asset beta * 0.640.16D/E ratio 0.610.86Fraction Equity 0.390.14Fraction Debt 0.900.65Stock beta Forest OilBerry Petroleum * Assumes debt beta = 0 and no taxes Say GE selects Berry Petroleum & Forest Oil as pure plays: Operationally similar firms, but Berry Petroleums E = 0.65 and Forest Oils E = 0.90 Why so different? Reason: Forest Oil uses debt for 39% of financing; Berry Petroleum: 14%.

15 Converting Equity Betas to Asset Betas for Two Pure Play Firms To determine correct A to use as discount rate for the project, GE must convert pure play E to A, then average. –Previous table lists data needed to compute unlevered equity beta. –Unlevered equity beta (same as A when taxes are zero) strips out effect of financial leverage, so always less than or equal to equity beta. –Berrys A = 0.56, Forests A = 0.55, so average A = 0.55 GE capital structure consists of 20% debt and 80% equity (D/E ratio = 0.25). Compute relevered equity beta:

16 Converting Equity Betas to Asset Betas for Two Pure Play Firms One more step to find the right discount rate for GEs investment in this industry: calculate project WACC. Using CAPM, compute rate of return GE shareholders require for the oil and gas investment. Assume risk-free rate of interest is 6% and expected risk premium on the market is 7%: E(R) = 6% + 0.69(7%) = 10.83%. –GEs financing is 80% equity and 20% debt. Assume investors expect 6.5% on GEs bonds:

17 Accounting for Taxes Have thus far assumed away taxes –Tax deductibility of interest payments favors use of debt. –Accounting for interest tax shields yields after-tax WACC. After-tax formula for equity beta changes to: –We are still assuming debt beta = 0. β U is the beta of an unlevered firm. Analogous to asset beta, but not strictly equal to β A due to taxes

18 Summary: Finding Discount Rate for Unique Projects 1) Identify pure play firms. 2) Calculate after-tax, unlevered betas for these firms and average them. 3) Relever beta to reflect the investing firms capital structure. 4) Plug relevered beta into CAPM to obtain r e.. 5) Use r e, r d, and capital structure weights to obtain after-tax project WACC.

19 A Closer Look at Risk Break-Even Analysis Managers often want to assess business value drivers: Useful to assessing operating risk is finding break-even point. Break-even point is level of output where all operating costs (fixed and variable) are covered.

20 Sensitivity Analysis Sensitivity analysis allows mangers to test importance of each assumption underlying a forecast. –Test deviations from base case and associated NPV. Best Electronics Inc has new DVD players project. Base case assumptions (below) yields Exp NPV = \$1,139,715. 1. The project s life is five years. 2. The project requires an up-front investment of \$41 million. 3. BEI will depreciate initial investment on S-L basis for five years. 4. One year from now, DVD industry will sell 3,000,000 units. 5. Total industry unit volume will increase by 5% per year. 6. BEI expects to capture 10% 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 \$100 in year one. 9. Selling price will decline by 5% per year after year one. 10. Variable production costs will equal 60% of the selling price. 11. The appropriate discount rate is 14 percent.

21 Sensitivity Analysis of DVD Project NPVPessimisticAssumptionOptimisticNPV -\$448,315\$43,000,000Initial investment\$39,000,000+2,727,745 -\$1,106,5742,800,000 unMarket size in year 13,200,000 un+3,386,004 -\$640,7272% per yearGrowth in market size8% per year+3,021,884 -\$4,602,8328%Initial market share12%+6,882,262 -\$3,841,884ZeroGrowth in market share2% per year+6,121,315 -\$2,229,718\$90Initial selling price\$110+4,509,149 -\$545,00262% of salesVariable costs58% of sales+2,824,432 -\$2,064,260-10% per yrAnnual price change0% per year+4,688,951 -\$899,41316%Discount rate12%+3,348,720 If all optimistic scenarios play out, projects NPV rises to \$37,635,010. If all pessimistic scenarios play out, projects NPV falls to -\$19,271,270!

22 Real Options in Capital Budgeting Embedded options arise naturally from investment; Called real options to distinguish from financial options. Option pricing analysis 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.

23 Real Options in Capital Budgeting Expansion options If a product is a hit, expand production. Abandonment options 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. WACC and CAPM are connected. Cost of debt and equity are driven by debt and equity betas. Use pure play equity betas when invest in unique projects. Risk And Capital Budgeting

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