CAPITAL STRUCTURE. 2 Two primary funding sources: debt and equity. 4 Each source has different risk level

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1 CAPITAL STRUCTURE 2 Two primary funding sources: debt and equity 4 Each source has different risk level 2 Each funding source must be compensated for opportunity cost of what suppliers of funds can earn elsewhere, on investments of equivalent risk 2 In order to be accepted, projects must increase owners expected utility of wealth Each project must provide, on a risk adjusted basis, enough CF to pay required returns to equity and debt holders, pay back original investments, and leave something extra to increase owners (equity holders ) EU of wealth. 2 Cost of capital: minimum risk adjusted return to shareholders

2 2 With no debt and CAPM: 4 Cost of Capital = E(k j ) ' k 0 % E(k m & k 0 ) j 2 We need to consider effect of debt on the cost of capital Also does capital structure really matter? That is, does a firm s capital structure impact the firm s value?

3 VALUE OF THE FIRM WITH CORPORATE TAXES 2 Value of a Levered Firm 4 Modigliani and Miller (1958, 63) 3 Capital markets are frictionless 3 Borrow and lend at the risk-free rate 3 No cost to bankruptcy 3 Two types of claims: risk-free debt and (risky) equity 3 All firm s in the same risk class 3 Only corporate taxes 3 All CFs are perpetuities (no growth) 3 No signaling opportunities 3 Managers maximize shareholder wealth 2 Many of the assumptions can be relaxed without changing major conclusions 4 e.g., risk-free assumption on debt can be relaxed without impacting results 2 Bankruptcy and personal tax assumptions do have critical impact on results

4 2 Clarification: All firms in the same risk class 2 Implication: Risky CFs vary only by a scale factor CF i ' CF j where = constant scale factor In other words, CFs are perfectly correlated Consider gross returns r it ' CF it & CF it&1 CF it&1 CF i ' CF j Y r it ' CF jt & CF jt&1 CF jt&1 ' CF jt & CF jt&1 CF jt&1 ' r jt So if CFs differ only by scale factor, they will have the same distribution of returns, the same risk, and will require the same expected return.

5 2 Assume the firm s assets generate the same distribution of operating CFs each period after-taxes forever. Thus value of the firm without any debt is where V u ' E( c) k u V u = present value of an unlevered firm E( c) = expected after-tax cash flow in perpetuity k u = discount rate for all equity firm Remember stuff on estimating CF ATCF ' NIAT % Dep ' ( R & Ṽ c & F c & Dep)(1 & t c ) % Dep 4 no other accruals 4 no interest cost because no debt 4 no growth

6 We've assumed c is generated in perpetuity. This implies depreciation each year must be replaced by investment in order to keep the same amount of capital in place. Thus we're assuming Dep = I where I is capital investment each year. c = NIAT % Dep & I = ( Rev & Ṽ c & F c & Dep)(1 & t c ) % Dep & I = ( Rev & Ṽ c & F c & Dep)(1 & t c ) = ( EBIT)(1 & t c ) ' NIAT When all CFs are perpetuities, CFs to investors is the same as NIAT, so V u ' E( c) ' E( EBIT)(1 & t c ) k u k u

7 2 Now assume the firm issues debt After-tax CFs must be split between debt and equity holders 2 Equity holders get: NIAT % Dep & I Debt holders get: k d D where k d = interest rate on debt D = face value of debt 2 Thus to total CF to debt and equity holders is ( NIAT % Dep & I) % k d D ' ( Rev & Ṽ c & F c & Dep & k d D)(1 & t c ) % Dep & I % k d D 2 Assuming no growth (Dep = I), the total CF is NIAT % k d D = EBIT(1 & t c ) % k d Dt c 8 8 CF to unlevered Tax shield from firm ( c). Will have using debt (risk-free same risk level. by assumption).

8 2 Discounting each CF by the appropriate discount rate for its risk class, we find the value of the levered firm to be V L ' E( EBIT)(1 & t c ) % k d Dt c k u k 0 where Note: V L = value of levered firm k 0 = risk-free rate k d D is the perpetual stream of risk-free payments to debt holders This implies the market value of the risk-free debt is k B = d D = market value of debt (bonds) k 0 2 Rewriting we find, V L = V u + Bt c Value of a levered firm is equal to the value of the unlevered firm plus the present value of the tax shield provided by debt.

9 Note that in the absence of any market imperfections (i.e. t c = 0), the value of the firm is not dependent on the capital structure of the firm V L ' V u (if t c ' 0) This famous result is known as Modigliani-Miller Proposition I (MMI).

10 MMI (Arbitrage argument) (t c = 0) 2 firms, identical except for capital structures Lever Company Unlevered Company E(EBIT) = $200 E(EBIT) = $200 V L =? V u = $1000 B L = 500 B u = 0 E L =? E u = 1000 k d =.10 k u =.20 V u ' E(EBIT) k u ' ' $1000 Strategy I: Buy 10% of Unlevered Investment Cash Flow.10($1000) = $100.10( EBIT) =.10(V u )

11 2 Strategy II: Buy 10% of Levered Company s Equity Investment Cash Flow.10(E L ) =.10(V L - B L ).10( EBIT & k d B L ) Common argument: V L (and E L /share) should be lower because of increased risk associated with leverage. 2 Strategy III: Buy 10% of Unlevered using combination of borrowed funds and equity funds Borrow 10% of B L and combine with equity funds to buy 10% of V u. Investment Cash Flow Borrow 10% of B L -.10B L -.10 k d B L Buy 10% of V u.10v u.10( EBIT) Total.10(V u - B L ).10 ( EBIT - k d B L )

12 Important Point: Cash flows from buying levered firm are identical to borrowing and buying unlevered firm. (CF to Strategy II = CF to Strategy III) Therefore: Cost of Strategy II Cost of each strategy must be the same. Cost of Strategy III.10 (V L - B L ).10(V u - B L ) Thus rational investors will require V L = V u (MMI) 2 Critically important result in finance 2 Before MMI, effects of leverage misunderstood

13 MMI shows if levered firms are priced too high, individuals will simply borrow on their own accounts and buy shares in unlevered firms. Y Leverage doesn t effect value of firm! Example Consider decision to use debt in BigAg Company. Financial Structure (t c = 0) Current Proposal Assets $8,000,000 $8,000,000 Debt 0 4,000,000 Equity 8,000,000 4,000,000 Interest Rate 10% 10% Shares 400, ,000 Value/Share $20 $20

14 IMPACT OF CAPITAL STRUCTURE ON RETURNS No Debt Debt = 10% Recession Expected Expansion Recession Expected Expansion ROA 5% 15% 25% 5% 15% 25% EBIT $400,000 $1,200,000 $2,000,000 $400,000 $1,200,000 $1,200,000 Int , , ,000 0 NIAT 400,000 1,200,000 2,000, ,000 1,600,000 ROE 5% 15% 25% 0 20% 40% EPS $1.00 $3.00 $ $4.00 $8.00 Analysis: Effect of financial leverage depends on company s income.

15 Possible Argument: Expected income is $1,200,000 so the firm should take on additional debt. 2 Invest $2,000 in levered Argument is flawed. Shareholders can borrow on personal accounts and duplicate effects of company s leverage. Leverage Plan Recession Expected Expansion EPS 0 $4 $8 EPS x 100 shares Initial Cost = 100 $20/sh. = $ Invest $2,000 in unlevered Homemade Leverage (Borrow $2,000 Buy 200 shares in Unlevered) Recession Expected Expansion EPS x 200 sh. $1 x 200 = x 200 = x 200 = 1000 Int =.10(2000) Initial Cost = 200($20) = $2000

16 2 This is another illustration of MMI. In a world without transaction costs, capital structure doesn t matter. Effectively, increases in expected returns from leverage are offset by additional risk (more later). 2 Doesn t match reality 2 Letting t c > 0, V L ' V u % Bt c giving debt preferential tax treatment (allowing a tax deduction for interest payments) increases the value of the firm as the firm takes on more and more debt. Y firms should use almost all debt financing. 2 Doesn t match reality

17 WEIGHTED AVERAGE COST OF CAPITAL (WACC) Suppose project is funded with B = $ by debt holders E = $ by equity holders I = $ of initial investment I = B + E The WACC is defined so that suppliers of capital receive their respective required return given the risk they must bear. Debt holders require k d. After-tax cost = k d (1 - t c ) Equity holders require k e. I k w = B k d (1 - t c ) + E k e k w = WACC

18 k w ' B I k d (1 & t c ) % E I k e Let w d ' B I and w e ' E I k w ' w d k d (1 & t c ) % w e k e (WACC) 2 Could allow multiple debt and equity types 2 w d and w e often assumed set at some "target level" (more later) 2 k w supplies required return to each contributor of capital

19 Relationship between k e and debt V L = V u + Bt c 2 Expected ATCF into levered firm V u (k u ) + Bt c 8 8 (k d ) same risk same risk as c as k d D 2 Expected ATCF to debt and equity holders Ek e % Bk d 2 Cash inflows = cash outflows (no growth) V u k u % t c Bk d ' Ek e % Bk d k e ' V u E k u & (1 & t c ) B E k d

20 Remember V L ' V u % t c B ' B % E so V u ' E % B(1 & t c ) Substituting, k e ' E % B(1 & t c ) E k u & (1 & t c ) B E k d 2 k e ' k u % (1 & t c )(k u & k d ) B E (MMII) 4 Opportunity cost of equity capital increases linearly B with a change in. E 4 With no debt, k e = k u.

21 Example: AGFIRM is currently unlevered. It is considering restructuring to allow $200 in debt. Company expects to generate $ in EBIT (perpetuity). Corporate tax rate = 34%. Cost of debt is 10%. Unlevered firms in the industry require a 20% return. 2 What will AGFIRM S value be if it restructures? E( ATCF u ) ' E( EBIT)(1 & t c ) ' $151.52(1 &.34) ' $100 V u ' E(ATCF u ) k u ' ' $500 V L ' V u % t c B ' $500 % 200(.34) ' $500 % $68 ' $568

22 Suppose AGFIRM started with 500 shares Share price u = V u shares ' $ ' $1 Share price L = V L & B shares ' $568&$ ' $1.23 Value of equity L = E L = V L - B = $568 - $200 = $368 2 What is the required return on AGFIRM s equity? k e ' k u % (1 & t c )(k u & k d ) B E '.20 % (1 &.34)(.20 &.10) ' Use of debt increased required return on equity from k u =.20 to k e =.2359

23 Check E L ' (E(EBIT) & k d B)(1 & t c ) k e ' ( &.10(200))(1 &.34).2359 = $368 2 Find AGFIRM s WACC w d ' B V L ' '.352 w e ' '.648 k w = w e k e + w d k d (1- t c ) = (.648)(.2359) + (.352) (.10)(1 -.34) = =.1761

24 The firms WACC decreased from k w = k u = 20% to k w = 17.61% as a result of the debt use. Check value of the firm V L ' E(EBIT)(1 & t c ) k w ' (1 &.34).1761 ' $568 Suppose the firm holds a $100 in assets. Required payment to capital suppliers = I k w = = $17.61 Funding Required Cash Source Investment Return Flow Equity.648(100) = $ $ Debt.352(100) = Govt. tax shield = $3.52(.34) (1.20) Total $17.60

25 2 No taxes GRAPHICAL LOOK AT COST OF CAPITAL % k e =k u +(k u -k d ) B/S k u k w = k u k d B/E Note: k w ' w e k e % w d k d ' E B%E k e % B B % E k d ' E B%E (k u % (k u & k d ) B E ) % B B%E k d ' E B%E k u % B B%E (k u & k d ) % B B%E k d ' k u

26 Corporate taxes (t c > 0) Note: % k e =k u +(1-t c )(k u -k d ) B/E k u k u (1-t c ) k w =k u (1-t c B/B+E) k d (1-t c ) B/E k w = = = E B % E (k u % (1 & t c )(k u & k d ) B E ) % E B % E k u % E B % E k u % = k u & B B % E t c k u 6 = k u 1 & t c B B % lim B64 ( B B % E (1 & t c )k u B B % E k u & E B B % E ) ' 1 Y lim B64 B B % E t c k u k w ' k u (1 & t c ) B B % E k d (1 & t c )

27 With or without taxes, increasing debt increases k e because of higher risk (also higher expected return). However, value of firm and equity claims only change as a result of tax shield. V L ' E(EBIT)(1 & t c ) k w % Bt c Without taxes reduces to V L ' EBIT k u Results so far: Without taxes Capital structure irrelevant Corporate taxes Firms should use almost all debt

28 CAPITAL STRUCTURE LIMITS TO DEBT USE 4 Remember: world without personal taxes V L ' V u % t c B 4 Firms should use all debt financing 4 Inconsistent with real world 4 MM theory help point out possible answers 3 Financial distress costs 3 Personal taxes

29 2 Bankruptcy: Risk or Cost? 4 Debt provides tax benefits 4 Debt also puts financial pressure on firm 4 Ultimate financial distress 6 bankruptcy 4 Bankruptcy costs can offset benefits of debt Example (no taxes) Day Company and Knight Company both plan to operate one more year. Knight Company: Day Company: $49 principle and interest obligation $60 principle and interest obligation Both companies have the same operating CFs.

30 Knight Company Day Company Boom Rec Boom Rec Prob. (.50) (.50) (.50) (.50) CF Debt Distribution to Stockholders Day Company bankrupt in regression Assume: Risk neutral investors Interest rate k e = k d = 10% E k ' (.5)(51)%(.5)(1) 1.10 '23.64 E D ' (.5)(40)%(.5)(0) 1.10 '$18.18 B k ' (.5)49%(.5)(49) 1.10 '44.54 B D ' (.5)(60)%(.5)(50) 1.10 '50 V k V D Firms have same value 2 Debt holders recognize bankruptcy impacts

31 Promised payment $60, but debt holders only willing to pay $50. Required payment without bankruptcy 60 (1 %.10) = $54.55 Actual yield on Day s debt & 1 '.20 or 20% (junk bond) Example is unrealistic Reality: lawsuits, liquidation, other cost increase realized bankruptcy costs Suppose these costs = $15

32 Day Company (.5) Boom (.5) Rec CF E D ' Debt 60 Distribution to Equity (.5)(40) % (.5)(0) 1.10 ' (.5)(60) % (.5)(35) B D = = V D Bankruptcy "costs" reduce value of firm 2 Bankruptcy "risk" did not impact firm value Without bankruptcy costs $100 $50 $60 Debt $40 Eq. $50 Debt With bankruptcy costs $100 $50 $60 Debt $40 Eq. $15 B. cost $35 Debt Debt and Equity holders no longer split earnings

33 Bondholders account for bankruptcy "costs" in returns $60 $43.18 & 1 ' 39.0% Bond holders pay fair price after accounting for prob. and costs of bankruptcy Suppose Repayment Amount Rec Prob Bankruptcy Cost Promise Borrowed $ $ Bankruptcy costs increase cost of debt 2 Financial distress causes same impact as bankruptcy costs

34 TYPES OF COSTS Direct Costs of Financial Distress 2 Legal and Administration Costs of Liquidation and Reorganization 4 Legal fees 4 Administrative fees 4 Accounting fees 4 Court fees (expert witnesses) Estimated Costs (publically traded firms) 3% of market value 2 Indirect Costs of Financial Distress 4 Impaired ability to conduct business 3 impacts relations with customers and suppliers Estimated direct and indirect costs 20%+ of market value

35 AGENCY COSTS Conflict of interest between shareholders and debt holders 1. Incentives to take large risks 4 Firms near bankruptcy take larger risks Suppose promised debt payment is $100 Low Risk Project Prob. Value = Equity + Debt Rec..5 $100 = Boom = V L ' (.5)(100) % (.5)(200) ' $150 High Risk Project Prob. Value = Equity + Debt Rec..5 $ 50 = (bankrupt) Boom = V H ' (.5)(50) % (.5)(240) ' $145

36 All equity firm would select low risk project However equity value is V L > V H E L = (.5)(0) + (.5)(100) = 50 E H = (.5)(0) + (.5)(140) = 70 Equity holders will want high risk project when debt is used. 2. Incentive toward under investment New investment may help debt holders at shareholders expense Consider firm $4,000 debt payment due at end of year Bankrupt in recession Project cost $1,000 and brings in $1,700

37 Firm without Project Firm with Project (.5) (.5) (.5) (.5) Boom Rec Boom Rec CFs 5,000 2,400 6,700 4,100 Debt 4,000 2,400 4,000 4,000 1, , Debt holders prefer project Suppose $1,000 cost of project comes from equity E w/o = (.5) 1,000 + (.5) 0 = $500 E w = (.5) (2,700) + (.5)(100) - 1,000 = $400 Equity holders prefer to reject project. Equity holders contribute entire investment but must share rewards.

38 3. Milk Property like strategy 2 except instead of deciding not to invest you actually divest through increasing dividends. 4 These strategies only occur when there is a possibility of bankruptcy Again increases the cost of debt 4 May be reduced through "protective covenants" in loon documents 3 Negative Covenants (limit actions) restrict dividends, collateral, mergers, asset sales, debt levels 3 Positive covenant (specify action) NWC, financial statements 3 Debt Consolidation also reduces bankruptcy costs

39 3 Combining the tax effects and financial distress costs Maximum Value Value of Firm PV of tax shield V L = V u + t c B PV of financial distress cost V u B * (Optional debt level) Debt Tax shield Y 8 value of firm Distress costs Y 9 value of firm

40 VALUATION UNDER PERSONAL AND CORPORATE TAXES 2 Earlier we saw gains in leverage with only corporate taxes: G ' V L & V u ' t c B 2 Now consider value of firm in a world with both corporate and personal taxes Equity holders receive (EBIT - k d B)(1 - t c )(1 - t e ) Debt holders get k d D(1 - t d ) Total CF to all stakeholders: or (EBIT & k d D)(1 & t c )(1 & t e ) % k d D(1 & t d ) EBIT (1 - t c )(1 - t e ) + k d D(1 - t d ) 1 & (1 & t c )(1 & t e ) (1 & t d ) 8 8 CF to unlevered CF to debt firm after taxes holders after taxes

41 So V L ' V u % B 1 & (1 & t c )(1 & t e ) (1 & t d ) where B = k d D (1 - t d ) / k d Gain from leverage in world with personal taxes Notes: G ' B 1 & (1 & t c )(1 & t e ) (1 & t d ) 2 When t e = t d, gain is same as in world without personal taxes 2 When t e < t d, gain from leverage is reduced from world without personal taxes 4 Reasons t e may be less than t d 3 capital gains tax break 3 capital gains may be delayed by reinvestment 3 gains and losses in a portfolio may offset each other 3 dividend exclusions for corporations when t e < t d, more taxes get paid in a levered firm, than an unlevered firm at the personal level

42 2 If (1 & t c )(1 & t e ) ' (1 & t d ), gain from leverage is zero. Lower corporate taxes from leverage are exactly offset by higher personal taxes. $ V L = V u + t c B when t e = t d V L = V u + B[1- (1-t c )(1-t e ) ] (1-t d ) when (1-t d ) > (1-t c )(1-t e ) V L = V u when (1-t d ) = (1-t c )(1-t e ) B

43 TAX POLICY AND FINANCING INCENTIVES Before 1986: Corporate Income 46% maximum Interest and Dividends 50% maximum Capital Gains 20% Suppose firm pays no dividends and capital gains are deferred so that the effective tax rates are t e = 10%, t d = 50% and t c = 46%. Interest Equity Income Income before tax $1.00 $1.00 Less Corporate 46% Income after Corporate tax Less Personal tax (t e =.10 and t d =.50) Income after tax $0.50 $0.496 Essentially no advantage to debt Small advantage to debt = $.004

44 1999: Corporate Income 35% maximum Interest and Dividend 39.6% maximum Capital Gains 20% Suppose effective capital gains rate is 20%/2 = 10% and that no dividends are paid. Interest Equity Income Income before tax $1.00 $1.00 Less Corporate tax (t c = 35) Income after Corporate tax Personal tax (t d =.396 and t e =.10) Income after tax $0.604 $0.585 Advantage to debt = $0.019

45 Now suppose the same firm in 1999 pays out 1/2 of equity income as dividends. Effective tax rate on equity ( )/2 =.248) Interest Equity Income Income before tax $1.00 $1.00 Less Corporate tax (t c =.35) Income after Corporate tax Personal tax (t d =.396 and t e =.248) Income after tax $.604 $0.489 Advantage to debt = $ Advantage tends to favor debt 2 Magnitude not clear and depends on tax rates of equity and debt holders as well as dividend payout rates

46 EXAMPLE E(EBIT) ' $100,00 (perpetuity) t c ' 34% t e ' 12% t d ' 28% k u (1 & t c ) ' 15% Currently all equity, but considering borrowing $120,000 at 10%. V u ' $100,000(1&.34)(1 &.12).15(1&.12) ' $440,000 V L ' $440,000 % $120,000 1 & (1 &.34)(1 &.12) (1 &.28) ' $463,200 G ' V L & V u ' 463,200 & 440,000 = $23,230 Smaller than t c B =.34(120,000) = $40,800 Extra tax on debt (t d > t e ) at personal level lowers gains from debt

47 2 Implications 4 Gains from leverage still positive (probably) but smaller than thought if t e < t d 4 "Grossed" up return on debt to equate after-tax returns (if t e < t d ) offsets same debt advantage Result 4 Framework also lays out arguments for equilibrium aggregate debt levels (another day)

48 2 How firms establish capital structure 2 Practical difficulties no "formula" for optimal debt structure 2 Empirical Evidence 4 Most firms have "low" D/E. U.S. average D/E :.3 to.5 Firms pay substantial taxes but clearly don't issue debt to point where tax shield is exhausted 4 Announced increases (decreases) in anticipated leverage tend to increase (decrease) firm value 4 Capital structures differ by industry 3 Profitability 3 Growth 3 Intangible assets 4 Firms tend to maintain target levels at D/E

49 FACTORS TO CONSIDER IN DETERMINING TARGET D/E 2 Taxes (tax shield) 2 Financial Distress Cost 4 Variable income 6 increase probability of financial distress 4 Tangible assets 6 less financial distress 4 Intangible assets 6 more financial distress 2 Credit Reserves 4 External equity can be expensive to issue relative to internal equity 4 Maintain credit capacity (low D/E) to allow capital expenditures without issuing new equity 2 Industry D/E Ratios

50 Reconciling M-M and CAPM Unifies approach to determining discount rate (cost of capital) Type of Capital CAPM MM Debt k d = k rf + (k m -k rf ) d k d = k rf, d = 0 Unlevered Equity k u = k rf + (k m -k rf ) u k u = k u Levered Equity k e = k rf + (k m -k rf ) L k e = k u + (ku -k d )(1-t c ) B/E WACC k w = w e k e + w d k d (1 - t c ) k w ' k u 1 & t c B B%E w d ' B B%E w c ' E B%E

51 Can easily modify MM risk-free debt assumption: k d ' k rf % (k m & k rf ) d Relationship between L + u k e ' k rf % (k m & k rf ) L ' k u % (k u & k d )(1 & t c ) B E Substitute k d ' k rf % (k m & k rf ) d Rearrange and simplify k u ' k rf % (k m & k rf ) u L ' u % ( u & d )(1 & t c ) B E ' u (1 % (1 & t c ) B E ) & d (1 & t c ) B E If we observe L, we can estimate u u ' L % d (1 & t c ) 1 % (1 & t c ) B E B E

52 EXAMPLE Currently w d =.2 (market value) Considering w d =.35 k d = k rf =.07 ( d = 0) t c =.5 k m =.17 L =.5 (w d =.20) 2 Find the current values of k e and k w k e ' k rf % (k m & k rf ) L '.07 % (.17 &.07).5 '.12 or 12% (at w d '.2) k w ' w e k e % w d k d (1 & t c ) ' (.8)(.12) % (.2)(.07)(1 &.5) '.103 or 10.3% (at w d '.2)

53 2 Find k w if the new target capital is w d =.35 Remember k e will increase as the debt level rises relative to equity MM s definition of k w says k w ' k u 1 & t c B B % E which implies (using observed results at w d =.20) k u ' k w 1 & t c B B % E ' &(.5)(.2) '.1144 So if w d =.35, MM s definition of k w says k w =.1144 (1 - (.5)(.35)) = or 9.438%

54 2 We could have calculated the new L and k e and preceded with the standard k w approach directly At w d =.2, Remember d = 0 1 % (1 & t c ) B E u ' L '.5 (1 % (1 &.5)(.25)) '.4444 So at w d =.35, the new L will be L ' 1 % (1 & t c ) B E u ' [1 % (1 &.5)(.5385)](.4444) '.5641 (at w d '.35) Thus k e = k rf + (k m - k rf ) L =.07 + ( ).5641 =.1264 and k w ' w d k e % w d k d (1 & t c ) (at w d '.35) ' (.65)(.1264) % (.35)(.07)(1 &.5) ' or 9.44% 2 Suppose project has same systematic risk as firm, L, and provides expected return at 9.25%. Should project be taken?

55 E(k p ) '.0925 < k w '.0944 % k e 12.6% 12% k u (1 - t c ) k d (1 - t c ) k w = k u (1 - t c (B/B+E)) 25% 53.85% B/E

56 2 Evaluating projects with different risk levels than the firm. 4 Find the required return assuming all equity investment. 4 Adjust for the firm s capital structure using the approach(s) from the previous section. Example: u j ' 1.2, k rf '.07, k m '.17 4 k u j = k rf + (k m - k rf ) u j =.07 + ( ) 1.2 =.19 or 19% 4 k w = k u (1 - (1 - t c ) B/B+E) =.19 (1 - (.5) (.20)) =.171 or 17.1% at w d =.2 =.19 (1 - (.5) (.35)) =.157 or 15.7% at w d =.35 2 Comment on RTA vs. RTE 2 Comment on business organizations