Capital Structure Question Solution

FINE 3100 Problems for Midterm Additional Capital Structure Problems head 1 Belgarion Enterprises Asset beta, the jeopardy of the house patronize, can be found as the weighted average of the betas of its debt and impartiality, where the weights argon fraction of the immobile financed by debt and impartiality ? A = D/V ? D + E/V ? E = . 5 ? 0 + . 5 ? 1. 4 = . 7 To find the beta of the self-colored with no debt, find ? o or ? u using the formula for levered equity ? E,L = ? o + ? o ? D D/E ( 1 TC) Rearrange to find ? o = ? E,L + ? D D/E ( 1 TC) 1 + D/E ( 1 TC) Since the debt beta is zero, the equation simplifies to ?o = ?E,L = 1. 4 / ( 1 + (. 5/. 5) ? (1 . 4) ) = . 875 1 + D/E ( 1 TC) The asset beta is laster if the cockeyedly has NO DEBT, in the otherwise perfect monetary markets world. The solid with debt has an asset that the debauched no debt does not the interest revenue enhancement shield. The take chancesiness of the task shield is set out than the riski ness of the incorruptibles operating assets (its business risk). In fact, in this case, the interest tax shield is risk little because the debt is riskless. The beta of the levered firms assets is lower than beta of the unlevered firms assets. Remember, nonstarter is beless in this problem. If bankruptcy is not costless, the result may not hold by increasing leverage, the probability of bankruptcy goes up and in that locationfore the expected costs of bankruptcy increase. In this case, the firms riskiness may well increase with leverage). Question 2 Little Industries a) received market reputes EL = 300,000 ? $3 = $900,000 Value per attachment (. 05 ? 1000)/. 1 = 50/. 1 = $ viosterol Total trammels D= (. 05? 100,000)/. 1 = $50,000 VL = D + EL = 50,000 + 900,000 = $950,000 b) Current required browses of return Debt rD = 10 % (given) Equity rE,L = (EBIT I) ? (1 TC) = (270,000 5,000) ? (1 . 4) = . 1766666 = 17. % EL 900,000 WACC = (D/VL) ? rD ? (1-TC) + (EL/VL) ? rE. L = ( 50,000/950,000) ? .1 ? (1-. 4) + 900,000/950,000 ? .177 = . 1708 c) For case of perpetual debt VL = Vu + Tc D Therefore Vu = VL Tc D = 950,000 . 4 ? 50,000 = 950,000 20,000 = 930,000 NOTE another bureau to solve for the unlevered firm hold dear is to first calculate the unlevered cost of equity and then use it to discount the unlevered firms cash flows 1. Unlevered cost of equity swall(a)ow rE. L = r0 + (r0 rD) D/E (1 Tc) Rearrange the formula for r0 0 = rE,L + rD D/E (1 Tc) / 1 + D/E (1 Tc) = (. 177 + . 1? 50,000/900,000 ?. 6)/(1+50,000/900,000?. 6) = . 1741935 VU = EU = EBIT ? (1- TC)/r0 = 270,000 ? .6/. 1741935 = 930,000 d) (i) After restructuring, the firm get out be 30% debt financed. Let D* be the integrality debt after refinancing and VL* be the total firm place after refinancing. It must be unbent that D* = . 3 ? VL* Since VL = Vu + Tc D, then VL* = Vu + Tc D* Substituting for D* VL* = Vu + Tc . 3 ? VL* Solve for VL* (1 . 3? TC) VL*= Vu VL*= Vu/ (1 . 3? TC) = 930,000/ ( 1 . 3 ?. 4) = 1,056,818. 2 And D* = . 3 ? VL*= . 3 ? 1,056,818. 2 = 317,045. 5 EL* = . ? VL*= . 7 ? 1,056,818. 2 = 739,772. 7 (ii) By issuing brisk debt and retiring uniform value of equity, total firm value increases VOLD= 950,000 VNEW = 1,056,818. 2 Increase in firm value = 1,056,818. 2 950,000 = 106,818. 2 Since the required rate of return to debt is unchanged, we can assume that all of the benefit of the restructuring is captured by the copeholders. On the announcement of the proposed restructuring, the total value of equity entrust increase by the increase in firm value Value of existing equity on the announcement = 900,000 + 106,818. 2 = 1,006,818. 2 New sh be outlay = 1,006,818. 2/300,000 = $3. 356To figure out the number of sh bes repurchased, first figure out the dollar value of the newborn debt issued New debt issued = New total debt previous total debt = 317,045. 5 50,000 = 267,045 Shares worth $267,045 are repurchased, at $3. 356 per share Total sha res repurchased = $267,045/$3. 356 per share = 79,572 shares Share remaining = 300,000 79,572 = 220,427 (iii) New required return to equity regularity 1 rE. L = r0 + (r0 rD) D/E (1 Tc) = . 17419 + (. 17419 . 1) ? (317,045. 5/739,772. 7) ? .6 = . 193 Method 2 recreate on total debt, I = . 1 ? 317,045. 5 = 31,704. 5 rE,L = (EBIT I) ? (1 TC) = (270,000 31,704. 5) ? 1 . 4) = . 193 EL 739,772. 7 New WACC = . 3 ? .1 ?. 6 + . 7?. 193 = . 1531 e) (i) Because the model assumes bankruptcy costs are zero, it does not consider the potential downside of increasing leverage. With bankruptcy costs, the expected costs of bankruptcy increase with leverage, offsetting the benefit of reduced taxes. (ii) Given D* = 317,045. 5 and Interest = 31,704. 5 EL = (EBIT I) ? (1 TC) = (270,000 31,704. 5) ? (1 . 4) = 571,909. 1 EL . 25 Total firm value V = D* + EL = 317,045. + 571,909. 1 = 888,955 Now, taking into account the impact of the bankruptcy costs, on the announcement of the increased lever age, the firm value FALLS Change in firm value = 950,000 888,955 = -61,045 New equity value on the announcement = 900,000 61,045 = 838,955 New share price on the announcement = 838,955/300,000 = $2. 80 Share price water hang from $3 to $2. 80 Therefore, the restructuring is a bad idea if the new required rate of return to equity rises to 25%. Question 3 Mighty Machinery Initial situation market value of debt = . 08? 50m/. 08 = 50 m market value of equity = 8 m ? 20/sh = 160 m market value of firm = 210After Restructuring Assume that all change in value is borne by the shareholders. So the mischief of the tax shield will impact shareholders only. Value of lost tax shield = Tax rate ? change in debt = . 35 (-10m) = 3. 5m New firm value = old value + value of tax shield = 210 3. 5 = 206. 5 m New debt value = old debt + change in debt = 50m 10 m = 40m New equity value (at the actual restructuring date) = new firm value new debt value = 206. 5 40 = 166. 5 m New share price Given that shareholders bear all of the impact of the reduced tax shield, given efficient financial markets, the value of the equity will fall by 3. m ON THE ANNOUNCEMENT of the plan. Thus, at the announcement, total equity is worth 160 3. 5 = 156. 5m or $19. 5625 per share ($156. 5m/8m = 19. 5625). Another way the NPV of the restructuring is -3. 5m, which is all borne by shareholders. The change in share price will be -3. 5m/8m = -$0. 4375, giving a new share price of $20 . 4375 or $19. 5625. ii) Shares issued = $10m/$19. 5625 or 511,182 Check final share value/new number of shares = 166. 5/8. 511182 = $19. 5625. (iii) drill the formula rE = r0 + (r0 rD) D/E (1 Tc) Rearrange the formula for r0 r0 = rE + rD D/E (1 Tc) / 1 + D/E (1 Tc) = . 5 + . 08 ? 50/160 ? (1-. 35)/1+50/160 ? (1-. 35) = . 138181818. Then New rE = r0 + (r0 rD) (new D/new E) (1 Tc) = . 138 + (. 138-. 08) (40/166. 5) (1-. 35) = . 1429 The restructuring causes rE to fall, as expected. The leverage is lower, the ri sk of equity is lower, shareholders required rate of return falls. b) You answer this question Question 4 NOTE This was a particularly tricky question. Part marks were given for wrong answers. Assume that it is logical to use the CAPMthis is ok, given the perfect financial markets assumption. Need to get all of the components of WACC rD = current yield-to-maturity, 9% market place value of D = (. 08 ? 2. 5m )/. 09 = 2. 22222m TC = 35% What about value of equity and cost of equity Use a competitor to figure outthe closest company to GLC is all told Lawn Chemicals. The most complete way to go is to figure out the unlevered cost of equity of All Lawn (reflecting the business risk), and value GLC at this rate. This will give us the unlevered value of GLC. Next, use GLCs current capital social system to get GLCs levered value of the firm and its equity. Next calculate the cost of equity, given GLCs current capital structure. 1. Find unlevered cost of capital for All LawnUse the same r earrangement of the cost of equity formula in question 6 rE = r0 + (r0 rD) D/E (1 Tc) Rearrange the formula for r0 r0 = rE + rD D/E (1 Tc) / 1 + D/E (1 Tc) Use CAPM to find current rE of All Lawn rE = rf + ? ? MRP = . 075 + 1. 2 ? .07 = . 159 r0 = . 159 + . 09 ?. 3? (1-. 35) / 1+. 3? (1-. 35) = . 14774 Value of firm for GLC V L = OCF ? (1 tc) + tcD RU V = 1. 5M * (0. 65) + 2. 222M*(0. 35) .1477 VL = 7. 37892M Value of Equity for GLC VL = Ve + VD = 7. 37892M = 2. 222M + Ve Ve = 7. 37892 2. 222 = 5. 1569M Ve = 5. 1569M = y R equity = (OCF Interest expense)(1 tax rate)/ Value of equity = ($1. million . 08x$2. 5 million) . 65/5. 1569= . 163858 =16. 39%. OR 1. Find unlevered cost of capital for All Lawn Use the same rearrangement of the cost of equity formula in question 6 rE = r0 + (r0 rD) D/E (1 Tc) Rearrange the formula for r0 r0 = rE + rD D/E (1 Tc) / 1 + D/E (1 Tc) Use CAPM to find current rE of All Lawn rE = rf + ? ? MRP = . 075 + 1. 2 ? .07 = . 159 r0 = . 159 + . 09 ?. 3? (1-. 35) / 1+. 3? (1-. 35) = . 14774 2. Value of Unlevered GLC Vu = OCF Taxes / r0 = 1. 5 ? (1-. 35) /. 14774 =6. 59943 3. Value GLC with its current capital structure VL = Vu + Tc D = 6. 59943 + . 35 ? . 22222 = 7. 37721 4. Value GLCs equity and its required rate of return Thus EL = VL D = 7. 37721 2. 22222 = 5. 15499 and rE = r0 + (r0 rD) D/E (1 Tc) = . 14774 + (. 14774 . 09)? (2. 22222/5. 15499)?. 65 = . 1639 5. Calculate GLCs WACC Wacc = (2. 22222/7. 37721)?. 09?. 65 + (5. 15499/7. 37721)?. 1639 = . 1322 Question 5 a) False. Although often increases in firm value increase equity value, it is not always the case. When debt is dubious (that is, there is a chance that the debt will not be paid the full promised interest and principal), improvements in firm value may go partly or totally to debt holders.This means that the debt has become less risky there is less chance that the bondholders wont get the promised interest and principal repayments. An example when a firm is in financial woe, a value-increasing investment may only increase the value of the debt and none of the value goes to shareholders. See kit and also the Barclay, Smith, Watts article. b) False. All that is necessary for the risk of equity to increase is that the firms operating cash flow be variable.Whenever you add the fixed interest payments, the result is to escalate the variability of the cash flows to shareholders (they get paid only after the fixed payments view been made to the debtholders). scene at the kit, risk of equity increased with the addition of debt and there is no chance of bankruptcy in this example (debt is riskless no matter what state of the world occurs, the debtholders get their promised payments). c) False. For this answer, assume perfect financial markets and keep the firms investment and borrowing ceaseless. If you dont fixate these assumptions, then we clear to make other assumptions about the state of the financial markets. These ones make our story easy). It is true that a shareholder may have to sell shares at the bottom of the market to create homemade dividends. But if the firm increases its dividend, they too will have to sell shares at the bottom of the market If we assume that the firm is soon paying out the cash they have, the rest is tied up in investment plans and no new borrowing is made, if the dividend is increased, THE FIRM WILL HAVE TO GO TO THE MARKET AND SELL SHARES to pay for the higher dividend.The risk of selling shares at the bottom of the market has not gone away and shareholders still get stuck with it all they pay for it directly when they sell their shares or indirectly when the firm brings in new shareholders who pay less for their shares than if it had been the top of the market. So this is not a valid reason why the firm paying a dividend will increase firm value. d) Uncertain. What the answer depends on is whether the bond holders anticipated correctly the chances and costs of distress /bankruptcy.If bondholders correctly anticipate distress and the costs associated with it, they will pay less for the bonds than if the costly distress did not occur. Shareholders end up paying the costs because the company gets less for the bonds sold raising the cost of debt financing. Of course, if bondholders do not correctly anticipate the distress, then they share in the costs. e) THIS IS A POST MIDTERM oppugn True. Cost savings are ofttimes more likely to be achievable than revenue increases firms have control over their production process solely not over their customers. f) False. This question is very much related to a).Shareholders will not be willing to contribute more money to positive NPV projects when the multitude of the benefit goes to bondholders. See the references in a). g) True. The messy formula for the impact on firm value of adding debt when some(prenominal) in-person and corporate taxes are considered is outlined in the kit. This happens when (1-TB) (1-Tc)(1-TS).. Translating 1-TB is the after-all-taxes cash flow of a $1 of bond income, (1-Tc)(1-TS) is the after-all-taxes cash flow of $1 of equity income (because first corporate taxes are paid and then personal taxes on equity income are paid).If investors get less in their pocket, after all taxes, when $1 of bond income is paid then after a $1 of equity income, they wont want the firm to borrow pay only dividend income and less total taxes (corporate irrefutable personal) are paid. Firm value will be lower if the company borrows h) True. This follows from the free cash flow problem discussed in Barclay, Smith and Watts. A company with lots of cash but few investment opportunities (low growth) puts management into temptation spend the money on projects they like but arent necessarily positive NPV.For such a firm, a high dividend payout (high dividends/net income) and high interest and principal obligations keeps the cash out of the hands of manager and gives them fewer opport unities to make negative NPV investments, increasing the value of the firm. i) True. Given these assumptions, adding debt creates a new asset a tax shield. The tax shield is a gift from the government, increasing the firms after-tax cash flows. This tax shield is lower risk than the assets of the business it depends on the riskiness of the firms debt (and we assume that the tax rate doesnt change).Thus total risk of the levered firm is lower than if it is unlevered (the levered firm has the same business risk plus the lower risk tax shield the overall risk is lower). j) THIS IS A POST MIDTERM QUESTIONS False. All valuation methods requiring assumptions to be made. Earnings capitalization is a simpler valuation method than discounted cash flow but it is loaded with strong assumptions about the future cash flows/earnings such as constant growth, constant dividend payout and unchanging capital structure. ) True the firm will have received the cash without having to issue new shares, however, the firm will also have missed out on raising equity when these warrants are not exercised and the warrant holders (and other potential investors) are disappointed and may not invest in this firm in subsequent rounds of equity financing if they were not able to benefit from their warrant purchase. Warrants are not like call options. With call options the firm in not involved in the transaction. With warrants the firms reputation and ability to raise financing is affected.