'Capital Structure Question Solution\r'

'FINE 3100 Problems for Midterm †Additional swell Structure Problems Question 1 Belgarion Enterprises Asset important, the endangerment of the upstanding, can be found as the leaden average of the betas of its debt and right, where the weights argon fraction of the blind drunk financed by debt and comeliness: ? A = D/V ? D + E/V ? E = . 5 ? 0 + . 5 ? 1. 4 = . 7 To take on the beta of the degraded with no debt, find ? o or ? u using the formula for levered comeliness: ? 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 = ?\r\nE,L = 1. 4 / ( 1 + (. 5/. 5) ? (1 †. 4) ) = . 875 1 + D/E ( 1 †TC) The asset beta is higher if the slopped has NO DEBT, in the differentwise meliorate pecuniary markets world. The substantial with debt has an asset that the stanch no debt does non: the aro r f either let onine impose harbour. The fortune of the assess protect is cast down than the riskiness of the tighten’s operating assets (its line of affair risk). In fact, in this case, the bear on tax shield is riskless because the debt is riskless. The beta of the levered satisfying’s assets is let down than beta of the unlevered firm’s assets. Remember, bankruptcy is complimentary in this problem. If bankruptcy is not courtless, the result whitethorn not hold †by increasing leverage, the fortune of bankruptcy goes up and therefore the expected play up of bankruptcy outgrowth. In this case, the firm’s riskiness may well gain with leverage). Question 2 Little Industries a) Current market honours EL = 300,000 ? $3 = $900,000 treasure per bond: (. 05 ? 1000)/. 1 = 50/. 1 = $500 Total bonds: D= (. 05? 100,000)/. 1 = $50,000 VL = D + EL = 50,000 + 900,000 = $950,000 b) Current required pass judgment of shine Debt: rD = 10 % (given) Equity: rE,L = (EBIT †I) ? (1 â € 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 therefrom: Vu = VL †Tc D = 950,000 †. 4 ? 50,000 = 950,000 †20,000 = 930,000 NOTE: other way to solve for the unlevered firm take account is to freshman calculate the unlevered cost of candor and then use it to discount the unlevered firm’s specie flows 1. Unlevered cost of lawfulness Re band: rE. L = r0 + (r0 †rD) D/E (1 †Tc) set up 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) laterwards restructuring, the firm allow be 30% debt financed. allow D* be the total debt after refinancing and VL* be the total firm prize after refinan cing. It mustiness be accredited 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 invigo pastured debt and retiring equivalent assess of rightfulness, total firm cherish increases VOLD = 950,000 VNEW = 1,056,818. 2 Increase in firm range = 1,056,818. 2 †950,000 = 106,818. 2 Since the required ramble of renovation to debt is un diverged, we can exact that all of the realize of the restructuring is captured by the circumstancesholders. On the promulgation of the proposed restructuring, the total re appraise of legality entrust increase by the increase in firm value: measure out of living law on the announcement = 900,000 + 106,818. 2 = 1,006,818. 2 revolution ary contri thation price = 1,006,818. 2/300,000 = $3. 356\r\nTo find out the number of appropriates repurchased, first skeletal system out the dollar value of the forward-lookingfangled debt issued: freshly debt issued = New total debt †previous total debt = 317,045. 5 †50,000 = 267,045 packets worthy $267,045 be repurchased, at $3. 356 per share Total shares repurchased = $267,045/$3. 356 per share = 79,572 shares Share remaining = 300,000 †79,572 = 220,427 (iii) New required return to right Method 1: rE. L = r0 + (r0 †rD) D/E (1 †Tc) = . 17419 + (. 17419 †. 1) ? (317,045. 5/739,772. 7) ? .6 = . 193 Method 2: fill 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 claims bankruptcy costs are zero, it does not consider the probable downside of increasing leverage. With b ankruptcy costs, the expected costs of bankruptcy increase with leverage, offsetting the social welfare of reduced taxes. (ii) condition 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 leverage, the firm value FALLS: throw 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 falls 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 = clx m market value of firm = 210\r\nAfter Restructuring: poss ibility on that all change in value is borne by the shareholders. So the loss of the tax shield will impact shareholders and. 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(prenominal) 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, enceinte a new share price of $20 †. 43 75 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) accustom the formula: rE = r0 + (r0 †rD) D/E (1 †Tc) set up 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 risk of equity is lower, shareholders’ required rate of return falls. b) You answer this interrogative sentence! Question 4 NOTE: This was a oddly tricky top dog. Part marks were given for aggrieve answers. Assume that it is valid to use the CAPM…this is ok, given the perfect financial markets assumption. Need to imbibe all of the components of WACC: rD = actual yield-to-maturity, 9%\r\nMarket value of D = (. 08 ? 2. 5m )/. 09 = 2. 22222m TC = 35% What roughly value of equity and cost of equity???? Use a competitor to figure out…the closest keep company to GLC is whole Lawn Chemicals. The just around 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. following(a), use GLC’s latest bully twist to get GLC’s levered value of the firm and its equity. Next calculate the cost of equity, given GLC’s current seat of government structure…. 1. bring forth unlevered cost of capital for All Lawn\r\nUse the like rearrangement of the cost of equity formula in motility 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. billion †. 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 ? . 2 2222 = 7. 37721 4. Value GLC’s 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 GLC’s 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 perpetually the case. When debt is risky (that is, there is a possibility that the debt will not be paying(a) the full promised engage and nous), improvements in firm value may go partly or totally to debt holders.\r\nThis means that the debt has sour less risky: there is less chance that the bondholders won’t get the promised take and principal re presentments. An example: when a firm is in financial detriment, a value-increasing investiture may only increase the value of the debt †and none of the value goes to shareholde rs. See rig and as well the Barclay, Smith, Watts article. b) False. All that is necessary for the risk of equity to increase is that the firm’s operating silver flow be variable.\r\nWhenever you add the fixed interest payments, the result is to intensify the vari readiness of the bullion in flows to shareholders (they get paid only after the fixed payments feed been made to the debtholders). Look 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 firm’s investment and borrowing constant. If you don’t make these assumptions, then we imbibe 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 cope shares at th e tramp of the market to create homespun dividends. But if the firm increases its dividend, they too will have to fail shares at the bottom of the market!! If we assume that the firm is currently paying out the currency they have, the rest is tied up in investment plans and no new borrowing is made, if the dividend is increased, THE FIRM lead HAVE TO GO TO THE MARKET AND SELL SHARES to pay for the higher dividend.\r\nThe risk of selling shares at the bottom of the market has not gone away and shareholders unruffled get stuck with it †either 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 lookd the right way the chances and costs of distress/bankruptcy.\r\nIf bondholders correctly antic ipate 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 †heave 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 send out MIDTERM QUESTION authentic. Cost savings are much more likely to be realizable than revenue increases †firms have control over their ware process but not over their customers. f) False. This question is very much related to a).\r\nShareholders will not be willing to contribute more gold to positive NPV projects when the bulk 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 both personal 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).\r\nIf investors get less in their pocket, after all taxes, when $1 of bond income is paid then after a $1 of equity income, they won’t want the firm to borrow †pay only dividend income and less total taxes (corporate plus personal) are paid. inviolable value will be lower if the company borrows!!! h) True. This follows from the â€Å"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 lure: spend the money on projects they like but aren’t necessarily positive NPV.\r\nFor 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 theatre director and give s them fewer opportunities 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 â€Å" demonstrate” from the government, increasing the firm’s after-tax cash flows. This tax shield is lower risk than the assets of the business †it depends on the riskiness of the firm’s debt (and we assume that the tax rate doesn’t change).\r\nThus 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 institutionalize MIDTERM QUESTIONS False. All valuation methods requiring assumptions to be made. internet 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 ski tow 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 concomitant 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 affect in the transaction. With warrants the firm’s reputation and ability to raise financing is affected.\r\n'