Capital Structure Question Solution

FINE 3100 Problems for Midterm – Additional Capital Structure Problems Question 1 Belgarion Enterprises Asset beta, the riskiness of the firm, can be found as the weighted average of the betas of its debt and equity, where the weights are fraction of the firm financed by debt and equity: ? A = D/V ? D + E/V ? E = . 5 ? 0 + . 5 ? 1. 4 = . 7 To find the beta of the firm 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 higher if the firm has NO DEBT, in the otherwise perfect financial markets world. The firm with debt has an asset that the firm no debt does not: the interest tax shield. The riskiness of the tax shield is lower than the riskiness of the firm’s operating assets (its business risk). In fact, in this case, the interest tax shield is riskless because the debt is riskless. The beta of the levered firm’s assets is lower than beta of the unlevered firm’s assets. Remember, bankruptcy is costless in this problem. If bankruptcy is not costless, the result may not hold – by increasing leverage, the probability of bankruptcy goes up and therefore the expected costs of bankruptcy increase. In this case, the firm’s riskiness may well increase with leverage). Question 2 Little Industries a) Current market values EL = 300,000 ? $3 = $900,000 Value 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 rates 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 way to solve for the unlevered firm value is to first calculate the unlevered cost of equity and then use it to discount the unlevered firm’s cash flows 1. Unlevered cost of equity Recall: 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 will be 30% debt financed. Let D* be the total debt after refinancing and VL* be the total firm value after refinancing. It must be true 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 new debt and retiring equivalent 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 shareholders. On the announcement of the proposed restructuring, the total value of equity will increase by the increase in firm value: Value of existing equity on the announcement = 900,000 + 106,818. 2 = 1,006,818. 2 New share price = 1,006,818. 2/300,000 = $3. 356 To figure out the number of shares repurchased, first figure out the dollar value of the new 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 shares repurchased = $267,045/$3. 356 per share = 79,572 shares Share remaining = 300,000 – 79,572 = 220,427 (iii) New required return to equity Method 1: rE. L = r0 + (r0 – rD) D/E (1 – Tc) = . 17419 + (. 17419 – . 1) ? (317,045. 5/739,772. 7) ? .6 = . 193 Method 2: Interest 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, offs etting 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 leverage, 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 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 = 160 m market value of firm = 210 After Restructuring: Assume that all change in value is borne by the shareholders. So the loss 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 pric e 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) Use 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 risk 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 valid to use the CAPM†¦this is ok, given the perfect financial markets assumption. Need to get all of the components of WACC: rD = current yield-to-maturity, 9% Market 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 out†¦the closest company to GLC is All 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 GLC’s current capital structure to get GLC’s levered value of the firm and its equity. Next calculate the cost of equity, given GLC’s current capital structure†¦. 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 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 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 always the case. When debt is risky (that is, there is a chance that the debt will not be paid the full promised interest and principal), improvements in firm val ue may go partly or totally to debt holders. This means that the debt has become less risky: there is less chance that the bondholders won’t get the promised interest and principal repayments. An example: when a firm is in financial distress, 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 firm’s operating cash flow be variable. Whenever you add the fixed interest payments, the result is to intensify the variability of the cash flows to shareholders (they get paid only after the fixed payments have 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 have 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 currently payi ng out the money 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 – 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 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 QUESTION True. Cost savings are much more likely to be achievable than revenue increases – firms have control over their production process but 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 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). 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 won’t want the firm to borrow – pay only dividend income and less total taxes (corporate plus personal) are paid. Firm 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 temptation: spend the money on projects they like but aren’t 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 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"gift† 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). 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 firm’s reputation and ability to raise financing is affected.