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1.a.. The EPS is the net income divided by the 5,000 shares outstanding. RecessionNormalExpansion

EBIT$12,600$21,000$26,250

NI$12,600$21,000$26,250

EPS$ 2.52$ 4.20$ 5.25

b.If the company undergoes the proposed recapitalization, it will repurchase:Share price = Equity / Shares outstanding= $275,000/5,000= $55Shares repurchased = Debt issued / Share price=$99,000/$45 = 1,800 Interest payment = $99,000(.08) = $7,920The last row shows the percentage change in EPS the company will experience in a recession or an expansion economy under the proposed recapitalization.RecessionNormalExpansion

EBIT$12,600$21,000$26,250

Interest 7,920 7,920 7,920

NI$ 4,680$13,080$18,330

EPS$1.46$ 4.09$ 5.73

2.a.share price is $55, and there are 5,000 shares outstanding. RecessionNormalExpansion

EBIT$12,600$21,000$26,250

Taxes 4,410 7,350 9,188

NI$8,190$13,650$17,063

EPS$1.64$2.73$3.41

b.s the proposed capitalization is shown below. The interest payment and shares repurchased are the same as in part b of Problem 1. RecessionNormalExpansion

EBIT$12,600$21,000$26,250

Interest7,9207,9207,920

Taxes 1,638 4,578 6,416

NI$3,042$8,502$11,915

EPS$0.95$2.66$3.72

Notice that the percentage change in EPS is the same both with and without taxes.2.a.Since the company has a market-to-book ratio of 1.0, the total equity of the firm is equal to the market value of equity.ROE = NI/$275,000RecessionNormalExpansion

ROE4.58%7.64%9.55%

The second row shows the percentage change in ROE from the normal economy.b.If the company undertakes the proposed recapitalization, the new equity value will be:Equity = $275,000 99,000 = $176,000 ROE = NI/$176,000RecessionNormalExpansion

ROE2.66%7.43%10.41%

%ROE64.22+40.14

c.If there are corporate taxes, the ROE is:ROE2.98%4.96%6.20%

If the company undertakes the proposed recapitalization, and there are corporate taxes, the ROE for each state of the economy is:ROE1.73%4.83%6.77%

Notice that the percentage change in ROE is the same as the percentage change in EPS. The percentage change in ROE is also the same with or without taxes.

3.a.Under Plan I, the unlevered company, net income is the same as EBIT with no corporate tax. The EPS under this capitalization will be:EPS = $750,000/265,000 shares EPS = $2.83Under Plan II, the levered company, EBIT will be reduced by the interest payment. The interest payment is the amount of debt times the interest rate, so:NI = $750,000 .10($2,800,000) = $470,000And the EPS will be: EPS = $470,000/185,000 shares = $2.54Plan I has the higher EPS when EBIT is $750,000.

b.Under Plan I, the net income is $1,500,000 and the EPS is: EPS = $1,500,000/265,000 shares = $5.66Under Plan II, the net income is:NI = $1,500,000 .10($2,800,000) = $1,220,000And the EPS is:EPS = $1,220,000/185,000 shares = $6.59Plan II has the higher EPS when EBIT is $1,500,000.

c.To find the breakeven EBIT for two different capital structures, we simply set the equations for EPS equal to each other and solve for EBIT. The breakeven EBIT is:EBIT/265,000 = [EBIT .10($2,800,000)]/185,000 ; EBIT = $927,500 4.a.The earnings per share are:EPS = $33,000/6,000 shares = $5.50 So, the cash flow for the shareholder is:Cash flow = $5.50(100 shares) = $550b.To determine the cash flow to the shareholder, we need to determine the EPS of the firm under the proposed capital structure. The market value of the firm is:V = $58(6,000) = $348,000 Under the proposed capital structure, the firm will raise new debt in the amount of:B = 0.35($348,000) = $121,800This means Shares repurchased = $121,800/$58 = 2,100Under the new capital structure, the company will have to make an interest payment on the new debt. The net income with the interest payment will be: NI = $33,000 .08($121,800) = $23,256This means the EPS under the new capital structure will be:EPS = $23,256 / (6,000 2,100 shares) = $5.96 Since all earnings are paid as dividends, the shareholder will receive:Shareholder cash flow = $5.96(100 shares) = $596.31

c.To replicate the proposed capital structure, the shareholder should sell 35 percent of their shares, or 35 shares, and lend the proceeds at 8 percent. The shareholder will have an interest cash flow of: Interest cash flow = 35($58)(.08) = $162.40The shareholder will receive dividend payments on the remaining 65 shares, so the dividends received will be: Dividends received = $5.96(65 shares) = $387.60The total cash flow for the shareholder under these assumptions will be:Total cash flow = $162.40 + 387.60 = $550This is the same cash flow we calculated in part d.The capital structure is irrelevant because shareholders can create their own leverage or unlever the stock to create the payoff they desire, regardless of the capital structure the firm actually chooses.

5.a.With the information provided, we can use the equation for calculating WACC to find the cost of equity. The equation for WACC is:WACC = (S/V)RS + (B/V)RB(1 tC) The company has a debt-equity ratio of 1.5, which implies the weight of debt is 1.5/2.5, and the weight of equity is 1/2.5, soWACC = .11 = (1/2.5)RS + (1.5/2.5)(.07)(1 .35); RS = .2068, or 20.68%

b.To find the unlevered cost of equity, we need to use M&M Proposition II with taxes, so:RS = R0 + (R0 RB)(B/S)(1 tC) .2068 = R0 + (R0 .07)(1.5)(1 .35) R0 = .1392, or 13.92%c.To find the cost of equity under different capital structures, we can again use M&M Proposition II with taxes. With a debt-equity ratio of 2, the cost of equity is:RS = R0 + (R0 RB)(B/S)(1 tC) RS = .1392 + (.1392 .07)(2)(1 .35) = .2293, or 22.93% With a debt-equity ratio of 1.0, the cost of equity is:RS = .1392 + (.1392 .07)(1)(1 .35) = .1842, or 18.42% And with a debt-equity ratio of 0, the cost of equity is:RS = .1392 + (.1392 .07)(0)(1 .35) RS = R0 = .1392, or 13.92%

6.a.For an all-equity financed company: WACC = R0 = RS = .11 or 11%b.To find the cost of equity for the company with leverage, we need to use M&M Proposition II with taxes, so:RS = R0 + (R0 RB)(B/S)(1 tC) RS = .11 + (.11 .08)(.25/.75)(1 .35) RS = .1165, or 11.65%c.Using M&M Proposition II with taxes again, we get:RS = R0 + (R0 RB)(B/S)(1 tC)RS = .11 + (.11 .08)(.50/.50)(1 .35) RS = .1295, or 12.95%d.The WACC with 25 percent debt is:WACC = (S/V)RS + (B/V)RB(1 tC) WACC = .75(.1165) + .25(.08)(1 .35) WACC = .1004 or 10.04%And the WACC with 50 percent debt is:WACC = (S/V)RS + (B/V)RD(1 tC) WACC = .50(.1295) + .50(.08)(1 .35) WACC = .0908 or 9.08%7.a.In a world with corporate taxes, a firms weighted average cost of capital is equal to:RWACC = [B / (B+S)](1 tC)RB + [S / (B+S)]RSB / (B+S) = 2.5 / (2.5 + 1) = .7143S / (B+S) = 1 / (2.5 + 1) = .2857We can now use the WACC equation to find the cost of equity, which is:.10 = (.7143)(1 0.35)(.06) + (.2857)(RS) ; RS = .2525, or 25.25%b.We can use Modigliani-Miller Proposition II with corporate taxes to find the unlevered cost of equity. Doing so, we find:RS = R0 + (B/S)(R0 RB)(1 tC).2525 = R0 + (2.5)(R0 .06)(1 .35); R0 = .1333, or 13.33%c.If debt-equity = .75B / (B+S) = .75 / (.75 + 1) = .4286S / (B+S) = 1 / (.75 + 1) = .5714The cost of levered equity will be:RS = R0 + (B/S)(R0 RB)(1 tC); RS = .1333 + (.75)(.1333 .06)(1 .35)= .1691, or 16.91%And the weighted average cost of capital will be:RWACC = [B / (B+S)](1 tC)RB + [S / (B+S)]RSRWACC = (.4286)(1 .35)(.06) + (.5714)(.1691)= .1133, or 11.33%

If debt-equity =1.50B / (B+S) = 1.50 / (1.50 + 1) = .6000; S / (B+S) = 1 / (1.50 + 1) = .4000The cost of levered equity will be:RS = R0 + (B/S)(R0 RB)(1 tC)RS = .1333 + (1.50)(.1333 .06)(1 .35)= .2048, or 20.48%And the weighted average cost of capital will be:RWACC = [B / (B+S)](1 tC)RB + [S / (B+S)]RSRWACC = (.6000)(1 .35)(.06) + (.4000)(.2048)= .1053, or 10.53%8. Given RD=12%, RF=10%, RM=18%, E=1.5, D/V=0.5thereforeRE=RF+E*Risk Premium=10%+1.5*8%=22%RA=D/V*RD+E/V*RE=0.5*12%+0.5*22%=17%E=(RD-RF)/Risk premium=2%/8%=0.25A=Excess Return/Risk premium=7%/8%=0.875

9.a.Debt issue:The company needs a cash infusion of $1.3 million. If the company issues debt, the annual interest payments will be:Interest = $1,300,000(.08) = $104,000The cash flow to the owner will be the EBIT minus the interest payments, or:40 hour week cash flow = $550,000 104,000 = $446,00050 hour week cash flow = $625,000 104,000 = $521,000Equity issue:Toms ownership percentage = $3,200,000 / ($3,200,000 + 1,300,000) = .71So, Toms cash flow under an equity issue will be 71 percent of EBIT, or:40 hour week cash flow = .71($550,000) = $391,11150 hour week cash flow = .71($625,000) = $444,444b.Tom will work harder under the debt issue since his cash flows will be higher. Tom will gain more under this form of financing since the payments to bondholders are fixed. Under an equity issue, new investors share proportionally in his hard work, which will reduce his propensity for this additional work.c.The direct cost of both issues is the payments made to new investors. The indirect costs to the debt issue include potential bankruptcy and financial distress costs. The indirect costs of an equity issue include shirking and perquisites.

10.a.Since this is the only project for the company, the company value will be the same as the project value, so:Low-volatility project value = .50($3,500) + .50($3,700)= $3,600High-volatility project value = .50($2,900) + .50($4,300)= $3,600The low-volatility project maximizes the expected value of the firm.b.If the low-volatility project is undertaken, the firms equity will be worth $0 if the economy is bad and $200 if the economy is good. Expected value of equity with low-volatility project = .50($0) + .50($200)= $100And the value of the company if the high-volatility project is undertaken will be:Expected value of equity with high-volatility project = .50($0) + .50($800)= $400c.The companys stockholders prefer the high-volatility project since it maximizes the expected value of the companys equity.d.Let X be the debt payment that bondholders will require if the high-volatility project is undertaken. In order for stockholders to be indifferent between the two projects, the expected value of equity if the high-volatility project is undertaken must be equal to $100, so:Expected value of equity = $100 = .50($0) + .50($4,300 X)X = $4,100

11.a.Using M&M Proposition I with taxes, the value of a levered firm is:

VL = [EBIT(1 tC)/R0] + tCB = [$975,000(1 .35)/.14] + .35($1,900,000)= $5,191,785.71

b.The CFO may be correct. The value calculated in part a does not include the costs of any non-marketed claims, such as bankruptcy or agency costs.12.