FINS3625T2Yr2018Wk9Solutions.pdf - 16-1 QBE = F(P – V = $500,000($75 $50 = 20,000 16-2 If wd = 0.2 then wce = 1 – 0.2 = 0.8 So D/S = wd/we = 0.2/0.8

FINS3625T2Yr2018Wk9Solutions.pdf - 16-1 QBE = F(P – V =...

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16-1 Q BE = F/(P – V) = $500,000/($75 - $50) = 20,000. 16-2 If w d = 0.2, then w ce = 1 – 0.2 = 0.8. So D/S = w d /w e = 0.2/0.8. b U = b/[1 + (1-T)(D/S)] = 1.15/[1 + (1-0.40)(0.2/0.8)] = 1.0. 16-3 If the company had no debt, its required return would be: r s,U = r RF + b U RP M = 5.5% + 1.0(6%) = 11.5%. With debt, the required return is: r s,L = r RF + b L RP M = 5.5% + 1.6(6%) = 15.1%. Therefore, the extra premium required for financial risk is 15.1% - 11.5% = 3.6%. 16-4 S Post = (1 – w d )(V opNew ) = (1 – 0.4)($500) = $300 million. 16-5 S Post = (1 – w d )(V opNew ) = (1 – 1/3)($900) = $600 million. P Post = (V opNew – D old )/n prior = ($900 – 0)/30 = $30 16-6 n Post = Original shares – shares repurchased = n Prior – (Dollar value of shares repurchased/Repurchase Price) = 60 – ($150/$7.5) = 60 – 20 = 40 million. Note that the formula n Post = n Prior [(V OpNew – D New )/(V OpNew – D Old )] can be used if you note that V OpNew = $60x$7.50 = $450 and D Old = $0 so that n Post = 60[($450 - $150)/($450 – 0)] = 40 million shares.
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16-8 a. Original value of the firm (D = $0): We are given that the book value of assets is equal to the market value of assets, so the value is $3,000,000. Alternatively, we can calculate the value as the sum of the debt (which is zero) and the stock (200,000 shares at a price of $15 per share): V = D + S = 0 + ($15)(200,000) = $3,000,000. Original cost of capital: WACC = w d r d (1-T) + w ce r s = 0 + (1.0)(10%) = 10%. With financial leverage (w d =30%): WACC = w d r d (1-T) + w ce r s = (0.3)(7%)(1-0.40) + (0.7)(11%) = 8.96%. Because growth is zero, FCF is equal to EBIT(1-T). The value of operations is: V op = . $3,348,214 0.0896 0.40) (1 ($500,000) WACC T) (EBIT)(1 WACC FCF = = = Increasing the financial leverage by adding $900,000 of debt results in an increase in the firm’s value from $3,000,000 to $3,348,214. b. Using its target capital structure of 30% debt, the company must have debt of: D = w d V = 0.30($3,348,214.286) = $1,004,464. Therefore, its value of equity is: S = V – D = $2,343,750. Alternatively, S = (1-w d )V = 0.7($3,348,214.286) = $2,343,750. The new price per share, P, is: P = [S + (D – D 0 )]/n 0 = [$2,343,750 + ($1,004,464.286 – 0)]/200,000 = $16.74.
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c. The number of shares repurchased, X, is: X = (D – D 0 )/P = $1,004,464.286 / $16.741 = 60,000.256 60,000. The number of remaining shares, n, is: n = 200,000 – 60,000 = 140,000. Initial position: EPS = NI/n 0 = [(EBIT – Int.)(1-T)] / n 0 = [($500,000 – 0)(1-0.40)] / 200,000 = $1.50. With financial leverage: EPS = [($500,000 – 0.07($1,004,464.286))(1-0.40)] / 140,000 = [($500,000 – $70,312.5)(1-0.40)] / 140,000 = $257,812.5 / 140,000 = $1.842. Thus, by adding debt, the firm increased its EPS by $0.342. d. 30% debt: TIE = I EBIT = 5 . 312 , 70 $ EBIT . Probability TIE 0.10 ( 1.42) 0.20 2.84 0.40 7.11 0.20 11.38 0.10 15.64 The interest payment is not covered when TIE < 1.0. The probability of this occurring is 0.10, or 10 percent.
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16-9 a. Present situation (50% debt): WACC = w d r d (1-T) + w ce r s = (0.5)(10%)(1-0.15) + (0.5)(14%) = 11.25%. V = 1125 . 0 ) 15 . 0 1 )( 24 . 13 ($ WACC ) T 1 )( EBIT ( WACC FCF = = = $100 million. 70 percent debt: WACC = w d r d (1-T) + w ce r s = (0.7)(12%)(1-0.15) + (0.3)(16%) = 11.94%. V = 1194 . 0 ) 15 . 0 1 )( 24 . 13 ($ WACC ) T 1 )( EBIT ( WACC FCF = = = $94.255 million. 30 percent debt: WACC = w d r d (1-T) + w ce r s = (0.3)(8%)(1-0.15) + (0.7)(13%) = 11.14%. V = 1114 . 0 ) 15 . 0 1 )( 24 . 13 ($ WACC ) T 1 )( EBIT ( WACC FCF = = = $101.023 million. 16-10 a. BEA’s unlevered beta is b U =b/(1+ (1-T)(D/S))=1.0/(1+(1-0.40)(20/80)) = 0.870. b. b = b U (1 + (1-T)(D/S)). At 40 percent debt: b L = 0.87 (1 + 0.6(40%/60%)) = 1.217. r S = 6 + 1.218(4) = 10.87% c. WACC = w d r d (1-T) + w ce r s = (0.4)(9%)(1-0.4) + (0.6)(10.872%) = 8.68%. V = 08683 . 0 ) 4 . 0 1 )( 933 . 14 ($ WACC ) T 1 )( EBIT ( WACC FCF = = = $103.20 million.
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16-11 Tax rate = 40% r RF = 5.0% b U = 0.8 r M – r RF = 6.0% From data given in the problem and table we can develop the following table: w d w ce D/S r d r d (1 – T) Levered beta a r s b WACC c 0 100% 0.00 6.0% 3.60% 0.80 9.80% 9.80% 0.2 80% 0.25 7.0% 4.20% 0.92 10.52% 9.26% 0.4 60% 0.67 8.0% 4.80% 1.12 11.72% 8.95% 0.6 40% 1.50 9.0% 5.40% 1.52 14.12% 8.89% 0.8 20% 4.00 10.0% 6.00% 2.72 21.32% 9.06% Notes: a These beta estimates were calculated using the Hamada equation, b = b U [1 + (1 – T)(D/S)].
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