16.9 A) ROE for XYZ is ROE=Net Income/Equity Value Net Income for XYZ=EBIT-Interest Expense=86000-30000=56000 ROE of XYZ=56000/375000=14.93% B) Since XYZ has a 1:1 debt-equity ratio, Richard should: 1) invest in ABC’s stock using both his own money and borrowed funds 2) borrow in the same proportion as XYZ’s capital structure 3) use the loan to invest in ABC’s stock Expected return on ABC’s stock: rABC=EBIT/Equity Value=86000/750000=11.47% Richard’s expected return: Return=11.47%×30000-8%×15000=2240 Rate of return=2240/15000=14.93% This shows homemade leverage, demonstrating that an investor can replicate firm leverage by borrowing personally. C) Cost of equity for ABC=rABC=EBIT/Equity Value=86000/750000=11.47% Cost of equity for XYZ=rXYZ= rABC+(D/E*(rABC-rD))=11.47%+(375000/375000 ×(11.47%−8%))=14.93% D) WACC=(E/V×rE)+(D/V×rD) For ABC, WACC=11.47% For XYZ, WACC=(375000/750000×14.93%)+(375000/750000×8%)=7.47%+4%=11.47% 16.14 A) Since Bruce currently has no debt, we use the formula for the value of unlevered firm Vunlevered=(EBIT×(1-T))/rE=(185000×(1-0.35))/0.16=751563 B) The value of the levered firm Vlevered=Vunlevered+TD=751563+(0.35×135000)=798813 16.15 New cost of equity after recapitalization is: New debt-to-equity ratio D/E’=135000/(Vlevered-D)=135000/(798813-1350000=0.2035 rE’=rE+((D/E) ×(rE-rD) ×(1-T))=16%+(0.2035×(16%-9%)×(1-0.35))=16.93% New WACC=((E’/Vlevered) ×rE’)+((D/Vlevered) ×rD×(1T))=(663813/798813)×16.93%+(135000/798813) ×9%×(1-0.35)=15.06% The implications are: - The firm’s cost of equity increased because shareholders now require a higher return due to increased financial risk. - However, the firm’s WACC decreased from 16% to 15.06%, showing a benefit from the tax shield of debt. - This demonstrates the tax advantage of debt financing, as the firm's overall cost of capital is lower after borrowing. If the firm continues to increase leverage, the WACC may decrease further, but at very high levels of debt, bankruptcy costs might outweigh the benefits. 16.20 A) Valpha=number of shares×price per share=15000×30=450000 B) According to MM Proposition I, Vbeta=Valpha Since capital structure does not affect firm value in a world without taxes, we have Vbeta=450000 So Beta Corp is also worth 450000 C) Since Beta Corp has 65000 in debt, the value of its equity=Ebeta=Vbeta-D=4500006500=385000 D) For Alpha Corp: cost=20%×450000=90000 For Beta Corp: cost=20%×385000=77000 E) The dollar return is calculated using net income: Alpha Corp: return=20%×75000=15000 Beta Corp: net income=75000-(65000×9%)=69150 Beta Corp: return=20%×6915-=13830 F) To replication the leverage of Beta while investing in Alpha, an investor can: - invest 90000 in Alpha’s equity(20%) - borrow proportionally like Beta, debt=14.44%×90000=13000 - net investment: 90000-13000=77000 which matches the cost of 20% of Beta’s equity - ROI in alpha: 15000 - interest on on borrowed amount=9%×13000=1170 - net return=15000-1170=13830 which matches Beta’s return G) - Beta’s equity is riskier than Alpha’s because it has financial leverage. - When a firm takes on debt, equity holders bear more risk because they are entitled to residual income after paying interest. - Since Beta has fixed debt payments, any fluctuations in EBIT disproportionately affect equity holders, making Beta’s equity riskier. - Alpha’s equity, on the other hand, bears only business risk without additional financial leverage. McKenzie Mini case 1) Without expansion: EV=(0.3×25000000)+(0.5×30000000)+(0.2×48000000)=32100000 With expansion: EV=(0.3×27000000)+(0.5×37000000)+(0.2×57000000)=38000000 2) Without expansion: EV=(0.3×25000000)+(0.5×29000000)+(0.2×29000000)=27800000 With expansion: EV=(0.3×27000000)+(0.5×29000000)+(0.2×29000000)=28400000 3) Total value created by expansion=EVexpansion-EVno expansion=5900000 Value increase for bondholders=D=28400000-27800000=600000 Value increase for shareholders=E=5900000-600000=5300000 4) If the company announces NO expansion, the expected debt value is $27.8M, which is lower than the bond's face value of $29M. This suggests that the bonds would trade at a discount (below face value), as the bondholders have a risk of not being fully repaid. If the company announces expansion, the expected debt value rises to $28.4M, meaning bondholders receive a slightly higher expected return. Since their expected payout improves, bond prices will increase, getting closer to the face value. 18.5 a) Beta of north pole=1.25×(1+((1-0.35) ×2900000)/3800000)=1.87 Beta of south pole=1.25×(1+((1-0.35) ×3800000)/2900000)=2.31 b) r of north pole=5.30%+(1.87×(12.40%-5.30%))=18.58% r of south pole=5.30%+(2.31×(12.40%-5.30%))=21.70% 18.16 A) Vunlevered=(EBIT×(1-T))/r=(83000×0.6)/0.15=332000 B) Vlevered=Vunlevered+T×D=332000+(0.4×195000)=410000 C) E=Vlevered-D=410000-195000=215000 rE=15%+(195000/215000) ×6%×0.6=18.26% D) Interest = D×rD=195000×9=17550 Net income=(83000-17550) ×(1-0.4)=39270 E=39270/0.1826=215000
