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• Reinaldo Rosero

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CORPORATE FINANCE WEIGHTED AVERAGE COST OF CAPITAL - HOMEWORK

NAME: Natalie Rosero Pasmay GROUP: 1801 DATE: 23/01/2020

EXERCISES 1. Calculating WACC Mullineaux Corporation has a target capital structure of 70 percent common stock and 30 percent debt. Its cost of equity is 15 percent, and the cost of debt is 8 percent. The relevant tax rate is 35 percent. What is Mullineaux’s WACC? DATA We: 70% Wd: 30% Re: 15% Rd: 8% TC: 35% WACC=? 𝑊𝐴𝐶𝐶 = 𝑊𝑒 ∗ 𝑟𝑒 + 𝑊𝑑 ∗ 𝑟𝑑(1 − 𝑡𝑐) 𝑊𝐴𝐶𝐶 = 0,70 ∗ 0,15 + 0,30 ∗ 0,08(1 − 0,35) 𝑊𝐴𝐶𝐶 = 0.105 + 0.0156 𝑊𝐴𝐶𝐶 = 0.1206 = 12.06%

2. Taxes and WACC Miller Manufacturing has a target debt–equity ratio of .45. Its cost of equity is 17 percent, and its cost of debt is 10 percent. If the tax rate is 35 percent, what is Miller’s WACC? DATA Debt-equity= 45 Rd= 10% Re= 17%

𝐷𝑒𝑏𝑡 𝐸𝑞𝑢𝑖𝑡𝑦 = 1

0.45 1

0.45

𝑊𝑑 = 1.45 = 0.3103 = 31%

𝑊𝑒 = 1.45 = 0.68.97 = 68.97%

Tc= 35% 𝑊𝐴𝐶𝐶 = 𝑊𝑒𝑟𝑒 + 𝑊𝑑𝑟𝑑(1 − 𝑇𝑐) 𝑊𝐴𝐶𝐶 = 0.68.97(0.17) + 0.3103 × 0.10(1 − 0.35) 𝑊𝐴𝐶𝐶 = 0.1374 = 13.74% 3. Finding the Capital Structure Fama’s Llamas has a weighted average cost of capital of 9.8 percent. The company’s cost of equity is 15 percent, and its cost of debt is 7.5 percent. The tax rate is 35 percent. What is Fama’s debt–equity ratio? WAAC= 9.8% Re= 15%

𝑊𝑒 + 𝑊𝑑 = 1

Rd= 7.5%

𝑊𝑒 = 1 − 𝑊𝑑

Tc= 35% 𝑊𝐴𝐴𝐶 = 𝑊𝑒 𝑅𝑒 + 𝑊𝑑 𝑅𝑑 (1 − 𝑇𝑐) 0,098 = 𝑊𝑒 0,15 + 𝑊𝑑 0,075 (1 − 0,35) 0,098 = (1 − 𝑊𝑑)0,15 + 𝑊𝑑 0.075 (1 − 0.35) 0,098 = 0,15 − 0,15𝑊𝑑 + 𝑊𝑑 0.075 − 0,02625 0,098 = 0,15 − 0,15𝑊𝑑 + 0,04875𝑊𝑑 0,098 = 0,15 − 0,10125𝑊𝑑 0,098 − 0,15 = −0,10125𝑊𝑑 −0,052 = −0,10125𝑊𝑑 −0,052 = 𝑊𝑑 −0,10125 0,513580 = 𝑊𝑑 ≅ 51,36% Wd

4. WACC Kose, Inc., has a target debt–equity ratio of .65. Its WACC is 11.2 percent, and the tax rate is 35 percent. DATA 0.65

WACC= 11.2%

𝑊𝑑 = 1+0.65 = 0.3939 = 39.39%

Tax rate (Tc) = 35%

𝑊𝑒 = 1+0.65 = 0.6061 = 60.61%

1

Debt-equity= 65% Wd=? We=? a) If Kose’s cost of equity is 15 percent, what is its pretax cost of debt? Cost of equity (re) =15% Cost of debt (rd) =? 𝑊𝐴𝐶𝐶 = 𝑊𝑒𝑟𝑒 + 𝑊𝑑𝑟𝑑(1 − 𝑇𝑐) 0.112 = 0.6061(0.15) + 0.3939𝑟𝑑(1 − 0.35) 0.112 = 0.090915 + 0.256035𝑟𝑑 0.112 − 0.090915 = 0.256035𝑟𝑑 0.021085 = 𝑟𝑑 0.256035 𝑟𝑑 = 0.0824 = 8.24%

b) If instead you know that the after tax cost of debt is 6.4 percent, what is the cost of equity? Cost of equity (re) =? Cost of debt (rd) = 6.4% 𝑊𝐴𝐶𝐶 = 𝑊𝑒𝑟𝑒 + 𝑊𝑑𝑟𝑑(1 − 𝑇𝑐) 0.112 = 0.6061𝑟𝑒 + 0.3939(0.064)(1 − 0.35) 0.112 = 0.6061𝑟𝑒 + 0.01638624 0.112 − 0.01638624 = 0.6061𝑟𝑒 0.09561376 = 𝑟𝑒 0.6061 𝑟𝑒 = 0.1578 = 15.78%

5. Calculating WACC Maxwell Industries has a debt–equity ratio of 1.5. Its WACC is 10 percent, and its cost of debt is 7 percent. The corporate tax rate is 35 percent. DATA WACC: 10% TC: 35% Rd: 7% Wd: 15%

1. What is the company’s cost of equity capital? 𝑊𝐴𝐶𝐶 = We ∗ Re + Wd ∗ Rd(1 − TC) + Wp ∗ Rp 1 1.5 ) 𝑅𝑒 + ( ) (0.07)(1 − 0.35) 2.5 2.5 1 1.5 0.10 − ( ) (0.07)(1 − 0.35) = ( ) 𝑅𝑒 2.5 2.5 0.0727 = 𝑅𝑒 1 2.5 0.10 = (

0.18175 = 𝑅𝑒 𝑅𝑒 = 18.18% 2. What is the company’s unlevered cost of equity capital? 𝐷 𝑅𝑒 = Ru + (Ru − Rd)( )(1 − TC) 𝐸 0.1818 = Ru + (Ru − 0.07)(1.5)(1 − 0.35) 0.1818 = Ru + (Ru − 0.07)(0.975) 0.1818 = Ru + 0.975Ru − 0.06825 0.1818 + 0.06825 = 1.975Ru 0.25005 = 𝑅𝑢 1.975 𝑅𝑢 = 0.1266 = 12.66%

3. What would the cost of equity be if the debt–equity ratio were 2? 𝐷 𝑅𝑒 = Ru + (Ru − Rd)( )(1 − TC) 𝐸 𝑅𝑒 = 0.1266 + (0.1266 − 0.07)(2)(1 − 0.35) 𝑅𝑒 = 0.1266 + 0.07358 𝑅𝑒 = 0.20018 = 20.02% 

What if it were1.0? 𝐷 𝑅𝑒 = Ru + (Ru − Rd)( )(1 − TC) 𝐸 𝑅𝑒 = 0.1266 + (0.1266 − 0.07)(1)(1 − 0.35) 𝑅𝑒 = 0.1266 + 0.03679

𝑅𝑒 = 0.16339 = 16.34% 

What if it were zero? 𝐷 𝑅𝑒 = Ru + (Ru − Rd)( )(1 − TC) 𝐸 𝑅𝑒 = 0.1266 + (0.1266 − 0.07)(0)(1 − 0.35) 𝑅𝑒 = 0.1266 + 0 𝑅𝑒 = 0.1266 = 12.66%

6. Calculating WACC Empress Corp. has no debt but can borrow at 8.2 percent. The firm’s WACC is currently 11 percent, and the tax rate is 35 percent. DATA Cost of debt (rd) = 8.2% WACC= 11% Tax rate (Tc) = 35% Wd= 0 We= 100% a) What is the company’s cost of equity? 𝑊𝐴𝐶𝐶 = 𝑊𝑒𝑟𝑒 + 𝑊𝑑𝑟𝑑(1 − 𝑇𝑐) 0.11 = 1𝑟𝑒 + 0(0.082)(1 − 0.35) 𝑟𝑒 =

0.11 = 0.11 = 11% 1

b) If the firm converts to 25 percent debt, what will its cost of equity be? 𝑊𝑒 = 1 − 𝑊𝑑 𝑊𝑒 = 1 − 25% 𝑊𝑒 = 75% 𝑊𝐴𝐶𝐶 = 𝑊𝑒𝑟𝑒 + 𝑊𝑑𝑟𝑑(1 − 𝑇𝑐) 0.11 = 0.75𝑟𝑒 + 0.25(0.082)(1 − 0.35) 0.11 = 0.75𝑟𝑒 + 0.013325 0.11 − 0.013325 = 0.75𝑟𝑒 0.09675 = 𝑟𝑒 0.75

𝑟𝑒 = 0.1289 = 12.89%

c) If the firm converts to 50 percent debt, what will its cost of equity be? 𝑊𝑒 = 1 − 𝑊𝑑 𝑊𝑒 = 1 − 50% 𝑊𝑒 = 50% 𝑊𝐴𝐶𝐶 = 𝑊𝑒𝑟𝑒 + 𝑊𝑑𝑟𝑑(1 − 𝑇𝑐) 0.11 = 0.50𝑟𝑒 + 0.50(0.082)(1 − 0.35) 0.11 = 0.50𝑟𝑒 + 0.02665 0.11 − 0.02665 = 0.50𝑟𝑒 0.08335 = 𝑟𝑒 0.50 𝑟𝑒 = 0.1667 = 16.67% d) What is the company’s WACC in part (b)? In part (c)? PART B 𝑊𝐴𝐶𝐶 = 𝑊𝑒𝑟𝑒 + 𝑊𝑑𝑟𝑑(1 − 𝑇𝑐) 𝑊𝐴𝐶𝐶 = 0.75(0.1289) + 0.25(0.082)(1 − 0.35) 𝑊𝐴𝐶𝐶 = 0.096675 + 0.013325 𝑊𝐴𝐶𝐶 = 0.110075 = 11% PART C 𝑊𝐴𝐶𝐶 = 𝑊𝑒𝑟𝑒 + 𝑊𝑑𝑟𝑑(1 − 𝑇𝑐) 𝑊𝐴𝐶𝐶 = 0.50(0.1667) + 0.50(0.082)(1 − 0.35) 𝑊𝐴𝐶𝐶 = 0.08335 + 0.02665 𝑊𝐴𝐶𝐶 = 0.11 = 11%

7. Longstreet Communications Inc. (LCI) has the following capital structure, which it considers to be optimal: debt = 25%, preferred stock = 15%, and common stock =60%. LCI’s tax rate is 40%, and investors expect earnings and dividends to grow at a constant rate of 6% in the future. LCI paid a dividend of $3.70 per share last year (D0), and its stock currently sells at a price of $60 per share. Preferred stocks are sold in the market at $50 with an annual dividend of $4.

According the last financial

statements, LCI issued 10,000 bonds that were sold at a face value of $10 which caused $20,000 in interest expenses paid to bondholders. What is the LCI´s W.A.C.C.? 4 = 0.08 ≅ 8% 50 2 𝑹𝑫 = = 0.2 ≅ 20% 10 3,70 𝑹𝑬 = + 0.06 = 0.1217 ≅ 𝟏𝟐. 𝟏𝟕% 60 𝑹𝑷 =

𝑊𝐴𝐴𝐶 = 𝑊𝑒 ∗ 𝑟𝑒 + 𝑊𝑑 ∗ 𝑟𝑑(1 − 𝑡𝑐) + 𝑊𝑝 ∗ 𝑟𝑝 𝑾𝑨𝑨𝑪 = 0,60(0,01217) + 0,25(0,20)(1 − 0,40) + 0,60(0,08) 𝑾𝑨𝑨𝑪 = 𝟎, 𝟎𝟖𝟓𝟑𝟎𝟐 ≅ 𝟖, 𝟓𝟑%