Williamson, Inc., has a debt–equity ratio of 2.55. The firm’s weighted average c
ID: 2750532 • Letter: W
Question
Williamson, Inc., has a debt–equity ratio of 2.55. The firm’s weighted average cost of capital is 11 percent, and its pretax cost of debt is 5 percent. Williamson is subject to a corporate tax rate of 30 percent.
What is Williamson’s unlevered cost of equity capital? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))
What would Williamson’s weighted average cost of capital be if the firm’s debt–equity ratio were .85 and 1.75? (Do not round intermediate calculations and round your final answers to 2 decimal places. (e.g., 32.16))
Williamson, Inc., has a debt–equity ratio of 2.55. The firm’s weighted average cost of capital is 11 percent, and its pretax cost of debt is 5 percent. Williamson is subject to a corporate tax rate of 30 percent.
Explanation / Answer
(a) CALCULATION OF COST OF EQUITY CAPITAL(KE)
GIVEN,
WEIGHTED AVERAGE COST OF CAPITAL(WACC)=11%
DEBT TO EQUITY RATIO=2.55 I.E WHERE DEBT IS 2.55
EQUITY=1
TOTAL OF DEBT AND EQUITY=2.55+1=3.55
WEIGHT OF DEBT(WD)=2.55/3.55=0.7183
WEIGHT OF EQUITY(WE)=1/3.55=0.2817
COST OF DEBT (KD)=5%(PRETAX)
AFTER TAX KD =5%(1-TAX RATE)
=5%(1-0.3)
=3.5%
APPLYING FORMULA,
WACC=KD*WD+KE*WE
11%=3.5%*0.7183+KE*0.2817
KE*0.2817=11%-0.0251405%
ke=0.0848595/0.2817
KE=0.30124 or 30.124%
HENCE COST OF EQUITY CAPITAL IS 30.124%
(b) CALCULATION OF COST OF UNLEVERED EQUITY CAPITAL
unlevered cost of equity = WACC /(1 - debt ratio* tax rate)
= 11/ (1- 0.7183*.30)
= 9 /(0.78541)
= 11.47
(c)CALCULATION OF WEIGHTED AVERAGE COST OF CAPITAL
WHEN DEBT EQUITY RATIO IS 0.85
APPLYING FORMULA,WACC=KD*WD+KE*WE
KD=3.5 CALCULATED ABOVE
WD=WEIGHT OF DEBT=0.85/(0.85+1)=0.85/1.85=0.4595
KE=30.124% CALCULATED ABOVE
WE=WEIGHT OF EQUITY=1/1.85=0.5405
HENCE WEIGHTED AVERAGE COST OF CAPITAL IS=3.5*0.4595+29.23*0.5405
1.60825+15.799=16.88%
WHEN DEBT EQUITY RATIO IS 1.75
APPLYING FORMULA,WACC=KD*WD+KE*WE
KD=3.5%
WD=1.75/(2.75)=0.6364
KE=30.124%
WE=1/(2.75)=0.3636
HENCE WEIGHTED AVERAGE COST OF CAPITAL=3.5%*0.6364+30.124%*0.3636
0.002274+0.109530=11.18%
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