Linexy is an all-equity firm where annual sales are expected to be $100 million
ID: 2800078 • Letter: L
Question
Linexy is an all-equity firm where annual sales are expected to be $100 million in perpetuity. The firm estimates its cost of production will be 65% of sales. The stock’s beta is currently 1.30 and faces a 30% tax rate. Further, there are 5 million shares outstanding. The current yield-to-maturity on T-Bills is 2.7%, and the market risk premium is 7%. The firm is considering buying back $50 million of equity by issuing debt. The firm can issue debt at 8%. Post recapitalization, what is the value of:
1. The firm
2 The firm’s equity?
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Explanation / Answer
Required rate of return=Risk free rate+ Beta *(Market risk premium)
Risk free rate=2.7%
Beta=1.30
Market risk premium=7%
Required rate of return=2.7+1.3*7=11.8%=0.118
Annual sales in perpetuity=$100 million
Cost of production =0.65*100million dollar
Cost of production=$65 million
Annual before tax cash flow in perpetuity=(100-65)=$35 million
Tax rate=30%
Annual after tax cash flow in perpetuity=35*(1-0.3)=$24.5 million
Present value of cash flow=$24.5million/(Required rate of return)
Present value of cash flow=24.5/0.118=$ 207.6271 million
Value of Equity=$ 207.6271million
Unlevered beta=(Levered Beta)/(1+(1-Tax rate)*(Debt/Equity))
Unlevered Beta=1.30
Tax rate=30%=0.3
Post capitalization:
Debt=$50million
Equity=( 207.6271-50) million dollar
Equity=$ 157.6271million
Debt/Equity=50/ 157.6271= 0.317204
Debt/Equity= 0.317204
Levered Beta post capitalization=(Unlevered beta)* (1+(1-Tax rate)*(Debt/Equity))
Post capitalization Beta=1.30*(1+(1-0.3)* 0.317204)=1.30*1.222043=1.588656
Post Capitalization:
Cost of Debt=8*(1-0.3)=5.6%
Cost of Equity= Required rate of return=Risk free rate+ Beta *(Market risk premium)
Cost of Equity=2.7+1.588656*7=13.82%
Weight of Debt=50/(50+157.6271)= 0.24
Weight of Equity=157.6271/(50+157.6271)=0.76
Weighted Average Cost of Capital(WACC)=0.24*5.6+0.76*13.82=11.85%=0.1185
Annual interest cost, post Capitalization=$50million*0.08=$4 million
Annual before tax cash flow=(35-4)=$31million
Annual after tax cash flow=(1-0.3)*31=$21.7 million
Present value of Annual cash flow in perpetuity=(21.7/WACC)=21.7/0.1185= $ 183.12 million
.1 Value of the firm=$183.12million
.2 The firm’s Equity=(Value of the firm)-(Debt)
The firm’s Equity=(183.12-50)= $ 133.12 million
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