Timpano Inc. can each period have good sales with 50% probability or bad sales w

Question

Timpano Inc. can each period have good sales with 50% probability or bad sales with 50% probability. In case of good sales the unlevered cash flow will be $80 million, in case of bad sales the unlevered cash flow will be $50 million. The unlevered beta of the company is 1.5, the expected return of the market portfolio is 4% while the risk-free return is 1%. Timpano's equity market value is $850 million and its debt is kept constant at $950 million.

What is the corporate tax rate? (Assume that the firm's cash flow is perpetual). Answer: 65.07%

Please answer only if you reach the answer 65.07

Explanation / Answer

Cash flows with good sales = 80*0.50 i.e 40

Cash flows with bad sales = 50*0.50 i.e 25

Total probability of unlevered cash flows = 40+25 i.e 65

Cost of equity = Risk Free return + Beta ( Market Return - Risk free return )

= 1% + 1.5 ( 4-1) i.e 5.5%

Total Value of company = Value of debt + Value of equity

= 850+950 i.e 1800

Weight of equity = 850/1800 i.e 47.22%

Weight of debt = 950/1800 i.e 52.78%

4% = 5.5*0.4722+X(0.5278)

0.5278X = 4-2.5971

X = 1.4029/0.5278 i.e 2.658%

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