Creating value with risk management - value of firm with taxes

[zript]

Hi,

In paragraph 3.2 from Creating Value with risk management document, Rene Stulz show us the formula of the value of a firm with taxes

He took Pure gold price as example. I understand that Value of firm = PV(Gold Sales) - PV(Taxes). I agree that PV(Gold Sales) = 333.33 but I do not understand where 0,5 comes from in PV(Sales). For me PV(Sales) should equal to 75/1,05. In fact we discount the 75 million taxes that will be paid in the future.

Could you help me finding where 0,5 comes from in PV(Sales formula)?

Thanks,

 

[David Harper CFA FRM]

Hi zript,

The 0.5 is the probability of the up-jump in the binomial alternative (to the guaranteed, hedged forward price $350) where the uncertain outcome (he simplifies with a one-step binomial tree) is $250 or $350. Key to his point is a differential tax rate: the hedged $350 guarantees a tax, but the unhedged is 50/50 to pay taxes, as under his simple progressive tax structure the down-jump outcome (250) pays no taxes.
(please note I put this on the second tab of this XLS @ http://www.bionicturtle.com/how-to/spreadsheet/1.b.4_stulz_bankruptcy_taxes_debt_overhang/) ... David

http://learn.bionicturtle.com/images/forum/0828_stulztaxes.png