According to Lund (2011), when depreciation deductions are taken into account, the after-tax cost of capital depends on the specific taxation rules. The commonly used WACC method fails to recognize the effects of taxation on the risk sharing pattern between the firm and the tax authority and thus is misleading. To find out correct asset betas for different tax systems, one needs not only to “unlever” but also “untax” and “unaverage” the observed equity betas. The thesis extends the one-period model for uncertain tax position of Lund (2011) and multi-period model for certain tax position of Lund (2002) to multi-period models under uncertain tax position. It is then possible to consider the more common tax rule, carryforwards. However, it is impossible to find the analytical solutions and the risk neutral valuation method using Monte Carlo simulation, originally developed for derivative pricing in financial markets, can be applied under reasonable assumptions. It is found that the number of periods can increase the risk but still the after-tax betas are significantly lower than the pre-tax cash flows. Under carryforwards tax rule the betas are even lower compared to no-loss-offset rule. Surprisingly, the interest payment from tax authority does not reduce the betas significantly compared to the no interest payment case. The sensitivity test on tax rate also suggests taxation does have a strong effect on the after-tax betas.