Introduction: A Stochastic Approach to Discounted Cash Flow -- Basic Elements: Cash Flow, Tax, Expectation, Cost of Capital, Value -- Corporate Income Tax: WACC, FTE, TCF, APV -- Personal Income Tax -- Corporate and Personal Income Tax -- Proofs -- Sketch of Solutions.

"We argue that a firm's aggregate risk is a key determinant of whether it manages its future liquidity needs through cash reserves or bank lines of credit. Banks create liquidity for firms by pooling their idiosyncratic risks. As a result, firms with high aggregate risk find it costly to get...