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Problem
Corporations in the United States are allowed to subtract depreciation allowances from their taxable income. The depreciation allowances are based on the purchase price of the capital; a corporation that buys a new capital good at time t can deduct fraction D(s ) of the purchase price from its taxable income at time t +s. Depreciation allowances often take the form of straight-line depreciation: D(s ) equals 1/T for s [0,T ], and equals 0 for s > T, where T is the tax life of the capital good.
(a) Assume straight-line depreciation. If the marginal corporate income tax rate is constant at τ and the interest rate is constant at i, by how much does purchasing a unit of capital at a price of PK reduce the present value of the firm's corporate tax liabilities as a function of T, τ, i, and PK ? Thus, what is the after-tax price of the capital good to the firm?
(b) Suppose that i = r +π, and that π increases with no change in r. How does this affect the after-tax price of the capital good to the firm?
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