Posted: November 11th, 2015

Economic

Economic

Suppose that you have been placed in charge of calculating the user cost of capital for a corporation. You know that capital costs are debt-financed at the margin and you have the following additional information (the time period is a year, and all percentages have been translated into fractions, i.e., a 10% interest rate is written as .1):

before-tax interest rate paid by the corporation = .1

depreciation rate (denoted d in class) = .05

In the absence of taxes, what is the user cost of capital? (Give a number, and make sure that you show all of your calculations.)

For the remaining questions, assume that corporate income is taxed at a 50% rate. (Assume no investment tax credits.)

If the firm is allowed no tax deductions for any of the costs associated with capital investments, then what is the user cost of capital?

If the firm is allowed to deduct both interest payments and actual economic depreciation from its taxable income, then what is the user cost of capital?

(d) If the firm is allowed to expense its capital investments but is not allowed to deduct interest payments, then what is the user cost of capital?

2. The following questions concern the general formula for the user cost of capital

Write the general formula for the user cost of capital (given in class, not in Rosen-Gayer).

(b) Which term is the cost of funds in this formula?

(c) Is the cost of funds higher when the firm finances its marginal investment by borrowing (debt finance), or by selling stock (equity finance)? Explain why, using the relevant tax laws for a corporate tax.

(d) Which term is the present value of the tax savings from the depreciation deductions that the firm gets from a dollar investment? Write out the present value formula for this term.

(e) Rank from lowest to highest the present value of the tax savings from the depreciation deductions for the following three methods: accelerated depreciation deductions; deductions for actual economic depreciation; expensing. Using your answer, rank from lowest to highest the user cost of capital for these three methods.

3. The following questions are about the effect of the personal income tax on the user cost of capital.

Which term in the user cost formula is affected by the personal income tax? How do the personal tax rates on interest income, dividends, and capital gains affect this term? Answer this question by giving an equation showing how this term depends on personal taxes for the following two cases: (1) additional investment is financed with debt (issuing bonds), and (2) additional investment is financed with new equity (selling stock). (Note: Your answer will be wrong if you use the user cost formula from Rosen-Gayer.)

Another method of finance is retained earnings. How does the tax on dividends affect the user cost in this case? You can use the argument presented in class.

Suppose that the existing income and corporate income taxes in the U.S. were replaced with either a Hall-Rabushka flat tax or a value-added tax.

Briefly describe the tax base(s) under each of these two new tax systems.

How would each tax system affect the user cost of capital? What deductions or exemptions described in part (a) are responsible for your answer.

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