Assume that a firm pays taxes on revenue and is allowed some deductions. 1.Deriv

Question

Assume that a firm pays taxes on revenue and is allowed some deductions.

1.Derive and explain the user cost of capital if the firm's nominal interest payments are tax deductible.

2.Derive and explain the user cost of capital if the firm's real interest payments are tax deductible.

3.Derive and explain the user cost of capital if the depreciation of capital is tax deductible.

4.Derive and explain the user cost of capital if the firm's real interest payments and the depreciation of capital are tax deductible.

5.What is the impact of the tax on the firm's desired level of capital in the last case?

Explanation / Answer

Dear sir/madam,

Let us take the example of effect of taxes and inflation on housing costs. In the US , interest payments on a principal residence are deductible from the personal income tax. The deduction, not available in many other countries, is part of a deliberate attempt to encourage individual homeownership. A further feature of the US tax system is that nominal interest payments are deductible and nominal interest payments are deductible and nominal capital gains due to inflation are essentially untaxed. This means that the combination of high nominal rates and high inflation strongly encourages housing investment. Consider payments on a $100000 mortgage when the nominal interest rate is 15 percent and the inflation rate is 10 percent. Annual interest is approximately $15000. For a homeowner in the 30 percent marginal tax bracket, the mortgage interest deduction is $4500, so the after-tax interest cost is approximately $10500. But at 10 percent inflation, this cost is offset by a $10000 increase in the nominal value of the house. In effect, the real cost of capital for the house is nearly zero.

Despite this analysis, high nominal interest rates do discourage homeownership because of two kinds of liquidity effects. First, the homeowner has to make the full nominal payments up front and receives the offsetting capital gain far in the future. Second, banks use rules of thumb to qualify mortgage applicants ( eg. that payment can be no more than 28 percent of income) that don't adjust very much in periods of high inflation. Both these liquidity effects depend on the nominal, not real, interest rate.

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