Your Firm Is In A 40% Combined Federal And State Marginal In

Your Firm Is In A 40 Combined Federal And State Marginal Income Tax

Your firm has an annual income of $500,000 for two years. You are considering financing a project with a $1.3 million mortgage at an 8% interest rate or paying cash. The goal is to compare the amount Uncle Sam (the government) will receive in taxes under each financing method and to determine the present value (PV) of the tax savings from financing the project with a mortgage, considering an expected rate of return of 10% by other firms.

Specifically, the tasks include calculating the tax benefit derived from the mortgage interest payments, estimating how much tax Uncle Sam receives under each scenario, and determining the PV of the tax savings by financing with a mortgage compared to paying cash. Additionally, the analysis considers the firm's tax rate of 40%, the interest expense, and the comparative rate of return in the market.

Paper For Above instruction

The financial decision to finance a project through debt or cash has significant tax implications for a firm, especially when considering the impact on tax savings and overall firm value. In this context, analyzing how mortgage financing at a specific interest rate affects tax liabilities and savings offers vital insights into optimal capital structuring.

Tax implications of mortgage financing

When a firm opts for debt financing, especially through a mortgage, interest expenses are deductible from pre-tax income, thereby reducing taxable income and subsequently decreasing the amount of taxes paid to Uncle Sam. Given the firm's income of $500,000 per year for two years and a mortgage of $1.3 million at an 8% interest rate, the annual interest expense becomes a critical factor in calculating tax benefits.

The annual interest on the mortgage can be computed as:

Interest Expense = Principal × Interest Rate

Interest Expense = $1,300,000 × 8% = $104,000 per year.

Since this interest expense is tax-deductible, the firm’s taxable income reduces by this amount each year, which in turn reduces its tax liability. The tax shield (tax savings) per year is:

Tax Shield = Interest Expense × Tax Rate

Tax Shield = $104,000 × 40% = $41,600 annually.

Over two years, total tax savings due to interest deductions amount to:

Total Tax Savings = $41,600 × 2 = $83,200.

If financed with cash

If the firm chooses to pay cash for the project without debt, it does not incur interest expenses, and thus, cannot benefit from the tax shield associated with interest payments. The entire project cost, $1.3 million, is paid upfront, but no interest deductions or tax savings related to debt are available.

Comparison of tax benefits

The key difference is that debt financing provides a tax shield, reducing taxable income and hence the tax liability each year. Without debt, the firm’s tax liability remains unaffected by the project expense beyond the initial deduction for depreciation or amortization, which in this simplified scenario is not considered.

Present value of tax savings

To evaluate the value of the tax shield over the two-year period, the present value (PV) of the tax benefits must be computed, considering the firm’s discount rate, which is aligned with the expected return of 10% by comparable firms. The PV of the tax shield is calculated as:

PV = Tax Shield × [1 - (1 + r)^-n] / r

where r is the discount rate (10%) and n is the number of years (2).

Calculating:

PV = $41,600 × [1 - (1 + 0.10)^-2] / 0.10

PV = $41,600 × [1 - (1.10)^-2] / 0.10

PV = $41,600 × [1 - 0.82645] / 0.10

PV = $41,600 × 0.17355 / 0.10

PV ≈ $41,600 × 1.7355

PV ≈ $72,124

This PV indicates the present value of the tax savings from debt financing over the two-year period, which adds value to the firm, highlighting the tax benefit of financing through debt rather than equity or cash.

Conclusion

Utilizing debt financing at an 8% interest rate in a 40% tax environment yields significant tax savings, with the total discounted value of these savings approximately $72,124. Conversely, financing with cash offers no tax shield benefits, making debt financing a more tax-efficient strategy. The comparison underscores the importance of considering tax implications when making financing decisions, especially in environments with high marginal tax rates.

References

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