Final answer:
The present value of the tax shield for the company is calculated using the tax rate, interest rate on the debt, and the calculated debt value. Subtracting the market capitalization from the total company value gives the debt value, which is then used to determine the present value of the tax shield, resulting in $12,800.
Step-by-step explanation:
The question asks to calculate the present value of the tax shield for a company with a specific set of financial parameters. The tax shield is the saving a company achieves due to the tax-deductibility of interest expenses. The formula for the present value of a tax shield is generally: (Tax Rate) x (Interest Expense) x (Debt Value) / (Cost of Debt), assuming perpetual debt, or the tax shield can be considered simply as (Tax Rate) x (Interest Expense) for the given period if the debt is not perpetual.
In this case, to find the present value of the tax shield, we will use the given interest rate on debt and the tax rate:
Present Value of Tax Shield = Tax Rate x Interest Rate x Debt Value
Since the company has 100,000 shares outstanding valued at $8/share, the debt value can be calculated by subtracting market capitalization from the total company value:
Debt Value = Total Company Value - (Shares Outstanding x Share Price)
Debt Value = $1,200,000 - (100,000 x $8)
Debt Value = $1,200,000 - $800,000
Debt Value = $400,000
Now, we can calculate the present value of the tax shield as follows:
Present Value of Tax Shield = 0.40 x 0.08 x $400,000
Present Value of Tax Shield = $12,800
The correct answer is b. $12,800.