Firm L has debt with a market value of $200,000 and a yield of 9%. The firm's equity has a market value of $300,000, its earnings are growing at a 5% rate, and its tax rate is 40%. A similar firm with no debt has a cost of equity of 12%. Under the MM extension with growth, what would Firm L's total value be if it had no debt?
358,421
To calculate Firm L's total value if it had no debt using the Modigliani-Miller (MM) extension with growth, we need to follow these steps:
Step 1: Calculate the cost of equity for Firm L
Since we are given that a similar firm with no debt has a cost of equity of 12%, we can assume that the cost of equity for Firm L is also 12%.
Step 2: Estimate the terminal value of Firm L's earnings
To estimate the terminal value of Firm L's earnings, we can use the Gordon Growth Model, which assumes a constant growth rate. The formula for the terminal value is:
Terminal Value = Earnings / (Cost of Equity - Growth Rate)
Given that the earnings of Firm L are growing at a 5% rate, we have:
Terminal Value = Earnings / (0.12 - 0.05)
Step 3: Calculate the present value of the terminal value
To calculate the present value of the terminal value, we need to discount it back to its present value using the cost of equity. The formula for the present value is:
Present Value = Terminal Value / (1 + Cost of Equity)^n
Where n represents the number of years.
Step 4: Calculate the present value of the tax shield
Since Firm L has debt, it benefits from the tax shield, which is the tax savings resulting from the tax deductibility of interest expense. The formula for the present value of the tax shield is:
Present Value of Tax Shield = (Tax Rate) * (Debt)
Given that the tax rate is 40% and debt is $200,000, we can calculate the present value of the tax shield.
Step 5: Calculate the firm's value with no debt
Finally, we can calculate the total value of Firm L with no debt by summing the present value of the terminal value and the present value of the tax shield. The formula is:
Firm Value = Equity Value + Present Value of Terminal Value + Present Value of Tax Shield
Since Firm L has no debt in this scenario, its Firm Value will be equal to its Equity Value.
Therefore, the total value of Firm L if it had no debt would be:
Firm Value = $300,000 (Equity Value) + Present Value of Terminal Value + Present Value of Tax Shield
To obtain the final value, you will need to calculate the present value of the terminal value and the present value of the tax shield as explained in the steps above.