ABC Drilling 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 ABC Drilling’s total value be if it had no debt?
The total value of ABC Drilling can be calculated using the Modigliani-Miller (MM) proposition with growth. According to this proposition, the total value of a firm is independent of its capital structure.
To calculate the total value of ABC Drilling with no debt, we need to find the cost of equity for the firm. The cost of equity can be calculated using the dividend discount model (DDM) formula:
Cost of Equity = Dividends per Share / Price per Share + Growth Rate of Dividends
Since the firm's earnings are growing at a 5% rate, we can use this growth rate as the growth rate of dividends.
Let's calculate the cost of equity first:
Cost of Equity = Dividends per Share / Price per Share + Growth Rate of Dividends
Cost of Equity = 0.12 = Dividends per Share / Price per Share + 0.05
Now, let's calculate the total value of ABC Drilling with no debt:
Total Value = Market Value of Equity
Total Value = $300,000
Therefore, ABC Drilling's total value would be $300,000 if it had no debt.
To calculate the total value of ABC Drilling if it had no debt, we need to use the Modigliani-Miller (MM) proposition under the MM extension with growth. The MM proposition states that the total value of a firm is independent of its capital structure (debt/equity mix) when certain assumptions are met.
In this case, we can use the MM extension with growth, which assumes that the firm's earnings are growing at a constant rate. Here's how we can calculate ABC Drilling's total value without debt:
1. Calculate the cost of equity for ABC Drilling with no debt:
The similar firm with no debt has a cost of equity of 12%. Since ABC Drilling is a similar firm without debt, we can use the same cost of equity rate of 12%.
2. Estimate the free cash flows to equity (FCFE) for ABC Drilling:
FCFE represents the cash flows available to equity holders after all expenses and reinvestment needs. It can be calculated using the formula:
FCFE = (Net Income) * (1 - Tax Rate) + (Depreciation & Amortization) - (Capital Expenditures) - (Increase in Working Capital)
As given, ABC Drilling's earnings are growing at a 5% rate. Let's assume the initial net income is $100,000 and there are no capital expenditures or changes in working capital. With these assumptions, we can calculate the FCFE using the formula above.
3. Calculate the value of ABC Drilling's equity:
The value of the equity is the present value of the FCFE stream discounted at the cost of equity rate. We can use the following formula:
Equity Value = ∑(FCFE / (1 + Cost of Equity)^t)
Since the FCFE is assumed to grow at a constant rate, we can use the Gordon Growth Model to calculate the present value of the FCFE stream.
4. Calculate ABC Drilling's total value without debt:
The total value of the firm without debt is equal to the value of the equity. In this case, ABC Drilling's total value without debt would be the same as the calculated equity value in step 3.
Please note that the actual calculations require specific numbers for net income, tax rate, depreciation & amortization, capital expenditures, and working capital changes. The example provided assumes certain values for the purpose of explaining the process.