Final answer:
To find the value of the firm, calculate the unlevered free cash flows using the Gordon Growth Model and adjust for the debt and tax shield. The calculations yield an enterprise value of $40M and, after adding the tax shield, the total value of the firm is $40.45M, which doesn't match any of the given options.
Step-by-step explanation:
To calculate the value of the firm, we first need to determine the after-tax operating cash flow. Given $10M in sales and annual costs at 20% of sales, we have operating income of $10M - 20% * $10M = $10M - $2M = $8M. After applying the 30% tax rate, the after-tax operating income is $8M - 30% * $8M = $8M - $2.4M = $5.6M.
Since the after-tax cash flow is expected to grow at 2% per year forever, we use the Gordon Growth Model to calculate the value of unlevered free cash flows (UFCF). The UFCF is calculated using the formula: UFCF = After-tax operating income / (Unlevered cost of capital - Growth rate), which is $5.6M / (10% - 2%) = $70M.To find the enterprise value, we must consider the firm's debt. The enterprise value is the value of unlevered free cash flows minus the firm’s perpetual debt. Therefore, the enterprise value is $70M - $30M = $40M.
However, the actual value of the firm equals the enterprise value plus the present value of the tax shield from the debt. The tax shield is calculated by multiplying the firm's perpetual debt by the tax rate and cost of debt. So, the tax shield is $30M * 30% * 5% = $0.45M. Adding this to the enterprise value, the value of the firm is $40M + $0.45M = $40.45M, which is not listed as one of the provided options, indicating a possible error in either the question or calculations. It's important to review and ensure the values and models are correctly applied.