The problem asks us to calculate the value of the firm and the value of common stock per share, given the following information: - Free cash flow per year = $460,000 - Firm's cost of capital = 9% or 0.09 - Firm's cost of equity capital = 16% or 0.16 - Market value of debt = $200,000 - Market value of preferred stock = $180,000 - Number of shares of common stock outstanding = 100,000

1. Problem Description

The problem asks us to calculate the value of the firm and the value of common stock per share, given the following information:

- Free cash flow per year = $460,000

- Firm's cost of capital = 9% or 0.09

- Firm's cost of equity capital = 16% or 0.16

- Market value of debt = $200,000

- Market value of preferred stock = $180,000

- Number of shares of common stock outstanding = 100,000

2. Solution Steps

Step 1: Calculate the value of the firm.

Since the free cash flow is expected to be constant forever, we can use the perpetuity formula to calculate the value of the firm:

$Value of Firm = Free Cash Flow / Cost of Capital$

$Value of Firm =$460,000 / 0.09$

$Value of Firm =$5,111,111.11$

Step 2: Calculate the value of common stock.

Value of Common Stock = Value of Firm - Market Value of Debt - Market Value of Preferred Stock

$Value of Common Stock =$5,111,111.11 - $200,000 -$180,000$

$Value of Common Stock =$4,731,111.11$

Step 3: Calculate the value of common stock per share.

Value of Common Stock Per Share = Value of Common Stock / Number of Shares of Common Stock Outstanding

$Value of Common Stock Per Share =$4,731,111.11 / 100,000$

$Value of Common Stock Per Share =$47.31$

3. Final Answer

Value of the firm: $5,111,111.11

Value of common stock per share: $47.31