Questions: A firm's end-of-year free cash flow is anticipated to be 50 million. The firm's free cash flows are expected to grow 11.5 percent a year, forever. The firm's weighted average cost of capital is 13.07 percent, and the firm has 12 million common stock outstanding shares. If the firm has 80 million in preferred stock and long-term debt, the firm's estimated intrinsic value of its common stock per share is . Calculate to two decimal points using the following formula: PV = ((FCF / (WACC - g)) - total debt) / common shares.

A firm's end-of-year free cash flow is anticipated to be 50 million. The firm's free cash flows are expected to grow 11.5 percent a year, forever. The firm's weighted average cost of capital is 13.07 percent, and the firm has 12 million common stock outstanding shares. If the firm has 80 million in preferred stock and long-term debt, the firm's estimated intrinsic value of its common stock per share is . Calculate to two decimal points using the following formula: PV = ((FCF / (WACC - g)) - total debt) / common shares.

Transcript text: A firm's end-of-year free cash flow is anticipated to be $\$ 50$ million. The firm's free cash flows are expected to grow 11.5 percent a year, forever. The firm's weighted average cost of capital is 13.07 percent, and the firm has 12 million common stock outstanding shares. If the firm has $\$ 80$ million in preferred stock and long-term debt, the firm's estimated intrinsic value of its common stock per share is $\$$ . Calculate to two decimal points using the following formula: $P V=((F C F /(W A C C-g))-$ total debt $) /$ common shares. $\square$

Solution

Solution Steps

To solve this problem, we need to calculate the intrinsic value of the firm's common stock per share using the given formula. Here are the steps:

Calculate the present value of the firm's free cash flow using the formula $ PV = \frac{FCF}{WACC - g} $.
Subtract the total debt (preferred stock and long-term debt) from the present value.
Divide the result by the number of common shares outstanding to get the intrinsic value per share.

Step 1: Calculate the Present Value of the Firm's Free Cash Flow

The present value (PV) of the firm's free cash flow (FCF) is calculated using the formula: \[ PV = \frac{FCF}{WACC - g} \] Given: \[ FCF = 50 \, \text{million} \] \[ g = 0.115 \] \[ WACC = 0.1307 \]

Substituting the values: \[ PV = \frac{50}{0.1307 - 0.115} = \frac{50}{0.0157} \approx 3184.7134 \, \text{million} \]

Step 2: Subtract Total Debt from the Present Value

The total debt includes preferred stock and long-term debt, which is given as: \[ \text{Total Debt} = 80 \, \text{million} \]

Subtracting the total debt from the present value: \[ \text{Value After Debt} = PV - \text{Total Debt} = 3184.7134 - 80 = 3104.7134 \, \text{million} \]

Step 3: Calculate the Intrinsic Value per Share

The number of common shares outstanding is given as: \[ \text{Common Shares} = 12 \, \text{million} \]

The intrinsic value per share is calculated by dividing the value after debt by the number of common shares: \[ \text{Intrinsic Value per Share} = \frac{\text{Value After Debt}}{\text{Common Shares}} = \frac{3104.7134}{12} \approx 258.7261 \]