Question

1. It is January 1, 2020.  Over the previous12 months XYZ Corp has generated nominal free cash flows of $1,000. This free cash flow is expected to grow at an annual rate of 5% forever. XYZ Corp has a 12% WACC and a 25% corporate tax rate. XYZ Corp has $1,125 excess cash; $5,000 debt; $1,500 of preferred stock, and 500 shares of common stock outstanding. Assume cash flows occur on December 31 of each year. what should be the price per share of XYZ Corp stock today?

Answer 1

XYZ Corp.

nominal free cash flows = 1000

free cash flow is expected to grow at an annual rate = 5%

WACC = 12%

corporate tax rate = 25%

Excess cash =1125

Debt = 5000

preferred stock = 1500

shares of common stock outstanding = 500

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what should be the price per share of XYZ Corp stock today

The firm’s free cash flows already follow a growing perpetuity pattern, so we can find the terminal value today. In the equation below, T = 0

VF=∑t1T FCFt / (1+wacc)^t+TVT / (1+wacc)^T + excess cash

VF=∑t1T FCFt / (1+wacc)^2+TVT / (1+wacc)^0 + excess cash

.

The free cash flow over the next 12 months will be

FCF1 = 1000*(1+0.05) = 1050

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The value of the firm today, assuming end of year cash flows, will be

TV0 = 1050 / 0.12 - 0.05 = 15000

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That is the present value of the future free cash flows today, assuming end of year cash flows. This problem assumes cash flows occur continuously, so the value of the firm is

Vf = 15000*(1+0.12)^0.5+1125 = 16999.5

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The value of the firm is divided among all providers of capital, so

Vf = D+PS+E

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Solve for the value of equity (E);

E=VF−D−PS=$16,999.5−$5,000−$1,500=$10,500

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Price is the value of equity divided by number of shares outstanding

P = 10500 / 500 = 21

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price per share of XYZ Corp stock today is $21.