Luxx Inc. currently has assets to $5 million, zero debt, is in the 40 percent federal- plus-state tax bracket, has a net income of $1 million, and pays out 40 percent of its earnings as dividends. Net income is expected to grow at a constant rate of 5 percent per year, 200,000 shares of stock are outstanding, and current WACC is 13.40 percent.

The company is considering a recapitalization where it will issue $1 million in debt and use the proceeds to repurchase stock. Investment bankers have estimated that if the company goes through with the recapitalization, its before-tax cost of debt will be 11%, and its cost of equity will rise to 14.5%.

A. What is the stock's current price per share (before the recapitalization)?
B. Assuming the company maintains the same payout ratio, what will be its stock price following the recapitalization?

a.)$25 ; b.) $30.96

Explanation:

A.) Stock's current price per share:

Net income = $1,000,000

Dividend paid = 0.40 x $1,000,000 = $400,000

Dividend per share before recapitalization = $400,000 / 200,000 = $2

Price of the share before recapitalization is calculated as:

D1 = $2 × 1.05  = $2.10

P0 = D1/Ke - g

= $2.10/ 0.134 - 0.05

= $25

B.) Portion of equity after recapitalization = (200, 000 x $25) - $1,000,000 = $4,000,000

Portion of debt = $1,000,000

Revised WACC after recapitalization = Ke x E/V + Kd(1-t) x D/V

= 0.145 x $4,000,000/$5,000,000 + 0.11 x (1-0.40) x $1,000,000/$5,000,000

= 0.1292

= 12.92%

Revised net income is calculated as:

Before tax income = $1,000,000/0.60 = $5M

Interest = 0.11 x $1,000,000 = $110,000

Earning before tax = $1556666

40% of tax = $622,666.4

Net income = $933,999.60

Revised dividend = $933,999.60 x 0.40 = $373599.84

DPS = $373599.84/(200,000 - ($1,000,000/$25))

$373599.84/160,000

= $2.335

Revised price of the share after recapitalization:

$2.335 x 1.05 / 0.1292 - 0.05

2.45175 / 0.0792

= $30.96

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