Stock and Market Value

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STEPHENSON REAL ESTATE
RECAPITALIZATION mini case by Vasily Kuznetsov, IFF 3-3

1. If Stephenson wishes to maximize the overall value of the firm, it should use debt to finance the $100 million purchase. Since interest payments are tax deductible, debt in the firm’s capital structure will decrease the firm’s taxable income, creating a tax shield that will increase the overall value of the firm.

2. Since Stephenson is an all-equity firm with 15 million shares of common stock outstanding, worth $32.50 per share, the market value of the firm is:

Market value of equity = $32.50(15,000,000)
Market value of equity = $487,500,000

So, the market value balance sheet before the land purchase is:

Market value balance sheet

Assets $487,500,000
Total assets $487,500,000

Equity $487,500,000
Debt & Equity $487,500,000

3. a. As a result of the purchase, the firm’s pre-tax earnings will increase by $25 million per year in perpetuity. These earnings are taxed at a rate of 40 percent. Therefore, after taxes, the purchase increases the annual expected earnings of the firm by:

Earnings increase = $25,000,000(1 – .40)
Earnings increase = $15,000,000

Since Stephenson is an all-equity firm, the appropriate discount rate is the firm’s unlevered cost of equity, so the NPV of the purchase is:

NPV = –$100,000,000 + ($15,000,000 / .125)
NPV = $20,000,000
b. After the announcement, the value of Stephenson will increase by $20 million, the net present value of the purchase. Under the efficient-market hypothesis, the market value of the firm’s equity will immediately rise to reflect the NPV of the project. Therefore, the market value of Stephenson’s equity after the announcement will be:

Equity value = $487,500,000 + 20,000,000
Equity value = $507,500,000

Market value balance sheet:

Old assets $487,500,000
NPV of project 20,000,000
Equity $507,500,000
Total assets $507,500,000
Debt & Equity $507,500,000

Since the market value of the firm’s equity is $507,500,000 and the firm has 15 million shares of common stock outstanding, Stephenson’s stock price after the announcement will be:

New share price = $507,500,000 / 15,000,000
New share price = $33.83

Since Stephenson must raise $100 million to finance the purchase and the firm’s stock is worth $33.83 per share, Stephenson must issue:

Shares to issue = $100,000,000 / $33.83
Shares to issue = 2,955,665

c. Stephenson will receive $100 million in cash as a result of the equity issue. This will increase the firm’s assets and equity by $100 million. So, the new market value balance sheet after the stock issue will be:

Market value balance sheet:

Cash $100,000,000
Old assets 487,500,000
NPV of project 20,000,000
Total assets $607,500,000

Equity $607,500,000
Debt & Equity $607,500,000

The stock price will remain unchanged. To show this, Stephenson will now have: Total shares outstanding = 15,000,000 + 2,955,665
Total shares outstanding = 17,955,665

So, the share price is:

Share price = $607,500,000 / 17,955,665
Share price = $38.33

d. The project will generate $25 million of additional annual pretax earnings forever. These earnings will be taxed at a rate of 40 percent. Therefore, after taxes, the project increases the annual earnings of the firm by $15 million. So, the aftertax present value of the earnings increase is:

PVProject = $15,000,000 / .125
PVProject = $120,000,000

So, the market value balance sheet of the company will be:

Market value balance sheet:

Old assets $487,500,000
PV of project 120,000,000
Total assets $607,500,000

Equity $607,500,000
Debt & Equity $607,500,000

4. a. Modigliani-Miller Proposition I states that in a world with corporate taxes:

VL = VU + tCB
As was shown in Question 3, Stephenson will be worth $607.5 million if it finances the purchase with equity. If it were to finance the initial outlay of the project with debt, the firm would have...
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