case finance

F13 BUS-F301 Solution to Minicase of Chapter 16 1/6

BUS-F301 Financial Management Fall 2013, Class No. 14301 (Online)/ 14973 (Face-to-Face) Answers to Minicase of Chapter 16 on Page 559 of your textbook.

Please print the minicase from Courseload on Oncourse and study it well before reading the following. You can find the instructions on how to print the textbook pages posted under Syllabus on Oncourse.

This minicase is a VERY CLOSE example for Case Study 3. Please learn the way below on how to present your answers to the questions in Case Study 3. You have to use your own words for your explanations to your answers for Case Study 3. 1. Should Stephenson want to maximize its overall firm value, it needs to consider using debt

financing for the $80 million purchase of the land. As interest payments are expenses to a firm and they are thus tax deductible (i.e. the interest payments reduce the taxable income and, in turn, the tax liability of the firm), debt in a firm’s capital structure will create a tax shield leading to a higher overall value of the firm. According to Modigliani-Miller Proposition I with corporate taxes, the value of a levered firm (firm that borrows – Firm L) is equal to the value of an unlevered firm (firm that does not borrow – Firm U) with identical assets and operations plus interest tax shield (i.e. the tax savings achieved by a firm from interest expenses resulted from borrowing). Therefore, VL = VU + TC × D where VL is the value of the levered firm, VU is the value of the unlevered firm, TC is the corporate tax rate,

D is the debt amount (this same amount is assumed to be borrowed by the firm perpetually) and

TC × D is the present value of the interest tax shield

This valuation model can also be applied to a firm before and after using debt. We can think of a firm before using any debt as an unlevered firm and when it starts using some debt, it turns itself into a levered firm. The present value of the interest tax shield is derived as below. Assuming that the debt, D, is perpetual and the annual interest rate is RD. Thus, the annual interest expense is D × RD. Suppose the corporate tax rate is TC, the annual interest payment (expense) will lower the tax liability by TC × D × RD per year (annual interest tax shield) for a levered firm as compared with an identical unlevered firm. Since the interest tax shields are generated by the need of paying interests, they are considered to have the same risk as the debt itself. As such, the appropriate discount rate for them is the cost of debt, i.e. the interest rate. As the debt is perpetual and the same amount of interest tax shield will be generated each year, the resulting interest tax shields will form a perpetuity to the firm.

F13 BUS-F301 Solution to Minicase of Chapter 16 2/6

Hence, Present value of the interest tax shields = Annual interest tax shield/Cost of debt = (TC × D × RD)/ RD = TC × D

[Please note that the PV of a perpetuity is calculated as PV = CF/r. Here CF = Annual interest tax shield = TC × D × RD and r = cost of debt = RD.]

2. Stephenson is currently an all-equity firm. It has 12 million shares of common stock outstanding, each worth $31.40. We can calculate the market value of the firm’s equity as in the following.

Market value of equity = $31.40(12,000,000) = $376,800,000 As Stephenson carries no debt, the market value of its assets should be entirely equal to the

market value of its equity.

Thus, the market value balance sheet of Stephenson before announcing the land purchase should look as below.

Stephenson Real Estate Company

Market Value Balance Sheet - Before Land Purchase

Assets $376,800,000 Equity $376,800,000 Total assets $376,800,000 Total Debt & Equity $376,800,000

3. a. Since the project will generate additional annual pretax earnings of $16 million forever

and these earnings will be taxed at 40 percent, Stephenson’s after taxes increase in the annual earnings = Pre-tax increase in annual earnings × (1 – TC) where TC is the corporate-tax rate

= $16 million × (1 – 40%) = $9.6 million

[ Please note that After-tax increase in annual earnings = Pre-tax increase in annual earnings – Taxes = Pre-tax increase in annual earnings – Pre-tax increase in annual earnings × TC = Pre-tax increase in annual earnings × (1 – TC) ]

As Stephenson is an all-equity firm with no debt financing, the appropriate discount rate for its expected cash flows is the firm’s unlevered cost of equity (RU) of 10.2%. Therefore, as the project increases the after-tax annual earnings of the firm by $9.6 million, the present value of the after-tax earnings increases is $94,117,647.

F13 BUS-F301 Solution to Minicase of Chapter 16 3/6

PVProject = After-tax increase in annual earnings/RU = $9,600,000 / 10.2% = $9,600,000 / .102 = $94,117,647

The NPV of the project can be calculated as below. NPV Project = – Cost Project + PV Project = –$80,000,000 + $94,117,647 = $14,117,647

[Please note that by formula, the NPV of the project is equal to negative of its cost plus the present value of all the expected future cash flows to be generated by the project, i.e. the present value of all the after-tax annual earnings increases. As the after-tax annual earnings increases are the same for all the years and such increases are assumed to be perpetual. They form a perpetuity to the firm.

In order to calculate the present value of a perpetuity, we use the formula, PV = CF/r.

Applying here, PVProject = After-tax annual earnings increase/RU.]

b. When Stephenson has made the announcement of purchasing the land using equity (i.e.

raising the required fund to pay for the purchase by issuing common stock), its value immediately increases by $14,117,647 (the same as the net present value of the project). According to the Efficient Market Hypothesis which advocates that all the relevant information about the securities of a firm such as stocks, bonds, should be reflected fully and immediately in their market prices; thus, the market value of Stephenson’s equity will immediately rise to reflect the NPV of the project.

[Please note that the market value of a firm’s equity is equal to the market price of the firm’s common stock times the number of shares of common stock outstanding.]

Therefore, Stephenson will have the market value of its equity after the announcement

as in the following. Equity value = $376,800,000 + $ 14,117,647 = $390,917,647

Stephenson Real Estate Company Market Value Balance Sheet – Immediate After

the Announcement of the Land Purchase Project

Old assets $376,800,000

NPV of project

14,117,647 Equity $390,917,647

Total assets $390,917,647 Total Debt & Equity $390,917,647

F13 BUS-F301 Solution to Minicase of Chapter 16 4/6

As you can see from above, the market value of the firm’s equity is $390,917,647 and the firm has 12 million shares of common stock outstanding. As a result, Stephenson’s stock price after the announcement of the project will be $32.58.

New share price = $390,917,647 / 12,000,000 = $32.576471

= $32.58 As Stephenson needs to raise $80 million in total to pay for the land and the firm’s

stock is currently worth $32.58 ($32.576471) per share, Stephenson will have to issue approximately 2,455,760 shares.

Shares to issue = $80,000,000 / $32.576471 = 2,455,760.203

= 2,455,760 c. By issuing the required number of shares (2,455,760 shares) of common stock,

Stephenson will receive $80 million in cash. This will in turn increase its assets (cash is a current asset) and equity both by $80 million. As such, the market value balance sheet after the stock issue will look as below.

Stephenson Real Estate Company

Market Value Balance Sheet – Immediately After the Stock Issue but Before the Purchase of Land

Cash $80,000,000 Old assets 376,800,000

NPV of project

14,117,647 Equity $470,917,647

Total assets $470,917,647 Total Debt & Equity $470,917,647 After the stock issue, Total shares outstanding = 12,000,000 + 2,455,760.203 = 14,455,760.203 = 14,455,760 Share price = $470,917,647 / 14,455,760.203

= $32.576471 = $32.58

You can see here that the stock price remains unchanged at this point.

F13 BUS-F301 Solution to Minicase of Chapter 16 5/6

d. Stephenson pays $80,000,000 to purchase the land, thus, its cash balance will be

lowered by the same amount. After Stephenson has paid for the land, the value of the project to the firm as an asset will be equal to the PV of the project. The market value balance sheet of the company after the purchase of the land will be as below:

Stephenson Real Estate Company

Market Value Balance Sheet – After the Purchase of Land

Old assets $376,800,000 PV of project 94,117,647 Equity $470,917,647

Total assets $470,917,647 Total Debt & Equity $470,917,647

4. a. As had been explained in Question 1, Modigliani-Miller Proposition I states that in a

world with corporate taxes:

VL = VU + TC × D

That is, a firm has a value of VU before using any debt as an unlevered firm and when it starts using some debt, it turns itself into a levered firm and will have a value of VL, which is increased by the present value of the interest tax shield that is calculated as TC × D.

As can be seen in Question 3, the value of Stephenson is $470,917,647 if it finances the

purchase of land with equity. On the other hand, if it were to finance the initial cost of the project (purchasing the land for $80 million) with debt, the firm would have $80 million worth of 6 percent debt outstanding. That means Stephenson will carry $80 million of debt and pays 6% interest annually.

[Please note that Stephenson is able to issue bonds at par value with an 6 percent coupon rate. That means the yield to maturity is also 6 percent. Remember that when a bond’ yield to mature is equal to its coupon rate, then the bond is selling at par? As such, the annual interest rate to Stephenson is also 6 percent (before-tax cost of debt).]

So, the value of Stephenson, if it finances the purchase of land with debt, can be

estimated as below. VL = VU + TC × D = $470,917,647+ .40($80,000,000) = $502,917,647

F13 BUS-F301 Solution to Minicase of Chapter 16 6/6

b. According to the Efficient Market Hypothesis, after the announcement of the debt

financing for the purchase of the land, the value of Stephenson will immediately increase by the present value of the interest tax shields.

PV of interest tax shields = TC × D = .40($80,000,000) = $32,000,000

Stephenson’s market-value balance sheet after both the debt issue and land purchase

will look as below:

Stephenson Real Estate Company Market value balance sheet – After Both the Debt Issue and Land

Purchase

Value unlevered

$470,917,647 Debt

$80,000,000

Tax shield 32,000,000 Equity 422,917,647

Total assets $502,917,647 Total Debt & Equity $502,917,647

Market value of total debt & equity should be equal to market value of total assets. Therefore, in the above market value balance sheet, Market value of equity = Market value of debt & equity – Market value of debt = Market value of total assets – Market value of debt = $502,917,647 - $80,000,000 = $422,917,647

[Please note that even after Stephenson has borrowed the $80,000,000. Its capital structure will be 84.09% (=$422,917,647/$502,917,647) of equity and 15.91% (=$80,000,000/$502,917,647) of debt, not yet reached the optimal capital structure which is thought to be 70% of equity and 30% of debt. Stephenson can still borrow more money to finance other projects if it wants to. ]

After borrowing the $80,000,000, the total number of shares of common stock outstanding remains at 12,000,000 but the market value of equity is estimated at $422,917,647.

Stock price = $422,917,647/ 12,000,000 = $35.243137 = $35.24

5. In sum, if Stephenson issues equity to finance the project (i.e. remains as an unlevered firm), its stock price will remain at $32.58 per share. If Stephenson obtains debt to finance the project (i.e. turns itself into a levered firm), its stock price will rise to $35.24 per share (see an increase of $2.66 per share). Now you can see how debt financing can be used to maximize the per share stock price of the firm’s equity.