Chapter 16, Problem 3M

a)

Summary Introduction

Case synopsis:

Company S is a real estate firm, whose CEO (chief executive officer) is Person R. The firm buys real estate and rents it to the tenants. The firm has a profit each year. Before the foundation of Company S, Person R was a CEO and the founder of Company A, which is a farming operation. Company A was a failure as a firm, which ended up with bankruptcy. This situation made Person R extremely averse towards debt financing.

Hence, the company is completely financed through equity. Company S is assessing a plan to buy a huge tract of land, which would be leased to tenant farmers. This purchase is predicted to raise the annual earnings before tax in perpetuity. Person J is the new CFO (chief financial officer) of Company S, who has determined the present capital cost of the company.

Person J felt that the company will be very valuable if it adds debt in its capital structure. While evaluating whether the company could issue debt to completely finance the project, she found that it can issue bonds at a par value with the coupon rate. She found an optimal range of capital structure between 70% equity and 30% debt.

Characters in the case:

• Company S
• Company A
• Person S
• Person J

Adequate information:

• If Company S moves beyond the 30% debt, the bonds issued by the company will have a lower rating and a greater coupon as the possibility of financial distress and the associated cost will increase.
• Company S also has a corporate rate of tax.

To compute: The NPV of the project.

Answer to Problem 3M

The NPV (net present value) of the project $14,117,647.06.

Explanation of Solution

Given information: Company S has an outstanding stock of 12 million shares, while financed completely through equity. The present trade of the stock is $31.40 for one share. The purchase price of the huge tract of land is $80 million. The expected increase in the earnings through the land purchase is $16 million.

The present capital cost of the company is 10.2%. The company will have an optimal capital structure if it is between 70% equity and 30% debt. The corporate rate of tax is 40%.

Explanation:

The purchase of land will result in an increase in the earnings of the company by $16 million in a year, in perpetuity. Such earnings are taxed at 40%. Hence, after taxes, the land purchase will increase the yearly-expected earnings of the company.

Formula to calculate the increase in the earnings:

$\text{Earnings increase}=\text{Increase in purchase before tax}\left(1-\text{Rate of tax}\right)$

Calculate the increase in the earnings:

$\begin{array}{c}\text{Earnings increase}=\text{Increase in purchase before tax}\left(1-\text{Rate of tax}\right)\\ =\$16,000,000\left(1-0.40\right)\\ =\$9,600,000\end{array}$

Hence, the increase in the earnings after tax is $9,600,000.

As Company S is an all-equity company, the appropriate rate of discount is the company’s unlevered cost of equity. Hence, the NPV of the purchase is as follows:

Formula to calculate the NPV:

$\text{NPV}=\frac{\text{Increase in the earnings after-tax}}{\text{Current cost of capital}}-\text{Initial cost}$

Calculate the NPV:

$\begin{array}{c}\text{NPV}=\frac{\text{Increase in the earnings after-tax}}{\text{Current cost of capital}}-\text{Initial cost}\\ =\frac{\$9,600,000}{0.102}-\$80,000,000\\ =\$14,117,647.06\end{array}$

Hence, the NPV is $14,117,647.06.

b)

Summary Introduction

Case synopsis:

Company S is a real estate firm, whose CEO (chief executive officer) is Person R. The firm buys real estate and rents it to the tenants. The firm has a profit each year. Before the foundation of Company S, Person R was a CEO and the founder of Company A, which is a farming operation. Company A was a failure as a firm, which ended up with bankruptcy. This situation made Person R extremely averse towards debt financing.

Hence, the company is completely financed through equity. Company S is assessing a plan to buy a huge tract of land, which would be leased to tenant farmers. This purchase is predicted to raise the annual earnings before tax in perpetuity. Person J is the new CFO (chief financial officer) of Company S, who has determined the present capital cost of the company.

Person J felt that the company will be very valuable if it adds debt in its capital structure. While evaluating whether the company could issue debt to completely finance the project, she found that it can issue bonds at a par value with the coupon rate. She found an optimal range of capital structure between 70% equity and 30% debt.

Characters in the case:

• Company S
• Company A
• Person S
• Person J

Adequate information:

• If Company S moves beyond the 30% debt, the bonds issued by the company will have a lower rating and a greater coupon as the possibility of financial distress and the associated cost will increase.
• Company S also has a corporate rate of tax.

To construct:

The balance sheet of Company S with its market value after its announcement that the company will use equity finance for the purchase. Calculate the new price for one share of the company’s stock and the number of shares to be issued by the company in order to finance the purchase.

Answer to Problem 3M

The new price per share after the announcement of land purchase is $32.58 and the number of shares Company S needs to be issued is $2,547,770.70.

Explanation of Solution

The value of Company S will maximize by $14,117,647.06, which is NPV of the purchase, after the announcement. As per the efficient-market hypothesis, the firm’s market value will immediately increase to reflect the project’s NPV. Hence, the market value equity of Company S after the purchase announcement is as follows:

Formula to calculate the value of equity:

$\text{Equity value}=\text{Market value of equity}+\text{NPV}$

Calculate the value of equity:

$\begin{array}{c}\text{Equity value}=\text{Market value of equity}+\text{NPV}\\ =\$376,800,000+\$14,117,647.06\\ =\$390,917,647.10\end{array}$

Hence, the equity value is $390,917,647.10.

Balance sheet showing the market value after its announcement of land purchase through equity finance:

Market value balance sheet
Equity	$39,09,17,647	Old assets	$37,68,00,000
		NPV of project	$1,41,17,647
Debt and equity	$39,09,17,647	Total assets	$39,09,17,647

As the market value of the company’s equity is $390,917,647 and the company has an outstanding stock of 9 million shares, the stock price of Company S after the announcement will be the following:

Formula to calculate the new share price:

$\text{New share price}=\frac{\text{Market value of the firm's equity}}{\text{Outstanding shares}}$

Calculate the new share price:

$\begin{array}{c}\text{New share price}=\frac{\text{Market value of the firm's equity}}{\text{Outstanding shares}}\\ =\frac{\$390,917,647}{\$12,000,000}\\ =\$32.58\end{array}$

Hence, the new share price is $32.58.

Company S should increase $80 million to finance the purchase of land and the worth of the company’s stock is $32.58 for one share. Hence, Company S must issue the following amount:

Formula to calculate the shares to be issued:

$\text{Shares to issue}=\frac{\text{Increase in the financing amount for land purchase}}{\text{New share price}}$

Calculate the shares to be issued:

$\begin{array}{c}\text{Shares to issue}=\frac{\text{Increase in the financing amount for land purchase}}{\text{New share price}}\\ =\frac{\$80,000,000}{\$32.58}\\ =\$2,455,494.168\end{array}$

Hence, the shares to be issued are $2,455,494.168.

c)

Summary Introduction

Case synopsis:

Company S is a real estate firm, whose CEO (chief executive officer) is Person R. The firm buys real estate and rents it to the tenants. The firm has a profit each year. Before the foundation of Company S, Person R was a CEO and the founder of Company A, which is a farming operation. Company A was a failure as a firm, which ended up with bankruptcy. This situation made Person R extremely averse towards debt financing.

Hence, the company is completely financed through equity. Company S is assessing a plan to buy a huge tract of land, which would be leased to tenant farmers. This purchase is predicted to raise the annual earnings before tax in perpetuity. Person J is the new CFO (chief financial officer) of Company S, who has determined the present capital cost of the company.

Person J felt that the company will be very valuable if it adds debt in its capital structure. While evaluating whether the company could issue debt to completely finance the project, she found that it can issue bonds at a par value with the coupon rate. She found an optimal range of capital structure between 70% equity and 30% debt.

Characters in the case:

• Company S
• Company A
• Person S
• Person J

Adequate information:

• If Company S moves beyond the 30% debt, the bonds issued by the company will have a lower rating and a greater coupon as the possibility of financial distress and the associated cost will increase.
• Company S also has a corporate rate of tax.

To construct:

The balance sheet of Company S, with its market value after the issue of equity prior to the purchase. Calculate the new price for one share of the company’s stock and the outstanding number of shares of the common stock that the company has.

Answer to Problem 3M

The outstanding number of shares of common stock that the company has is $14,547,770.70 and the price for one share of the company’s stock is $32.58.

Explanation of Solution

Company S will receive a cash of $80 million due to equity issues. This will raise the assets and equity of the firm by $80 million. Hence, the balance sheet with the new market value after the issue of stock will be as follows:

Balance sheet showing the market value before the land purchase after the issue of stock:

Market Value Balance Sheet
Equity	$470,917,647	Cash	$80,000,000
		Old assets	$376,800,000
		NPV of project	$1,41,17,647
Debt and equity	$470,917,647	Total assets	$470,917,647

The stock price will be unchanged. Hence, compute the total outstanding shares to show the constant stock price.

Formula to calculate the total outstanding shares:

$\text{Total shares outstanding}=\text{Outstanding shares}+\text{Number of shares to be issued}$

Calculate the total outstanding shares:

$\begin{array}{c}\text{Total shares outstanding}=\text{Outstanding shares}+\text{Number of shares to be issued}\\ =\$12,000,000+\$2,455,494.168\\ =\$14,455,494.17\end{array}$

Hence, the total outstanding shares are $14,455,494.17.

Formula to calculate the share price:

$\text{Share price}=\frac{\text{Equity}}{\text{Total shares outstanding}}$

Calculate the share price:

$\begin{array}{c}\text{Share price}=\frac{\text{Equity}}{\text{Total shares outstanding}}\\ =\frac{\$470,917,647}{\$14,455,494.17}\\ =\$32.58\end{array}$

Hence, the share price is $32.58.

d)

Summary Introduction

Case synopsis:

Company S is a real estate firm, whose CEO (chief executive officer) is Person R. The firm buys real estate and rents it to the tenants. The firm has a profit each year. Before the foundation of Company S, Person R was a CEO and the founder of Company A, which is a farming operation. Company A was a failure as a firm, which ended up with bankruptcy. This situation made Person R extremely averse towards debt financing.

Hence, the company is completely financed through equity. Company S is assessing a plan to buy a huge tract of land, which would be leased to tenant farmers. This purchase is predicted to raise the annual earnings before tax in perpetuity. Person J is the new CFO (chief financial officer) of Company S, who has determined the present capital cost of the company.

Person J felt that the company will be very valuable if it adds debt in its capital structure. While evaluating whether the company could issue debt to completely finance the project, she found that it can issue bonds at a par value with the coupon rate. She found an optimal range of capital structure between 70% equity and 30% debt.

Characters in the case:

• Company S
• Company A
• Person S
• Person J

Adequate information:

• If Company S moves beyond the 30% debt, the bonds issued by the company will have a lower rating and a greater coupon as the possibility of financial distress and the associated cost will increase.
• Company S also has a corporate rate of tax.

To construct: The balance sheet of Company S after the purchase.

Explanation of Solution

The project will increase $16 million of extra pre-tax earnings yearly forever. Such earnings will be taxed at 40%. Hence, after taxes, the project will raise the yearly earnings of the firm by $9.6 million. Compute the present value of the increase in the earnings after-tax:

Formula to calculate the market value balance sheet:

$\text{Present value of the project}=\frac{\text{Increase in the yearly earnings of the firm }}{\text{Present capital cost}}$

Calculate the market value balance sheet:

$\begin{array}{c}\text{Present value of the project}=\frac{\text{Increase in the yearly earnings of the firm }}{\text{Present capital cost}}\\ =\frac{\$9,600,000}{\$0.102}\\ =\$94,117,647.06\end{array}$

Hence, the present value of the project is $94,117,647.06.

Balance sheet showing the market value after the land purchase after the issue of stock:

Market Value Balance Sheet
Equity	$470,917,647.1	Old assets	$376,800,000
		PV of project	$94,117,647.06
Debt and equity	$470,917,647.1	Total assets	$470,917,647.1