Chapter 29, Problem 14QP

a.

Summary Introduction

To determine: The value of each company before the merger.

Merger:

The merger is the combination of two entities into one in which shareholders of both the companies merge their resources into a new company. The ownership is also transferred to the new company.

Debt:

Debt is a secured liability of a company. It is a long-term liability. Debt carries a flat rate of interest on its value.

Equity:

Equity is the amount invested by the shareholders of the company. Shareholders are known as the owner of the company as they have invested their capital in the company. Equity shareholders get dividend which is not fixed and depends upon the profitability of the company.

Explanation of Solution

Given,

The probability of boom state is 0.65.

The probability of recession state is 0.35.

Value of Company B in boom state is $290,000.

Value of Company B in recession state is $110,000.

Value of Company R in boom state is $260,000.

Value of Company R in recession state is $80,000.

Calculation of the value of the company before the merger:

The formula to calculate the value of the company in the possible states of the economy,

$\text{Value}\text{of}\text{company}=\left[\begin{array}{l}\left(\begin{array}{l}\text{Probability}\text{of}\text{state}\text{boom}\times \\ \text{Value}\text{of}\text{company}\text{in}\text{boom}\text{state}\end{array}\right)\\ +\left(\begin{array}{l}\text{Probability}\text{of}\text{recession}\text{state}\times \\ \text{Value}\text{of}\text{company}\text{in}\text{recession}\text{state}\end{array}\right)\end{array}\right]$

Calculation of total value of Company B:

Substitute 0.65 for the probability of boom state, 0.35 for the probability of recession state, $290,000 for the value of the company in boom state and $110,000 for the value of the company in recession state.

$\begin{array}{c}\text{Value}\text{of}\text{Company}\text{B}=\left(0.65\times \$290,000\right)+\left(0.35\times \$110,000\right)\\ =\$188,500+\$38,500\\ =\$227,000\end{array}$

Hence, the value of Company B is $227,000.

Calculation of total value of Company R

Substitute 0.65 for the probability of boom state, 0.35 for the probability of recession state, $260,000 for the value of Company R in boom state and $80,000 for the value of Company R in a recession state

$\begin{array}{c}\text{Value}\text{of}\text{Company}\text{R}=\left(0.65\times \$260,000\right)+\left(0.35\times \$80,000\right)\\ =\$169,000+\$28,000\\ =\$197,000\end{array}$

Hence, the value of Company R is $197,000.

Conclusion

Thus, the value of Company B before the merger is $227,000 and the value of Company R before the merger is $197,000.

b.

Summary Introduction

To determine: The value of each Company’s debt and equity before the merger.

Explanation of Solution

Given,

The probability of boom state is 0.65.

The probability of recession state is 0.35.

Calculated,

Value of equity in boom state is $165,000 (working note).

Value of equity in recession state is $0 (working note).

The total value of the Company B is $227,000 (refer a part).

For company B,

Calculation of value of equity before merger:

The formula to calculate the value of equity before the merger,

$\text{Value}\text{of}\text{equity}=\left[\begin{array}{l}\left(\begin{array}{l}\text{Probability}\text{of}\text{boom}\text{state}\times \\ \text{Value}\text{of}\text{equity}\text{in}\text{boom}\text{state}\end{array}\right)\\ +\left(\begin{array}{l}\text{Probability}\text{of}\text{recession}\text{state}\times \\ \text{Value}\text{of}\text{equity}\text{in}\text{recession}\text{state}\end{array}\right)\end{array}\right]$

Substitute 0.65 for the probability of boom state, $165,000 for the value of equity in boom state, 0.35 for the probability of recession state and $0 for the value of equity in recession state in the above formula,

$\begin{array}{c}\text{Value}\text{of}\text{equity}=\left(0.65\times \$165,000\right)+\left(0.35\times \$0\right)\\ =\$107,250+\$0\\ =\$107,250\end{array}$

Hence, the value of equity of Company B before the merger is $107,250.

Calculation of value of debt before the merger,

The formula to calculate the value of debt,

$\text{Value}\text{of}\text{debt}=\left[\begin{array}{l}\text{Total}\text{value}\text{of}\text{company}\\ -\text{Value}\text{of}\text{equity}\text{of}\text{company}\end{array}\right]$

Substitute $227,000 for the total value of the company and $107,250 for the value of equity of company in the above formula,

$\begin{array}{c}\text{Value}\text{of}\text{debt}=\$227,000-\$107,250\\ =\$119,750\end{array}$

Hence, the value of debt of Company B before the merger is $119,750.

For Company R,

Given,

Company R is an all-equity company.

So Company R has no debt.

So the value of equity of Company R before the merger is equal to the total value of the company.

Hence, the value of equity before the merger is $197,000.

The value of debt before the merger is $0.

Working Note:

For Company B,

Calculation of value of equity of Company B in boom state:

Given,

The total value of Company B in boom state is $290,000.

Value of debt of Company B in boom state is $125,000.

The formula to calculate the value of equity in boom state,

$\begin{array}{c}\text{Value}\text{of}\text{equity}\text{in}\text{boom}\text{state}=\left[\begin{array}{l}\text{Total}\text{value}\text{in}\text{boom}\text{state}\\ -\text{Value}\text{of}\text{debt}\text{in}\text{boom}\text{state}\end{array}\right]\\ =\$290,000-\$125,000\\ =\$165,000\end{array}$

Calculation of value of equity of Company B in recession state,

Given,

The total value of Company B in recession state is $110,000.

Value of debt of Company B in recession state is $125,000.

Since the value of debt of Company B is higher than the total value of Company B in recession state.

So there is no value equity value of Company B in recession state.

Conclusion

Thus, the value of equity of Company B before the merger is $107,250, the value of debt of Company B before the merger is $119,750. The value of equity of Company R before the merger is $197,000 and value of debt of Company R before the merger is $0.

c.

Summary Introduction

To determine: The total value of the companies, the total value of the equity and total value of the debt.

Explanation of Solution

Given,

The total value of Company B before the merger is $227,000(refer part a).

The total value of Company R before the merger is $197,000(refer part a).

Calculation of the total value of companies:

The formula to calculate the total value of companies,

$\text{Total}\text{value}\text{of}\text{companies}=\left[\begin{array}{l}\text{Total}\text{value}\text{of}\text{Company}\text{B}\\ +\text{Total}\text{value}\text{of}\text{Company}\text{R}\end{array}\right]$

Substitute $227,000 for a total value of Company B and $197,000 for a total value of Company R in the above formula,

$\begin{array}{c}\text{Total}\text{value}\text{of}\text{companies}=\$227,000+\$197,000\\ =\$424,000\end{array}$

Hence, the total value of the companies is $424,000.

Calculation of total value of equity:

Given,

Value of equity of Company B before the merger is $107,250 (refer part a)

Value of equity of Company R before the merger is $197,000(refer part a).

The formula to calculate the total value of equity,

$\text{Total}\text{value}\text{of}\text{equity}=\left[\begin{array}{l}\text{Value}\text{of}\text{equity}\text{of}\text{Company}\text{B}\\ +\text{Value}\text{of}\text{equity}\text{of}\text{Company}\text{R}\end{array}\right]$

Substitute $107,250 for the value of equity of Company B and $197,000 for the value of equity of Company R,

$\begin{array}{c}\text{Total}\text{value}\text{of}\text{equity}=\$107,250+197,000\\ =\$304,250\end{array}$

Hence, the total value of equity is $304,250.

Calculation of total value of debt:

Given,

Value of debt of Company B before the merger is $119,750(refer part b)

Value of debt of Company R before the merger is $0 (refer part b).

The formula to calculate the total value of debt,

$\text{Total}\text{value}\text{of}\text{debt}=\left[\begin{array}{l}\text{Value}\text{of}\text{debt}\text{of}\mathrm{C}\text{ompany}\text{B}\\ +\text{Value}\text{of}\text{debt}\text{of}\text{Company}\text{R}\end{array}\right]$

Substitute $119,750 for the value of debt of Company B and $0 for the value of debt of Company R.

$\begin{array}{c}\text{Total}\text{value}\text{of}\text{debt}=\$119,750+\$0\\ =\$119,750\end{array}$

Hence, the total value of debt is $119,750.

Conclusion

Thus, the total value of companies is $424,000, the total value of equity is $304,250 and the total value of debt is $119,750.

d.

Summary Introduction

To determine: The value of the merged company, the value of the merged company’s debt and the value of merged company’s equity.

Explanation of Solution

Given,

The probability of boom state is 0.65.

The probability of recession state is 0.35.

Calculated,

Value of merged company in boom state is $550,000(working note).

Value of merged company in recession state is $190,000 (working note)

Value of merged company’s equity in boom state is $425,000 (working notes).

Value of merged company’s equity in recession state is $110,000(working notes)

Calculation of value of the merged company:

The formula to calculate the value of the merged company,

$\text{Value}\text{of}\text{merged}\text{company}=\left[\begin{array}{l}\left(\begin{array}{l}\text{Probabiility}\text{of}\text{boom}\text{state}\times \\ \text{Value}\text{of}\text{merged}\text{company}\text{in}\text{boom}\text{state}\end{array}\right)\\ +\left(\begin{array}{l}\text{Probabilitty}\text{of}\text{recession}\text{state}\times \\ \text{Value}\text{of}\text{merged}\text{company}\text{in}\text{recession}\text{state}\end{array}\right)\end{array}\right]$

Substitute 0.65 for the probability of boom state, 0.35 for the probability of recession state, $550,000 for the value of the merged company in boom state and $190,000 for the value of the merged company in recession state in the above formula,

$\begin{array}{c}\text{Value}\text{of}\text{merged}\text{company}=\left(0.65\times \$550,000\right)+\left(0.35\times \$190,000\right)\\ \text{=}\$357,500+\$66,500\\ \text{=}\$424,000\end{array}$

Hence, the value of the merged company is $424,000.

Calculation of value of merged company’s equity:

The formula to calculate the value of merged company’s equity,

$\text{Value}\text{of}\text{merged}\text{company's equity}=\left[\begin{array}{l}\left(\begin{array}{l}\text{Probabiility}\text{of}\text{boom}\text{state}\times \\ \text{Value}\text{of}\text{merged}\text{company's}\text{equity}\text{in}\text{boom}\text{state}\end{array}\right)\\ +\left(\begin{array}{l}\text{Probabilitty}\text{of}\text{recession}\text{state}\times \\ \text{Value}\text{of}\text{merged}\text{company's}\text{equity}\text{in}\text{recession}\text{state}\end{array}\right)\end{array}\right]$

Substitute 0.65 for probability for the probability of boom state, 0.35 for probability for recession state, $425,000 for the value of merged company’s equity in boom state and $110,000 for the value of merged company’s equity in recession state.

$\begin{array}{c}\text{Value}\text{of}\text{merged}\text{company's}\text{equity}=\left(0.65\times \$425,000\right)+\left(0.35\times \$110,000\right)\\ =\$276,250+\$38,500\\ =\$314,750\end{array}$

Hence, the value of merged company’s equity is $341,750.

Calculation of value of merged company’s debt:

Given,

Since Company R is an all-equity company, so, Company R has no debt.

Company B has a bond of face value $125,000.

The formula to calculate the value of merged company’s debt,

$\text{Value}\text{of}\text{merged}\text{company's}\text{debt}=\left[\begin{array}{l}\text{Value}\text{of}\text{debt}\text{of}\text{company}\text{R}+\\ \text{Value}\text{of}\text{debt}\text{of}\text{company}\text{B}\end{array}\right]$

Substitute $0 for the value of debt of Company R and $125,000 for the value of debt of company B in the above formula,

$\begin{array}{c}\text{Value}\text{of}\text{merged}\text{company's}\text{debt}=\$0+\$125,000\\ =\$125,000\end{array}$

The value of merged company’s debt is $125,000.

Working Notes:

Calculation of value of the merged company in boom state,

Given,

Value of Company B in boom state is $290,000.

Value of Company R in boom state is $260,000.

The formula to calculate the value of the merged company in boom state,

$\begin{array}{c}\text{Value}\text{of}\text{merged}\text{company}\text{in}\text{boom}\text{state}=\left[\begin{array}{l}\text{Value}\text{of}\text{Company}\text{B}\text{in}\text{boom}\text{state}\\ +\text{Value}\text{of}\text{Company}\text{R}\text{in}\text{boom}\text{state}\end{array}\right]\\ \text{=}\$290,000+\$260,000\\ \text{=}\$550,000\end{array}$

Hence, the value of the merged company in boom state is $550,000.

Calculation of value of the merged company in recession state,

Given,

Value of Company B in recession state is $110,000.

Value of Company R in recession state is $80,000.

The formula to calculate the value of the merged company in recession state,

$\begin{array}{c}\text{Value}\text{of}\text{merged}\text{company}\text{in}\text{recession}\text{state}=\left[\begin{array}{l}\text{Value}\text{of}\text{Company}\text{B}\text{in}\text{recession}\text{state}\\ +\text{Value}\text{of}\text{Company}\text{R}\text{in}\text{recession}\text{state}\end{array}\right]\\ =\$110,000+\$80,000\\ =\$190,000\end{array}$

Hence, the value of the merged company in recession state is $190,000.

Given,

Company R is an all-equity company.

Value of equity of Company R in boom state is $260,000.

Value of equity of Company B in boom state is $165,000 (refer part b)

Calculation of value of merged company’s equity in boom state:

$\begin{array}{c}\left[\begin{array}{l}\text{Value}\text{of}\text{merged}\text{company's}\\ \text{equity}\text{in}\text{boom}\text{state}\end{array}\right]=\left[\begin{array}{l}\text{Value}\text{of}\text{equity}\text{of}\text{Company}\text{B}\text{in}\text{boom}\text{state}\\ \text{+Value}\text{of}\text{equity}\text{of}\text{Company}\text{R}\text{in}\text{boom}\text{state}\end{array}\right]\\ =\$165,000+\$260,000\\ =\$425,000\end{array}$

Hence, the value of merged company’s equity in boom state is $425,000.

Calculation of value of merged company’s equity in recession state:

Given,

Company R is an all-equity company.

Value of equity of Company R in recession state is $110,000

Value of equity of Company B in recession state is $0 (refer part b).

The formula to calculate the value of merged company’s equity in recession state,

$\begin{array}{c}\left[\begin{array}{l}\text{Value}\text{of}\text{merged}\text{company's}\\ \text{equity}\text{in}\text{recession}\text{state}\end{array}\right]=\left[\begin{array}{l}\text{Value}\text{of}\text{equity}\text{of}\text{Company}\text{B}\text{in}\text{recession}\text{state}\\ \text{+Value}\text{of}\text{equity}\text{of}\text{Company}\text{R}\text{in}\text{recession}\text{state}\end{array}\right]\\ =\$0+\$110,000\\ =\$110,000\end{array}$

Hence, the value of the merged company’s equity in recession state is $110,000.

Conclusion

Thus, the value of the merged company is $424,000, the value of merged company’s equity is $341,750 and the value of merged company’s debt is $125,000.

e.

Summary Introduction

To explain: Whether there is a transfer of wealth and the reason for that.

Answer to Problem 14QP

No, there is no transfer of wealth.

Explanation of Solution

The newly merged company neither issued the new shares nor pay off the debt. So, there is no transfer of wealth.

Conclusion

No, transfer of wealth is there.

f.

Summary Introduction

To explain: Whether the face value of the B’s debt will affect the transfer of wealth.

Answer to Problem 14QP

No, it will not affect the transfer of wealth.

Explanation of Solution

The face value of debt if is $90,000, it is less than the lowest value of the firm, so there will be no co-insurance effect. So, it will not affect the transfer of wealth.

Conclusion

No, the face value of the debt will not affect the transfer of wealth.