Chapter 13, Problem 9QP

a)

Summary Introduction

To calculate: The cash flow of Person R (a shareholder of the company), having 100 shares as per the current capital structure and with an assumption that the company has a rate of dividend payment at 100%.

Introduction:

Leverage refers to the borrowing of amount or debt to utilize for the purchase of equipment, inventory, and other assets of the company.

Answer to Problem 9QP

The dividend received by the shareholder is $1,868.85.

Explanation of Solution

Given information:

Company S is a consumer products’ firm that is planning to convert its all-equity financing to debt financing at 25%. The outstanding shares are 6,100 and the price for each share is $60. The EBIT is expected to be $38,000 for one year forever. The rate of interest for the debt is 7%.

Note: It is necessary to compute EPS (Earnings per share) to compute the cash flow.

Formula to compute the total value of the company:

$\text{Total value of the company }V=\text{Price per share}\times \text{Outstanding shares}$

Compute the total value of the company:

$\begin{array}{c}\text{Total value of the company }V=\text{Price per share}\times \text{Outstanding shares}\\ =\$60\left(6,100\right)\\ =\$366,000\end{array}$

Hence, the total value of the company is $366,000.

Formula to calculate the dividend received by Person R:

$\text{Dividend received}=\text{EBIT}\left(\frac{\text{Person R's owned stock}}{\text{Total value of the company}}\right)$

Calculate the dividend received by Person R:

$\begin{array}{c}\text{Dividend received}=\text{EBIT}\left(\frac{\text{Person R's owned stock}}{\text{Total value of the company}}\right)\\ =\$38,000\left(\frac{\$18,000}{\$366,000}\right)\\ =\$1,868.85\end{array}$

Hence, the dividend received is $1,868.85.

b)

Summary Introduction

To calculate: The cash flow of Person R as per the proposed capital structure assuming that she has the same 100 shares.

Note: It is necessary to compute EPS (Earnings per share) under the planned capital structure to calculate the cash flow.

Introduction:

Leverage refers to the borrowing of amount or debt to utilize for the purchase of equipment, inventory, and other assets of the company.

Answer to Problem 9QP

The cash flow of Person R under the proposed capital structure is $2,070.

Explanation of Solution

Formula to compute the new debt:

$\text{New debt amount}=\text{Debt percent}\left(\text{Market value of the firm}\right)$

Compute the new debt:

$\begin{array}{c}\text{New debt amount}=\text{Debt percent}\left(\text{Market value of the firm}\right)\\ =0.25\left(\$366,000\right)\\ =\$91,500\end{array}$

Hence, the new debt amount is $91,500.

Formula to calculate the repurchased shares:

$\text{Shares repurchased}=\frac{\text{New debt amount}}{\text{Price of outstanding shares}}$

Calculate the repurchased shares:

$\begin{array}{c}\text{Shares repurchased}=\frac{\text{New debt amount}}{\text{Price of outstanding shares}}\\ =\frac{\$91,500}{\$60}\\ =\$1,525\end{array}$

Hence, the repurchased shares are $1,525.

Note: The firm must make an interest payment on the new debt amount. Hence, compute the net income along with the payment of interest.

Formula to compute the net income:

$\text{Net income}=\text{EBIT}-\text{New interest payment}\left(\text{New debt amount}\right)$

Compute the net income:

$\begin{array}{c}\text{Net income}=\text{EBIT}-\text{New interest payment}\left(\text{New debt amount}\right)\\ =\$38,000-0.07\left(\$91,500\right)\\ =\$31,595\end{array}$

Hence, the net income is $31,595.

Compute the EPS:

$\begin{array}{c}\text{EPS}=\frac{\text{Net income}}{\left(\text{Outstanding shares}-\text{Repurchased shares}\right)}\\ =\frac{\$31,595}{\left(\$6,100-\$1,525\right)\text{ shares}}\\ =\$6.90\end{array}$

Hence, the EPS is $6.90.

Formula to compute the shares owned by the shareholders:

$\text{Shares owned}=\frac{\text{Stock owned by Person R}}{\text{Price of oustanding shares}}$

Compute the shares owned by the shareholders:

$\begin{array}{c}\text{Shares owned}=\frac{\text{Stock owned by Person R}}{\text{Price of oustanding shares}}\\ =\frac{\$18,000}{\$60}\\ =\$300\end{array}$

Hence, the shares owned by the shareholder is $300.

Formula to compute the cash flow:

$\text{Shareholder cash flow}=\text{EPS}\left(\text{Share of Person R}\right)$

Compute the cash flow:

$\begin{array}{c}\text{Shareholder cash flow}=\text{EPS}\left(\text{Share of Person R}\right)\\ =\$6.90\left(300\text{ shares}\right)\\ =\$2,070\end{array}$

Hence, the cash flow is $2,070.

c)

Summary Introduction

To calculate: How Person R would convert her shares to re-establish the original capital structure.

Introduction:

Leverage refers to the borrowing of amount or debt to utilize for the purchase of equipment, inventory, and other assets of the company.

Answer to Problem 9QP

The total cash flow of Person R under recreation of the original capital structure is $1,867.5.

Explanation of Solution

Formula to calculate the interest cash flow:

$\text{Interest cash flow}=\left[\begin{array}{l}\text{Sale of shareholders shares}\left(\text{Price of outstanding shares}\right)\\ \left(\text{Rate of interest}\right)\end{array}\right]$

To replicate the projected capital structure, the shareholder must sell their shares at 25% or 75 shares at an interest rate of 7%. Hence, compute the interest cash flow of the shareholder.

Calculate the interest cash flow:

$\begin{array}{c}\text{Interest cash flow}=\left[\begin{array}{l}\text{Sale of shareholders shares}\left(\text{Price of outstanding shares}\right)\\ \left(\text{Rate of interest}\right)\end{array}\right]\\ =75\left(\$60\right)\left(0.07\right)\\ =\$315\end{array}$

Hence, the interest cash flow is $315.

Note: The shareholders will obtain the dividend payment on the balance 225 shares, compute the dividend received by the shareholders.

Formula to calculate the dividend received:

$\text{Dividend received}=\text{Earnings per share}\left(\text{Remaining shares}\right)$

Calculate the dividend received:

$\begin{array}{c}\text{Dividend received}=\text{Earnings per share}\left(\text{Remaining shares}\right)\\ =\$6.90\left(\text{225 shares}\right)\\ =\$1,552.5\end{array}$

Hence, the dividend received by the shareholders is $1,552.5.

Formula to calculate the total cash flow:

$\text{Total cash flow}=\text{Interest cash flow}+\text{Dividend received}$

Calculate the total cash flow:

$\begin{array}{c}\text{Total cash flow}=\text{Interest cash flow}+\text{Dividend received}\\ =\$315+1,552.5\\ =\$1,867.5\end{array}$

Hence, the total cash flow is $1,867.5.

d)

Summary Introduction

To explain: The reason for the irrelevance in the capital structure of the company.

Introduction:

Leverage refers to the borrowing of amount or debt to utilize for the purchase of equipment, inventory, and other assets of the company.

Explanation of Solution

The reason for the irrelevance in the capital structure is that the shareholders create their own leverage to generate the payoff they wish, irrespective of the capital structure the company selects.