Chapter 15, Problem 20P

a.

Summary Introduction

To calculate: Net proceeds to Tyson Iron Works.

Introduction:

Net Proceeds:

It is the amount received by the seller of shares after the deduction of all the expenses and costs incurred for making such sales.

Answer to Problem 20P

The net proceeds on the sale of shares to Tyson Iron Works is $11,845,000.

Explanation of Solution

Calculation of net proceeds:

$\begin{array}{c}\text{Net Proceeds}=\text{Proceeds before out-of-pocket cost}-\text{Out-of-Pocket Costs}\\ =\$12,125,000-\$280,000\\ =\$11,845,000\end{array}$

Working Notes:

Calculation of net price:

$\begin{array}{c}\text{Net Proceeds}=\text{Share Price}\times \left(100\%-3\%\text{spread}\right)\\ =\$25\times 97\%\\ =\$24.25\end{array}$

Calculation of proceeds before out-of-pocket expenses:

$\begin{array}{c}\text{Proceeds before Out-of-Pocket costs}=\text{New Shares}\times \text{Net Price}\\ =500,000\times \$24.25\\ =\$12,125,000\end{array}$

b.

Summary Introduction

To calculate: The EPS of Tyson Iron Works immediately prior to the issue of stock.

Introduction:

Earnings per share (EPS):

It is the profit earned by shareholders on each share. A higher EPS indicates a higher value of the company because investors are ready to pay a higher price for one share of the company.

Answer to Problem 20P

The EPS of Tyson Iron Works immediately prior to the issue of stock is $1.05.

Explanation of Solution

Calculation of the EPS immediately prior to the issue of stock:

$\begin{array}{c}{\text{EPS}}_{\text{Before Stock Issue}}=\frac{\text{Earnings}}{\text{Number of Shares}}\\ =\frac{\$4,400,000}{4,200,000}\\ =\$1.05\end{array}$

c.

Summary Introduction

To calculate: The EPS of Tyson Iron Works immediately post the issue of stock.

Introduction:

Earnings per share (EPS):

It is the profit earned by shareholders on each share. A higher EPS indicates a higher value of the company because investors are ready to pay a higher price for one share of the company.

Answer to Problem 20P

The EPS of Tyson Iron Works immediately post the issue of stock is $0.94.

Explanation of Solution

Calculation of the EPS immediately post the issue of stock:

$\begin{array}{c}{\text{EPS}}_{\text{After Stock Issue}}=\frac{\text{Earnings}}{\text{Number of Shares including new shares}}\\ =\frac{\$4,400,000}{4,200,000+500,000}\\ =\frac{\$4,400,000}{4,700,000}\\ =\$0.94\end{array}$

d.

Summary Introduction

To determine: The rate of return that must be earned by Tyson Iron Works on its net proceeds without any dilution in its EPS during the year it went public.

Introduction:

Rate of Return (ROR):

A measurement of the profit earned or loss incurred on an investment over a specific time-period is the ROR. It compares the gain/loss to the costs incurred on the initial investment.

Answer to Problem 20P

The ROR that must be earned to prevent any dilution in an EPS of $1.05 is 4.52%.

Explanation of Solution

The calculation of ROR without the dilution of EPS is shown below.

$\begin{array}{c}\text{Rate of Return}=\frac{\text{Incremental Earnings}}{\text{Net Proceeds}}\\ =\frac{\$535,000}{\$11,845,000}\\ =4.52\%\end{array}$

Hence, 4.52% is the rate of return required to be earned on the net proceeds to earn an EPS of $1.05.

Working Notes:

Calculation of incremental earnings:

$\begin{array}{c}\text{Incremental Earnings}=\text{Earnings}-{\text{Aftertax Earnings}}_{\text{Current}}\\ =\$4,935,000-\$4,400,000\\ =\$535,000\end{array}$

Calculation of earnings:

$\begin{array}{c}\text{Earnings}={\text{EPS}}_{\text{Before}}\times \text{Number of shares including new shares}\\ =\$1.05\times 4,700,000\\ =\$4,935,000\end{array}$

e.

Summary Introduction

To determine: The rate of return that must be earned by Tyson Iron Works on its proceeds to earn a 10% increase in its EPS during the year it went public.

Introduction:

Rate of Return (ROR):

A measurement of the profit earned or loss incurred on an investment over a specific time-period is the ROR. It compares the gain/loss to the costs incurred on the initial investment.

Answer to Problem 20P

The ROR that must be earned to earn an increase of 10% in EPS is 8.88%.

Explanation of Solution

The calculation of ROR to earn an increase of 10% in EPS is shown below.

$\begin{array}{c}\text{Rate of Return}=\frac{\text{Incremental Earnings}}{\text{Net Proceeds}}\\ =\frac{\$1,052,000}{11,845,000}\\ =8.88\%\end{array}$

Hence, 8.88% is the rate of return required to be earned on the net proceeds to earn an increase of 10% in the EPS.

Working Notes:

Calculation of incremental earnings:

$\begin{array}{c}\text{Incremental Earnings}={\text{Earnings}}_{\text{After 5\% Increase}}-{\text{Aftertax Earnings}}_{\text{Current}}\\ =\$5,452,000-\$4,400,000\\ =\$1,052,000\end{array}$

Calculation of earnings with a 10% increase:

$\begin{array}{c}{\text{Earnings}}_{\text{After 10\% Increase}}={\text{EPS}}_{\text{Before}}\left(1+\%\text{increase}\right)\times \\ \text{Number of shares including new shares}\\ =\$1.05\left(1+0.10\right)\times 4,700,000\\ =\$1.16\times 4,700,000\\ =\$5,452,000\end{array}$