Question

Tyson Iron Works is about to go public. It currently has after-tax earnings of \(4,400,000, and 4,200,000 shares are owned by the present stockholders. The new public issue will represent 500,000 new shares. The new shares will be priced to the public at \)25 per share with a 3 percent spread on the offering price. There will also be $280,000 in out-of-pocket costs to the corporation.

d. Determine what rate of return must be earned on the net proceeds to the corporation so there will not be a dilution in earnings per share during the year of going public.

Short answer

The rate of return required is 4.38%.

Step-by-step solution

Information available

After-tax earnings = $4,400,000

Shares outstanding = 4,200,000

Shares issued in new public issue = 500,000 shares

Selling price for new public issue = $25 per share

Spread = 3%

Out-of-pocket costs = $280,000

Net proceeds = $11,845,000

Calculation of net earnings required after stock issue to maintain before issue EPS

The net earnings required is $4,920,900.

$\begin{array}{rcl}\mathrm{Net}\mathrm{earnings}& =& \mathrm{EPS}\times \mathrm{Shares}\mathrm{outstanding}\\ & =& \$1.047\times 4,700,000\\ & =& \$4,920,900\end{array}$

Calculation of additional earnings required

The additional earnings required is $520,900.

$\begin{array}{rcl}\mathrm{Additional}\mathrm{earnings}& =& \mathrm{Earnings}\mathrm{required}\mathrm{after}\mathrm{stock}\mathrm{issue}-\mathrm{After}\mathrm{tax}\mathrm{earnings}\\ & =& \$4,920,900-\$4,400,000\\ & =& \$520,900\end{array}$

Calculation of rate of return to be generated on the net proceeds

The rate of return required is 4.38%.

$\begin{array}{rcl}\mathrm{Rate}\mathrm{of}\mathrm{return}& =& \frac{\mathrm{Additional}\mathrm{earnings}\mathrm{required}}{\mathrm{Net}\mathrm{proceeds}}\\ & =& \frac{\$520,900}{\$11,845,000}\\ & =& 4.38\%\end{array}$