Question

Walker Machine Tools has 5.5 million shares of common stock outstanding. The current market price of Walker common stock is \(52 per share rights-on. The company’s net income this year is \)17.5 million. A rights offering has been announced in which 550,000 new shares will be sold at $46.50 per share. The subscription price plus 5 rights is needed to buy one of the new shares.

b. What would the earnings per share be immediately after the rights offering? What would the price-earnings ratio be immediately after the rights offering? (Assume there is no change in the market value of the stock, except for the change when the stock begins trading ex-rights.) Round all answers to two places after the decimal point.

Short answer

The earnings per share is $2.89 and price-earnings ratio is 17.67.

Step-by-step solution

Information provided in the question

Earnings = $17,500,000

Shares outstanding = 5,500,000

New shares issued = 550,000

Rights-on share price = $52

Subscription price = $46.50

Calculation of earnings per share

The earnings per share is $2.89

$\begin{array}{c}\mathbf{EPS}\mathbf{=}\frac{\mathbf{Earnings}}{\mathbf{Number}\mathbf{}\mathbf{of}\mathbf{}\mathbf{shares}\mathbf{}\mathbf{outstanding}\mathbf{+}\mathbf{New}\mathbf{}\mathbf{shares}\mathbf{}\mathbf{issued}}\\ \mathbf{=}\frac{\mathbf{\$}\mathbf{17}\mathbf{,}\mathbf{500}\mathbf{,}\mathbf{000}}{\mathbf{5}\mathbf{,}\mathbf{500}\mathbf{,}\mathbf{000}\mathbf{+}\mathbf{550}\mathbf{,}\mathbf{000}}\\ \mathbf{=}\frac{\mathbf{\$}\mathbf{17}\mathbf{,}\mathbf{500}\mathbf{,}\mathbf{000}}{\mathbf{6}\mathbf{,}\mathbf{050}\mathbf{,}\mathbf{000}}\\ \mathbf{=}\mathbf{\$}\mathbf{2}\mathbf{.}\mathbf{89}\end{array}$

Calculation of price-earnings ratio

The price-earnings ratio is 17.67.

$\begin{array}{c}\mathbf{R}\mathbf{=}\frac{{\mathbf{M}}_{\mathbf{0}}\mathbf{-}\mathbf{S}}{\mathbf{N}\mathbf{+}\mathbf{1}}\\ \mathbf{=}\frac{\mathbf{\$}\mathbf{52}\mathbf{-}\mathbf{\$}\mathbf{46}\mathbf{.}\mathbf{50}}{\mathbf{5}\mathbf{+}\mathbf{1}}\\ \mathbf{=}\frac{\mathbf{\$}\mathbf{5}\mathbf{.}\mathbf{50}}{\mathbf{6}}\\ \mathbf{=}\mathbf{\$}\mathbf{0}\mathbf{.}\mathbf{92}\end{array}$

$\begin{array}{c}\mathbf{Value}\mathbf{}\mathbf{of}\mathbf{}\mathbf{ex}\mathbf{-}\mathbf{right}\mathbf{}\mathbf{share}\mathbf{=}\mathbf{Share}\mathbf{}\mathbf{price}\mathbf{-}\mathbf{Value}\mathbf{}\mathbf{of}\mathbf{}\mathbf{one}\mathbf{}\mathbf{right}\\ \mathbf{=}\mathbf{\$}\mathbf{52}\mathbf{-}\mathbf{\$}\mathbf{0}\mathbf{.}\mathbf{92}\\ \mathbf{=}\mathbf{\$}\mathbf{51}\mathbf{.}\mathbf{08}\end{array}$

$\begin{array}{c}\mathbf{PE}\mathbf{}\mathbf{ratio}\mathbf{=}\frac{\mathbf{Share}\mathbf{}\mathbf{price}}{\mathbf{EPS}}\\ \mathbf{=}\frac{\mathbf{\$}\mathbf{51}\mathbf{.}\mathbf{08}}{\mathbf{\$}\mathbf{2}\mathbf{.}\mathbf{89}}\\ \mathbf{=}\mathbf{17}\mathbf{.}\mathbf{67}\end{array}$