Question

The Hamilton Corporation Company has 4 million shares of stock outstanding and will report earnings of \(6,910,000 in the current year. The company is considering the issuance of 1 million additional shares that can only be issued at \)30 per share.

a. Assume that Hamilton Corporation Company can earn 7.0 percent on the proceeds. Calculate the earnings per share.

b. Should the new issue be undertaken based on earnings per share?

Short answer

a. Earnings per share is $1.382.

b. Yes, the new issue should be undertaken.

Step-by-step solution

Computation of earnings per share

$$\begin{gathered} \mathrm{Earning}\mathrm{per}\mathrm{share}=\frac{\mathrm{Earnings}}{\mathrm{Shares}\mathrm{outstanding}+\mathrm{Additional}\mathrm{shares}} \\ =\frac{\$6,910,000}{4,000,000+1,000,000} \\ =\$1.382 \end{gathered}$$

Computation of growth in EPS

$$\begin{gathered} \mathrm{New}\mathrm{income}=\mathrm{Expected}\mathrm{earnings}\left(\mathrm{Additional}\mathrm{shares}\times \mathrm{value}\mathrm{per}\mathrm{share}\right) \\ =7\%\left(1,000,000\times \$30\right) \\ =\$2,100,000 \\ \mathrm{Total}\mathrm{income}=\mathrm{New}\mathrm{income}+\mathrm{Previous}\mathrm{income} \\ =\$2,100,000+\$6,910,000 \\ =\$9,010,000 \\ \mathrm{New}\mathrm{earnings}\mathrm{per}\mathrm{share}=\frac{\mathrm{Total}\mathrm{income}}{\mathrm{Outstanding}\mathrm{stock}+\mathrm{Additional}\mathrm{issue}} \\ =\frac{\$9,010,000}{5,000,000} \\ =\$1.802 \\ \mathrm{Growth}\mathrm{in}\mathrm{EPS}=\mathrm{New}\mathrm{EPS}-\mathrm{Old}\mathrm{EPS} \\ =\$1.802-\$1.382 \\ =\$0.42 \end{gathered}$$

Conclusion:Hence, the new issue should be undertaken because earnings per share will grow by$0.42.