Question

American Health Systems currently has 6,400,000 shares of stock outstanding and will report earnings of \(10 million in the current year. The company is considering the issuance of 1,700,000 additional shares that will net \)30 per share to the corporation.

a. What is the immediate dilution potential for this new stock issue?

b. Assume that American Health Systems can earn 9 percent on the proceeds of the stock issue in time to include them in the current year’s results. Calculate earnings per share. Should the new issue be undertaken based on earnings per share?

Short answer

a. Immediate dilution is $0.328.

b. New EPS is $1.8012 and the new issue should be undertaken.

Step-by-step solution

Computation of immediate dilution

$$\begin{gathered} EPSbeforestockissue=\frac{Earnings}{Outs\tan dingstock} \\ =\frac{\$10,000,000}{6,400,000} \\ =\$1.5625 \\ EPSafterstockissue=\frac{Earnings}{Outs\tan dingstock+Additionalissue} \\ =\frac{\$10,000,000}{6,400,000+1,700,000} \\ =\frac{\$10,000,000}{8,100,000} \\ =\$1.2345 \\ Dilution=EPSbeforestockissue-EPSafterstockissue \\ =\$1.5625-\$1.2345 \\ =\$0.328 \end{gathered}$$

Computation of New EPS

$$\begin{gathered} Newincome=Expectedearnings\left(Additionalissue\times pricepershare\right) \\ =9\%\left(1,700,000\times \$30\right) \\ =9\%\left(51,000,000\right) \\ =\$4,590,000 \\ Totalincome=Newincome+Reportedearnings \\ =\$4,590,000+\$10,000,000 \\ =\$14,590,000 \\ NewEPS=\frac{Totalincome}{Numberofshares} \\ =\frac{\$14,590,000}{8,100,000} \\ =\$1.8012 \end{gathered}$$

Undertaking of new issue

$$\begin{gathered} GrowthinEPS=NewEPS-EPSbeforestockissue \\ =\$1.8012-\$1.5625 \\ =\$0.2387 \end{gathered}$$

The new issue should be undertaken because there will be no dilution and EPS will grow by $0.2387.