Question

The investment banking firm of Einstein & Co. will use a dividend valuation model to appraise the shares of the Modern Physics Corporation. Dividends (D1) at the end of the current year will be \(1.64. The growth rate (g) is 8 percent and the discount rate (Ke) is 13 percent.

a. What should be the price of the stock to the public?

b. If there is a 7 percent total underwriting spread on the stock, how much will the issuing corporation receive?

c. If the issuing corporation requires a net price of \)31.30 (proceeds to the corporation) and there is a 7 percent underwriting spread, what should be the price of the stock to the public? (Round to two places to the right of the decimal point.)

Short answer

1. The stock price to the public is $32.8.
2. The net amount that the corporation will receive is $30.504.
3. The stock price to the public is $33.655 when $31.30 is the required net price of the corporation.

Step-by-step solution

Computation of stock price to the public

$\begin{array}{rcl}\mathrm{Stock}\mathrm{price}& =& \frac{\mathrm{Current}\mathrm{year}\text{'}\mathrm{s}\mathrm{dividend}\left(\mathrm{D}1\right)}{\left(\mathrm{Discount}\mathrm{rate}\left(\mathrm{Ke}\right)-\mathrm{Growth}\left(\mathrm{G}\right)\right)}\\ & =& \frac{\$1.64}{\left(13\%-8\%\right)}\\ & =& \$32.8\end{array}$

Computation of net amount received by the corporation

$\begin{array}{rcl}\mathrm{Net}\mathrm{amount}\mathrm{received}\mathrm{by}\mathrm{the}\mathrm{corporation}& =& \mathrm{Stock}\mathrm{price}-\left(\mathrm{Underwriting}\mathrm{spread}\times \mathrm{Stock}\mathrm{price}\right)\\ & =& \$32.8-\left(7\%\times \$32.8\right)\\ & =& \$32.8-\$2.296\\ & =& \$30.504\end{array}$

Computation of stock price to the public when the required net price is given

Assuming the issue price is $100.

The underwriting spread is 7% (given).

Net received by the corporation is $93, i.e., the difference between the issue price and underwriting spread.

$\begin{array}{rcl}\mathrm{Issue}\mathrm{price}& =& \frac{\mathrm{Desired}\mathrm{price}}{\mathrm{Amount}\mathrm{received}\mathrm{by}\mathrm{corporation}}\times 100\\ & =& \frac{\$31.30}{93}\times 100\\ & =& \$33.655\end{array}$