Question

b. The firm proposes to offer new common stock to the preferred stockholders to wipe out the deficit. The common stock will pay the following dividends over the next four years:

D1	\(1.15
D2	\)1.25
D3	\(1.35
D4	\)1.45

The company anticipates earnings per share after four years will be $4.09 with a P/E ratio of 10.

The common stock will be valued as the present value of future dividends plus the present value of the future stock price after four years. The discount rate used by the investment banker is 14 percent. Round to two places to the right of the decimal point. What is the calculated value of the common stock?

Short answer

Answer

The present value of the common stock is $28.

Step-by-step solution

Step-by-step solutionStep 1: Information provided in the question

EPS = $4.09

P/E ratio = 10

Discount rate = 14 years

Calculation of future price of stock

The future price of stock will be $40.9.

$\begin{array}{c}\mathbf{Futureprice}\mathbf{=}\mathbf{EPS}\mathbf{\times }\mathbf{P}\mathbf{/}\mathbf{Eratio}\\ \mathbf{=}\mathbf{\$}\mathbf{4}\mathbf{.}\mathbf{09}\mathbf{\times }\mathbf{10}\\ \mathbf{=}\mathbf{\$}\mathbf{40}\mathbf{.}\mathbf{9}\end{array}$

Calculation of present value of stock

The present value of stock will be $28.

$\begin{array}{c}\mathbf{PV}\mathbf{}\mathbf{of}\mathbf{}\mathbf{stock}\mathbf{=}\frac{\mathbf{Dividend}}{{\mathbf{(}\mathbf{1}\mathbf{+}\mathbf{Discount}\mathbf{}\mathbf{rate}\mathbf{)}}^{\mathbf{N}}}\mathbf{+}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{+}\frac{\mathbf{Dividend}\mathbf{+}\mathbf{Future}\mathbf{}\mathbf{price}\mathbf{}\mathbf{of}\mathbf{}\mathbf{stock}}{{\mathbf{(}\mathbf{1}\mathbf{+}\mathbf{Discount}\mathbf{}\mathbf{rate}\mathbf{)}}^{\mathbf{N}}}\\ \mathbf{=}\frac{\mathbf{1}\mathbf{.}\mathbf{15}}{{\mathbf{(}\mathbf{1}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{14}\mathbf{)}}^{\mathbf{1}}}\mathbf{+}\frac{\mathbf{1}\mathbf{.}\mathbf{25}}{{\mathbf{(}\mathbf{1}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{14}\mathbf{)}}^{\mathbf{2}}}\mathbf{+}\frac{\mathbf{1}\mathbf{.}\mathbf{35}}{{\mathbf{(}\mathbf{1}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{14}\mathbf{)}}^{\mathbf{3}}}\mathbf{+}\frac{\mathbf{1}\mathbf{.}\mathbf{45}\mathbf{+}\mathbf{40}\mathbf{.}\mathbf{9}}{{\mathbf{(}\mathbf{1}\mathbf{+}\mathbf{0}\mathbf{.}\mathbf{14}\mathbf{)}}^{\mathbf{4}}}\\ \mathbf{=}\mathbf{\$}\mathbf{28}\end{array}$