You want to value the stock of Vigrosoft, a software company. Vigrosoft just

generated annual earnings per share of $$10.$ Without any new investment, it is

expected that the company would be able to generate these earnings at the end of

every year forever. However, like many of its competitors, Vigrosoft is reinvesting a lot

of its current earnings into the development of new products. As a matter of fact, the

annual earnings that were just generated were completely reinvested in new projects.

The company expects to reinvest all of its earnings again at the end of this year. In

every year after that, it plans to distribute $50\%$ of its earnings in dividends to its

shareholders, and reinvest the balance.

New investments are expected to generate a return of $40\%$ this year, $30\%$ next year,

and then a constant $20\%$ in every subsequent year. For example, an investment of

$$100$ made today will generate earnings of $$40$ at the end of this year, $$30$ at the end

of next year $($end of year $2),$ and $$20$ at the end of every year after that. Similarly, an

investment of $$100$ made at the end of this year will generate $$30$ in two years, and

$$20$ at the end of every year after that.

The equity cost of capital is $23\%.$

Estimate stock price