The hotel company Alpha S$.$A$.$ has estimated that the cash flows and initial costs required to implement an investment project are $4,000,000$ euros. The company is going to finance the investment project by issuing a bond loan worth $2,000,000,$ taking a bank loan of $1,000,000$ and covering the rest with equity $($retained earnings of the company$).$

Also, the following information is given on the financial structure of the project:

For equity, it is given that the current share price of the company Alpha SA$.$ is equal to $6$ euros. The company just paid a dividend of $1$ euro per share and the annual growth rate of the dividend is $2\%$ stable which is estimated to remain at this level for the next period.

The following data are given for foreign funds:

$$ The bank loan will have a duration of $10$ years and will be repaid in $10$ equal installments. The annual interest rate of the loan is estimated to be $10\%.$

$$ The bonds issued by the company also have a duration of $10$ years and an interest rate equal to $4\%.$ The nominal value of the bonds amounts to $1000$ euros, while their market value is equal to $789\mathrm{.}29$ euros.

Use the information above to calculate:

The cost of equity capital.