A company has the following capital structure as at $31$st December $2023$

Ordinary share $(100,000$ shares$)$ sh$.5,000,000$

Retained Earnings $2,000,000$

$12\%$ bonds $3,000,000$

Total $10,000,000$

The company expects to pay a dividend of sh$.3$ per share and its expected growth rate is $12\%$ forever. The current market price of the share is sh$.24$ with no floatation costs. The company is planning to venture into a lucrative business opportunity from next year which will require financing worth sh$.13$M$.$ This will require a new issue of ordinary shares at sh$.30$ and floatation costs of $10\%$ will be incurred. New bonds issued beyond break point have a cost of $15\%.$ Assume a tax rate of $30\%$

Required:

a$)$ Weighted average cost of capital

b$)$ Break point in terms of retained earnings