BagelChat Limited ("BCL") is listed on the stock exchange with 10 million shares in issuance. Its current share price is $8. The company's beta is 1.4. BCL has also issued 20,000, 4% coupon bonds outstanding with par value of $1,000. The bonds are currently trading at par. The corporate tax rate is 20%.

In addition, the following information has been obtained:

The expected market return is 10%.

The current 10-year Treasury bond yield is 4%.

The current AAA-rated bond yield is 4.5%.

BCL is considering whether to issue an additional $10 million of bonds at par.

(a) Compute the current weighted average cost of capital for BCL. (6 marks)

(b) Based on Modigliani and Miller's Propositions, calculate the value of the firm and the cost of equity of the company if it has no debt. (6 marks)

(c) Based on Modigliani and Miller's Propositions, appraise the value of the firm and the cost of equity of BCL if the company decides to issue an additional $10 million of debt. (6 marks)

(d) Without calculating, infer if BCL's weighted average cost of capital has increased or decreased with the additional issuance of $10 million of debt. (5 marks)

(e) Discuss the impact on the value of the firm if BCL should continue to increase its leverage. (7 marks)