HiTech is an established software developer based in the Silicon Valley. In November 2017 the company is unlevered, and it has 4 million shares trading at $40 per share. The firm faces a marginal tax rate of 40%. The CFO is considering a permanent increase in leverage. The proceeds of the debt issue will be used to repurchase stock. The following table summarises the estimated probabilities of default for HiTech at different levels of debt: Value of debt (million) Default probability $0 $20 $40 $60 0% 2% 5% 10% 30% 60% $80 $100 You have been hired by HiTech to help the CFO team determine the amount of new debt to be issued. After carefully analysing its business, you have estimated the direct and indirect default costs for HiTech to be 20% of the unlevered firm value. (a) Estimate the optimal debt level for the firm using the APV approach. Present in a table the tax shields, expected default costs and market value of the firm associated with each debt level. (10 marks) (b) The firm follows your advice and announces a leveraged recapitalisation to implement the optimal debt level you have determined. Assuming efficient markets, at which price will the firm be able to repurchase the stock? What will the market value balance sheet be after the recap announcement? And after the recap is completed? (8 marks) (c) Assume you revise your estimation of default costs to just 10% of the firm's unlevered value. How much debt should the firm issue in this case? Explain, providing a simple intuition for your answer. (10 marks)