Please show work: answer is given

An analyst constructs a privately held firms cost of equity using the buildup method. The 10-year Treasury bond rate is 4% and the historical equity risk premium for the S&P 500 stock index is 5.5%. The risk premium associated with firms of this size is 3.8% and for firms within this industry is 2.4%. Based on due diligence, the analyst estimates the risk premium specific to this firm to be 2.5%. What is the firms cost of equity based on this information? Answer: 18.2%

An investor is interested in making a minority equity investment in a small privately held firm. Because of the nature of the business, she concludes that it would be difficult to sell her interest in the business quickly. She believes the discount for the lack of marketability to be 25%. She also estimates that if she were to acquire a controlling interest in the business, the control premium would be 15%. Based on this information, what should be the discount rate for making a minority investment in this firm? What should she pay for 20% of the business if she believes the value of the entire business to be $1 million? Answer: Discount rate = 9.78% and purchase price for a 20% interest = $180,440.