Neon Corp. stock returns have a covariance with the market portfolio of 0.05. The standard deviation of the returns on the market portfolio is 15 percent, and the expected market risk premium is 8 percent. The company has bonds outstanding with a total market value of $55 million and a yield to maturity of 5 percent. The company also has 4 million shares of common stock outstanding, each selling for $20. The company's CEO considers the firm's current debt-to-equity ratio optimal. The corporate tax rate is 30 percent, and Treasury bills currently yield 2 percent. The company is considering the purchase of additional equipment that would cost $42 million. The expected unlevered cash flows from the equipment are $12 million per year for six years. Purchasing the equipment will not change the risk level of the firm. Assume the MM world with corporate taxes. a) Use the WACC approach to determine whether Neon should purchase the equipment. (7 pts) b) Suppose the company decides to fund the purchase of the equipment entirely with equity. What happens to the cost of capital for the project now?

This is the answer :

a) Market value of equity = 4*20=80; MV of debt = 55; D/V= 55/135; E/V = 80/135 beta = .05/.15^2 = 2.22; rs = .02+2.22*.08 = 19.76% wacc = 55/135*(1-.3)*.05+80/135*19.76% = 13.14%; NPV = -42+12*A(13.14%, 6) = $5.79 million

I want to know what the A is in the NPV formula and how does the answer suddenly become 5.79 million, Also when finding rs where did the 2.22 come from. Also i noticed there are a few 0.05 values in the answer , i wanted to know which 0.05 are the yield to maturity and which are from market portfolio. ( I dont have much knowledge in finance but am trying to understand this question)

b) All equity financing wacc = 19.76% NPV = -1.85 <0 then the firm should not undertake the investment. Nonetheless, the firm should stick to its optimal debt to equity ratio, which will also improve the value of the firm by undertaking this investment.

For part B what is the 1.85 showing and can you explain this in more simple terms to someone with limited finance knowledge?