Individual assignment Mathematics & Economics Math Problem

ABC Corp. stock returns have a covariance with the market portfolio of 0.0415. The standard deviation of the returns on the market portfolio is 20 percent, and the expected market risk premium is 6.0 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 4.5 million shares of common stock outstanding, each selling for $25. The company’s CEO considers the firm’s current debt-to-equity ratio to be optimal. The corporate tax rate is 35 percent, and Treasury bills currently yield 2.9 percent. The company is considering the purchase of additional equipment that would cost $42 million. The expected unlevered cash flows from the equipment are $11.8 million per year for five years. Purchasing the equipment will not change the risk level of the firm. Calculate the NPV to determine whether ABC should purchase the equipment. (Hint: β = Covariance / Variance of Market Returns)
Question 2 – Capital Structure (20 Marks)
XYZ International is a shipping firm with a current share price of $5.50 and 10 million shares outstanding. Suppose that XYZ announces plans to lower its corporate taxes by borrowing $20 million and repurchasing shares. XYZ pays a corporate tax rate of 35% and shareholders expect the change in debt to be permanent.
a. If the only imperfection is corporate taxes, what will the share price be after this announcement?
b. Suppose the only imperfections are corporate taxes and financial distress costs. If the share price rises to $5.80 after this announcement, what is the present value of financial distress costs XYZ will incur as the result of this new debt?
Question 3 – Valuation (50 Marks)
Calculate the share price for company DEF using 2 methods: (1) WACC and (2) APV (note: for APV assume debt is retired after 10 years – with linear amortization)
Assumptions:
 Sales (for the last fiscal year): $555M
 Years 1 to 10
o EBIT Margin: 16% CapEx: 10% of sales
o Depreciation and Amortization: 5% of sales Working Capital: 2% of sales
 Sales growth: 4% per year (Years 1 to 5)
 Sales growth: 3% per year (Years 6 to 10)
 Terminal Horizon (Years 11+): Perpetual (Long-Term) FCF growth rate (g = 1%)
 Tax Rate: 30%
 WACC: 12%
 Net Debt (at t = 0): $125M
 # of shares: 10 Million
 KD = 3.5% (with leverage ratio “D/E” = 30%)