Suppose a large institutional investor Ant’s portfolio has an expected return of 8 percent and a standard deviation of 10 percent. Another institutional investor Beast’s portfolio has an expected return of 12 percent and a standard deviation of 18 percent. The correlation between the two portfolios is 1, and the market portfolio can be described as a portfolio comprising these two with equal weights. Suppose there is a firm called Cats & Dogs Services (CDS), whose equity beta is 1.8 and the interest rate for its debt is 4 percent. CDS’s equity value is £1 million and its debt is £1.5 million. The present value of CDS’s tax shield is £0.3 million. Assume that CAPM holds.
a) What is the market portfolio’s expected return?
b) What is the Sharpe ratio of Ant’s portfolio? What about Beast’s portfolio’s Sharpe ratio?
c) What is the effective corporate tax rate for CDS?
d) Assuming the Modigliani-Miller theorem with corporate taxes, what should be the cost of equity for CDS when it is unlevered?
e) What is the present value of financial distress costs for CDS? Assume the tradeoff theory by setting the case in which CDS can borrow at the risk free rate as the benchmark case, and that the cost of equity remains the same.
f) Suppose CDS’s WACC is lowest with the current capital structure. According to the trade-off theory, which increases more when CDS increases its leverage, costs of financial distress or the present value of tax shield? Explain.