Solution to Part I
What is important? Perfect capital market, no taxes; M&M propositions apply here; total market value of GP is 300 m composed of 200 m equity and 100 m debt; the expected return on equity is 15% and the market value weight of equity is 2/3 while the expected return on debt is 6% with market value weight of 1/3. Therefore the firm’s pre-transaction WACC is 12% WACC (pre-transaction) = 2/3 * 15% + 1/3 * 6% = 10% + 2% = 12%
a) (4 points) After the transaction GP will be all equity financed. The firm’s cost of equity the equals the WACC. As there are no taxes the firm’s WACC is independent of its capital structure and remains at 12%. WACC (post-transaction) = 12% = rE,U * 1/1 => rE,U = 12%
b) (4 Points) In this case the debt-to-value ratio will increase to 0.5 (from 0.333 pre-transaction). If the debt remains riskless all the risk from financial leverage is borne by the equityholders. As the WACC stays constant at 12% the new cost of equity (which is presumably higher than 15%) could be derived from the following equation:
WACC = 12% = 0.5 * rE,L + 0.5 * 6% => rE,L = (12%-3%) / 0.5 = 18%
or alternatively, using M&M proposition II reL=rU+(rU-rD)*D/E =>12%+6%*1 = 18%
c) (4 points) If the risk of the debt increased in b) this would lower the cost of equity well below 18% as this would mean that some risk sharing is taking place. This should remind us that capital structure is a sharing rule of the firm’s cash flows and cash flow risk. The risk is generated by the firm’s assets and operations (the asset side of the economic balance sheet) and shared among the firm’s financiers (the liability side of the economic balance sheet) according to their weight in the firm’s capital structure.
d) (3 points) The argument is wrong because it assumes that the risk of default is responsible for the higher cost of equity following higher leverage. According to this false argument if leverage increases but the risk of default does not increase, this will have no effect on the firm’s cost of equity. But any
leverage raises the equity cost of capital. In fact, risk-free leverage raises it the most (because it does not share any of the risk).
Part II - Cost of capital (15 points) In a world without taxes Weston Enterprises is an all-equity firm with two divisions. The soft drink division has an asset beta of 0.60, expects to generate free cash flow of $50 million until the end of this year, and anticipates a 3% perpetual growth rate. The industrial chemicals division expects to generate free cash flow of $70 million until the end of this year, and anticipates a 2% perpetual growth rate. The asset beta of the industrial chemicals division is yet unknown. Only information on a levered pure-play comparable firm active in the industrial chemicals sector is available. It is given in the following table:...