Consider a simple firm that has the following market-value balance sheet Assets
ID: 2794252 • Letter: C
Question
Consider a simple firm that has the following market-value balance sheet Assets Liabilities & Equity S1,000 Debt 3400 600 Equity Next year, there are two possible values for its assets, each equally likely $1,200 and $960. Its debt will be due with 5.0% interest. Because all of the cash flows from the asset m t go either to the debt o the equity if you hold a portfolio of the debt and equity in the same proportions as he firm's capital structure your portfolio should earn exactly the expected return on the firm's assets. Show that a portfolio invested 40% in the firm's debt and 60% in its equity will have the same expected return as the assets of the firm. That is, show that the firm's WACC is the same as the expected return on its assets. Round to one decimal placa.) If the assets will be worth $1,200 in one year, the expected return on assets will be If the assets will be worth $960 in one year, the expected return on assets will be | %. (Round to one decimal place.) The expected retum on assels will be For a portfolio of 40% debt and 60% equity, the expected return on the debt will be 1 %. (Round to one decimal place.) If the equity will be worth $780.00 in one year, the expected return on equity will be If the equity will be worth $540.00 in one year, the expected return on equity will be The expected return on equity will be The expected pre-tax return on a portfolio of 40% debt and 60% equity will be % ( %. Round to one decimal place.) 96 Round to one decimal place.) (Round to one decimal place.) (Round to one decimal place.) Round to one decimal place. There may be a slight difference due to rounding.)Explanation / Answer
If the assets are worth $1200 in the next year, the expected return on the assets would be
= (Forecasted assets - previous year)/Previous year =
= [(1200 -1000)/1000] * 100 = 20.0%
If the assets are worth $960 in the next year, the expected return on the assets would be
= (Forecasted assets - previous year)/Previous year
= [(960 -1000)/1000] * 100 = - 4.0%
As both outcomes are equally likely,
The expected return on the assets would be = 0.5 * (20% - 4%) = 8.0%
For a portfolio of 40% debt and 60% equity, the expected return on the debt = 5.0% (given)
If the equity will be worth $780 in one year, the expected return on equity
=[(780 - 600)/600] * 100 = 30.0%
If the equity will be worth $540 in one year, the expected return on equity
=[(540 -600)/600] * 100 = -10.0%
The expected return on equity will be = 0.5 * (30%-10%) = 10.0%
The expected pre tax return on a portfolio of 40% debt and 60% equity
= weight of debt*cost of debt + weight of equity * cost of equity
= 40%*10%+60%*8%
= 8.80%