Consider a simple firm that has the following market-value balance sheet: Next y
ID: 2774384 • Letter: C
Question
Consider a simple firm that has the following market-value balance sheet: Next year, there are two possible values for its assets, each equally likely: $I,190 and S970. Its debt will be due with 4. 9% interest. Because all of the cash flows from the assets must go either to the debt or the equity, if you hold a portfolio of the debt and equity in the same proportions as the firm's capital structure, your portfolio should earn exactly the expected return on the firm's assets. Show that a portfolio invested 43% in the firm's debt and 57% 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. If the assets will be worth $1,190 in one year, the expected return on assets will be %. (Round to one decimal place.) If the assets will be worth $970 in one year, the expected return on assets will be %. (Round to one decimal place.)The expected return on assets will be %. (Round to one decimal place.)For a portfolio of 43% debt and 57% equity, the expected return on the debt will be %. (Round to one decimal place.)If the equity will be worth $717. 95 in one year, the expected return on equity will be Q%. (Round to one decimal place.) If the equity will be worth $497. 95 in one year, the expected return on equity will be %. (Round to one decimal place.)The expected return on equity will be %. (Round to one decimal place.) The expected pre-tax return on a portfolio of 43% debt and 57% equity will be %. (Round to one decimal place. There may be a slight difference due to rounding.)Explanation / Answer
If the assets are worth $1190 in the next year, the expected return on the assets would be
= [(1190 -1040)/1040] * 100 = 14.4%
If the assets are worth $970 in the next year, the expected return on the assets would be
= [(970 -1040)/1040] * 100 = - 6.7%
Since both outcomes are equally likely,
The expected return on the assets would be = 0.5 * (14.4 - 6.7) = 3.8%
For a portfolio of 43% debt and 57% equity, the expected return on the debt = 4.9%
If the equity will be worth $717.95 in one year, the expected return on equity
=[(717.95 -590)/590] * 100 = 21.7%
If the equity will be worth $497.95 in one year, the expected return on equity
=[(497.95 -590)/590] * 100 = -15.6%
The expected return on equity will be = 0.5 * (21.7 -15.6) = 3%
The expected pre tax return on a portfolio of 43% debt and 57% equity
= 0.43 * 4.9% + 0.57 * 3% = 2.1 + 1.7 = 3.8%
which is same as the expected return on the assets of the firm, thus showing that the firm's WACC is the same as the expected return on it's assets.