Question

3. Consider a simple firm that has the following market value balance sheet: Assets Liabilities & Equity $1,000 $430 Debt Equity 570 Next year, there are two possible values for its assets, each equally likely: $1,200 and $960. Its debt will be due with 4.8% 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 $1,200 in one year, the expected return on assets will be decimal place.) %. (Round to one %. (Round to one If the assets will be worth $960 in one year, the expected return on assets will be decimal place.) The expected return on assets will be %. (Round to one decimal place.) %. (Round to one For a portfolio of 43% debt and 57% equity, the expected retum on the debt will be decimal place.) %. (Round to one If the equity will be worth $749.36 in one year, the expected return on equity will be decimal place.) %. (Round to one If the equity will be worth $509.36 in one year, the expected return on equity will be decimal place.) The expected return on equity will be %. (Round to one decimal place.) %. (Round to one The expected pre-tax return on a portfolio of 43% debt and 57% equity will be decimal place. There may be a slight difference due to rounding.)

Answer 1

Formulas:

ROA = (worth of asset after one year/current worth) -1

ROE = (equity value after one year/current equity value) -1

1). Asset is worth $1,200 in one year then ROA = (1,200/1,000) -1 = 20.0%

2). Asset is worth $960 after one year then ROA = (960/1,000) -1 = -4.0%

3). Asset will be worth either $1,200 or $960 next year so probability for both is 0.5

Expected asset worth after one year = average of expected asset values = (0.5*1,200) + (0.5*960) = 1,080

Expected return on assets = (1,080/1,000) -1 = 8.0%

4). Expected return on debt will equal the interest rate of debt which is 4.8%.

5). If equity is $749.36 in one year then return on equity = (749.36/570)-1 = 31.5%

6). If equity is $509.36 in one year then return on equity = (509.36/570)-1 = -10.6%

7). Equity will be worth either $749.36 or $509.36 next year, so both have a probability of 0.5

Expected equity value after 1 year = average of expected values = (0.5*749.36)+(0.5*509.36) = 629.36

Expected return on equity = (629.36/570) -1 = 10.4%

8). Expected pre-tax return on a portfolio of 43% debt and 57% equity = sum of weighted returns = (weigh of debt*return on debt) + (weight of equity*return on equity)

= (43%*4.8%) + (57%*10.4%) = 8.0%