Question

Consider a simple firm that has the following market-value balance sheet: 3. Assets Liabilities & Equity Debt $1,000 $430 570 Equity 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 eam exactly the expected retum 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 retum as the assets of the firm. That is, show that the firm's WACC is the same as ther 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.) For a portfolio of 43% debt and 57 % equity , the expected retum on the debt will be decimal place.) % . ( Round to one % ( 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 retum on equity will be decimal place.) % ( Round to one decimal place.) The expected return on equity will be The expected pre-tax return on a portfolio of 43 % debt and 57 % equity will be decimal place. There may be a slight ditference due to rounding.) (Round to one %.

Answer 1

Part a)

The expected return on the assets (if value of assets in one year will be $1,200) is calculated as below:

Expected Return on Assets = (Value of Assets in One Year - Value of Assets Today)/Value of Assets Today*100

Substituting values in the above formula, we get,

Expected Return on Assets (if value of Assets in One Year will be $1,200) = (1,200 - 1,000)/1,000*100 = 20%

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Part b)

The expected return on the assets (if value of assets in one year will be $960) is determined as below:

Expected Return on Assets = (Value of Assets in One Year - Value of Assets Today)/Value of Assets Today*100

Substituting values in the above formula, we get,

Expected Return on Assets (if value of Assets in One Year will be $960) = (960 - 1,000)/1,000*100 = -4%

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Part c)

The value of expected return on assets is arrived as follows:

Expected Return on Assets = Expected Return on Assets (if value of Assets in One Year will be $1,200)*Probability of $1,200 Value of Assets in One Year + Expected Return on Assets (if value of Assets in One Year will be $960)*Probability of $960 Value of Assets in One Year

Substituting values in the above formula, we get,

Expected Return on Assets = 20%*50% + (-4%)*50% = 8%

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Part d)

The value of expected return on debt is calculated as follows:

Expected Return on Debt = (Current Value of Debt*(1+Interest Rate on Debt) - Current Value of Debt)/Current Value of Debt*100

Substituting values in the above formula, we get,

Expected Return on Debt = (430*(1+4.8%) - 430)/430*100 = 4.8%

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Part e)

The expected return on equity (if value of equity in one year is $749.36) is arrived as below:

Expected Return on Equity = (Value of Equity in One Year - Current Value of Equity)/Current Value of Equity*100

Substituting values in the above formula, we get,

Expected Return on Equity (if value of Equity in One Year is $749.36) = (749.36 - 570)/570*100 = 31.5%

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Part f)

The expected return on equity (if value of equity in one year is $509.36) is determined as below:

Expected Return on Equity = (Value of Equity in One Year - Current Value of Equity)/Current Value of Equity*100

Substituting values in the above formula, we get,

Expected Return on Equity (if value of Equity in One Year is $509.36) = (509.36 - 570)/570*100 = -10.6%

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Part g)

The value of expected return on equity is calculated as follows:

Expected Return on Equity = Expected Return on Equity (if value of Assets in One Year will be $749.36)*50% + Expected Return on Equity (if value of Assets in One Year will be $509.36)*50%

Substituting values in the above formula, we get,

Expected Return on Equity = 31.5%*50% + (-10.6%)*50% = 10.5%

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Part h)

The expected pre-tax return is calculated as below:

Expected Pre-Tax Return = Investment Percentage in Debt*Expected Return on Debt + Investment Percentage in Equity*Expected Return on Equity

Substituting values in the above formula, we get,

Expected Pre-Tax Return = 43%*4.8% + 57%*10.5% = 8%

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Notes:

There can be a slight difference in final answers on account of rounding off value.