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Disregard your answers to the previous question. Now, assume that the cosmetic business has a valuation of $1,427 million and a beta of 0.7 with a perpetual growth rate of 4%, and the coal mining business has a valuation of $997 million and a beta of 1.2 with a perpetual growth rate of 1%. Suppose the risk-free rate is 2% and the market risk premium is 5%. Eastern Inc. is an all-equity firm. What is Eastern Inc’s current cost of capital? (Hint: first, need to calculate the current equity beta for Eastern Inc.) Note: Enter your final answers in percentage points in X.X format. e.g. if your answer is 10.654%, enter 10.7 Your answer is:

Question

Disregard your answers to the previous question. Now, assume that the cosmetic business has a valuation of 1,427millionandabetaof0.7withaperpetualgrowthrateof41,427 million and a beta of 0.7 with a perpetual growth rate of 4%, and the coal mining business has a valuation of 997 million and a beta of 1.2 with a perpetual growth rate of 1%. Suppose the risk-free rate is 2% and the market risk premium is 5%. Eastern Inc. is an all-equity firm. What is Eastern Inc’s current cost of capital? (Hint: first, need to calculate the current equity beta for Eastern Inc.) Note: Enter your final answers in percentage points in X.X format. e.g. if your answer is 10.654%, enter 10.7 Your answer is:

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Solution

Sure, I can do that. Here are the steps to calculate Eastern Inc's current cost of capital:

  1. Calculate the equity beta for Eastern Inc. The equity beta is a weighted average of the betas of the two divisions, with the weights being the proportion of the firm's total value that each division represents.

    Equity Beta = (Cosmetic Division Beta * Cosmetic Division Value / Total Value) + (Coal Mining Division Beta * Coal Mining Division Value / Total Value)

    Total Value = Cosmetic Division Value + Coal Mining Division Value = 1,427million+1,427 million + 997 million = $2,424 million

    Equity Beta = (0.7 * 1,427million/1,427 million / 2,424 million) + (1.2 * 997million/997 million / 2,424 million) = 0.42 + 0.49 = 0.91

  2. Calculate the cost of capital using the Capital Asset Pricing Model (CAPM). The formula for CAPM is:

    Cost of Capital = Risk-free rate + Equity Beta * Market Risk Premium

    Substituting the given values into the formula:

    Cost of Capital = 2% + 0.91 * 5% = 6.55%

So, Eastern Inc's current cost of capital is 6.55%. According to the instruction, we should round it to one decimal place, so the final answer is 6.6%.

This problem has been solved

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