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Eastern Inc. is an all-equity firm with two divisions.The cosmetic division has an asset beta of 0.6, expects to generate a free cash flow of $79 million by the end of this year (year 1), and anticipates a 4% perpetual growth rate.The coal mining division has an asset beta of 1.1, expects to generate a free cash flow of $236 million by the end of this year (year 1), and anticipates a 2% perpetual growth rate.Suppose the risk-free rate is 2% and the market risk premium is 5%. What is the value of cosmetic division in million dollars?

Question

Eastern Inc. is an all-equity firm with two divisions.The cosmetic division has an asset beta of 0.6, expects to generate a free cash flow of 79millionbytheendofthisyear(year1),andanticipatesa479 million by the end of this year (year 1), and anticipates a 4% perpetual growth rate.The coal mining division has an asset beta of 1.1, expects to generate a free cash flow of 236 million by the end of this year (year 1), and anticipates a 2% perpetual growth rate.Suppose the risk-free rate is 2% and the market risk premium is 5%. What is the value of cosmetic division in million dollars?

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Solution

To calculate the value of the cosmetic division, we first need to calculate the cost of equity using the Capital Asset Pricing Model (CAPM). The formula for CAPM is:

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

Substituting the given values into the formula:

Cost of Equity = 2% + 0.6 * 5% = 5%

Next, we use the Gordon Growth Model to calculate the value of the division. The Gordon Growth Model is:

Value = Free Cash Flow * (1 + growth rate) / (Cost of Equity - growth rate)

Substituting the given values into the formula:

Value = 79million(1+479 million * (1 + 4%) / (5% - 4%) = 79 million * 1.04 / 0.01

Value = $8,236 million

So, the value of the cosmetic division is $8,236 million.

This problem has been solved

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