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Company DEF has book value of $10 per share, is expected to earn $2.00 forever, and pays out all of its earnings as dividends. Its required return on equity is 12.5 percent. Value the stock of DEF using the residual income model. (1 mark)

Question

Company DEF has book value of 10pershare,isexpectedtoearn10 per share, is expected to earn 2.00 forever, and pays out all of its earnings as dividends. Its required return on equity is 12.5 percent. Value the stock of DEF using the residual income model. (1 mark)

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Solution

The Residual Income Model is a method of valuation that estimates the worth of a company by adding its book value and the present value of its expected future residual income, discounted at the appropriate cost of equity.

Step 1: Calculate the Residual Income Residual Income = Net Income - (Equity Capital * Cost of Equity) In this case, the company pays out all of its earnings as dividends, so the Net Income is 2.00.TheEquityCapitalisthebookvaluepershare,whichis2.00. The Equity Capital is the book value per share, which is 10. The Cost of Equity is 12.5%.

Residual Income = 2.00(2.00 - (10 * 12.5%) Residual Income = 2.002.00 - 1.25 Residual Income = $0.75

Step 2: Calculate the Present Value of the Residual Income Since the company is expected to earn this residual income forever, we can use the formula for the present value of a perpetuity to calculate this.

Present Value = Residual Income / Cost of Equity Present Value = 0.75/12.5PresentValue=0.75 / 12.5% Present Value = 6

Step 3: Add the Book Value and the Present Value of the Residual Income Value of the Stock = Book Value + Present Value of Residual Income Value of the Stock = 10+10 + 6 Value of the Stock = $16

So, according to the Residual Income Model, the stock of DEF is valued at $16 per share.

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