Dooley Wilson Company presently pays a dividend of $3.00 per share on its common stock. The company expects to increase the dividend at a 20% annual rate for the next two years, at a 15% annual rate for the following two years, and at a 10% rate thereafter. This phased-growth pattern aligns with the expected life cycle of earnings. You require a 17% return to invest in Dooley Wilson Company.

What value should you place on a share of this stock?

The value of a share of Dooley Wilson Company can be calculated by applying the Dividend Discount Model. By calculating the future dividends and adding them together, the intrinsic value of the stock is $65.58.

Explanation:

The value of a share of Dooley Wilson Company's stock can be calculated using the Dividend Discount Model (DDM). This model is used to calculate the value of a stock by forecasting the future dividends. The model is based on the future cash flow concept which holds the belief that the present value of a business is the result of its future cash flows.

The Dividend Discount Model simplifies the calculation by considering the only future cash flow will be the dividends paid by the company.

As given, the company expects to increase the dividends at a 20% rate for the next two years, 15% rate for the subsequent two years, and a 10% constant rate thereafter. Let's calculate the future dividends:Year 1 Dividend = 3 * 1.20 = $3.60.Year 2 Dividend = 3.60 * 1.20 = $4.32.Year 3 Dividend = 4.32 * 1.15 = $4.97.Year 4 Dividend = 4.97 * 1.15 = $5.72. The dividend for year 5 and onwards will grow at a constant rate of 10% per year.

Using the Dividend Discount Model, the price of the stock is calculated as following:P = D1 / (r - g) , where P = price of the stock, D1 = dividend expected next year, r = required return, and g = growth rate. Given that the required return is 17% and the future growth rate is 10%, we can set up the equation.

The price of the stock for the first 4 years is the present value of the dividends of each year: P = 3.6 / (1.17) + 4.32 / (1.17)^2 + 4.97 / (1.17)^3 + 5.72 / (1.17)^4 = $12.65.

For the 5th year and onwards, the price is calculated using the Dividend Discount Model formula with the g value of 10%: P = D5 / (r - g) = 5.72 * 1.10 / (0.17 - 0.10) = $89.89. However, the $89.89 must be discounted back to today's dollars, P= 89.89 / (1.17)^4 = $52.93.

Finally, by adding the two parts together, the intrinsic value of the stock = $12.65 + $52.93 = $65.58.

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