Sunnyfax Publishing pays out all its earnings and has a share price of $38. In order to expand, Sunnyfax Publishing decides to cut its dividend from $3.00 to $2.00 per share and reinvest the retained funds. Once the funds are reinvested, they are expected to grow at a rate of 12%. If the reinvestment does not affect Sunnyfax's equity cost of capital, what is the expected share price as a consequence of this decision?

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The expected share price can be calculated using the Gordon Growth Model (also known as the Dividend Discount Model for a perpetuity), which is given by the formula: $$ P_0 = \frac{D_1}{r - g} $$ where $P_0$ is the price of the stock today, $D_1$ is the dividend next year, $r$ is the cost of equity, and $g$ is the growth rate of dividends.Given that the dividend is cut from $3.00 to $2.00 and the funds are expected to grow at a rate of 12%, we can use the information to find the cost of equity ($r$) before calculating the new share price. The original dividend of $3.00 at a share price of $38 gives us a dividend yield of $\frac{3}{38}$, but since the company pays out all its earnings as dividends, the growth rate ($g$) was initially 0. Therefore, the original cost of equity ($r$) is the same as the original dividend yield, which can be calculated as $\frac{3}{38}$.However, since the question states that the equity cost of capital remains unchanged even after the reinvestment, we use the original cost of equity for our calculation. The new dividend is $2.00, and the growth rate is 12% (or 0.12). Plugging these values into the Gordon Growth Model formula gives us:$$ P_0 = \frac{2.00}{r - 0.12} $$To find $r$, we use the original dividend and share price:$$ r = \frac{3}{38} \approx 0.0789 $$Substituting $r$ and $g$ into the formula:$$ P_0 = \frac{2.00}{0.0789 - 0.12} $$This calculation will not give a correct result because of a mistake in the interpretation of $r$. The correct approach to find the new share price after the dividend cut and reinvestment should directly apply the expected growth rate and the new dividend into the Gordon Growth Model without recalculating $r$ from the original dividend and price, as $r$ represents the required rate of return or the cost of equity, not the dividend yield. The mistake was in the interpretation and calculation of $r$.The correct calculation, assuming the cost of equity ($r$) remains the same and is not directly provided, would involve understanding that the equity cost of capital is implied to be the rate that equates the original dividend payments to the share price, considering growth. However, without the explicit cost of equity or a clear way to calculate it from the provided information (as the initial assumption about calculating $r$ from the dividend yield was incorrect in this context), the focus should be on the decision's impact given the growth rate and the new dividend.Given the growth rate (12% or 0.12) and the new dividend ($2.00), and assuming we had the correct cost of equity or could accurately derive it from the given information, we would plug these into the Gordon Growth Model formula to find the new expected share price. The error in the explanation was in the misinterpretation of how to use the given data to find $r$ and in the calculation process that followed.The correct approach to solving the problem with the given information (dividend cut to $2.00, growth at 12%, and the implication that the cost of equity remains unchanged) would involve correctly applying the Gordon Growth Model with the accurate values for $r$, $D_1$, and $g$. However, without the explicit value of $r$ or a correct method to derive it from the given information, the calculation process described does not lead to a correct answer under the standard application of the model.Given the mistake in the calculation process and the explanation, the focus should be on understanding how the dividend cut, the reinvestment at a certain growth rate, and the unchanged cost of equity would theoretically affect the share price according to the Gordon Growth Model, with an emphasis on the importance of accurately determining or being provided with the cost of equity to perform the calculation.

Sunnyfax Publishing Pays Out All Its Earnings and Has a Share