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?

Question

Quizplus · Accepted Answer

The expected share price after the dividend cut and reinvestment can be calculated using the Gordon Growth Model (also known as the Dividend Discount Model for a perpetuity) formula: P = D / (r - g), where P is the price of the stock, D is the dividend per share, r is the cost of equity, and g is the growth rate. Before the reinvestment, the cost of equity (r) can be calculated using the original dividend and share price: r = D / P + g, where D is $3.00, P is $38, and g is 0 because the company pays out all its earnings. However, since the company is now retaining some earnings, we focus on the new scenario where D is $2.00, and g is 12% (or 0.12). The cost of equity (r) remains unchanged as the reinvestment does not affect Sunnyfax's equity cost of capital. We use the original scenario to find r: r = 3 / 38 + 0 = 0.0789 or 7.89%. Using the new D and g in the formula gives us P = 2 / (0.0789 - 0.12), which is not directly solvable with the given information because we incorrectly calculated r without considering growth initially. Correcting the approach: Since the company pays out all its earnings initially, the growth rate (g) is 0, and the dividend yield plus growth rate gives us the cost of equity. After the dividend cut, the expected growth rate is 12%, but we need to find the cost of equity (r) correctly. The initial calculation of r was incorrect because it assumed a growth rate of 0 which was not needed for the initial r calculation. Given the dividend cut and reinvestment leading to growth, and without the exact cost of equity (r) provided or a way to calculate it directly from the given information (since the initial calculation of r was based on a misunderstanding), we focus on the growth impact. The correct approach involves understanding that the share price is expected to increase due to the reinvestment of funds at a higher growth rate than before, but without the exact r, we cannot directly calculate the new price using the formula provided in the explanation. The correct approach to find the new share price involves recognizing that the reduction in dividend and the subsequent reinvestment at a 12% growth rate would generally lead to an expectation of share price increase due to the value of future dividends increasing. However, without the precise cost of equity or a clear method to calculate it from the provided information, the calculation cannot be directly completed as initially attempted. The expectation of a share price increase is based on the principle that reinvesting at a higher rate of return (12% in this case) should increase the company's value, but the exact new share price requires additional information or assumptions not provided in the question.

Sunnyfax Publishing Pays Out All Its Earnings and Has a Share