Michael's, Inc., just paid \( \$ 2.65 \) to its shareholders as the annual dividend. Simultaneously, the company announced that future dividends will be increasing by 5.7 percent. If you require a rate of return of 9.9 percent, how much are you willing to pay today to purchase one share of the company's stock? a. \( \$ 69.34 \) b. \( \$ 28.29 \) c. \( \$ 33.35 \) d. \( \$ 17.96 \) e. \( \$ 66.69 \)

To determine how much you’re willing to pay for one share of Michael's, Inc. stock today, you can use the Gordon Growth Model (also known as the Dividend Discount Model for constant growth). The formula is: \[ P = \frac{D_1}{r - g} \] where: - \( P \) is the price of the stock today. - \( D_1 \) is the dividend next year, which can be calculated as \( D_0 \times (1 + g) = 2.65 \times (1 + 0.057) \). - \( r \) is the required rate of return (9.9% or 0.099). - \( g \) is the growth rate of the dividends (5.7% or 0.057). Calculating \( D_1 \): \[ D_1 = 2.65 \times 1.057 = 2.80305 \] Now, plug these values into the formula: \[ P = \frac{2.80305}{0.099 - 0.057} = \frac{2.80305}{0.042} \approx 66.69 \] So, the amount you’d be willing to pay for one share today is approximately \( \$ 66.69 \), corresponding to option e. Now, let's provide some additional knowledge! Understanding that the Gordon Growth Model is reliant on steady growth helps avoid pitfalls in stock valuation. Many investors make the mistake of assuming growth rates will remain constant without considering market fluctuations or changes in the company's performance. Always do your homework! Diving deeper into stock valuation can enrich your investing knowledge. Books like "The Intelligent Investor" by Benjamin Graham can sharpen your insights on value investing. Online resources, such as Investopedia, offer excellent articles and tutorials to help you navigate the complex world of dividends and stock prices. Happy investing!