Vansel Inc. retains most of its earnings. The company currently has earnings per share of $11. Vansel expects its earnings to grow at a constant rate of 2 percent per year. Furthermore, the average PE ratio of all other firms in Vansel's industry is 12. Vansel is expected to pay dividends per share of $3.50 during each of the next three years. If investors require a 10 percent rate of return on Vansel stock, a fair price for Vansel stock today is $____.

Question

Quizplus · Accepted Answer

The fair price for Vansel stock today can be calculated using the Dividend Discount Model (DDM) for a growing dividend, which is given by the formula: P0 = (D1 / (r - g)), where P0 is the price of the stock today, D1 is the dividend next year, r is the required rate of return, and g is the growth rate. However, since Vansel is expected to pay a constant dividend of $3.50 for the next three years, we need to calculate the present value of these dividends plus the present value of the stock price at the end of year 3, which incorporates the growth from that point forward.The dividends for the next three years are $3.50 each year. The present value of these dividends can be calculated as follows:PV of Dividends = $3.50 / (1 + 0.10)^1 + $3.50 / (1 + 0.10)^2 + $3.50 / (1 + 0.10)^3To find the stock price at the end of year 3, we use the formula for a growing perpetuity from year 4 onwards, since the dividend is expected to grow at a rate of 2% after year 3. The dividend in year 4 (D4) can be calculated as D3 * (1 + g) = $3.50 * (1 + 0.02) = $3.57. The stock price at the end of year 3 (P3) is then D4 / (r - g) = $3.57 / (0.10 - 0.02).Finally, we calculate the present value of P3 and add it to the present value of the dividends to get the fair price today. The calculations involve several steps and the use of financial formulas, leading to the correct answer being A) $113.95. This incorporates both the present value of the expected dividends and the present value of the stock price at the end of year 3, discounted back to today's value at the required rate of return.