Final answer:
To calculate the present value of the Graphical Designs preferred stock, we use the present value of a perpetuity formula, accounting for the delayed start of the dividend payments. The present value of Babble, Inc.'s stock is the sum of the discounted future dividend payments. Both cases use fundamental finance principles to assess stock value.
Step-by-step explanation:
The student is asking how to determine the present value of a stock given the future dividend payments and the required rate of return. When computing the price of the stock in question, we apply the concept of the time value of money, which includes discounting future payments to their present value. The formula to calculate the value of perpetuity, starting at a future date, is used in this case. Using the details provided for Graphical Designs preferred stock, with a $20 annual dividend beginning 20 years from now and a 4.90% required rate of return, we would calculate the present value of the stock as follows:
The formula for the present value of a perpetuity is PV = D / r, where PV is the present value, D is the dividend, and r is the required rate of return. Since the dividend payments begin in 20 years, we must discount the perpetuity value back to the present using the formula PV = $(PV of perpetuity) / (1 + r)^t, where t is the number of years before payments begin. This must be done to obtain the actual price of the stock today. For Babble, Inc., the value of one share can be found by calculating the present value of expected dividends. Babble will disband in two years, so we take the sum of present values of expected dividends for each year. This involves dividing by (1 + required rate of return) raised to the power of the number of years from now to each dividend payment.