During the immediately preceding 4 years, the annual dividend paid on the Perez Construction's common stock has grown from $3.91 to $4.58 (Do), or by approximately a dollar, which equates to a 4% growth rate. Sophia Perez believes that without a proposed investment, the historical annual dividend growth rate will continue into the future. Currently the required rate of return on the common stock is 13% and the stock price is $52.92.

Sophia Perez' research indicates that if a proposed expansion is undertaken, the annual rate of dividend growth will rise. She feels that in thebest case, the dividend would continue to grow at this rate each year forever into the future. Or, essentially, that she would replace this expansion project with a similar project repeatedly in the future. In theanticipated case, the higher annual rate of dividend growth would continue for only two years, and then at the beginning of the third year the dividend growth rate would return fall back to a more normal level. In theworst case, the firm's growth rate would over time drop, due to the use of valuable managerial resources managing inventory assignment across Perez Construction and the losses incurred if the economy were to deteriorate in a world where it had amassed extra inventory.

As a result of the increased risk associated with the proposed risky investment, the required rate of return on the common stock is expected to increase by 1% to an annual rate of 14%. This required rate of return applies regardless of which dividend growth outcome occurs. Armed with the preceding information, Sophia has tasked you with assessing the impact of the proposed risky investment on the market value of Perez Construction's stock. In this scenario analysis, your examination has shown that the best case scenario is likely to happen 10 percent of the time, optimistic case 15 percent of the time, anticipated case 50 percent of the time, low growth case 15 percent of the time and negative growth 10 percent of the time. {Note on grading: Correct prices have the correct inputs, so you should report the inputs (D₁, D₂, D₃, r_s, g) in computing P_o. Reporting inputs also allows you to earn partial credit in instances wherein you have not computed the correct share price.}

1. Best case. Find the value of Perez Construction's common stock in the event that it undertakes the proposed investment and the subsequent dividend growth rate stays at 9% forever. (3 points)

2. Anticipated case. Recalculate the current price assuming that after two years the average annual dividend growth rate returns from 8% to 4%. (5 points)

3. Worst case. Recalculate the current price assuming that project is undertaken and that in addition to the required return rising, costs exceed revenues after the initial customers are satiated. Hence, the growth rate for the overall company is only 6 percent for one year, falls back to 5 percent in Year 2, and then drops to 2 percent from that point onward. (5 points)