The Blinkelman Corporation has just announced that it plans to introduce a new solar panel that will greatly reduce the cost of solar energy. As a result, analys now expect the company’s earnings, currently (year 0) $1 per share to grow by 50 percent per year for the next three years, by 25 percent per year for the following 3 years, and by 8 percent per year thereafter. Blinkelman does not currently pay a dividend but it expects to pay out 20 percent of its earning beginning 2 years from now. The payout ratio is expected to become 50 percent in 5 years and to remain at that level. The company’s marginal tax rate is 40 percent. If you require a 20 percent rate of return on a stock such as this, how much would you be willing to pay for it today?

To determine how much you would be willing to pay for the stock today, you need to calculate the present value of its future dividends and terminal value.

First, let's calculate the dividends for each year:
- Year 0: No dividend
- Year 1: No dividend
- Year 2: 20% of earnings (0.20 * 1) = $0.20
- Year 3: 20% of earnings (0.20 * 1.50) = $0.30
- Year 4: 20% of earnings (0.20 * 2.25) = $0.45
- Year 5: 50% of earnings (0.50 * 2.81) = $1.41
- Year 6: 50% of earnings (0.50 * 3.51) = $1.76
- Year 7: 50% of earnings (0.50 * 4.38) = $2.19
- Year 8 and beyond: Growing at a rate of 8% per year

Next, let's calculate the present value of each dividend using the discount rate of 20%:
- Year 0: No dividend
- Year 1: No dividend
- Year 2: $0.20 / (1 + 0.20) ^ 2 = $0.166
- Year 3: $0.30 / (1 + 0.20) ^ 3 = $0.186
- Year 4: $0.45 / (1 + 0.20) ^ 4 = $0.252
- Year 5: $1.41 / (1 + 0.20) ^ 5 = $0.774
- Year 6: $1.76 / (1 + 0.20) ^ 6 = $0.874
- Year 7: $2.19 / (1 + 0.20) ^ 7 = $1.039

Then, let's calculate the terminal value using the Gordon Growth Model:
Terminal Value = (Dividends at Year 8) / (Discount Rate - Growth Rate)
= $2.19 / (0.20 - 0.08) = $21.90

Now, calculate the present value of the terminal value at Year 2:
Present Value of Terminal Value = Terminal Value / (1 + Discount Rate) ^ (8 - 2)
= $21.90 / (1 + 0.20) ^ 6 = $10.06

Finally, calculate the total present value of all the dividends:
Total Present Value = Present Value of Year 2 Dividend + Present Value of Terminal Value
= $0.166 + $0.186 + $0.252 + $0.774 + $0.874 + $1.039 + $10.06
= $13.35

Therefore, if you require a 20% rate of return on the stock, you would be willing to pay approximately $13.35 for it today.