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?
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To determine the value of the stock today, we can use the dividend discount model (DDM), which calculates the present value of all expected future dividends. Here's how you can solve this problem:
1. Determine the expected dividends per share for each year:
- Year 0: No dividend currently
- Year 1: $1 * (1 + 50%) = $1.50
- Year 2: $1.50 * (1 + 50%) = $2.25
- Year 3: $2.25 * (1 + 50%) = $3.38
- Year 4: $3.38 * (1 + 25%) = $4.23
- Year 5: $4.23 * (1 + 25%) = $5.29
- Year 6: $5.29 * (1 + 25%) = $6.61
- Year 7 onwards: $6.61 * (1 + 8%) = $7.14 (assuming an 8% growth rate)
2. Determine the payout ratio for each year:
- Year 0: No dividend payout currently
- Year 1: No dividend payout currently
- Year 2: 20%
- Year 3: 20%
- Year 4: 20%
- Year 5: 50%
- Year 6 onwards: 50%
3. Calculate the dividends paid out each year:
- Year 0: No dividend paid out
- Year 1: No dividend paid out
- Year 2: $2.25 * 20% = $0.45
- Year 3: $3.38 * 20% = $0.68
- Year 4: $4.23 * 20% = $0.85
- Year 5: $5.29 * 50% = $2.65
- Year 6 onwards: $7.14 * 50% = $3.57
4. Determine the present value of each dividend using the required rate of return (20%):
- Year 2: $0.45 / (1 + 20%)^2 = $0.31
- Year 3: $0.68 / (1 + 20%)^3 = $0.45
- Year 4: $0.85 / (1 + 20%)^4 = $0.51
- Year 5: $2.65 / (1 + 20%)^5 = $1.46
- Year 6 onwards: $3.57 / (1 + 20%)^6 = $1.55
5. Calculate the intrinsic value of the stock by summing the present value of dividends:
Intrinsic value = $0.31 + $0.45 + $0.51 + $1.46 + ($1.55 / (20% - 8%))
6. Calculate the terminal value using the constant growth dividend formula:
Terminal value = $1.55 / (20% - 8%)
7. Calculate the present value of the terminal value:
Present value of terminal value = Terminal value / (1 + 20%)^6
8. Calculate the final intrinsic value by summing the present value of dividends and the present value of the terminal value:
Final intrinsic value = Intrinsic value + Present value of terminal value
Therefore, the amount you would be willing to pay for the stock today is the final intrinsic value calculated in step 8.