your investment advisor has sent you three reports for a young growing company named vegas chips incorporated. these three reports depict the company as speculative but each one poses different projections of the companys future growth in earnings and dividends. all three reports show that vegas chips earned$1.20 per share in the year ended previously. there is consensus that a fair rate of return to investors for this common stock is 14% and that management expects to consistently earn 15% return on the book value of equity (ROE = 15%. the analyst who produced report c makes the assumption that vegas chips will enter the national market but expects a high level of initial excitement for the product that is then followed by growth at a constant rate. earnings and dividend is expected to grow at a rate of 50% over the next year, 20% for the following two years and then revert back to a constant growth of 9% thereafter. management is expected to elect to pay out 40% of the recently reported earnings to current stockholders. based on this report what model can you use to value a share of common stock in vegas chip and what is the value of the stock?
To value a share of common stock in Vegas Chips Incorporated based on the information provided in report C, you can use the Dividend Discount Model (DDM).
The DDM calculates the present value of all expected future dividends by discounting them back to the present using the required rate of return. In this case, the required rate of return for investors is given as 14%.
Using the information provided in the report, let's calculate the value of the stock step by step:
1. Calculate the expected dividends for the next three years:
- Year 1: Earnings and dividends are expected to grow at a rate of 50%. So, the expected dividend per share in Year 1 will be $1.20 * 1.50 = $1.80.
- Year 2: Earnings and dividends are expected to grow at a rate of 20%. So, the expected dividend per share in Year 2 will be $1.80 * 1.20 = $2.16.
- Year 3: Earnings and dividends are expected to grow at a rate of 20%. So, the expected dividend per share in Year 3 will be $2.16 * 1.20 = $2.59.
2. Determine the constant growth rate:
- After the first three years, the earnings and dividend growth is expected to revert to a constant rate of 9%.
3. Calculate the expected dividends in perpetuity:
To calculate the expected dividends in perpetuity, we need to determine the expected dividend in Year 4 and discount it to the present value.
- Year 4: Earnings and dividends are expected to grow at a constant rate of 9%. So, the expected dividend per share in Year 4 will be $2.59 * 1.09 = $2.82.
4. Determine the payout ratio:
- The report mentions that management will elect to pay out 40% of the recently reported earnings to current stockholders. Since the recently reported earnings per share were $1.20, the dividend payout per share will be $1.20 * 40% = $0.48.
5. Calculate the present value of future dividends:
Using the DDM formula, we can calculate the present value of future dividends. The formula is as follows:
Stock Value = (D1 / (1 + r)) + (D2 / (1 + r)^2) + (D3 / (1 + r)^3) + ... + (Dn / (1 + r)^n)
Where D1, D2, D3...Dn represent the expected dividends for each year, r represents the required rate of return, and n represents the number of years.
In this case, n is infinite because we are assuming perpetual dividends.
Considering a required rate of return of 14%, the present value of future dividends can be calculated as follows:
Stock Value = ($1.80 / (1 + 0.14)) + ($2.16 / (1 + 0.14)^2) + ($2.59 / (1 + 0.14)^3) + ... + ($2.82 / (1 + 0.14)^n)
Note: In this calculation, we only considered the first three years and the fourth year with a constant growth rate, but in reality, the calculation should continue indefinitely.
By summing up the present values of expected dividends for each year, you will get the value of the stock.