Final answer:
An investor should pay no more than $5.00 for a share of Crozet Scenic Railways' stock, calculated using the Dividend Discount Model with a decreasing dividend and a required rate of return of 14%.
Step-by-step explanation:
To calculate the price an investor should be willing to pay for Crozet Scenic Railways' stock, given a declining dividend, we must use the Dividend Discount Model (DDM) for stocks with a non-constant growth rate. We know the company just paid a dividend of $1.20 and plans to reduce dividends by 10% annually. With a required rate of return of 14%, the value of each dividend payment in the future must be discounted back to its present value.
The first dividend to be reduced will be next year's dividend, which can be calculated as follows:
- Dividend year 1 = $1.20 * (1 - 0.10) = $1.08
- Dividend year 2 = $1.08 * (1 - 0.10) = $0.972
- ...and so on.
To calculate the present value of each of these future dividends, we use the formula:
Present Value = Dividend / (1 + required rate of return)^number of years
Once all individual present values are determined, they must be summed to obtain the total value of the stock. However, the series of declining dividends theoretically continues indefinitely, so we can use the formula for the sum of a perpetuity with decay:
Stock Price = Dividend / (required rate of return - rate of dividend decline)
In this case:
Stock Price = $1.20 / (0.14 - (-0.10)) = $1.20 / 0.24 = $5.00
The investor should not pay more than $5.00 per share for this stock.