Th e Seneca Maintenance Company currently (that is, as of year 0) pays a common stock

dividend of $1.50 per share. Dividends are expected to grow at a rate of 11 percent per
year for the next four years and then to continue growing thereaft er at a rate of 5 percent
per year. What is the current value of a share of Seneca common stock to an investor who
requires a 14 percent rate of return?

To find the current value of a share of Seneca common stock, we can use the dividend discount model (DDM) formula.

The formula for the DDM is:
Price = Dividend / (Required rate of return - Dividend growth rate)

Step 1: Calculate the dividends for the next four years.
Year 0 dividend = $1.50
Dividend growth rate for the next four years = 11%

Year 1 dividend = Year 0 dividend * (1 + Dividend growth rate)
Year 1 dividend = $1.50 * (1 + 0.11)

Year 2 dividend = Year 1 dividend * (1 + Dividend growth rate)
Year 2 dividend = Year 1 dividend * (1 + 0.11)

Year 3 dividend = Year 2 dividend * (1 + Dividend growth rate)
Year 3 dividend = Year 2 dividend * (1 + 0.11)

Year 4 dividend = Year 3 dividend * (1 + Dividend growth rate)
Year 4 dividend = Year 3 dividend * (1 + 0.11)

Step 2: Calculate the dividend growth rate after the fourth year.
Dividend growth rate after the fourth year = 5%

Step 3: Calculate the current value of a share of Seneca common stock using the DDM formula.
Price = Year 0 dividend / (Required rate of return - Dividend growth rate) + Year 1 dividend / (Required rate of return - Dividend growth rate)^2 + Year 2 dividend / (Required rate of return - Dividend growth rate)^3 + Year 3 dividend / (Required rate of return - Dividend growth rate)^4 + Year 4 dividend / (Required rate of return - Dividend growth rate)^5

Note: The dividend after the fourth year will be growing indefinitely, so we consider it as a growing perpetuity in the formula.

Let's calculate the value using the given values:

Price = $1.50 / (0.14 - 0.11) + Year 1 dividend / (0.14 - 0.11)^2 + Year 2 dividend / (0.14 - 0.11)^3 + Year 3 dividend / (0.14 - 0.11)^4 + Year 4 dividend / (0.14 - 0.11)^5

Substituting the calculated values for Year 1, Year 2, Year 3, and Year 4 dividends:

Price = $1.50 / (0.14 - 0.11) + Year 1 dividend / (0.14 - 0.11)^2 + Year 2 dividend / (0.14 - 0.11)^3 + Year 3 dividend / (0.14 - 0.11)^4 + Year 4 dividend / (0.14 - 0.11)^5

Calculating each term:
Price = $1.50 / 0.03 + (Year 0 dividend * (1 + Dividend growth rate)) / 0.03^2 + (Year 0 dividend * (1 + Dividend growth rate) * (1 + Dividend growth rate)) / 0.03^3 + (Year 0 dividend * (1 + Dividend growth rate) * (1 + Dividend growth rate) * (1 + Dividend growth rate)) / 0.03^4 + (Year 0 dividend * (1 + Dividend growth rate) * (1 + Dividend growth rate) * (1 + Dividend growth rate) * (1 + Dividend growth rate)) / 0.03^5

Calculating the value of each term:
Price = $1.50 / 0.03 + ($1.50 * (1 + 0.11)) / 0.03^2 + ($1.50 * (1 + 0.11) * (1 + 0.11)) / 0.03^3 + ($1.50 * (1 + 0.11) * (1 + 0.11) * (1 + 0.11)) / 0.03^4 + ($1.50 * (1 + 0.11) * (1 + 0.11) * (1 + 0.11) * (1 + 0.11)) / 0.03^5

Calculating the final value:
Price = $1.50 / 0.03 + ($1.50 * 1.11) / 0.0009 + ($1.50 * 1.11 * 1.11) / 0.000729 + ($1.50 * 1.11 * 1.11 * 1.11) / 0.000531441 + ($1.50 * 1.11 * 1.11 * 1.11 * 1.11) / 0.000387420489

Calculating the final value:
Price ≈ $50 + $1,815 + $2,808.33 + $5,393,165.38 + $10,461,319.65

Adding up all the terms:
Price ≈ $5,407,303.36

Therefore, the current value of a share of Seneca common stock to an investor who requires a 14 percent rate of return is approximately $5,407,303.36.

To find the current value of a share of Seneca common stock, we can use the Dividend Discount Model (DDM). The DDM calculates the present value of all future dividends a stock is expected to pay.

Step 1: Calculate the future dividends for the next four years.
The current dividend is $1.50 per share. Dividends are expected to grow at a rate of 11 percent per year for the next four years. So, we can calculate the dividends for the next four years as:
Year 1 dividend = $1.50 * (1 + 0.11) = $1.665
Year 2 dividend = Year 1 dividend * (1 + 0.11) = $1.665 * (1 + 0.11) = $1.847
Year 3 dividend = Year 2 dividend * (1 + 0.11) = $1.847 * (1 + 0.11) = $2.051
Year 4 dividend = Year 3 dividend * (1 + 0.11) = $2.051 * (1 + 0.11) = $2.277

Step 2: Calculate the future dividends from year 5 and beyond.
Dividends are expected to continue growing at a rate of 5 percent per year after the fourth year. We can calculate the future dividends using the formula for a growing annuity:
Future dividends from year 5 = Year 4 dividend * (1 + 0.05) = $2.277 * (1 + 0.05) = $2.391

Step 3: Calculate the present value of future dividends.
To calculate the present value of future dividends, we need to find the present value of each annual dividend and sum them up. We can use the formula for the present value of a growing perpetuity to calculate the present value of the dividends from year 5 and beyond:
Present value of future dividends = Year 5 dividend / (rate of return - growth rate) = $2.391 / (0.14 - 0.05) = $2.391 / 0.09 = $26.5667

Step 4: Calculate the present value of the dividends for the next four years.
To calculate the present value of the dividends for the next four years, we use the discounted cash flow (DCF) formula:
Present value of Year 1 dividend = Year 1 dividend / (1 + rate of return) = $1.665 / (1 + 0.14) = $1.4579
Present value of Year 2 dividend = Year 2 dividend / (1 + rate of return)^2 = $1.847 / (1 + 0.14)^2 = $1.3603
Present value of Year 3 dividend = Year 3 dividend / (1 + rate of return)^3 = $2.051 / (1 + 0.14)^3 = $1.2707
Present value of Year 4 dividend = Year 4 dividend / (1 + rate of return)^4 = $2.277 / (1 + 0.14)^4 = $1.187

Step 5: Calculate the current value of a share of Seneca common stock.
The current value is the sum of the present values of future dividends and the present values of the dividends for the next four years:
Current value = Present value of future dividends + Present value of Year 1 dividend + Present value of Year 2 dividend + Present value of Year 3 dividend + Present value of Year 4 dividend
Current value = $26.5667 + $1.4579 + $1.3603 + $1.2707 + $1.1870
Current value = $31.8426

So, the current value of a share of Seneca common stock to an investor who requires a 14 percent rate of return is approximately $31.84.