The 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 4 years and then to continue growing thereafter 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 calculate the current value of a share of Seneca common stock, we can use the dividend discount model (DDM). The DDM formula is:

PV = D1 / (r - g)

Where:
PV = Present value of the stock
D1 = Dividend expected to be received in Year 1
r = Required rate of return
g = Growth rate of the dividends

In this case, the dividend in Year 1 (D1) can be calculated as follows:
D1 = D0 * (1 + g) = $1.50 * (1 + 0.11) = $1.665

The required rate of return (r) is given as 14%, and the growth rate (g) for the first 4 years is 11%.

Let's calculate the present value (PV):

PV = $1.665 / (0.14 - 0.11)

PV = $1.665 / 0.03

PV = $55.50

So, the current value of a share of Seneca common stock is $55.50 to an investor who requires a 14% rate of return.

To calculate the current value of a share of Seneca common stock, we can use the dividend discount model (DDM) approach. The DDM calculates the present value of future dividends to determine the stock's intrinsic value.

Here's how you can calculate the current value of a share of Seneca common stock:

1. Determine the expected future dividends:
- In year 0, the dividend is given as $1.50 per share.
- Dividends are expected to grow at a rate of 11 percent per year for the next 4 years and then at a rate of 5 percent per year thereafter.

2. Calculate the annual dividends for the next 4 years using the growth rate:
Year 1 dividend = $1.50 * (1 + 0.11) = $1.665
Year 2 dividend = $1.665 * (1 + 0.11) = $1.850
Year 3 dividend = $1.850 * (1 + 0.11) = $2.055
Year 4 dividend = $2.055 * (1 + 0.11) = $2.286

3. Determine the future dividend stream beyond year 4:
After year 4, dividends are expected to grow at a rate of 5 percent per year. We can assume the growth rate is constant.

4. Calculate the present value of the future dividends:
To calculate the present value, we need to discount each future dividend using the investor's required rate of return. In this case, the required rate of return is 14 percent.

Present value = (Year 1 dividend / (1 + required rate of return)^1) +
(Year 2 dividend / (1 + required rate of return)^2) +
(Year 3 dividend / (1 + required rate of return)^3) +
(Year 4 dividend / (1 + required rate of return)^4) +
(Year 5 dividend / (1 + required rate of return)^5) + ...

Present value = ($1.665 / (1 + 0.14)^1) +
($1.850 / (1 + 0.14)^2) +
($2.055 / (1 + 0.14)^3) +
($2.286 / (1 + 0.14)^4) +
($2.286 * (1 + 0.05) / (1 + 0.14)^5) + ...

Note: The summation of future dividends continues indefinitely, assuming the growth rate remains constant beyond year 4.

5. Sum up the present values of the future dividends to get the current stock value.

It's important to note that this calculation assumes that the dividends will be paid as planned and the growth rates will remain constant.

I hope this explanation helps you understand how to calculate the current value of a share of Seneca common stock.