Question

Consolidated Software does not currently pay any dividends but is expected to start doing so in four years. That is, Consolidated will go for three more years without paying any dividends and then is expected to pay its first dividend ($1) at the end of the 4th year. Once the company starts paying dividends, it is expected to continue to do so. The company is expected to have a dividend payout ratio of 60% and to maintain a return on equity of 20%. Based on the Dividend Discount Model, and given a required rate of return of 12%, what is the maximum price you should be willing to pay for this stock today?

Answer 1

The maximum price you should pay for Consolidated Software's stock today, considering it's not currently paying dividends but is expected to start in four years, is $17.79. This is based on the computed present value using the adjusted Gordon Growth Model to account for the future dividend growth and the required rate of return.

Step-by-step explanation:

To calculate the maximum price you should be willing to pay for Consolidated Software stock today, we will use the Gordon Growth Model (a version of the Dividend Discount Model) which is suitable for valuing a stock with dividends that are expected to grow at a constant rate in perpetuity. However, in this case, the dividends start after four years, so we need to adjust our formula accordingly.

First, let's find the expected dividend growth rate. Since the company will maintain a return on equity (ROE) of 20% and has a dividend payout ratio of 60%, the expected growth rate (g) of the dividends is:

g = ROE × (1 - Dividend Payout Ratio)
g = 0.20 × (1 - 0.60)
g = 0.20 × 0.40
g = 0.08 or 8%

Now, using the Dividend Discount Model, the value of the stock at the end of year 3 (just before the first dividend payment) can be calculated as follows:

P3 = D1 / (k - g)
P3 = $1 / (0.12 - 0.08)
P3 = $1 / 0.04
P3 = $25

To find the present value of this price today (year 0), we need to discount it back for three years using the required rate of return (k) of 12%.

Present Value = P3 / (1 + k)³
Present Value = $25 / (1 + 0.12)³
Present Value = $25 / (1.404928)
Present Value = $17.79

This means that the maximum price you should be willing to pay for the stock today, to achieve a required rate of return of 12%, is $17.79.

Answer 2

The maximum that should be paid for a share today is $17.79

Step-by-step explanation:

We need to calculate the sustainable growth rate first to calculate the price of the stock using the constant growth model of DDM. The growth rate can be calculated as,

g = ROE * (1 - Dividend Payout Ratio)

g = 0.2 * (1-0.6) = 0.08 or 8%

The price of the stock today can be calculated using the constant growth model of DDM. The formula for price under this model is,

P0 = D1 / r-g

We can calculate the price at year 3 using the dividend D4 that is given to us and discount it back for three periods to calculta the price of the stock today.

P3 = 1 / (0.12 - 0.08)

P3 = 25

P0 = 25 / (1+0.12)^3

P0 = $17.79