JRN Enterprises just announced that it plans to cut its dividend from $2.50 to $1.50 per share and use the extra funds to expand its operations. Prior to this announcement, JRN's dividends were expected to grow at 4% per year and JRN's stock was trading at $25.00 per share. With the new expansion, JRN's dividends are expected to grow at 8% per year indefinitely. Assuming that JRN's risk is unchanged by the expansion, the value of a share of JRN after the announcement is closest to:

P0 = $25

Explanation:

To calculate the value of JRN after the announcement, we will use the constant growth model of DDM as the dividends are expected to grow at a constant rate. The formula for price under this model is,

P0 = D0 * (1+g)  /  (r - g)

Where,

As the risk will remain the same, so we can say that the r or required rate of return will remain the same. To calculate r, we will input the pre announcement values in the formula above.

25 = 2.5 / (r - 0.04)

25 * (r - 0.04)  =  2.5

25r  -  1  = 2.5

25r = 2.5 + 1

r = 3.5 / 25

r = 0.14 or 14%

Using the same formula for post announcement values, we calculate teh price to be,

P0 = 1.5 /  (0.14 - 0.08)

P0 = $25