# Consider a firm that has been priced using a 10% growth rate and a 15% required rate. The firm...

Consider a firm that has been priced using a 10% growth rate and a 15% required rate. The firm recently paid a $1.30 dividend. The firm has just announced that because of a new joint venture it will likely grow at a rate of 12%. How much should stock price change in dollars and percentage? ## Dividend Growth Model As per the dividend growth model, the cost of equity is the division of expected dividend and current price including the growth rate. The dividend model is used to compute the expected rate or the current price of the share. However, this model works only when the growth in the future year is constant and does not change. There are different assumptions of this model which are needed to be followed. ## Answer and Explanation: The change in price is of$19.93 and in percentage term the change is of 69.69%

Explanation

Step 1

Price (when growth is 10%) = Expected Dividend / (Required Return - Growth Rate)

• Expected Dividend = Current Dividend * (1 + growth rate) => $1.30 * (1 + 0.1) =$1.43
• Required Return = 15%
• Growth Rate = 10%

So,

Price (when growth is 10%) = $1.43 / (15% - 10%) =$28.6

Step 2

Price (when growth is 12%) = Expected Dividend / (Required Return - Growth Rate)

• Expected Dividend = Current Dividend * (1 + growth rate) => $1.30 * (1 + 0.12) =$1.456
• Required Return = 15%
• Growth Rate = 12%

So,

Price (when growth is 12%) = $1.456 / (15% - 12%) =$48.53

Step 3

Change in price (dollars) = $48.53 -$28.6 = $19.93 Change in price (percentage) = ($19.93 / \$28.6) * 100 = 69.69%