Question

Sisters Corp. expects to earn $6 per share next year. The firm’s ROE is 15% and its plowback ratio is 60%. The firm’s market capitalization rate is 10%. a. Calculate the price with the constant dividend growth model. (Do not round intermediate calculations.)

Answer 1

Using the Gordon Growth Model with the provided earnings, ROE, plowback ratio, and market capitalization rate, the calculated stock price for Sisters Corp. is $240 per share.

Step-by-step explanation:

The question pertains to calculating the price of a company's stock using the constant dividend growth model, a concept in finance.

Firstly, we determine the growth rate of dividends which can be calculated as the product of the return on equity (ROE) and the plowback ratio. In this instance, the growth rate is 15% (ROE) multiplied by 60% (plowback ratio), giving us 9%.

Since Sister Corp. expects to earn $6 per share next year, we can use the Gordon Growth Model. According to this model, the price of a stock is the dividend per share divided by the market capitalization rate minus the growth rate, which is:

P = D / (k - g)

Where P is the price, D is the dividend per share, k is the market capitalization rate, and g is the growth rate.

As the firm plows back 60%, it will pay out 40% (100% - 60%) as dividends. The dividends per share thus would be $6 * 40% = $2.4.

Substituting the values into the equation:

P = $2.4 / (0.10 - 0.09)

P = $240

The price of the stock would be $240 per share using the constant dividend growth model.

Answer 2

Stock price = $240.

Step-by-step explanation:

Here,

Plowback ratio is the ratio which estimates the amount of money a company retains after paying the dividend to the stockholders.

To calculate the stock price, the plowback ratio is the growth rate for the firm.

Here, Expected earn, D1 = $6; ROE = 15% = 0.15; Plowback Ratio = 60% = 0.60; Market capitalization rate, K = 10% = 0.10.

We know,

Stock price =
`D_(1) / (K - g)`

Stock price =
`(D_(1) (1 - plowback ratio))/(Market capitalization rate - (ROE * plowback ratio))`

Stock price =
`(6 (1 - 0.60))/(0.10 - (0.15*0.60))`

Stock price = $2.4/0.01 = $240