# Bill's Bakery expects earnings per share of $2.26 next year. The current book value is$4 per...

## Question:

Bill's Bakery expects earnings per share of $2.26 next year. The current book value is$4 per share. The appropriate discount rate for Bill's Bakery is 14%.

Calculate the share price for Bill's Bakery if earnings grow at 3.2% forever.

## Dividend Discount Model:

The Dividend Discount Model is one of the financial approach to determine the stock price according to given information about the dividends, the dividend growth rate and the required rate of return.

We can use the dividend growth model to compute the price per share as follows

• price per share = next dividend / (required return - dividend growth rate)

We first need to to compute the next dividend. To do so we first compute the dividend payout ratio, using the formula for sustainable growth rate:

• sustainable growth rate = ROE *(1 - dividend payout ratio)
• 3.2% = (2.26 / 4) *(1 - dividend payout ratio)
• dividend payout ratio = 0.943

Given expected earnings per share of 2.26, the next dividend per share = 2.26 *0.943 = 2.13. The growth rate is 3.2%, and the discount rate is 14%. Applying the formula, the price per share is:

• price per share = 2.13 / (14% - 3.2%)
• price per share = 19.72 