Question

Bill’s Bakery has current earnings per share of $3.06. Current book value is $5.00 per share. The appropriate discount rate for Bill’s Bakery is 12 percent. Calculate the share price for Bill’s Bakery if earnings grow at 3.3 percent forever. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

Answer:

For this case let X represent the earnings per share. And we know that:

$X_0 = 3.06$ represent the earnings per share at year 0

The increasing factor on this case is i = 3.3% = 0.033

So then we can find the earnings per share at year 1 like this:

$X_1 = (1+i) x_o = (1+0.033)*3.06 = 3.16098$

Then we can use the dividen growth model given by the following expression:

$P0 = \frac{X_1}{R-i}$

Where P0 represent the share price and R=12% =0.12 the discount rate and if we replace we got:

$P0 = \frac{3.16098}{0.12-0.033}= 36.3331$

So then the share price for Bill's Bakery on this case would be $ 36.33

Explanation:

For this case let X represent the earnings per share. And we know that:

$X_0 = 3.06$ represent the earnings per share at year 0

The increasing factor on this case is i = 3.3% = 0.033

So then we can find the earnings per share at year 1 like this:

$X_1 = (1+i) x_o = (1+0.033)*3.06 = 3.16098$

Dividend growth model is defined as a valuation model, used to "calculate the fair value of stock, assuming that the dividends grow either at a stable rate in perpetuity or at a different rate during the period at hand".

Then we can use the dividend growth model given by the following expression:

$P0 = \frac{X_1}{R-i}$

Where P0 represent the share price and R=12% =0.12 the discount rate and if we replace we got:

$P0 = \frac{3.16098}{0.12-0.033}= 36.3331$

So then the share price for Bill's Bakery on this case would be $ 36.33