Answer:
The p/e ratio for this firm is 12.70.
Step-by-step explanation:
The price-to-earnings ratio (P/E ratio) refer to the ratio that is employed to value a company as it measures current price of share of the company relative to the earnings per share (EPS) of the company.
From the question, we are given the following:
r = Market capitalization rate = 10%
roe = Expected return on equity = 11%
eps = Expected earning per share = $4
pb = Plowback ratio = 68%
Therefore,
po = payout ratio = 100% - pb = 100% - 68% = 32%
To calculate the price earning (P/E), we use the P/E ratio formula as follows:
P/E ratio =Price / EPS .............................. (1)
Where;
Price = d / (r - g) ........................................ (2)
d = Expected dividend = eps * pb = $4 * 32% = $1.28
g = growth rate = pb * roe = 68% * 11% = 7.48%
Substituting for d, r and d into equation (2), we have:
Price = $1.28 / (10% - 7.48%) = $1.28 / 2.52% = $50.79
Substituting for Price and eps into equation (1), we have:
P/E ratio = $50.79 / $4 = 12.70
Therefore, p/e ratio for this firm is 12.70.