Question

The market capitalization rate on the stock of Aberdeen Wholesale Company is 10%. Its expected ROE is 12%, and its expected EPS is $5. If the firm's plowback ratio is 60%, its P/E ratio will be A.7.14 B.14.29 C.16.67 D.22.22

Answer 1

The P/E ratio for Aberdeen Wholesale Company is approximately 0.1042.

Step-by-step explanation:

To calculate the P/E ratio, we can use the formula P/E = (ROE - g) / r where ROE is the return on equity, g is the growth rate, and r is the market capitalization rate.

Given that the plowback ratio is 60%, the growth rate can be calculated as g = ROE * plowback ratio = 12% * 60% = 7.2%.

Therefore, P/E = (12% - 7.2%) / 10% = 4.8% / 0.1 = 48.

Since the earning per share (EPS) is $5, the P/E ratio will be $5 / 48 = $0.1042.

Answer 2

If the market capitalization rate on the stock of Aberdeen Wholesale Company is 10%. its P/E ratio will be B.14.29.

What is the P/E ratio?

The ROE formula is:

ROE = Net Income / Equity

Dividend payout ratio (DPR) = 1 - Plowback ratio

So,

ROE = Expected ROE * Plowback ratio

ROE = 0.12 * 0.60

= 0.072

Next, we calculate the dividend per share (DPS) using the formula:

DPS = EPS * DPR

DPS = $5 * (1 - 0.60)

= $5 * 0.40

= $2

Market price per share (P) using the formula:

P = EPS / (Market capitalization rate - ROE)

P = $2 / (0.10 - 0.072)

= $2 / 0.028

= $71.43

P/E ratio is:

P/E ratio = Market price per share / Earnings per share (EPS)

= $71.43 / $5

≈ 14.29

Therefore the correct answer is B. 14.29.