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 _________.

Answer 1

14.29

Step-by-step explanation:

Data provided in the question:

The market capitalization rate on the stock = 10%

Expected ROE = 12%

Expected EPS = $5

Firm's plowback ratio = 60%

Now,

Payout ratio = (1 - plowback ratio )

= ( 1 - 0.6 )

= 0.4

Growth rate = ROE × Retention ratio

= ( 0.12 × 0.6 )

= 7.2%

Thus,

Dividend for next period, D1 = EPS × Payout ratio

= $5 × 0.4

= $2

Therefore,

Current price = D1 ÷ ( Market capitalization rate - Growth rate )

= $2 ÷ ( 0.10 - 0.072 )

= $71.43

Hence,

P/E ratio = ( Current price ) ÷ ( EPS )

= $71.43 ÷ $5

= 14.29