Question

using the P/E ratio approach to evaluation calculate the value of a share of stock under the following

Conditions:

The investors required rate of return is 15% , The expected level of earnings at the end of this year ( E1 ) is $8.00

• · The firm follows a policy of retaining 30% of its earnings
• · The return on equity ( ROE )is 20% and
• · Similar shares of stock sell at multiples of 7.7778 times earnings per share.
  Show that you get the same answer using the discounted dividend model.

Answer 1

value of a share of stock using P/E multiple.

P/E ratio or multiple = Price per share/earnings per share

7.7778 = Price per share/$8

Price per share = $8*7.7778 = $62.22

discounted dividend model

Price per share = expected dividend/(required rate of return - dividend growth rate)

expected dividend = expected earnings*(1-retention rate) = $8*(1-0.30) = $8*0.70 = $5.6‬

dividend growth rate = ROE*retention rate = 0.20*0.30 = 0.06 or 6‬%

Price per share = $5.6/(0.15 - 0.06) = $5.6/0.09 = $62.22

You get the same value of stock per share of $62.22 either you use P/E multiple valuation or dividend discount model.