Question

Using the ​P/E ratio approach to​ valuation, calculate the value of a share of stock under the following​ conditions:

• the​ investor's required rate of return is 14 ​percent,

• the expected level of earnings at the end of this year ​(E1​) is ​$5​,

• the firm follows a policy of retaining 20 percent of its​ earnings,

• the return on equity ​(ROE​) is 15 ​percent, and

• similar shares of stock sell at multiples of 7.272 times earnings per share.

Now show that you get the same answer using the discounted dividend model.

a. The stock price using the ​P/E ratio valuation method is ​$ (?). ​ (Round to the nearest​ cent.)

b. The stock price using the dividend discount model is $_________ (round to the nearest cent.)

Answer 1

Part A:

Price at the end of Year 1 = EPS for Year 1 * PE Ratio

= $ 5 * 7.272

= $ 36.36

Div for Year 1 = EPS for Year 1 * ( 1 - Retention Ratio)

= $ 5 ( 1 - 0.2 )

= $ 56 * 0.8

= $ 4.00

Price of STock Today = [ P1 + D1 ] / [ 1 + Ke ]

= [ $ 36.36 + $ 4.00 ] / [ 1 + 0.14 ]

= $ 40.36 / 1.14

= $ 35.40

Part B:

g = Retention Ratio * ROE
= 0.2 * 15%

= 3%

P0 = D1 / [ Ke - g ]

= $ 4.00 / [ 14% - 3% ]

= $ 4.00 / 11%

P0 - Price Today

D1 - Div after 1 Year

Ke -Required Ret

g - Growth Rate

= $ 36.36