company A recently reported earning of $1.5 million. The firm plan to
retain 30% of its earnings. The historical return on equity for the
firm has been 12% ad this figure is expected to continue in the
future. If the firm has 1000,000 shares outstanding, calculate the
price of each share. assume the company's beta is 1.2, the risk free
rate is 4% and the market risk premium is 11%.

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Request for Question Clarification by juggler-ga on 26 Mar 2003 21:52 PST

When you write, "1000,000 shares," do you mean 1,000,000 (i.e., one million) shares?

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Clarification of Question by hang-ga on 26 Mar 2003 22:08 PST

my mistake, it is 1,000,000. thanks for help.

Hello.

First, we use the Capital Asset Pricing Model to calculate the
expected rate of return. Source:
Financial Concepts: Capital Asset Pricing Model (CAPM)
http://www.investopedia.com/university/concepts/concepts8.asp

Expected Return = RF Rate + (Market Return - RF Rate) * Beta 
Expected Return = RF Rate + (market risk premium) * Beta
Expected Return = 4% + (11%) * (1.2) 
Expected Return = 4% + 13.2%
Expected Return = 17.2%

We will use this expected return as the discount rate in the dividend
discount model below.

Next, we calculate the growth rate.
See: "Financial Statements Ratio Analysis," hosted by CSUN.edu:
http://dcary.csun.edu/csun/fin435/ratios.pdf

sustainable growth rate = (return on equity) * (retention ratio)
sustainable growth rate = 12% * 30%
sustainable growth rate = 4%


Next, we calculate the amount of earnings that are paid out as
dividends.

Total payout = total earnings * ( 1 - retention rate) 
Total payout = 1500000 * ( 1 - .30)
Total payout = 1050000

Next, we calculate the current dividend payout per share, D(0).

D(0) = 1050000 / 1000000 
D(0) = 1.05

Next we calculate the expected dividend for next year, D(1)

D(1) = DIV0 * (1 + growth rate)
D(1) = 1.05 * (1 + .04)
D(1) = 1.05 * 1.04 
D(1) = 1.092


Finally, we use the Dividend Discount Model (DDM - Constant Perptual
Growth) to calculate the value of each share.
Source: "Chapter 6 Common Stock Valuation," hosted by dom.edu:
http://domin.dom.edu/faculty/esbittme/gsb731/chap6.doc

share value = D(1) / (discount rate - growth rate)
share value = 1.092 / ( .172 - .04)
share value = 1.092 / .132
share value = 8.27
 
Thus, using the DDM - Constant Perptual Growth model, the expected
price of each share is $8.27.

I hope this helps.

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Clarification of Answer by juggler-ga on 27 Mar 2003 01:36 PST

search terms:
capm, "market risk premium", beta
"growth rate", "return on equity", "retention ratio"
"dividende discount model", growth

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Request for Answer Clarification by hang-ga on 27 Mar 2003 04:47 PST

hi, actually I have 5 possible answers, the answer must be one of
them:A$6.1,B$8.00,C$20.2,D,$22.6,E $112.5. Can you recheck the answer?

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Clarification of Answer by juggler-ga on 27 Mar 2003 10:55 PST

Hi.

I see that I made a computational error here:

sustainable growth rate = (return on equity) * (retention ratio) 
sustainable growth rate = 12% * 30% 
sustainable growth rate = 3.6%   (not 4% that I absentmindedly wrote down)

Now redoing the share value:
share value = D(1) / (discount rate - growth rate) 
share value = 1.092 / ( .172 - .036) 
share value = 1.092 / .136 
share value = 8.02

Thus, rounding down, I'd say that the answer is:
B. $8

Sorry about that mistake.