Analysts forecast that Dixie Chicks, Inc. (DCI) will pay a dividend of $2.50 a s

Question

Analysts forecast that Dixie Chicks, Inc. (DCI) will pay a dividend of $2.50 a share now, continuing a long-term growth trend of 10% per year. If this trend is expected to continue indefinitely, and investors' required rate of return for DCI is 12%: What is the market value per share of DCIs common stock? What is the market value per share of DCIs common stock if required rate of return is 16%? If there is expected to be non-constant growth of 20% for the first year, then 18% for the next year, then 16% for next year, finally stabilizing to a constant growth of 10% per year in the 4^th year what is the market value per share?

Explanation / Answer

a.

Market value per share = dividend in next year/ (R – g)

g = 10%

Next year dividend = 2.5*(1+g) = 2.5*1.10 = $2.75

R =12%

Thus,

Market value per share = 2.75/ (.12 - .10) = $137.5

b.

If R=16%

Market value per share = 2.75/ (.16 - .10) = $45.84

c.

As per the given yearly growth rate in dividend

D1=D0* (1+20%)=2.5*1.2 = $3

D2=D1*1.18=3*1.18= $3.54

D3=D2*1.16 = 3.54*1.16=$4.106 or $4.11

D4=D3*1.10 =4.11*1.10 = $4.52

D5=4.52*1.1 = $4.972

Thus,

Market value per share = D1/ (1+R) + D2/ (1+R) ^2 + D3/ (1+R) ^3 + D4/ (1+R) ^4 + share price in year4 / (1+R) ^4

Share price in year4 = Dividend in year 5 / (R – g) = D5/( R – g)

Market value per share = D1/ (1+R) + D2/ (1+R) ^2 + D3/ (1+R) ^3 + D4/ (1+R) ^4 + (D5/( R – g))/ (1+R) ^4

R=12% (original R given in the question)

Market value per share = 3/1.12 + 3.54/1.12^2 + 4.11/1.12^3 + 4.52/1.12^4 + (4.972/(.12-.1))/ 1.12^4

Market value per share = $169.29 approx.

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