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Common stock valuelong dashVariable growth Lawrence​ Industries' most recent annual dividend was ​$1.80 per share ​(D0equals$ 1.80​), and the​ firm's required return is 11​%. Find the market value of​ Lawrence's shares when dividends are expected to grow at 8​% annually for 3​ years, followed by a 5​% constant annual growth rate in years 4 to infinity.

Respuesta :

Answer:

market value of​ Lawrence's shares is $34.113

Explanation:

given data

annual dividend = ​$1.80 per share

Current year dividend  Do = $ 1.80

required return = 11​%

dividends expected  grow = 8​% annually

time = 3 year

growth rate = 5%

to find out

the market value of​ Lawrence's shares

solution

we will apply here Gordon Growth Model for terminal value in year 3 that is

Gordon Growth Model P3  = [tex]\frac{D4}{r-G}[/tex]

and [tex]\frac{D4}{r-G}[/tex] = [tex]\frac{D3(1+G)}{r-G}[/tex]

here r is required return and G is growth rate and D1  is Expected dividend of next 1 year

so here we get D1, D2, D3 and D4 they are as

D1 = $1.8×(1+0.08)

D1 = $1.944

and

D2 = $1.944×(1+0.08)

D2 =$2.0995

and

D3 = $2.0995×(1+0.08)

D3 = $2.267

and

D4 = $2.267×(1+0.05)

D4= $2.38

so

we get here now market value of the share year 3rd end that is

P3 =  [tex]\frac{2.38}{0.11-0.05}[/tex]

P3 = $39.67

and  

Market value of the share today is

Market value = [tex]\frac{D1}{(1.11)1} + \frac{D2}{(1.11)2} + \frac{D3}{(1.11)3} + \frac{D4}{(1.11)4}[/tex]  

put here all value

Market value = [tex]\frac{1.944}{(1.11)1} + \frac{2.0995}{(1.11)2} + \frac{2.267}{(1.11)3} + \frac{39.67}{(1.11)4}[/tex]  

solve we get

Market value = $34.113

so  market value of​ Lawrence's shares is $34.113