Question

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.

Answer 1

market value of​ Lawrence's shares is $34.113

Step-by-step 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 =
`(D4)/(r-G)`

and
`(D4)/(r-G)` =
`(D3(1+G))/(r-G)`

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 =
`(2.38)/(0.11-0.05)`

P3 = $39.67

and

Market value of the share today is

Market value =
`(D1)/((1.11)1) + (D2)/((1.11)2) + (D3)/((1.11)3) + (D4)/((1.11)4)`

put here all value

Market value =
`(1.944)/((1.11)1) + (2.0995)/((1.11)2) + (2.267)/((1.11)3) + (39.67)/((1.11)4)`

solve we get

Market value = $34.113

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