Question

Common stock value: Variable growth Lawrence Industries’ most recent annual dividend was $1.80 per share (D0 = $1.80), and the firm’s required return is 11%. Find the market value of Lawrence’s shares when:

a. Dividends are expected to grow at 8% annually for 3 years, followed by a 5% constant annual growth rate in years 4 to infinity.
b. Dividends are expected to grow at 8% annually for 3 years, followed by a 0% constant annual growth rate in years 4 to infinity.
c. Dividends are expected to grow at 8% annually for 3 years, followed by a 10% constant annual growth rate in years 4 to infinity.

Answer 1

Given Annual Dividend paid( D0) = $ 1.80

Rate of interest = 11%

Year	Dividend Amount
1	$ 1.80*1.08= $ 1.944
2	$ 1.944*1.08 =$ 2.09952
3	$ 2.09952*1.08 = $ 2.26748

* Formula for calculation of Dividend Amount = Last year dividend ( 1+ Growth rate )

Case a) Dividends are expected to grow at 8% annually for 3 years, followed by a 5% constant

We know that Market Value of a Share represents Present value of future cash inflows

So let us findout the Present value of cash flows accruing from year 1 to infinity

Present value = Future value / ( 1+r)

Step 1 : Present value of cash flows accruing from year 1 to year 3

Present value = Future value / ( 1+r)

Present value = $ 1.944/ ( 1+11%) + $ 2.09952/( 1+11%)^2 + $ 2.26748/ ( 1+11%)^3

= $ 1.944*0.9009 + $ 2.09952*0.81162+ $ 2.26748*0.73119

= $ 1.7514+ $ 1.7040+ $ 1.6580

= $ 5.1133

Step 2 : Present value of Cash flows accruing from year 4 to infinity

Present value of Cash flows accruning from year 4 to infinity at the end of 3rd year = D4/ Ke - g

Here D4 = D3( 1+g)

=  $ 2.26748( 1+0.05)

=  $ 2.380854

Ke = 11%

g= Growth rate i.e 5%

PV of Cash flows at the end of year 3 = $ 2.380854/( 0.11-0.05)

= $2.380854/0.06

= $ 39.6809

Present value of Cash flows at year 0 = FV / ( 1+r)^3

= $ 39.6809/( 1+11%)^3

=   $ 39.6809* 0.73119

= $ 29.01428

Step 3 : Calculation of the Market Price

PV of Future cash flows = Step 1+ Step 2

=  $ 5.1133+$ 29.01428

=  $ 34.12758

Hence the Market price of a share = $ 34.12758 .

Case b) Dividends are expected to grow at 8% annually for 3 years, followed by a 0% constant annual growth rate in years 4 to infinity.

Step 1 : Present value of cash flows accruing from year 1 to year 3

Present value = Future value / ( 1+r)

Present value = $ 1.944/ ( 1+11%) + $ 2.09952/( 1+11%)^2 + $ 2.26748/ ( 1+11%)^3

= $ 1.944*0.9009 + $ 2.09952*0.81162+ $ 2.26748*0.73119

= $ 1.7514+ $ 1.7040+ $ 1.6580

= $ 5.1133

Step 2 : Present value of Cash flows accruing from year 4 to infinity

Present value of Cash flows accruning from year 4 to infinity at the end of 3rd year = D4/ Ke - g

Here D4 = D3( 1+g)

= $ 2.26748( 1+0%)

= $ 2.26748

Ke = 11%

g= Growth rate i.e 0%

PV of Cash flows at the end of year 3 = $ 2.26748/( 0.11-0%)

= $2.26748/0.11

= $20.6134

Present value of Cash flows at year 0 =    FV / ( 1+r)^3

= $ 20.6134/( 1+11%)^3

=   $ 20.6314* 0.73119

= $ 15.07230

Step 3 : Calculation of the Market Price

PV of Future cash flows = Step 1+ Step 2

=  $ 5.1133+$ 15.07230

=  $ 20.1856

Hence the Market price of a share = $ 20.1856

Case c ) Dividends are expected to grow at 8% annually for 3 years, followed by a 10% constant annual growth rate in years 4 to infinity.

Step 1 : Present value of cash flows accruing from year 1 to year 3

Present value = Future value / ( 1+r)

Present value = $ 1.944/ ( 1+11%) + $ 2.09952/( 1+11%)^2 + $ 2.26748/ ( 1+11%)^3

= $ 1.944*0.9009 + $ 2.09952*0.81162+ $ 2.26748*0.73119

= $ 1.7514+ $ 1.7040+ $ 1.6580

= $ 5.1133

Step 2 : Present value of Cash flows accruing from year 4 to infinity

Present value of Cash flows accruning from year 4 to infinity at the end of 3rd year = D4/ Ke - g

Here D4 = D3( 1+g)

= $ 2.26748( 1+10%)

= $ 2.494228

Ke = 11%

g= Growth rate i.e 10%

PV of Cash flows at the end of year 3 = $ 2.494228/( 0.11-0.10)

=  $2.494228/0.01

= $ 249.4228

Present value of Cash flows at year 0 = FV / ( 1+r)^3

= $ 249.4228/( 1+11%)^3

=   $ 249.4228* 0.73119

= $ 182.37540

Step 3 : Calculation of the Market Price

PV of Future cash flows = Step 1+ Step 2

=  $ 5.1133+$ 182.37540

=  $ 187.4887

Hence the Market price of a share = $ 187.4887

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