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P7-15: Common stock value: Variable growth Lawrence Industriesā€™ most recent annual dividend was $1.80 per share (D0=$1.80), and the firmā€™s required return is 11%. Find the market value of Lawrenceā€™s shares when: a. Dividends are expected to grow at 8% annually for 3 years, followed by a 5% constant annual growth rate in year 4 to infinity. b. Dividends are expected to grow at 8% annually for 3 years, followed by a 0% constant annual growth rate in year 4 to infinity.c. Dividends are expected to grow at 8% annually for 3 years, followed by a 10% constant annual growth rate in year 4 to infinity.

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Answer:

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

Dā‚€ = $1.80

Dā‚ = $1.944

Dā‚‚ = $2.10

Dā‚ƒ = $2.2675

Dā‚„ = $2.38

terminal value at year 3 = $2.38 / (11% - 5%) = $39.68

current Pā‚€ = $1.944/1.11 + $2.10/1.11Ā² + $41.9484/1.11Ā³ = $1.75 + $1.70 + $30.67 = $34.12

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

Dā‚€ = $1.80

Dā‚ = $1.944

Dā‚‚ = $2.10

Dā‚ƒ = $2.2675

Dā‚„ = $2.38

terminal value at year 3 = $2.38 / 11% = $21.6364

current Pā‚€ = $1.944/1.11 + $2.10/1.11Ā² + $23.90/1.11Ā³ = $1.75 + $1.70 + $17.48 = $20.93

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

Dā‚€ = $1.80

Dā‚ = $1.944

Dā‚‚ = $2.10

Dā‚ƒ = $2.2675

Dā‚„ = $2.38

terminal value at year 3 = $2.38 / (11% - 10%) = $238

current Pā‚€ = $1.944/1.11 + $2.10/1.11Ā² + $240.2675/1.11Ā³ = $1.75 + $1.70 + $175.68 = $179.13

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