Common stock value: Variable growth Lawrence Industries’ most recent annual divi

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.

Explanation / Answer

a.) D1 ( at end of first year) = 1.80 + 8% = 1.94 (approx)

D2 ( at end of Second year) = 1.94 + 8% = 2.09 (approx)

D3 ( at end of Third year) = 2.09 + 8% = 2.26 (approx)

D4 (  at end of Fourth year) = 2.26 + 5% = 2.37 (approx)

P3 ( Market price at end of Third year) = 2.37 / 0.11 - 0.05 = 39.5

The market value of Lawrence’s shares

= [1.94 * 0.901] + [ 2.09 * 0.812 ] + [ (2.26 + 39.5) * 0.731]

= $ 33.97 i.e., $ 34 (approx)

b.) D1 ( at end of first year) = 1.80 + 8% = 1.94 (approx)

D2 ( at end of Second year) = 1.94 + 8% = 2.09 (approx)

D3 ( at end of Third year) = 2.09 + 8% = 2.26 (approx)

   D4 (  at end of Fourth year) = 2.26 (No growth)

   P3 ( Market price at end of Third year) = 2.26 / 0.11 = $ 20.54 (approx)

The market value of Lawrence’s shares

= [1.94 * 0.901] + [ 2.09 * 0.812 ] + [ (2.26 + 20.54) * 0.731]

= $ 20.11 i.e., $ 20 (approx)

c.)   D1 ( at end of first year) = 1.80 + 8% = 1.94 (approx)

D2 ( at end of Second year) = 1.94 + 8% = 2.09 (approx)

D3 ( at end of Third year) = 2.09 + 8% = 2.26 (approx)

D4 (  at end of Fourth year) = 2.26 + 10 % = 2.49 (approx)

P3 ( Market price at end of Third year) = 2.49 / 0.11 - 0.10 = $ 249

The market value of Lawrence’s shares

= [1.94 * 0.901] + [ 2.09 * 0.812 ] + [ (2.26 + 249) * 0.731]

= $ 187.12 i.e., $ 187 (approx)

Conclusion:-

Market value of Lawrence’s shares :-

Note:- 0.901, 0.812 and 0.731 are the P.V. Factors @ 11% for Year 1,2, and 3.

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