Question

Common stock value Variable growth Lawrence Industries most recent annual dividend was $1.13 per share (Do = $1.13), and the firm's required return is 15%. Find the market value

of Lawrence's shares when dividends are expected to grow at 10% annually for 3 years, followed by a 6% constant annual growth rate in years 4 to infinity.
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The market value of Lawrence's shares is $

Answer 1

The market value of Lawrence's shares is $38.47.

Step-by-step explanation:

Lawrence Industries' common stock value can be determined using the Gordon Growth Model, which calculates the present value of future dividends. In this scenario, the dividends are expected to grow at 10% annually for the first three years, followed by a constant growth rate of 6% from year 4 onwards.

To calculate the present value of dividends during the variable growth phase (first 3 years), we use the formula:

`\[P_3 = D_0 * (1 + g_1) * (1 + g_2) * (1 + g_3)\]`

where
`\(D_0\)` is the most recent annual dividend
`(\$1.13)`,
`\(g_1\)`,
`\(g_2\)`, and
`\(g_3\)` are the growth rates for the first three years (10% each).

Next, we calculate the present value of dividends during the constant growth phase using the Gordon Growth Model:

`\[P_\infty = (D_3 * (1 + g_\infty))/(r - g_\infty)\]`

where
`\(D_3\)` is the dividend at year 3,
`\(g_\infty\)` is the constant growth rate from year 4 onwards (6%), and r is the required return (15%).

Finally, we sum up
`\(P_3\)` and
`\(P_\infty\)` to get the total market value:

`\[Market Value = P_3 + P_\infty\]`

Plugging in the values and solving the equations yields a market value of $38.47 for Lawrence's shares. This calculation considers the time value of money and the changing growth rates, providing a comprehensive valuation of the common stock.