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Tin-Tin Waste Management, Inc., is growing rapidly. Dividends are expected to grow at rates of 30 percent, 35 percent, 25 percent, and 18 percent over the next four years. Thereafter, management expects dividends to grow at a constant rate of 7 percent. The stock is currently selling at $47.85, and the required rate of return is 16 percent. Compute the dividend for the current year (D0).

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Answer:

The dividend for the current year (D0) is $2.15.

Explanation:

This can be calculated as follows:

Current dividend = D0

Next dividend = (1 + relevant growth rate) * Current dividend ........... (1)

Based on equation (1), we have:

D1 = (1 + 0.30) * D0 = 1.30D0

D2 = (1 + 0.35) * D1 = 1.35 * 1.30D0 = (1.35 * 1.30)D0 = 1.755D0

D3 = (1 + 0.25) * D2 = 1.25 * 1.755D0 = (1.25 * 1.755)D0 = 2.19375D0

D4 = (1 + 0.18) * D3 = 1.18 * 2.19375D0 = (1.18 * 2.19375)D0 = 2.588625D0

D5 = (1 + 0.07) * D4 = 1.07 * 2.588625D0 = (1.07 * 2.588625)D0 = 2.76982875D0

Using Gordon Growth stable formula, we have price in year 4 (P4) as follows:

P4 = D5/(required rate of return - Perpetual dividend growth rate) ........ (2)

Substituting all the relevant values to equation (2), we have:

P4 = 2.76982875D0/(0.16 - 0.07)

P4 =2.76982875D0/0.09

P4 = 30.775875D0

Since the market price is the sum of all the present values of dividends from year 1 to 4 and P4, we have:

$47.85 = (D1 / (1 + required rate of return)^1) + (D2 / (1 + required rate of return)^2) + (D3 / (1 + required rate of return)^3) + (D4 / (1 + required rate of return)^4) + (P4 / (1 + required rate of return)^4) ...........(3)

Substituting all the relevant values to equation (3), we have:

$47.85 = (1.30D0 / 1.16^1) + (1.755D0 / 1.16^2) + (2.19375D0 / 1.16^3) + (2.588625D0 / 1.16^4) + (30.775875D0 / 1.16^4)

$47.85 = [(1.3 / 1.16^1) + (1.755 / 1.16^2) + (2.19375 / 1.16^3) + (2.588625 / 1.16^4) + (30.775875 / 1.16^4)]D0

$47.85 = 22.2572996535323D0

D0 = $47.85 / 22.2572996535323

D0 = $2.15

Therefore, the dividend for the current year (D0) is $2.15.

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