Respuesta :
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.
