2.Calculate the growth rate of Asset J dividends, we have to assume that future dividend payments will grow at a constant rate into the future forever. This constant rate can be estimated by calculating the average growth rate from the past dividends. Calculate Asset J’s dividend growth rate for the past 8 years.
Year 1 2 3 4 5 6 7 8
Dividend $0.86 $2.00
Let:
Dj = $ .86,
D8 = $2.00,
n = 8.
The equation for calculating the growth rate of dividends is the future value equation. FV=PV(1+i)n
where:
Dj = PV,
D8 = FV,
n = time
Growth Rate = I
To calculate the growth rate of Asset J dividends for the past 8 years, we can use the future value equation:
FV = PV(1 + i)^n
where FV is the future value (D8 = $2.00), PV is the present value (Dj = $0.86), i is the interest rate (growth rate), and n is the number of years (8).
Rearranging the equation to solve for i, we have:
(1 + i)^n = FV / PV
Substituting the given values:
(1 + i)^8 = 2.00 / 0.86
To solve for i, we need to take the 8th root of both sides of the equation:
1 + i = (2.00 / 0.86)^(1/8)
Now, subtract 1 from both sides to isolate i:
i = (2.00 / 0.86)^(1/8) - 1
Using a calculator,
i ≈ 0.0901
Therefore, the dividend growth rate for Asset J over the past 8 years is approximately 0.0901 or 9.01%.