Final answer:
The expected dividend in year 5, after applying a 20% growth for the first four years and then a 6% growth rate from year 4 to year 5 to an initial $2.00 dividend, results in approximately $4.95, option (c).
Step-by-step explanation:
The expected dividend in year 5 from Michigan Co., considering an initial dividend of $2.00 growing at 20% per year for four years before switching to a 6% growth rate, can be calculated using the formula for compound growth. For the first four years, we can calculate the dividend at the end of each year and then apply the 6% growth rate to the year 4 dividend to find the expected dividend for year 5.
The calculation for year 1 would be $2.00 × (1 + 0.20) = $2.40; for year 2, it's $2.40 × (1 + 0.20) = $2.88, continuing this for year 3 and year 4.
Finally, we apply the 6% growth to the year 4 dividend ($4.6656) to get the year 5 dividend: $4.6656 × (1 + 0.06) = $4.9451, which, when rounded, should give us the closest option, making the correct answer (c) $4.95.