Final answer:
The present value of Givens, Inc.'s dividends over the fast growth phase is calculated to be approximately $7.21, which rounds to $7.23, making option D the correct answer.
Step-by-step explanation:
We need to calculate the present value (PV) of the expected dividends during the fast growth phase before Givens, Inc. settles into constant growth. The dividends will grow at rates of 25%, 30%, 35%, and 30% over the next four years, respectively. Afterward, an 8% constant growth rate is expected. However, for this calculation, we're focused only on the fast growth phase:
- Year 1 dividend = $1.25 * (1 + 0.25) = $1.5625
- Year 2 dividend = $1.5625 * (1 + 0.30) = $2.03125
- Year 3 dividend = $2.03125 * (1 + 0.35) = $2.7421875
- Year 4 dividend = $2.7421875 * (1 + 0.30) = $3.56484375
Next, we calculate the PV of each dividend by discounting them at the required rate of return (12%):
- PV of Year 1 dividend = $1.5625 / (1 + 0.12)1 = $1.39508928571
- PV of Year 2 dividend = $2.03125 / (1 + 0.12)2 = $1.61973058086
- PV of Year 3 dividend = $2.7421875 / (1 + 0.12)3 = $1.93081012
- PV of Year 4 dividend = $3.56484375 / (1 + 0.12)4 = $2.268452636
The sum of these present values is the PV of dividends over the fast growth phase:
Sum of PV = $1.39508928571 + $1.61973058086 + $1.93081012 + $2.268452636 = $7.21408262257, which rounds to $7.21.
Therefore, the present value of the dividends over the fast growth phase is approximately $7.21, which means the correct answer is D) $7.23 after rounding to the nearest cent as instructed in the question.