Math Problem Statement

Thress Industries just paid a dividend of $3.25 a share (i.e., D0 = $3.25). The dividend is expected to grow 6% a year for the next 3 years and then 12% a year thereafter. What is the expected dividend per share for each of the next 5 years? Do not round intermediate calculations. Round your answers to the nearest cent.

D1 = $

D2 = $

D3 = $

D4 = $

D5 = $

Solution

To calculate the expected dividend per share for each of the next five years, we will use the dividend growth formula:

Dn=D0×(1+g)nD_n = D_0 \times (1 + g)^n

Where:

  • DnD_n is the dividend in year nn,
  • D0=3.25D_0 = 3.25 is the dividend just paid,
  • gg is the growth rate, which is 6% for the first 3 years and 12% thereafter.

Step-by-Step Calculation:

1. Year 1 (D1):

For the first year, the growth rate is 6%, so: D1=3.25×(1+0.06)=3.25×1.06D_1 = 3.25 \times (1 + 0.06) = 3.25 \times 1.06 D1=3.445D_1 = 3.445

2. Year 2 (D2):

For the second year, the growth rate is again 6%, so: D2=3.445×(1+0.06)=3.445×1.06D_2 = 3.445 \times (1 + 0.06) = 3.445 \times 1.06 D2=3.6517D_2 = 3.6517

3. Year 3 (D3):

For the third year, the growth rate is still 6%, so: D3=3.6517×(1+0.06)=3.6517×1.06D_3 = 3.6517 \times (1 + 0.06) = 3.6517 \times 1.06 D3=3.8708D_3 = 3.8708

4. Year 4 (D4):

From year 4 onward, the growth rate increases to 12%. For the fourth year: D4=3.8708×(1+0.12)=3.8708×1.12D_4 = 3.8708 \times (1 + 0.12) = 3.8708 \times 1.12 D4=4.3353D_4 = 4.3353

5. Year 5 (D5):

For the fifth year, the growth rate remains 12%, so: D5=4.3353×(1+0.12)=4.3353×1.12D_5 = 4.3353 \times (1 + 0.12) = 4.3353 \times 1.12 D5=4.8555D_5 = 4.8555

Final Results (rounded to the nearest cent):

  • D1=3.45D_1 = 3.45
  • D2=3.65D_2 = 3.65
  • D3=3.87D_3 = 3.87
  • D4=4.34D_4 = 4.34
  • D5=4.86D_5 = 4.86

Would you like further details or explanations?


Related Questions:

  1. What is the total dividend growth over the 5-year period?
  2. How would the dividend change if the growth rates were different?
  3. What is the present value of the dividends if discounted at 10%?
  4. How does this dividend growth affect the stock price?
  5. What happens if the 12% growth rate is only sustained for 2 years instead of permanently?

Tip: Always keep track of different growth rates across multiple time periods when forecasting dividends.

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Math Problem Analysis

Mathematical Concepts

Dividend Growth Model
Exponential Growth
Algebra

Formulas

Dividend Growth Formula: D_n = D_0 * (1 + g)^n

Theorems

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Suitable Grade Level

Undergraduate Finance or Economics