Question

the home market has adopted a policy of increasing the annual dividend on their common stock at a constant rate of 3.75% annually. the firm is paying an annual dividend of $1.10 today. what will the dividend be five years from now?

Answer 1

To calculate the future dividend given a growth rate, you use the future value of a growing annuity formula. For an annual dividend of $1.10 growing at a rate of 3.75% annually, the dividend after five years will be approximately $1.32.

Step-by-step explanation:

You’ve asked how to calculate the future dividend of a stock given a current dividend and a constant growth rate. We'll use the formula for future value of a growing annuity to determine the dividend in five years. Given a current annual dividend of $1.10 and a constant annual growth rate of 3.75%, the formula is:

FV = D₀ × (1 + g)⁵

Where:

• FV is the future value of the dividend.
• D₀ is the current dividend, which is $1.10.
• g is the growth rate, which is 3.75% or 0.0375 when expressed as a decimal.

Plugging the values into the formula gives us:

FV = $1.10 × (1 + 0.0375)⁵

Calculating the future value gives us:

FV = $1.10 × 1.1990

FV = $1.3189

Therefore, the annual dividend five years from now will be approximately $1.32.