A7X Corp. just paid a dividend of $1.70 per share. The dividends are expected to grow at 20 percent for the next eight years and then level off to a growth rate of 5 percent indefinitely. If the required return is 15 percent, what is the price of the stock today? (Do not round intermediate calculations and round your answer to 2 decimal places, e. g., 32.16.)

$41.64

Explanation:

The computation of the price of the stock today is shown below

Price of stock today = Dividend per share × (1 + growth rate)^n ÷ (1 + required rate of return)^n  + Dividend per share × (1 + growth rate)^n ÷ (1 + required rate of return)^n + Dividend per share × (1 + growth rate)^n ÷ (1 + required rate of return)^n + Dividend per share × (1 + growth rate)^n ÷ (1 + required rate of return)^n + Dividend per share × (1 + growth rate)^n ÷ (1 + required rate of return)^n + Dividend per share × (1 + growth rate)^n ÷ (1 + required rate of return)^n + Dividend per share × (1 + growth rate)^n ÷ (1 + required rate of return)^n + Dividend per share × (1 + growth rate)^n ÷ (1 + required rate of return)^n + Dividend per share × (1 + growth rate)^n × 1 + decreased growth rate ÷ (required rate of return - decreased in growth rate) ÷ (1 + required rate of return)^n

= ($1.70 × 1.2 ÷ 1.15) + ($1.70 × 1.2^2 ÷ 1.15^2) + $1.70 × 1.2^3 ÷ 1.15^3) + $1.70 × 1.2^4 ÷ 1.15^4) + ($1.70 × 1.2^5 ÷ 1.15^5) + ($1.70 × 1.2^6 ÷ 1.15^6) + ($1.70 × 1.2^7 ÷ 1.15^7) + ($1.70 × 1.2^8 ÷ 1.15^8) + (1.70*1.2^8*1.05 ÷ (15% - 5%)) ÷ 1.15^8)

= $41.64

We simply applied the above formula

The N represents the time period

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