Question

I HAVE THE SOLUTION FOR THE QUESTION. BUT DIDN'T UNDERSTAND FORMULA USED CAN YOU PROVIDE THE FORMULA AND EXPLAIN IT.
19. CX Enterprises has the following expected dividends: $1 in one year, $1.15 in two years, and $1.25 in three years. After that, its dividends are expected to grow at 4% per year forever (so that year four's dividend will be 4% more than $1.25 and so on). If CX's equity cost of capital is 12%, what is the current price of its stock?

Answer 1

Price of stock = present value of next 3 years dividends + present value terminal value at end of year 3

terminal value at end of year 3 = year 4 dividend / (equity cost of capital - constant growth rate after year 3)

year 4 dividend = year 3 dividend * (1 + constant growth rate after year 3)

year 4 dividend = $1.25 * (1 + 0.04) = $1.30

terminal value at end of year 3 = $1.30 / (0.12 - 0.04)

Present value = future value / (1 + discount rate)^{number of years}

Here, the discount rate is the equity cost of capital.

Present value of next 3 years dividends = ($1 / 1.12¹) + ($1.15 / 1.12²) + ($1.25 / 1.12³)

Present value of terminal value = [$1.30 / (0.12 - 0.04)] / 1.12³

Price of stock =  ($1 / 1.12¹) + ($1.15 / 1.12²) + ($1.25 / 1.12³) + [[$1.30 / (0.12 - 0.04)] / 1.12³]

Price of stock = $14.27