Question

Thirsty Cactus Corp. just paid a dividend of $1.25 per share. The dividends are expected to grow at 40 percent for the next 10 years and then level off to a 7 percent growth rate indefinitely. Required : If the required return is 12 percent, what is the price of the stock today?

$301.09

$295.06

$307.11

$249.13

$5.85

Answer 1

Year 1 dividend = 1.25 * 1.4 = 1.75

Year 2 dividend = 1.75 * 1.4 = 2.45

Year 3 dividend = 2.45 * 1.4 = 3.43

year 4 dividend = 3.43 * 1.4 = 4.802

year 5 dividend = 4.802 * 1.4 = 6.7228

year 6 dividend = 6.7228 * 1.4 = 9.41192

year 7 dividend = 9.41192 * 1.4 = 13.176688

year 8 dividend = 13.176688 * 1.4 = 18.447363

year 9 dividend = 18.447363 * 1.4 = 25.826308

year 10 dividend = 25.826308 * 1.4 = 36.156832

year 11 dividend = 36.156832 * 1.07 = 38.68781

Present value at year 10 using dividend discount model = D1 / require rate - growth rate

Present value at year 10 = 38.68781 / 0.12 - 0.07

Present value at year 10 = 38.68781 / 0.05

Present value at year 10 = 773.756205

Present value of 1,012.3913 today = 773.756205 / ( 1 + 0.12)¹⁰

Present value of 1,012.3913 today = 249.12879

Present value of year 10 dividend = 36.156832 / ( 1 + 0.12)¹⁰ = 11.641532

Present value of year 9 dividend = 25.826308 / ( 1 + 0.12)⁹ = 9.313226

Present value of year 8 dividend = 18.447363 / ( 1 + 0.12)⁸ =  7.450581

Present value of year 7 dividend = 13.176688 / ( 1 + 0.12)⁷ = 5.960464

Present value of year 6 dividend = 9.41192 / ( 1 + 0.12)⁶ = 4.768372

Present value of year 5 dividend = 6.7228 / ( 1 + 0.12)⁵ = 3.814697

Present value of year 4 dividend = 4.802 / ( 1 + 0.12)⁴ = 3.051758

Present value of year 3 dividend = 3.43 / ( 1 + 0.12)³ = 2.441406

Present value of year 2 dividend = 2.45 / ( 1 + 0.12)² = 1.953125

Present value of year 1 dividend = 1.75 / ( 1 + 0.12) = 1.5625

Price of stock = 1.5625 + 1.953125 + 2.441406 + 3.051758 + 3.814697 + 4.768372 + 5.960464 + 7.450581 + 9.313226 + 11.641532 + 249.12879

Price of stock = $301.09