Question

Compute the stock price for a firm that expects to pay a $1.50 dividend in one year and will experience such rapid growth that it expects to increase the dividend by 80% for years 2, 3, and 4. During year 5, however, the dividend growth rate will return to its more normal level of 3.6%. Shareholders in this firm require a 12.9% return.

Answer 1

Year 1 dividend = 1.5

Year 2 dividend = 1.5 (1 + 80%) = 2.7

Year 3 dividend = 2.7 (1 + 80%) = 4.86

Year 4 dividend = 4.86 (1 + 80%) = 8.748

Year 5 dividend = 8.748 (1 + 3.6%) = 9.062928

Value at year 4 = D5 / required rate growth rate

Value at year 4 = 9.062928 / 0.129 - 0.036

Value at year 4 = 9.062928 / 0.093

Value at year 4 = 97.450839

Stock price = Present value of dividends and terminal value

Stock price = 1.5 / (1 + 0.129)¹ + 2.7 / (1 + 0.129)² + 4.86 / (1 + 0.129)³ + 8.748 / (1 + 0.129)⁴ + 97.450839 / (1 + 0.129)⁴

Stock price = $72.19