Question

Kellogg Co. (K) recently earned a profit of $2.82 earnings per share and has a P/E ratio of 19.65. The dividend has been growing at a 6 percent rate over the past few years.

If this growth rate continues, what would be the stock price in five years if the P/E ratio remained unchanged? What would the price be if the P/E ratio declined to 14 in five years?

Answer 1

We know that

P/E ratio = Price of a Share / Earnings per Share

Where P/E ratio = 19.65

Recent earnings = $2.82 per share

Therefore Expected price of share = P0

Therefore

19.65 = P0 / $2.82

Or P0 = 19.65* $2.82 = $55.413

If earnings growth rate is 6% per year on the stock

Expected earnings per share after 5 year = Recent earnings * (1+ growth rate) ^years

= $2.82 * (1+6%) ^5 = $3.77 per share

Therefore the stock price in five years if the P/E ratio remained unchanged

P5 = 19.65 *$3.77 = $74.16 per share

The price be if the P/E ratio declined to 14 in five years

P5 = 14 *$3.77 = $52.83 per share