) Andrew plans to retire in 32 years. He plans to invest part of his retirement funds in stocks, so he seeks out information on past returns. He learns that over the entire 20th century, the real (that is, adjusted for inflation) annual returns on U.S. common stocks had mean 8.7% and standard deviation 20.2%. The distribution of annual returns on common stocks is roughly symmetric, so the mean return over even a moderate number of years is close to Normal. (a) What is the probability (assuming that the past pattern of variation continues) that the mean annual return on common stocks over the next 32 years will exceed 12%? (b) What is the probability that the mean return will be less than 8%?

Deere & Company (DE)

1. Calculation of Ratios:

a) Return on total assets = Net income divided by the average total assets, multiplied by 100.

Year 3  = $1,523.9/$57,965 x 100 = 2.6%

Year 2  = $1,940.0/$ 59,642 x 100 = 3.3%

Year 1 =  $3,161.7 /$ 60,429  x 100 = 5.2%

b) Return on stockholders' equity: Earnings after taxes/Stockholders' equity x 100.

Year 3  = $1,523.9/$ 6,644  x 100 = 22.9%

Year 2  = $1,940.0/$7,912 x 100 = 24.5%

Year 1 =  $3,161.7 /$ 9,667  x 100 = 32.7%

c) Earnings per share: Net Income/No. of outstanding shares.

Year 3  = $1,523.9/315 = $4.84

Year 2  = $1,940.0/334 = $5.81

Year 1 =  $3,161.7 /363 = $8.71

d) Dividend yield:  This is equal to the annual dividend per share divided by stock price per share, and multiplied by 100.

Year 3  = $2.40/$92.03 x 100 = 2.61%

Year 2  = $2.40/$81.10 x 100 = 2.96%

Year 1 = $2.22/$85.58 x 100 = 2.59%

e) Price-earnings ratio:  This is equal to market price per share divided by the earnings per share.

Year 3  = $92.03/$4.84 = 19.0 times

Year 2  = $81.10/$5.81 = 13.9 times

Year 1 = $85.58/$8.71 = 9.8 times

Explanation:

a) Data

                                                Year 3          Year 2         Year 1

                                               ('millions)     ('millions)     ('millions)

Net income (loss)                   $1,523.9       $1,940.0     $3,161.7

Preferred dividends                    $ 0.00          $ 0.00       $ 0.00

Interest expense                      $763.7        $ 680.0     $ 664.0

Shares outstanding                    315              334            363

for computing earnings per share

Cash dividend per share          $ 2.40      $ 2.40        $ 2.22

Average total assets             $57,965    $ 59,642     $ 60,429

Average stockholders' equity  $ 6,644     $7,912       $ 9,667

Average stock price per share  $ 92.03   $ 81.10      $ 85.58

b) Return on total assets = Net income divided by the average total assets, multiplied by 100.  It shows how well a company generates net income from assets.

Year 3  = $1,523.9/$57,965 x 100 = 2.63%

Year 2  = $1,940.0/$ 59,642 x 100 = 3.25%

Year 1 =  $3,161.7 /$ 60,429  x 100 = 5.23%

c) Return on stockholders' equity: Earnings after taxes/Stockholders' equity x 100.  It demonstrates how much of the earnings after taxes are available to stockholders.

Year 3  = $1,523.9/$ 6,644  x 100 = 22.94%

Year 2  = $1,940.0/$7,912 x 100 = 24.52%

Year 1 =  $3,161.7 /$ 9,667  x 100 = 32.71%

d) Earnings per share: Net Income/No. of outstanding shares.  It shows in dollar terms how much of the earnings made by a company is available to stockholders on the average of each share.

Year 3  = $1,523.9/315 = $4.84

Year 2  = $1,940.0/334 = $5.81

Year 1 =  $3,161.7 /363 = $8.71

e) Dividend yield:  This is equal to the annual dividend per share divided by stock price per share, and multiplied by 100.  It shows how a company pays dividend each year in relation to its share price.

Year 3  = $2.40/$92.03 x 100 = 2.61%

Year 2  = $2.40/$81.10 x 100 = 2.96%

Year 1 = $2.22/$85.58 x 100 = 2.59%

f) Price-earnings ratio:  This is equal to market price per share divided by the earnings per share.  It shows if a company is overvalued or undervalued.

Year 3  = $92.03/$4.84 = 19.0 times

Year 2  = $81.10/$5.81 = 13.9 times

Year 1 = $85.58/$8.71 = 9.8 times

g) Ratios are used to present a picturesque view of a company's financial performance and position to make easily understood and compared with other companies in the industry and over the years (trend analysis).  They are important financial management and investment tools, which should, however, not be taken in isolation.