The calculation is simple. If Intel is actually making any money, then the shareholder's equity per share this quarter plus the dividend paid would exceed the shareholder's equity per share from last quarter. That's what shareholder's equity is meant to show.
Unfortunately, Intel reports several different numbers for shares outstanding, so in the interest of completeness, I'll work out the numbers for all of them. The numbers are common shares outstanding and common shares outstanding assuming dilution. But then, they report two numbers for each, labelled "three months ended" and "six months ended". I don't know what calculation they're using, as to me it would seem self-evident that the number of shares outstanding at the end of a 3 month period ending on a certain date is the same as the number outstanding at the end of a 6 month period ending on the same date. Perhaps someone can offer an explanation. Be that as it may, the figures are available from:
And the calculation is shareholder's equity / number of shares from October + dividend received (8 cents) less shareholder's equity / number of shares from July. If we are to believe that Intel earned 32 cents a share, that value should be somewhere around 32 cents.
Here are the numbers, with each matching share total on a separate line, pick the one you like:
Common shares outstanding as reported for 3 month period: 36676 / 6062 + 0.08 - 37614 / 6144 = 0.00807815335
Common shares outstanding as reported for 6 (or 9) month period: 36676 / 6139 + 0.08 - 37614 / 6177 = -0.0351008596
Diluted shares outstanding as reported for 3 month period: 36676 / 6144 + 0.08 - 37614 / 6215 = -0.00273089719