Buying back shares will boost EPS and save Apple $1.5 billion a year in dividends.

Source: Posts at Eventide's Robert Paul Leitao. Clock to enlarge.

FORTUNE -- By the time it decided in April to increase its stock buyback program five fold -- from $10 billion to $60 billion -- Apple (AAPL) already spent $1.95 billion of the original $10 billion fund and had bought and retired nearly 4.1 million shares of Apple common stock. Average share price, according to the company's latest Form 10-Q: $478.20.

That leaves, by Robert Paul Leitao's calculations, $58 billion to be spent over the next 11 quarters.

Leitao, who writes the Posts at Eventide blog and oversees the Braeburn Group of independent analysts, used two assumptions to create the charts above: That the $58 billion would be spent in equal parts of approximately $5.272 billion each, and that Apple's share price would rise $25 each quarter from $475 per share this quarter to $725 per share in fiscal Q1 2016 (the last calendar quarter of 2015).

As a result of the exercise, Leitao made several interesting discoveries:

• The repurchase program represents a material boost to Apple's bottom line. For example, even if September's net income were to be flat, Apple would report nearly $.25 more in EPS (earnings per share) because there will be that many fewer shares in the denominator.
• By the end of the program, Apple will have repurchased just under 100 million shares, or approximately 10.55% of its current diluted share count.
• The company will save more than $2.230 billion in dividend payouts on the retired shares -- even if it  increases its dividends 10% each May. That works out to a savings of nearly $370 million each quarter, or nearly $1.5 billion per year moving forward.

"The dividends saved each year will go a long way to covering the interest costs on the funds borrowed to facilitate the share repurchases," Leitao nots, "while Apple continues to earn interest on the off-shore funds not repatriated and used for the share repurchases."

NOTE:  Included in the numbers is the expectation the 1,494,992 shares received on April 1, 2013 will be included in the June quarter reduction in the share count. Not included are any new shares used for stock-based compensation during the 11-quarter period.