Warren Buffett’s Berkshire Hathaway, which has one of the highest share prices in the world — Buffett doesn’t believe in stock splits — announced today its first buyback plan in at least four decades.

Companies buy back their own shares when they believe they are especially cheap, and Berkshire Hathaway is going for fire-sale prices these days. The shares closed Friday at $100,320 each, down 17 percent this year. They jumped $5,700 today on the news of the buyback, even though the Omaha, Neb.-based company didn’t say how many shares it would repurchase.

In a statement, the company simply said: ”The underlying businesses of Berkshire are worth considerably more than this amount. If we are correct in our opinion, repurchases will enhance the per-share intrinsic value of Berkshire shares.”

Berkshire owns diverse businesses including insurance, retail, railroads, furnishings, newspapers and electric and gas utilities.  The firm has a pile of cash: $47.9 billion as of June 30.

But shareholders don’t get to see any of that cash. Over the years, Berkshire hasn’t paid a dividend; instead it plows the money back into the company and uses the earnings from it to boost profits.

One big cloud over the business is Buffett himself, who, at age 81, won’t stay as CEO forever.  Earlier this month, he said 50-year-old hedge fund manager Ted Weschler will join Berkshire from his current employer, Peninsula Capital Advisors.  Weschler is not a bold-face name on Wall Street and it’s anybody’s guess whether the master’s legendary investment ability can be continued.

Buffett has been in the spotlight lately for his stand on taxes. He doesn’t pay enough, he says.  He called on Congress to commit to “shared sacrifice” and raise taxes on people earning more than $1 million. Buffett said the rich are “coddled” by Congress “as if we were spotted owls or some other endangered species.”

President Obama wants to oblige, putting a “Buffett Rule” in his jobs plan, which requires that millionaires pay at least the same tax rate as the middle class.