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Title: Settling the Stock Buyback Controversy with Simple Mathematics

Unraveling a fundamental mathematical concept can shed light on numerous disputes related to stock buybacks.

Ray Davies, the brains behind The Kinks, is a music legend whose impact on the industry is...
Ray Davies, the brains behind The Kinks, is a music legend whose impact on the industry is unquestionable. As the group's primary songwriter, his uncensored creativity and unique perspective have shaped their iconic sound.

Title: Settling the Stock Buyback Controversy with Simple Mathematics

"Skimping is small, and not too steep,But best of all, skimping is cheap.Circumstances forced my hand,To be a frugal person in a thrifty land."

In my initial piece published in May 2023, titled "Using the Money of the Masters (The Shareholders) Against the Masters (Fellow Shareholders)", I touched upon a fundamental aspect of capitalism often overlooked - that "The masters of a company are its shareholders."

Analogically, there's a fundamental principle of corporate finance related to share repurchase programs or stock buybacks, which can be grasped even by individuals who had algebra lessons in the 8th or 9th grade. The similarity ends promptly as the topic of stock buybacks has sparked substantial debate, while the mathematical basis for this practice, evidently obvious, remains frustratingly misunderstood.

This principle is elegant and grounded in mathematics: "Every share bought back at a discount to the per-share intrinsic value of a company results in an increase in the per-share intrinsic value of the remaining shares."

Let's analyze a simple instance (Exhibit #1). Assume a debt-free company with an underlying business worth $900 million, $300 million in cash, and 30 million shares in circulation, valued at $40 per share. If this corporation uses its $300 million of cash to purchase 10 million shares of stock at $30 per share (a discount to its initial per-share intrinsic value), the remaining shares' intrinsic value skyrockets to $45, a 12.5% increase.

Exhibit #2 presents a matrix demonstrating this increase (or decrease) in per-share intrinsic value under various repurchase prices. When the company acquires shares at a discount to its initial intrinsic value, the remaining shares' worth increases. Conversely, when the company purchases shares at a premium, the remaining shares' worth decreases.

Warren Buffett, the legendary value investor and Chairman of Berkshire Hathaway, beautifully explained this principle during Berkshire Hathaway's Annual Meeting of Shareholders in 2019. He stated: "We will repurchase shares when they fall below a conservative estimate of their intrinsic value. We ensure that the remaining shareholders are worth more after repurchasing shares than before."

A company intending to implement a share repurchase program should adopt the mindset of the narrator in "Low Budget" and only consider purchasing shares when they're "on sale" or discounted, which means purchasing below intrinsic value. Repurchasing shares at a discount is value-creating, whereas purchasing shares at a premium is value-destructive. By understanding this simple principle, much strife could be avoided, and numerous shareholders' funds could be saved.

However, the question arises, "How do you determine intrinsic value?" Since companies do not have a dedicated line item for "Intrinsic Value" on their balance sheet, the answer is subjective. Well-established financial theory defines intrinsic value as the present value of the future stream of cash flows generated by a business, discounted to the present by its cost of capital, which represents the rate of return required for the risk associated with those future cash flows.

For entities whose underlying business is primarily the ownership of stocks in other companies and/or other assets like cash or real estate, intrinsic value is more straightforward; it becomes merely the sum of the market value of the stocks and other assets, reduced by any debt. To illustrate, the example presented in Exhibit 1 is a mix of these two types of entities, which is an atypical amalgam of both.

Activists aiming to enhance shareholder value often advocate for share repurchase programs, as they believe the stock is undervalued. Non-activist investment professionals, managers, and public influencers should also understand the basic math surrounding stock buybacks. Sadly, the debate surrounding share repurchases is often influenced by misinformation.

In response to misguided commentary regarding stock buybacks, Warren Buffett wrote to Berkshire Hathaway's shareholders in 2023: "Whenever you are told that all repurchases harm shareholders or the country, or are particularly beneficial to CEOs, you're listening to an economic illiterate or a persuasive demagogue. They are not mutually exclusive."

Hopefully, understanding the basic mathematics debunks the controversy surrounding stock buybacks.

In the context of shareholder activism, some advocates argue for companies to engage in share repurchase programs, as they believe that buying back shares at a discount is a value-creating strategy, increasing the intrinsic value of the remaining shares. This principle was succinctly explained by Warren Buffett, who stated that Berkshire Hathaway would repurchase shares when they fall below their intrinsic value, ensuring that remaining shareholders benefit from the transaction.

Additionally, Warren Buffett, in his response to misguided commentary on stock buybacks, emphasized that the idea that all share repurchases harm shareholders or the country is economically illiterate, and such statements often originate from individuals lacking a deep understanding of the mathematical basis for this practice.

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