Prime Numbers: Share repurchases <em>still </em>don’t prop up value (2024)
As executives consider the pros and cons of issuing share repurchases, they are asking themselves (and their finance teams) some good questions about the value of doing so.
Don’t repurchases artificially prop up a company’s value?Share repurchases and dividendsboth decrease the market value of a fairly traded company by the same amount (since cash is being paid out). Dividends lower the price per share (since the share count stays the same), while share repurchases lower the share count and don’t affect the price per share. Repurchases do boost earnings per share (EPS), helping managers hit their EPS-based compensation targets, but the associated share price generally stays the same. In addition, finance professionals tend to use TSR rather than EPS in their market performance analyses and incentive systems, which helps them adjust for the short-term effects of share repurchases and dividends.
Is the net-neutral effect on returns consistent? In 2011, McKinsey analysis showed that US companies returned, on average, 60 percent of their net income in dividends and share repurchases to shareholders between 1965 and 2008. There was no clear impact on returns or multiples. We recently repeated this analysis, and the findings hold true. The total payout by US companies to shareholders between 1995 and 2021, on average, is up to 78 percent, with slightly more repurchases than dividends. But neither the payout size nor the mix automatically affects EBITA multiple (Exhibit 1) or TSR (Exhibit 2) for nonfinancial companies in the S&P 500.
If there is no net benefit to shareholders, why do companies give any money back, regardless of the mechanism? Because good companies have more cash than they can invest. Think about a company with $1 billion a year in after-tax profits projected to grow at 5 percent a year with a 25 percent return on capital. It could have $800 million of excess cash (after R&D and capital expenditures) that could be invested or returned to shareholders. But how easy would it be to find new value-creating investments for 80 percent of the company’s net income each year? The short answer: it would be very tough, regardless of industry—especially since a lot of high-performing companies already deploy billions of dollars in R&D and capital expenditures.
Overall, companies may be better off by returning cash to shareholders rather than investing in businesses and assets that they have no competence to run or grow (which would be value destroying). In most cases, shareholders will not sit on the cash; they will redeploy it to other, better value-creating opportunities.
Aya Benlakhder is a capabilities and insights analyst in McKinsey’s Lisbon office; Vartika Gupta is a solution manager in the New York office, where David Kohn is an associate partner; Tim Koller is a partner in the Denver office; and Werner Rehm is a partner in the New Jersey office.
For a full discussion of market dynamics, see Valuation: Measuring and Managing the Value of Companies, seventh edition (John Wiley & Sons, 2020), by Marc Goedhart, Tim Koller, and David Wessels.
Step 1: Find the factors of the given number and list them. Step 2: Check the total number of factors of that number. Step 3: If the number has just two factors- one and the number itself, then the given number is a prime number. However, if it has more than two factors, then it is a composite number.
One of the reasons primes are important in number theory is that they are, in a certain sense, the building blocks of the natural numbers. The fundamental theorem of arithmetic (the name of which indicates its basic importance) states that any number can be factored into a unique list of primes.
Two consecutive numbers which are natural numbers and prime numbers are 2 and 3. Apart from 2 and 3, every prime number can be written in the form of 6n + 1 or 6n – 1, where n is a natural number. Note: These both are the general formula to find the prime numbers.
The oldest unsolved problem in mathematics is to determine if any odd perfect numbers exist. The only even perfect numbers known to the ancient Greeks were 6, 28, 496, and 8,128. Euclid discovered a pattern that generates even perfect numbers: (2^{p-1} \times (2^p - 1)), where (p) is a prime number.
(ii) if none of the prime numbers are odd, then both the prime numbers would be odd and hence sum of the prime numbers would be even as sum of two odd numbers is always even. No, because 2 is a prime number, i.e., divisible by only 1 or itself. Adding 2 to 3, 5, 7, etc, results in an odd number.
Until now, there is no known efficient formula for primes, nor a recognizable pattern or sequence the primes follow. All recent publications dealing with this issue established that primes are distributed at random and looked more to a white noise distribution [7] .
There are actually several prizes related to finding large prime numbers . The Great Internet Mersenne Prime Search gives $3,000 to anyone who discovers a Mersenne prime with fewer than 100 million digits while using their software. The EFF offers a $150,000 prize for a prime with more than 100 million digits.
The first few unique primes are 3, 11, 37, 101, 9091, 9901, 333667, ... (OEIS A040017), which have periods 1, 2, 3, 4, 10, 12, 9, 14, 24, ... (OEIS A051627), respectively.
What is a prime number in math? A prime number is a number that can only be divided by itself and 1 without remainders. What are the prime numbers from 1 to 100? The prime numbers from 1 to 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
The largest known prime number is 282,589,933 − 1, a number which has 24,862,048 digits when written in base 10. It was found via a computer volunteered by Patrick Laroche of the Great Internet Mersenne Prime Search (GIMPS) in 2018.
An even number by definition has no remainder when divided by two. So adding it to another even number will still generate no remainder. Hence an even result.
Because 2 is the only even prime, all other primes must have at least one number in between them (since every two odd numbers are separated by an even). Multiplying two primes will always produce an odd number: This is also only true of odd primes. 2 * odd prime = even.
Introduction: My name is The Hon. Margery Christiansen, I am a bright, adorable, precious, inexpensive, gorgeous, comfortable, happy person who loves writing and wants to share my knowledge and understanding with you.
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