In my book, Money Machine: The Surprisingly Simple Power of Value Investing, I analyzed Apple stock using the most recently available data (August 2016) and concluded that “the S&P 500 was an attractive investment and that Apple was even more so.” At the time, the S&P500 was around 2180 and Apple was $25/share (all prices are adjusted for Apple’s 4-for-1 split on August 28, 2020).

A year later, on November 6, 2017, with Apple around $40, I concluded that, even though Apple’s growth had slowed, “Apple is now a money machine that, with reasonable, conservative assumptions, should be far more rewarding that Treasury bonds over the long-run.” On July 2, 2018 with Apple getting close to $50, I renewed my faith: “Apple looks to be a stock you can buy and hold, and be happy you did.”

Now, in January 2023, Apple is around $150, far higher than its value 5, 6, or 7 years ago, but down 18% from a high price of $182 on January 3, 2022. Even down 18%, Yahoo Finance says that Apple is overvalued at $150.

Let’s look at some numbers from the perspective of a value investor. The intrinsic value of a stock is what an investor who has no intention of ever selling would pay to receive all the cash generated by the stock—including both dividends and share repurchases. The simplest way to see this is to imagine that a single person owns all of Apple stock and receives all the cash that Apple pays out in dividends and share repurchases. The intrinsic value of all the company’s stock is clearly the value of all the dividends and share repurchases. It follows that the value of a single share is equal to the total value divided by the number of shares outstanding.

This logic is important for analyzing Apple because it has been giving far more cash to shareholders though repurchases than through dividends—which is a wise move because stock buybacks are better than dividends from a tax perspective. In the fiscal year ending on September 30, 2022, Apple distributed a total of $14.8 billion in dividends and $89.4 billion in repurchases ($0.91/share versus $6.38/share).

The Gordon model that was derived by John Burr Williams, the father of value investing, says that when a company’s dividends plus share repurchases *D* is growing at a constant rate *g*, and investors require a rate of return *R*, the intrinsic value *V* is given by this well-known equation

I will work with real, inflation-adjusted values for these various parameters.

Over the past 10 years, Apple’s inflation-adjusted sum of dividends plus repurchases has grown at an annual rate of 17% a year. That is clearly not sustainable, so I will calculate an extremely conservative valuation using a long-run 2% average real growth rate. This is somewhat lower than the 3% average annual growth rate of U.S. real GDP since 1950 and roughly equal to current long-run projections for the U.S. economy. Apple is not an average company, but I want to be conservative and the long run is, well, the long run.

The current real yield on 30-year Treasury Inflation Protected Securities (TIPS) is 1.47%. I will use a 5.5% real required rate of return, a 4% risk premium. (You should use your own personal inflation-adjusted required rate of return). With these assumptions, Apple’s intrinsic value is $182.29 per share:

There is uncertainty, of course, about this valuation. It is standard practice to measure a stock’s riskiness by either the standard deviation of its price fluctuations or by its beta coefficient, which relates a stock’s price fluctuations to the overall market’s price fluctuations. These measures are of little concern for value investors, who don’t try to predict future prices and care little about day-to-day price fluctuations. Remember Warren Buffett’s famous aphorisms:

*My favorite holding period is forever.*

*I buy on the assumption that they could close the market the next day and not reopen it for five years.*

If anything, short-run price fluctuations are a boon because they offer opportunities to buy when prices are low and sell when prices are high.

For value investors, the real uncertainty is about the future income from an investment—here, the long-run growth of Apple’s dividends plus share repurchases. (The required return in this model depends on *current* interest rates and there is no uncertainty about these.) We can model our uncertainty about Apple’s long-run growth by specifying a probability distribution for the growth rate and using this to determine a probability distribution for the intrinsic value—in most cases, using Monte Carlo simulations. For example, working with real, inflation-adjusted data, an investor might summarize his or her uncertainty about Apple’s growth rate with a normal distribution with a mean of 2% and a standard deviation of 0.5%. This assumption implies that the investor believes with 95% certainty that Apple’s long-run inflation-adjusted growth rate is between 1% and 3%. With these assumptions, there is only an 8% chance that the current intrinsic value of Apple is less than $150.

Remember that these calculations assume that Apple’s long-run real growth rate is only 2%, the same as the projected growth rate for the overall U.S. economy, beginning immediately. If it takes 5, 10, or 20 years for Apple’s long-run growth rate to slow to 2%, the case for buying Apple stock now is even more compelling.