Intrinsic Value and the Equity Perpetuity Theory

This is Part 1 of a Series

Flat cash payments into infinity. To think of stocks as "equity" perpetuities can be a useful, conservative mindset to quickly assess a reasonable purchase price. Despite projecting perpetual annual cash payments, they're still assumed, nonetheless, flat!

Thanks to that contemplation on how relevant and useful the P/E Ratio and Earnings Yields are, I’ve been thinking about perpetuities often these days. And because of that, I’m starting to think of stocks as perpetuities. It’s reasonable, after all, if you intend to indefinitely hold on to an excellent business which would continuously and unendingly generate you bucks passively year after year after year (and beyond). And the great thing about perpetuities is that, they’re conservative! They’re conservative primarily because of their flat or fixed annual payments assumption. We do all know that a good company shall be able to expand or grow its cash profits year after year. So if we’re going to assume flat earnings, then that’s definitely being conservative, don’t you agree? To think of stocks as perpetuities shall be a conservative, appropriate mindset, for a prospecting, long-term rational investor conscious of a reasonable purchase price.

What are Perpetuities again?

Perpetuities are assets that give fixed annual payments to its holder forever. In contrast to bonds (which has a maturity date) it doesn’t have an expiration; consequently, it also doesn’t have a lump principal payout that is natural to bonds at maturity. Its value, therefore, shall, and is only derived from those fixed annual payments. It’s somewhat logical (yet kinda weird) if we view businesses this way: from a perpetuity point of view, a business is only worth all the annual earnings it’s gonna provide its shareholder (and that’s consciously not counting the present net assets of the company particularly its property, plant and equipment accounts). We consciously do not count the liquidation values of the company’s assets because of this reason: If the business shall be a going-concern and be a perpetuity (operate forever), then these assets are gonna be tied up to the unending business activity (theoretically, we won’t be receiving them—or their liquidation value—unlike having a lump principal payout as in bonds when they mature) and they shall therefore only be worth or as good as all the future earnings they’re gonna provide.

So how do we logically value a perpetuity which shall give us, say, Php100 every year if we want to earn 15% return from it? The answer lies on discounting all those Php100 annual payments projected to infinity and beyond. Creating an infinite tabulation of cash flows and discounting them sounds like an impossible task, right? But good thing the clever mathematicians already did this dirty job for us by coming up with a simple perpetuity formula. The worth of a perpetuity is the present values of all its infinite future cash flows discounted at a rate which would be subject to the investor’s requirement or preference. Mathematically, this is simply expressed as:

Fixed annual payments / Required rate of return = Perpetuity worth

Now doesn’t that look simple? Our above Php100 perpetuity example, therefore, should be worth:

Php100 (fixed annual payments) /15% (required rate of return) = Php666.67 (perpetuity worth)

That is to say, if we intend to earn 15% from a Php100-paying perpetuity, then we'd have to pay Php666.67.

Now comes the next question: When it comes to alive, operating business, which “fixed annual payments” should we discount...? Continue to Part 2: Rate of Return on Equity Perpetuity: Dividend Yield and Free Cash Flow Yield