DDM: There is no discounting!

Manage
1

So the DDM (dividend discount model) is pretty cool—not that I fully understand it. And not that I wouldn’t like to (need to) take some courses on this.

Still, I was reading an article by Lyn Alden: Interest Rate Effects on Equities: Valuation Impacts

It occurred to me that mathematically there is no discounting when interest rates are zero (and are expected to stay zero). While I do not have a degree in finance, I think this is absolutely true given the math.

Below is an image from a link in the link I provided. The discounting—as in dividend dicount model (DDM)–all comes from the denominator.

If interest rates (r) are zero (for a long time) then the denominator is 1(one) for a long time. There is no discounting unless you think interest rates will be going up sometime.

To asses the value of a company we have to consider cash flows 20 or 30 years from now. But the cash flows are not discounted at all with zero interest rates. There is no discounting, mathematically speaking, if one expects interest rates to remain this low.

Sure your value stock is making money now but so what? If there is a growth company that may surpass this company 30 years from now then the DDM says you should buy the growth company based on those revenues 30 years from now, doesn’t it?

Lyn Alden looks out 25 years in the article but she implies that some of this is to simplify the discussion (and poor ability to predict that far out). So 25 years for sure and maybe more. BTW, I have read serious discussion that Warren Buffett does well because he tends to buy old companies that have been around for a while, and because of this fact alone, can be expected to be around a while in the future and have (discounted) cash flows for a very long time (the Lindy effect).

So, I guess this is probably one reason why growth has done particularly well recently. Or better than value I would say.

Looks like Marc may have had it right all along. Or at least I think he offers an explanation as to what has happened in the market.

The caveat to the idea that there is no discounting is that interest rates could go up in the future. I deleted all of my speculation about what will happen to interest rates going forward. I think I will just paraphrase an educated opinion on this (as I understand it). I think Marc does not think interest rates can stay low forever. There is, I think, some signs of life in value recently. So he may be right (I kind of hope he is) Anyway, I think I will let Marc and other pros speculate about the future and its interest rates.

I get that this is obvious for many. But I had never really thought that for some—those that expect interest rates to remain low or even go negative—there is no discounting whatsoever in their analysis. And they have had an impact on the market, I think.

Jim

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What about the equity risk premium? You don’t discount future cash flows based on interest rates, but on the risk-free rate plus the equity risk premium. And the proper interest rate to use is the 10-year or 30-year treasury note. Those rates are not 0, and are not expected to be.

3

Can you be more specific about how you come to this Yuval? I am not aware of a standard to calculate ERP.
Per P123 Fed Model, it seems ERP is 3.41% (using forward current year aggregate P/E estimate I guess). Using current month P/E estimate (time-weighting latest quarter real number and next quarter estimate), I come to about half that.

4

Yuval,

You are right about them using the ten year which is not zero now.

But I do not think the equity risk premium is in the DDM equation itself and would not be called discounting.

Either way: point taken. There is some discounting.

The equity risk premium is used somewhere in all of this to be sure. There has to be a reward for the risk or no one would take the risk. Lyn Alden gives a nice example in the link above.

And I wonder if a pro might look at real (inflation adjusted) interest rates at some point too—before his final decision on what to buy. TIPS or levered TIPS are being purchased by some funds.

At the end of the day interest rates (and speculation about inflation and the direction of the economy) are different than during the dot.com bubble. I wonder if being in growth companies will prove to be more rational (or not).

Jim

5

No matter where the ERP belongs in one’s equations on what to buy it is important, I think

I do not have an opinion on this (or what assets belong in a portfolio). Uh…well not Silver I guess;-) But FWIW this article puts the ERP at 3%.

Jim

6

There are so many ways to calculate the ERP that it’s ridiculous.

Here’s what makes sense to me.

Method 1.

ERP = D*(1 + G) / P + G – Rf, where D is levered free cash flow (unlevered free cash flow minus interest expense plus debt increase), G is the terminal growth rate (the average of the projected inflation rate and long-term GDP growth), P is the market value of equity, and Rf is the risk-free rate (ten-year treasury bonds).

Why?

Because P = D * (1 + G) / (R - G) and R = Rf + ERP. So P = D * (1 + G) / (Rf + ERP - G). Isolate ERP and you get my equation.

Currently the sum of the market’s levered free cash flow is $5.24 trillion; inflation expectation is 2.5%; long-term GDP growth is estimated at 2%; the market value of all equity is $61.451 trillion; and the risk-free rate is 1.15%.

ERP is then 5.24 * 1.0225 / 61.451 + 0.0225 - 0.0115 = 9.8%.

Method 2.

Over the last twenty years, shareholder yield has averaged 3.58% (using a cap-weighted average). Annual sales growth has averaged 5.84% (also using a cap-weighted average). The 10-year T-bill has averaged 3.37%. Again, we’ll go back to P = D / (R - G). D / P = shareholder yield; G = sales growth; R = T-bill plus ERP. D / P = R - G, so ERP = G + D / P - T-bill = 6.05%. If we assume that the next twenty years are going to look like the last twenty, then 6% seems a reasonable guess for the ERP.

7

Yuval,

Some of this is a little ridiculous, IMHO. In medicine anyway, if there is more than one way of doing something it is because none of them are particularly good methods. Otherwise, everyone would be using what always works.

Anyway, ridiculous or not thank you for helping me understand this better… I was oversimplifying the formula quite a bit and learned a few things.

Seems like there are quite a few things that go into the “required rate of return”. Not just the risk-free interest rates as I was implying. I imagine a lot of factors can be rolled-up into the equity risk premium.

That is how it is done and I am not debating that. I have learned something.

So maybe this is a little better:

Both Marc and Lyn Alden present simple and effective formulas for understanding how changes in factors including interest rates (which are pretty low now) can affect the net present value of cash flows 10, 20 or even 30 years from now. But as you point out interest rates are not the only consideration and are not zero. And even if one focuses on just interest rates, they can change. And actually, it is probably what people expect interest rates and other factors to do in the future that affects equity prices now. As difficult as this can be to pin down, maybe this helps explain what has happened in the past to value stocks.

Much appreciated.

Jim