# Valuation

Anonymous

there is definitely a flaw in saying a company will never die (well, maybe not with BO in charge) and GGM and spin-offs used in DDM, DCF and related models.

would it be more appropriate creating a formula that incorporates the average life of a company of that size? such that moving from one cap to another would have an impact on valuation in that way? i think its impossible to use anything but relative valuation methods for smaller companies but relative valuations still need to reflect earnings valuations in the long-run. at what point will we have enough history to draw reasonable estimates of company life expectancies?

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basically i’m saying k, with little evidence, is a piece of crap at measuring bankruptcy risk. gonna look into it more, but could use a little discussion around the subject. how about different k’s for different time periods?

Remember that direct comparison of ratios like P/E assumes

1) The risks of the company are comparable.

2) The “shape” of the futures earning streams are identical.

If not, then there are “justifiable” differences in the PE ratio.

You want a quote? Haven’t I written enough already???

bchadwick Wrote:

——————————————————-

> Remember that direct comparison of ratios like P/E

> assumes

>

> 1) The risks of the company are comparable.

>

> 2) The “shape” of the futures earning streams are

> identical.

>

> If not, then there are “justifiable” differences

> in the PE ratio.

so holding the above true would also make it extremely difficult to measure average life expectancy and/or apply the correct life expectancy to each company.

what if we held k constant for all companies (small cap, large cap), calling it total equity risk and used average life expectancy as the differentiating factor between large and small cap. if k is a result of volatility, does it truly reflect the risk inherent in a small cap company in all circumstances accurately? as life expectancy and risk are generally constant for large caps, can you really use the same methodology of volatility (and the assumption of going concern) with small caps? does the current equity risk premium even take into factor the possibility of bankruptcy at this point.

i think using average life expectancy would reign in price inflation in large caps while maintaining steady values for small caps.

thanks for responding to my random thoughts bchad. i know they must be tough to picture on an online forum relative to a whiteboard.

*all of the above assumes you have an infinite time horizon (or the typical LT view) to match the infinite pricing (GGM).

There is strong empirical support for a small-cap premium (more support than the value premium, in fact).

Financial theorists have been trying to figure out where this premium might come from. One theory is that smallcap companies have risks that are not included in their covariance with the market, and hence deserve a special risk premium. This is plausible since smallcap companies may have fewer resources to rely on to stave off bankruptcy and thus might have a lower survival rate. But they also tend to be more adaptable because they tend not to have as much sunk capital and can rearrange their organizations more easily.

The other dominant explanation for the small-cap premium is that large institutional investors often have investment policies that prevent them from holding, more than X percent of a company. With smallcap companies, a huge pension fund like GM may find that it is stuck between owning so much of the company that it breaches these restrictions, particularly if it is using an active management approach. Or the transaction costs of rebalancing smallcaps don’t justify having them in a large portfolio. As a result, there is less demand for smallcap equity because institutional investors are locked out, and the risk premium goes up to compensate until you reach equilibrium.

There’s also interesting stuff on where the value premium comes from. Again, there is the idea that there must be a special risk to value companies that isn’t captured in their market covariance. My own sense is that the risks of high PE companies (that you’re misjudging the growth potential) is qualitatively different than the risks of low PE companies (that maybe prices are low because the company really is going into the toilet), and therefore a manager’s ability to distinguish one from another may be different (Aswath Damodaran reports that Growth tends to underperform Value, but Growth Managers outperform their benchmarks more than Value Managers do).

I read some stuff by Cliff Assness about Fundamental Indexing which suggested that a typical cap-weighted benchmark systematically overweights overvalued security (if they are overvalued, their prices are too high, and therefore the capweighted index has too much of them). If that’s true, the implication is that you would need to have a portfolio that has extra value securities in them to compensate, and that may be a simple structural reason that Value tends to outperform Growth. I like this explanation.

You want a quote? Haven’t I written enough already???

Thanks for the much more through and eloquent analysis BChad, always helpful :)

would it be possible to isolate liquidity risk so that

k (for small caps) = Rf + k (for large caps) + liquidity premium (for small caps)

then instead of using a risk premium to calculate bankruptcy risk, you use historical life expectantcy averages by company sector and size?

in this case, the liquidity premium would be reflected at all times. one could use probabilities of advancement from one cap to the next. in each probability branch where the company does not advance to the next cap, the average life expectancy for ‘non-advancers’ could be used to determine the expected value of that branch. expected time-to-cap advancement would be used to determine time frame, etc.

definitely a little more complicated than the GGM but at least valuation between large caps and small caps would be in-line and an attempt would be made in truly discounting future bankruptcy possibilities.

again, thanks for your thoughts. since JDV left, you’re the only one who seems to respond to my ramblings.

The assumption that relative valuation is less complex is a myth. So do a good comp analysis requires as much work as putting a DCF valuation together - but it lacks the transparency of being able to give you some insight into what’s driving a firms value, and what kind of assumptions are built into current prices. Not to mention the fact that RV models make the same assumption about perpetual earnings, so that doesn’t really solve anything in that regard either.

One approach some DCF models use is to created a “continuing value” forecast after the explicit 5 year forecast, and then the valuation stream can be modeled more realistically. Additionally, by tacking on another 15 years before adding the perpetuity value, the impact on the total firm valuation is a lot lower.

if I understand correctly, you don’t think the perpetuity assumption in GGM is reasonable?

infinity is an awfully long time, but when you do the math it doesn’t seem that bad.

if CFo is your current cash flow, g is growth in perpetuity and k is the discount rate, you’ll get a value of CFo*(1+g)/(k-g) by applying GGM.

if you instead assume the same parameters, but life of (N+1) years instead of infinite, you will get a value of CFo*(1+g)/(k-g)*[1-(1+g)^N/(1+k)^N]

in other words, by reducing the life to (N+1) years, your value is reduced by (1+g)^N/(1+k)^N percent. Does it really matter? Not for some reasonable k>=12%, g<=3%, and N>25.

Mobius Striptease Wrote:

——————————————————-

> if I understand correctly, you don’t think the

> perpetuity assumption in GGM is reasonable?

>

> infinity is an awfully long time, but when you do

> the math it doesn’t seem that bad.

> if CFo is your current cash flow, g is growth in

> perpetuity and k is the discount rate, you’ll get

> a value of CFo*(1+g)/(k-g) by applying GGM.

>

> if you instead assume the same parameters, but

> life of (N+1) years instead of infinite, you will

> get a value of

> CFo*(1+g)/(k-g)*[1-(1+g)^N/(1+k)^N]

>

> in other words, by reducing the life to (N+1)

> years, your value is reduced by (1+g)^N/(1+k)^N

> percent. Does it really matter? Not for some

> reasonable k>=12%, g<=3%, and N>25.

thats fine and dandy but think of it as an actual scenario where some who is say, 30-35 holds this stock until they are 50-60. so 15-30 year timeframe.

assuming that the stock will be sold for the DDM value at t=15 assuming an infinite time period at that time, the stock’s value has a much larger impact on the return of the trade. if you were to hold a stock with a dividend of 4% for 18 years, but at that time the stock’s future looks dismal and the stock is near zero, your rate of return is zero.

and to directly address the DCF, it is most only appropriate for non-dividend paying companies that have a cash flow, so basically large cap growth companies. a lot of growth companies will not reach LT growth phase until N>25 and for years 1 to 25, the g & k have a much smaller discreptancy. this means that the cash flow value expected in N=26 would be extremely high and thus yes, it would be material to valuation. again, you have to assume that you can sell it in 25 years for the total expected discounted cash flows as of N=25, if you can’t get that, you have likely made nothing on the investment.

I am not sure I follow this argument. If you were to hold a stock for 18 years, and the stock was paying 4% dividend annually, why would the stock’s future look dismal at the end of the period? if you are trying to calculate the cost of the “insurance protection” against the stock declining below a certain threshold value K in 18 years, why don’t you just value a put option with a strike K to find what that is.

Also regarding the DCF argument - what are these companies that grow for 25 years before they reach a significant cash flow in year 26? venture capital is a lot more impatient than this in my opinion

Mobius Striptease Wrote:

——————————————————-

> I am not sure I follow this argument. If you were

> to hold a stock for 18 years, and the stock was

> paying 4% dividend annually, why would the stock’s

> future look dismal at the end of the period? if

> you are trying to calculate the cost of the

> “insurance protection” against the stock declining

> below a certain threshold value K in 18 years, why

> don’t you just value a put option with a strike K

> to find what that is.

the stock’s future wouldn’t necessarily look dismal, but using an average life span over ‘into perpetuity’ would reduce the life expectancy from infinity to x number of years. if you were to calculate this at t=0, it would have a major impact on the price at t=0. if you are valuing the same company, ten years down the line, the value at t=0 would be similar to the value at t=10 b/c time has passed w/o the company going belly up. you’re basically discounting the ‘perpetuity’ argument to factor in accounting scandals and unforeseen bankfuptcies in the distant future.

> Also regarding the DCF argument - what are these

> companies that grow for 25 years before they reach

> a significant cash flow in year 26? venture

> capital is a lot more impatient than this in my

> opinion

sorry. i only used 25 b/c it was the number you used. more realistically, above average earnings growth for some companies is expected to be in excess of 10+ years. apple, rim, etc. the only point i was trying to make is that the gap between g and k can be thin for quite some time, making the 15th, 20th, and 25th year’s cash flows and share valuation significant to today’s valuation and return.

It would be interesting to see the empirical statistics on company survival rates. Not all companies disappear in bankruptcy. Some are bought, which may follow a period of decline or could be because a competitior wants control of a profitable challenger or technology or brand. Others go private, by choice or otherwise.

You want a quote? Haven’t I written enough already???