Cap of Excess Earnings vs. DCF

The Cap of Excess Earnings is the lazy way to value a business,

but does that make it the wrong way?  I rarely use the method since I’m a believer that you should attempt to forecast the business you are appraising for at least a few years before you just assume that the business will grow at a constant rate into perpetuity.  Plus why be lazy?

Let’s start with why I decided to write about these two methods.  First, I’m a nerd, I’ll admit it.  This means that my nightmares are very detailed and force me to jump out of bed and do math.  Yeah, strange right?  No, I’m not chased by clowns or “bad guys” as my 3 year old would call them.

Rather, I’m harassed by attorneys in my nightmares.  Last night in my dream an attorney asked me questions about things that I take for granted.  My answer of, “that’s finance 101, everyone knows that the cap of excess earnings method yields the same results as the DCF method when growth is held constant”,  just doesn’t fly.  Attorneys are smart people, but they know how to play dumb when they want to trip you up or get you frustrated.  So in my nightmare, I start to explain it to him and the jury.  I shrug to the judge “do I really need to explain something that everyone knows?  Just look it up on google, crack open any how to value a business book, or open up your Finance text book.”

The Judge looks at me and says, “we don’t have any of those here today” so he points to the white board.  I walk over there and I’m start to describe the Gordon growth method, which is used in the cap of excess earnings method.  I draw up the formula

Value=Cash Flow1/(Discount Rate-growth) or V=CF1/(Dr-G)

The DCF method is more complex you need to Sum up a stream of Cash Flows

So your value= Cashflow1/Discount Rate + CF2/(Dr)(Dr)+CF3/(Dr)(Dr)Dr)+ etc.

Then I go through an example, and I try to make it easy since there is no way I have lost my audience with these boring formulas.  So, I assume the following:

CF0=100

Discount rate = .1

Growth =1%

I then wake up and run to my computer, no pit stop for the restroom.  Didn’t stop at the fridge for some water, right to Excel.  I couldn’t do the math in my head during my nightmare, but I know that I have proven it before.  Had I forgotten how to do the math?  Could I answer my own nightmare question?

I know that the cap of excess earnings = DCF when growth is held constant, but could I prove it to the judge and jury in real life?

So as I cracked open excel I took on the cap of excess earnings method first.  I used my givens from my nightmare.

If CF0=100 and growth is 1% that means that CF1=101.  So that’s my first input.

Value=101/

Next the Dr is plugged in and the growth is subtracted.

Value=101/(.1-.01) or Value = $1,122.22222

Easy right?  Well I couldn’t do it in my head so that’s what drug me out of bed.  Can you visualize why an appraiser is likely to default to this method?  Think, all I need to come up with a value for your business is: an estimate of cash flow for next year, a discount rate (which is an art to take all of the information available and apply it to your subject company) and an assumed rate of growth.  For argument’s sake let’s just assume the discount rate is given to the appraiser.

Now let’s look at the DCF method given the same assumptions.

Value= Sum(Cashflow1/Discount Rate + CF2/(Dr)(Dr)+CF3/(Dr)(Dr)Dr)+ etc)

Value = Sum(101/1.1+102.01/1.21+103.03/1.331 + CF4……CF200/(Dr)^200)  I took this out to 200 periods rather than to infinity.  Since, we get 99.98% of the expected answer after 100 time periods and 99.999996% of the way to the Gordon growth method after 200 periods.

It took me about 5 minutes to write the formula in Excel to get me to $1,122.00 after 100 time periods.  Then I got $1,122.22218 after 200 time periods.

Did you notice that as we approach infinity we get the same value as we calculated in the Cap of Excess Earnings method?  We are 99% of the way to the correct answer after 54 time periods, but Ross this is taking way too long!  There has to be a short cut…

Welcome to the multistage DCF method.

What we do now is we assume that at some point the business we are appraising will achieve a steady rate of growth.  Here we can assume that at any point on the CF stream we could substitute the Gordon growth formula for our CFx through CFx to CF200.

Let me introduce you to the magic of mathematics.  Were I to sum my results from CF1-CF20 and then for CF21+ substitute in the Gordon growth method.  I would then calculate $1,122.22.  Go ahead I’ll wait for you to calculate it.  Did you get $918.68 for the CF1-CF20?  Did you then add in your Gordon Growth result of $203.54?  Well, you made it to $1,122.22 didn’t you!

Let’s try that with a different time period lets cut it off after CF5.  After 5 years you are only 35% of the way to proving the math.  You don’t really want to do the math another 95 times to get 99.98% of the correct answer do you?  So after 5 years you have $389.87 and you add that to your Gordon growth of $732.35, you get $1,122.22 again right?  Imagine taking it after say CF2, what do you get, $1,122.22.  So if we cut it off at CF1 we get $1,122.22.  Therefore, we have proven that if you have the same growth rate into perpetuity the DCF method will yield the same results as the cap of excess earnings method.

Did I win my case?  Does the jury applaud?  Do I get to go back to sleep?  Will I be haunted by more lawyers in my dreams?

So why do I use the DCF Method in 99% of my Appraisals?

As you can see by the math, taking the capitalization of excess earnings is the easy way out.  Am I trying to impress my clients by doing more work?  No, although I have to admit my reports are a lot thicker than they would be were I to use the cap of excess earnings method.

I just don’t believe that all businesses have hit their steady state growth rate.  I mainly deal with doctors who are in the transition process.  This generally means, that an older doctor is on the way out and a new one is on the way in.  Is it reasonable, to assume that there won’t be any disruptions in the practice?  In my opinion, no.  If they overlap will there be a temporary boost in revenue and with that an increase in expenses.  My bet is yes.  Will the new doctor be as productive as the old one?  Well, there is the art part in forecasting.

Nobody has a crystal ball, so an appraiser needs to either rely on assumptions/forecasts/or budgets provided by the client, or make their own judgements.  Many people will argue that they aren’t experts so they can’t be relied upon to forecast the cash flow of the business that they are appraising.  Typically, when confronted with that response, I ask myself: do my clients have more financial training and expertise than I?  If, the answer is yes, I ask them for guidance and their upcoming forecast or budget.

However, the majority of the time my clients aren’t going to be experts on the field of finance.  So, I feel duty bound to show them how I believe their practice will preform given the history of the practice and my experience with similar practices or situations.  Given my attempts, my crystal ball has NEVER been exact it couldn’t possibly be, or else I would be a world famous sports gambler, who has been banned by all Casinos.  I do smile a bit when my previous clients come back to me years later and say the projections I made were pretty close to where they are this year.  Of course, I pull out the frowny face when I find out that I have over projected revenue due to something like a lost associate doctor or a hygienist who left the practice.  Generally, those things are out of my control and just don’t get thrown into my crystal ball.

Although I admire the cap of excess earnings for its simplicity and mathematical beauty.  I just don’t feel like it serves the best interest of my clients to take the short cut and assume that things will continue on forever exactly as they are today.

About the Author

Ross Landreth is an appraiser and owner of Medical Valuations Inc.  His firm appraises medical and dental practices throughout the US.  He is an Accredited Senior Appraiser with the American Society of Appraisers.  Ross holds a BS degree from the University of California at Berkeley and a MBA from California State University East Bay.  Although he has nightmares about lawyers he gladly accepts cases to provide expert witness testimony for divorces, injury claims and partnership dissolutions.

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