Jul 27th 2009

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Here is a discussion of a very simple business valuation formula I believe is frequently misused. The formula converts a discount rate (used in the discounted earnings valuation method) into a capitalization rate (used in the capitalization of earnings valuation method) when company earnings are expected to grow at a stable rate. The formula is:

Capitalization Rate = Discount Rate - Growth

My assertion is the above formula is often inappropriately applied. I welcome your comments, challenges, or whatever you might want to add.

Establishing a capitalization rate by adjusting a discount rate for growth is a fundamental business valuation principle. As an illustration, let’s take a hypothetical where $100,000 is earned annually, in perpetuity, and when discounted by 25% per year, is equal to $400,000. The value can be alternatively computed by dividing $100,000 by 25%. Discounting values represents the discounted earnings valuation method, and the division formula represents the capitalization of earnings (or capitalization of cash flows) valuation method. The two methods should, and do, yield identical results.

If we add to the example that earnings for a company in question might be expected to grow by 4% per year, then $100,000 increased by 4% per year, discounted by 25% per year equals $476,190. This can be alternatively computed by dividing $100,000 by the “discount rate” minus “growth” ($100,000 divided by 21% (25% - 4%)).

Unfortunately, in many situations, and for many valuations, this is so fundamental that no further thought or discussion is seen as necessary.

So let’s introduce some additional facts that more closely reflect the complexities of the real world.

Presume earnings so far represent net cash flow to equity (NCF), but we are performing our valuation based on earnings before income taxes (EBT), because we believe EBT is more appropriate for our subject valuation. Based on a presumption that EBT to NCF will be 1.30, initial EBT should be $130,000 ($100,000 times 1.3). If our EBT to NCF ratio will remain at 1.30, then EBT should grow at the same rate as NCF (4%). To determine our EBT discount rate, we use another common business valuation technique. We multiply the NCF discount rate (25%) by 1.30. This gives us a 32.5% EBT discount rate.

So let’s test our work. Using EBT as the alternative earnings value, $130,000 per year in perpetuity, discounted at 32.5% per year equals $130,000 divided by 32.5%, or $400,000. As should be the case, virtually by definition, using NCF or EBT results in an identical valuation.

So here comes the issue (and the confusion). Let’s include 4% growth. Previously, we discussed NCF growth; so let’s now introduce EBT growth. If we deduct 4% from the 32.5% EBT discount rate we get 28.5%. $130,000 increased by 4% per year, discounted by 28.5% per year results in a value of $456,140 ($130,000 divided by 28.5%). Unfortunately, this is $20,050 less than our NCF valuation of $476,190. This means we need to modify our formula or values, or accept that using EBT instead of NCF for valuation purposes creates a markedly lower valuation?

From my perspective it seems clear we need to modify our EBT growth rate. We need to multiply 4% by 1.30 to more accurately convert NCF growth to EBT growth

__consistent with the way the EBT discount rate was established based on the NCF discount rate__. Deducting 5.2% (4% times 1.3) from 32.5% gives us 27.3%, and $130,000 divided by 27.3% gives us $476,190. This balances with our NCF valuation.Unfortunately, not multiplying the NCF growth rate by the EBT to NCF ratio is common, and most valuators deduct 4% from the EBT discount rate in establishing the EBT capitalization rate. I am suggesting this approach be revisited.

Are you persuaded by the merits of my position? If so, I am pleased we have a shared opinion. If not, please share with us why you believe no such adjustment should be made. Regardless of one’s opinion in this matter, none of us can escape the likelihood of being challenged at some point on the valuation processes we subscribe to. Given the importance of the issue here, I believe the debate might be long and vigorous.

Author’s Note: You can obtain a similar result by converting the NCF discount rate (25%), into a NCF capitalization rate (21%), and multiplying the NCF capitalization rate by 1.30 in arriving at an EBT capitalization rate. Unfortunately, such a methodology is in conflict with most valuation literature that addresses build-up capitalization and discount rates.

About the author:

*Thomas Beatty, CPA, has over 25 years of business valuation experience and is the author and founder of*

*www.TheValuationSite.com**, a website dedicated to professional level business valuation tools and educational modules.*

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