Valuating Tax Indifference Points

There are a lot of things valuators disagree on. Surprisingly, tax affecting is one of them. This seems silly to me, since taxes can be forecast with a relatively high degree of precision. I’m going to present a straightforward scenario and step through my valuation philosophy for addressing tax rates.

Assume you’re in an advisory role for a client in the following situation:

  • The business will generate $100,000 of net income on January 1st of 2015, 2016, 2017 and 2018. It will generate no subsequent income, and no cash flow adjustments are necessary.
  • You are valuing the business as of January 1st 2014.
  • You will apply a discount factor of 20%.

Figure 1 outlines a standard DCF valuation of the business before considering taxation. Each cash flow item is multiplied by discount factor of (1+d)^{-t}. Summing the discounted cash flows yields a present value of $258,873.
Figure 1

Does this mean the business will be worth $258,873 of post-tax money to the client? Absolutely not. Assuming the corporation will file as an 1120S, like most small businesses, this will result in no corporate taxes, but earnings will be taxed at the client’s personal income rate. Assuming a marginal tax rate of 25% decreases the post-tax valuation to $194,155.

Figure 2

Here’s where things start to get interesting. Would you advise your client to sell the business for $200,000? One might be tempted to say yes because $200,000 is greater than $194,155, resulting in a $5,845 increase in present value. However, just as we should not ignore the tax affects of holding onto the business, we should not ignore the tax affects of selling the business early. Like it or not, a capital gains rate of 15% will be assessed on the sale. Assuming a cost basis of zero, the client will have to pay $30,000 in capital gains taxes.

This means that instead of increasing their present value by $5,845, your advice decreased their present value by $24,155. That’s an instant simple return of -12.44%. In the world of advisory services, this qualifies as abject failure.

Figure 3 v2

When considering a potential sale (or a forced sale in some litigation environments), I like to calculate a tax indifference point. At what sales price would my client be indifferent between selling and holding the business? Assuming no cost basis, this can be calculated by multiplying the post-income tax present value by (1-t)^{-1}.

Figure 4

Your client should not sell his or her business unless the sales price is above $228,418. This yields an imputed tax rate of 11.76%, which happens to be equal to 1-\frac{1-t_1}{1-t_2} where t_1 is the personal tax rate and t_2 is the corporate tax rate.

A few common objections to this methodology followed by my responses:

  1. Capital gains tax is a cost of doing business and not the responsibility of the seller. True, capital gains tax is, literally, a cost of doing business, and it’s my responsibility to calculate the costs and benefits of a sale. If costs exceed benefits, then a sale shouldn’t happen.
  2. Does this mean that mergers and acquisitions should never happen since sellers have to pay capital gains taxes? Of course not. Buyers might have lower discount rates, synergies with existing product lines or asymetric information. Something to keep in mind: The above method doesn’t generate the price for which a business should sell. It generates the minimum value at which a business should consider selling. Sales happen if the bid price is at or above the ask price. I may not know where in that range a sale might occur, but the tax-indifference point gives the minimum sales price. Anything below that and your client is losing money.
  3. That’s fine and good for an advisory setting, but it doesn’t hold in litigious settings. For example, in the context of minority shareholder oppression, our job is to find the fair value of the company, not to advise on fair selling prices. Actually, this context has all the more reason to consider capital gains taxes as a credit. The defendant’s oppressive conduct forced my client to sell his shares and take on a capital gains liability. The court must consider this alongside any other damage claims to make our client whole.
  4. I don’t think this reasoning is valid in X legal setting. You might be right. We should examine that legal setting closely.
  5. I’ve never heard that argument before. Then you should really hire me as your forensic accountant! Not only does this methodology make sense, it also yields the same answer determined to be reasonable by the Delaware court in Open MRI Radiology Associates, P.A. v. Kessler, et al, although they may have come to the answer through different reasoning.