Do company valuations react to market sentiment with a lag?

According to their website, Duff & Phelps “is the premier global valuation and corporate finance advisor with expertise in complex valuation” and other fields. According to their annual Valuation Handbook – Guide to Cost of Capital, most stock valuations react to market news with a lag.

Often, valuators use conclusions of this model to make meaningful decisions about pricing company risk.

If the model isn’t true, then we will need to rethink the way we value companies — likely in a way which increases the value of closely held businesses. They will systemically overstate the risk of publicly traded corporations and therefore understate the value of closely held firms.

If the model were true, one could utilize the predictions to almost effortlessly make untold fortunes in the stock market.

I’m publicly sharing the results of my research, so I imagine you can guess where I stand on the question.

I am not comfortable using the “sum beta” methodology to estimate the riskiness of an individual stock. Any observed difference between the normal beta and the sum beta is likely the result of statistical noise. Unfortunately, this invalidates the conclusions of the Duff & Phelps methodology. Their industry risk estimates are likely biased in an upward direction.

I didn’t want this to be the result. I wanted to find an easy way to consistently beat the stock market, but I’m going to have to keep looking.

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.

Are Equities Riskier than Bonds?

Because individual companies are inherently riskier than entire nations, investors will apply a greater discount to future cash flows. This means that, if the business plan works out, investors will achieve a higher return on their invested capital. That’s why it is common to assume an equity risk premium when building a discount rate for companies. Valuators usually start with yields on government bonds and then add an additional risk premium for securities. A simple model suggested in the 2012 Ibbotson Valuation Yearbook is a 2.48 percent riskless discount rate (20-year U.S. Treasury Coupon Bond Yield) and a 6.62 percent equity premium (large company stock total returns minus long-term government bond income returns) with additional premiums that can be added for size, risk, industry, et cetera.

An article in February’s print copy of The Economist challenged this standard formulation. It is entitled Beware of the bias: Investors may have developed too rosy a view of equity returns. I’m open to the idea that investors are too rosy about equity returns, but I find almost every example cited spurious. I’ll quote liberally from the article and proceed point by point. Emphasis added throughout. Continue reading →

What is a discount rate?

Receiving $200 is strictly better than receiving $100. Receiving $100 now is strictly better than receiving $100 in a year. But it is not clear whether it is better to receive $90 now or $100 in a year.

Similarly, it is always better to receive $100 with absolute certainty than to receive $100 80 percent of the time. However, some would rather receive $79 with absolute certainty than $100 with 80 percent certainty.

This is a problem that must be solved in order to make perform discounted cash flows (or make simple investment decisions). A company’s value will vary not only with the magnitude of future cash flows, but when the cash flows occur and with what level of risk.

For valuation practitioners, both problems are usually solved through the discount rate or required rate of return. The discount rate is the rate of return for which an investor is indifferent between investing and not investing. For example, if one can achieve a 4 percent return without risk, then one would be indifferent between receiving $100 now and $104 a year from now since $100 could be invested at the risk free rate. If an investment is riskier, then investors will require a higher rate of return to set aside money.

Applying a discount rate to a future cash flow yields a present value via the following formula:


  • PV is the present value. This is the current value of the future payment.
  • NCF is the net cash flow. This is the amount of money the investor will receive after netting all expenses. Higher cash flow yields a higher value.
  • d is the discount rate or required rate of return, as discussed above. If investors demand a higher rate of return, then they will pay less for a future cash flow.
  • t is the time until the payment. Investors will pay less for payments further into the future.

According to the discounted cash flow methodology, the value of a company is equal to the present value of all future payments to investors.

Valuation Methods

All valuation methodologies can be classified into one of three approaches:

  1. Income Approach
  2. Asset Approach
  3. Market Approach

The Income Approach values a business by predicting cash flows to the owners. After making adjustments for fringe benefits, non-recurring events and future taxes paid (tax affecting), the analyst must apply a discount rate that adjusts future dollars into current dollars. If one can receive a risk-less 2 percent annual return, then one is theoretically indifferent between receiving $100 today and $102 a year from now. For risky investments, such as equity ownership, this discount rate will be far higher. In real terms, this means investors will demand a higher return in order to invest money into the business. A promise of $100 from a treasury bond is worth more than a promise of $100 from a business. The following factors might make a company riskier than the average equity position:

  • High financial leverage
  • Small size
  • Participation in a risky industry

Asset-based approaches to business valuation values a business as the sum of its parts less outstanding liabilities. Theoretically, a business owner would not be willing to buy a business for more than the cost of acquiring the individual parts of the business. For asset-intensive and distressed businesses, this may be a reasonable approach. However, many modern businesses consist of intangible assets that are hard to value and/or impossible to buy such as:

  • Specialized employees.
  • Goodwill with customers.
  • Reputation and brand value.
For this and other reason, many companies trade or sell at a multiple of their asset-based value.

Market approaches to business valuation attempt to use the value of comparable companies as a guideline to the subject company’s value. Comparable market valuations are commonly obtained through two methods:

  1. Market Capitalization — Market capitalization is the outstanding value of all publicly traded shares.
  2. Similar transactions — Some private data sources aggregate voluntarily-reported selling prices of privately held businesses.

Once similar companies have been identified, the analyst can scale their valuations to the subject company through any of numerous multiples, including:

  • Price to Sales Ratio — The ratio of the business’s value to gross revenue, total sales less no expenses.
  • Price to Book Ratio — The ratio of the business’s value to the asset based approach.
  • Price to EBITDA Ratio —The ratio of the business’s value to earnings before interest, taxes, depreciation and amortization. This can be computed by adding depreciation and amortization back to net income.

Numerous other approaches exist and are occasionally applied both to small companies and large, publicly traded companies.