Adjusting Discount Rates for Illiquidity

The other approach to dealing with illiquidity is to adjust the discount rate used in discounted cashflow valuation for illiquidity. In practical terms, this amounts to adding an illiquidity premium to the discount rate and deriving a lower value for the same set of expected cashflows. Earlier, we presented asset pricing models that attempt to incorporate illiquidity risk but they are not specific about how we should go about estimating the additional premium (other than saying that it should be larger for investments which are illiquid when the market is illiquid). There are three practical solutions to the estimation problem:

1. Add a constant illiquidity premium to the discount rate for all illiquid assets to reflect the higher returns earned historically by less liquid (but still traded) investments, relative to the rest of the market. This is akin to another very common adjustment made to discount rates in practice, which is the small stock premium. The costs of equity for smaller companies are often augmented by 3-3.5% reflecting the excess returns earned by smaller cap companies over very long periods. The same historical data that we rely on for the small stock premium can provide us with an estimate of an "illiquidity premium".

• Practitioners attribute all or a significant portion of the small stock premium reported by Ibbotson Associates to illiquidity and add it on as an illiquidity premium. Note, though, that even the smallest stocks listed in their sample are several magnitudes larger than the typical private company and perhaps more liquid.

• An alternative estimate of the premium emerges from studies that look at venture capital returns over long period. Using data from 1984-2004, Venture Economics, estimated that the returns to venture capital investors have been about 4% higher than the returns on traded stocks.72 We could attribute this difference to illiquidity and add it on as the "illiquidity premium" for all private companies.

72 The sample of several hundred venture capital funds earned an annual average return of 15.7% over the period whereas the annual average return was 11.7% on the S&P 500 over the same period. They did not adjust for risk. Broken down into classes, venture capital investments in early stage companies earned 19.9% whereas investments in late stage ventures earned only 13.7%.

The key is to avoid double counting the cost of illiquidity since some of the small stock premium may be compensation for the illiquidity of small cap companies.

2. Add a firm-specific illiquidity premium, reflecting the illiquiidy of the asset being valued: For liquidity premiums that vary across companies, we have to estimate a measure of how exposed companies are to liquidity risk. In other words, we need liquidity betas or their equivalent for individual companies. Drawing on the work done on the liquidity based capital asset pricing model, these liquidity betas should reflect not only the magnitude of trading volume on an investment but how that trading volume varies with the market trading volume over time. It may be possible to do this for some real assets (such as real estate) where there are transactions from time to time, but may be impossible to do for unique private businesses.

3. Relate the observed illiquidity premium on traded assets to specific characteristics of those assets. Thus healthier firms with more liquid holdings should have a smaller liquidity premium added on to the discount rate than distressed firms with non-marketable assets. While this can be done subjectively, it would make more sense to have a sold quantitative basis for the adjustment.

The three different approaches to adjusting discount rates are similar to the approaches used to estimate illiquidity discounts on value. The constant liquidity premium approach mirrors the fixed liquidity discount whereas the firm-specific liquidity premium approaches resemble the approaches used to adjust the illiquidity discount for individual firms. In fact, we could build regression models that relate expected returns on stocks to measures of illiquidity and use these regressions to forecast discount rates for private firms.

There are practitioners who have tried to develop models that incorporate illiquidity. One widely publicized model is called the Quantitative Marketability Discount Model (QMDM).73 The QMDM allows analysts to adjust the discount rate for illiquidity factors, though the adjustment is subjective, and then values illiquidity as a percent of firm value for different holding periods. To illustrate how the model works,

73 The model was developed by Chris Mercer, a principal at Mercer Capital. A fuller discussion of the model is available in Mercer, Z. C., 2004, The Integrated Theory of Business Valuation, Peabody

Publishing.

consider a firm with an expected cash flow next period of $ 1.00. Assume that the appropriate discount rate, based upon fundamental risk but before adjusting for liquidity risk is 9% and that the expected growth in the cashflows in perpetuity is 4%. This firm would have an intrinsic value of $ 20.74 In the QMDM, the analyst would adjust the discount rate for illiquidity (assume that he would add 3% to the discount rate to arrive at a required return of 12%), specify a holding period (say, 5 years) and the percent of the available cashflows that will be paid out (say 60%). The new firm value would then be computed as follows:

New Firm Value = PV of cashflows during holding period + PV of terminal value = PV of $ 0.60 growing 4% a year for 5 years + 20 (1.04)5/(1.12)5 = $ 16.13

The first term is the present value of annual cashflows during the holding period- $ 0.60 (60% of $ 1) growing at 4% a year for the next 5 year- and the second term is the present value of the terminal value ($ 20 growing at 4% a year for the next 5 years), all discounted back at the liquidity adjusted discount rate of 12%. Comparing the estimated value ($16.13) to the unadjusted value ($20) yields an illiquidity discount of 19.35%.

While the QMDM model is well intentioned, it fails on three levels. First, the cashflow that does not get paid out over the next 5 years is assumed to be wasted by the controlling stockholders for private benefits that do not accrue to the business.75 If this is indeed the case, the firm value should have been computed at $ 12 initially, rather than $ 20.76 Second, the illiquidity discount computed in the model is a consequence of both control and illiquidity. While Mercer makes the reasonable point that the two are interrelated, one can very easily exist without the other. In other words, you can have a completely liquid investment with absolutely no control over how a firm is run, as is often the case with stock in a large publicly traded company. The fact that you can sell your stock at any time will not protect you from management or controlling stockholder

75 If the cash is held back in the firm (rather than wasted), it will add on to the terminal value and the value of the firm should not be affected.

76 The model seems to assume that the firm will revert back to being optimally run at the end of the illiquidity period. There is no reason why this should happen. If you did not expect it to happen, the value of the firm would be based upon $ 0.60 in cashflow, growing at 4% a year in perpetuity:

actions since the price you sell at will reflect management foibles. Third, for a model that claims to quantify non-marketability, the QMDM is surprisingly elusive on the adjustment made to the discount rate for illiquidity, other than to note that it can be backed out of observed illiquidity discounts in restricted stock studies.

Illustration 14.2: Estimating the illiquidity adjusted discount rate for a private firm

Earlier in the chapter, we applied various estimates of the illiquidity discount to the estimated value of $1.796 billion to arrive liquidity-adjusted values. As an alternative, we could have adjusted the discount rate that we used to value Kristin Kandy to reflect the illiquidity.

• Adding an illiquidity premium of 4% (based upon the premium earned across all venture capital investments) to the cost of equity yields a cost of equity of 20.26% and a cost of capital of 15.17%. Using this higher cost of capital lowers the value of equity in the firm to $1.531 million, about 15.78% lower than the original estimated. 77

• Allowing for the fact that Kristin Kandy is an established business that is profitable would allow us to lower the illiquidity premium to 2% (based upon late stage venture capital investments). This will lower the cost of equity to 18.26%, the cost of capital to 13.77% and result in a value of equity of $1.658 million. The resulting illiquidity discount is 7.66%.

Two general points should be made about adjusting discount rates for illiquidity. The first is that small adjustments to the discount rate will translate into large illiquidity discounts. The second is that the length of the period that we make the illiquidity adjustment for will affect the magnitude of the discount. If we increase discount rates for illiquidity in perpetuity rather than the 5 years that we used in both calculations above, the resulting discounts will be much larger (31.77% for the 4% illiquidity premium and 17.66% for the 2% illiquidity premium).

77 The higher cost of capital was used only for the first 5 years. Extending into perpetuity reduces the value of equity to $1.225 million, a decline of 31.77%.

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    How to adjust illiquidity premium in cost of equity?
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