#3 – Quantifying Expected Holding Period Premiums from Restricted Stock Transactions

This is the third in a series of posts about restricted stock discounts.  In the first post, we examined the Silber Study, which should have told all appraisers that the use of averages of restricted stock studies to estimate marketabilty discounts for illiquid minority interests of private companies.  The second post proved that the only explanation for the difference in restricted share prices and publicly traded prices of issuing companies is something we called the expected holding period premium or HPP.

This third post examines a hypothetical restricted stock transaction from the earlier two year holding period requirement under SEC Rule 144 (prior to the change to a one year holding period in 1997).

We examine a hypothetical transaction.

• The freely traded price is \$10.00 per share
• The restricted stock transaction price is \$7.50 per share
• The issuing company pays no dividends and reinvests earnings to finance future growth
• The restricted stock discount is 25%
• The restricted stock minimum holding period is two years
• There are additional restrictions under the “dribble-out” rules for large blocks, and this is a large block

We show the restricted stock discount in Exhibit 8.13 from the third edition of Business Valuation: An Integrated Theory, which will be available on Amazon.com and from other booksellers in mid-October.  Look first at the vertical axis, which shows the two prices noted above.

To address the 25% restricted stock discount, we must look at expectations regarding the public company and for the restricted stock purchasers on the transaction date.  In the last post, we showed that the discount is caused by additional risk to the restricted shares relative to freely traded shares.  In this post, we unpack that observation.

Assume in Exhibit 8.13 that the required return for the issuing public company is 10%.  The expected growth in value, given no dividends, is 10% per year.  So the expectations embedded in the public stock pricing is for growth in value of 10% per year – to \$11.00 per share in year one, and to \$12.10 per share by the end of year two.

Given the size of the block at issue and the trading volume in the public company’s shares, the dribble-out rules will require somewhere between an additional year or two for the investor to obtain full liquidity.  The expected growth in value to three years is \$13.31 per share and to four years is \$14.64 per share.

The expected return for public shareholders is therefore 10% per year over this period based on the transaction date price of \$10.00 per share.  What about for the restricted share purchasers who purchased their shares for \$7.50 per share?

The question for analysis is this: what is the incremental return, or HPP, or expected holding period premium to the 10% discount rate for the public company, that can be inferred by the restricted stock transaction.  The answer requires our assumption regarding the expected holding period, which is effectively three to four years. Given the information thus far, we can calculate expected holding period premiums to three and four year expected holding periods.  We do so in Exhibit 8.14.

In the exhibit, we calculate the expected future price per share after three and four year holding periods showing the expected future share prices noted just above (\$13.31 per share and \$14.64 per share, respectively).  We have expected future values.  The present value from the perspective of restricted share purchasers is \$7.50 per share.  Given present values for three and four expected holding periods and future values, we can calculate the implied required returns to justify the discounted \$7.50 per share transaction price.

The implied Rhps (or expected returns over the holding periods) are 21.1% (three year holding periods) and 18.2% (four year expected holding period).  Given the discount rate for the public company of 10%, the implied holding period premiums are 11.1% (three years) and 8.2% (four years).

Astute readers may note that I selected an implied discount rate of 10% for the public company, and that might impact the result.  Based on our analysis, the range of implied holding period premiums is only modestly impacted by changes, even significant changes, in the assumed underlying public company discount rate.

If you are reading this series and you are using averages of restricted stock studies as a primary basis for estimating marketability discounts (or DLOMs) for illiquid minority interests of private companies, I hope your discomfort level is rising.  In the next post, we will examine some basic and summary information from existing restricted stock studies.  Your comfort level will not be helped by this analysis.

This discussion of restricted discounts is based on Chapter 8 of the third edition of Business Valuation: An Integrated Theory (by Travis Harms and me).  The book is published by John Wiley & Sons, Inc.  You can pre-order your copies on Amazon.com or from your favorite bookseller.  You should order personal copies for all of your professionals.  We understand that Kindle and other electronic versions will be available by the end of September and that physical books can be delivered by mid-October. The book is approximately 300 pages in length and in a smaller than textbook size.  It will not, as many valuation texts, overwhelm you with its length.  But it will inform you about valuation theory better than any book on the market.

Travis and I look forward to your comments about this series of blog posts and about the third edition of  Business Valuation: An Integrated Theory.

Until the next post on restricted stock discounts and more, be safe and be well!

Chris

Please note: I reserve the right to delete comments that are offensive or off-topic.

4 thoughts on “#3 – Quantifying Expected Holding Period Premiums from Restricted Stock Transactions”

1. A little confused. Chart says 10.1% but Table shows 11.1% for 3 year HPP.

• Chris Mercer says:

I think that is what they call a typo. Graph should read 11.1%. I would tell you it is the first time that’s ever happened to me, but it wouldn’t be the truth. Thanks! ☺

2. gilbert ostrick says:

How did you calculate the implied rate of returns of 21.1% and 18.2% to back into the holding period premiums?

• Chris Mercer says:

Here is how for three years. Four years is conceptually the same.

1. Calculate future value of public stock in three years (discount rate assumed to be 10%). That is: (1 + 10%)^3 = \$13.31 per share. (Raised to 3 years)
2. The restricted stock transaction occurred at \$7.50 per share, today for calculation purposes.
3. The rate of return between \$7.50 per share (PV) and \$13.31 per share (FV) for three years is 21.1%

The same calculations with four years will yield the 18.2% required return in the table in the post.

Hope this helps