Saturday, December 20, 2014

How to Value an Investor's Stake

I'm currently looking at a draft version of an entrepreneurship course written by, among others, people from
Cambridge's Judge Institute, and hosted by Epigeum.
Something that I found particularly helpful was how to decide what
percentage of a company to sell to an investor for the particular amount
of money the company needs. I've summarised it here.

The Value of a Stake

If the company is seeking capital worth c, then the issue is to calculate s, the percentage of the equity that should go to the investor providing that capital.

Firstly, assuming this is venture capital, the investor will look to exit probably within five years. Call this number of years y. Let r be the amortised annual rate of return that they desire, say 45%.

Hence, we can say that when the business is sold after those y years, the investor's stake should be worth w = c(1 + r)y, as this provides the desired rate of return.

Therefore, the stake is simply the fraction that w is of the selling price (market value), p, of the business. Of course, how does one estimate p?

answer lies in using the Price/Earnings (PE) ratio for a similar,
established, company, which details their worth as compared to their
sales. Assuming that we can predict the likely earnings of the company
y years' time, then we can multiply this by the PE ratio in order to obtain p.

may well discount the PE ratio, either because they do not believe it
to be realistic, or because of the perceived risk, or because the
expected revenue is uncertain.

As an example, assume a £1 million investment is needed, that r = 45%, and y
= 5. This means that w = £6.4 million. If projected sales in year 5 are
£1 million, with a PE ratio of 15, p = £15 million. Thus, the initial
stake would be 6.4/15 or 43%.

Which is food for thought. It does
very clearly show how VC investors "need" to take very large equity
stakes in order to make the desired rates of return. Hardly surprising,
but it's nice to at least vaguely understand the mathematics behind it

Understanding Dilution

This brings us neatly on to what actually happens when you sell the stake.

say that an investor offers you the £1 million for 43% of the equity.
That means that the investor is valuing the entire company (prior to the
investment) at £2.33 million, and in particular, valuing the 57% stake
you will be left with at £1.33 million.

Suppose that prior to the
investment the total number of issued shares (all owned by the
founders) is 10,000. This means that the price placed on those shares is

Why is it not the case that the
price is calculated based on £1 million for 43% of 10,000 (giving
£233/share), leaving the founders' 57% stake being worth £1.33 million?

Whilst the ownership percentages would be correct, this is not done because dilution takes place. In other words, the company issues new shares to the investor, rather than re-assigning existing shares.

the above example, given a price of £133/share, the investor must be
given £1 million/£133 = 7,518 shares. Post-investment, the company will
be worth a total of £2.33 million, divided into 17,518 shares. The
founders will hold their 10,000 shares (as before), but these are now
only 57% of the company, whilst the investor will hold 43% (17,518
shares), worth a total of £2.33 million * 0.43 = £1 million.

you have it: the end result is as proposed, i.e. the investor bought
the agreed percentage for the agreed price. The only somewhat
potentially confusing part is how this is brought about by dilution,
rather than share re-distribution.


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