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?

The 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 in y years' time, then we can multiply this by the PE ratio in order to obtain p.

Investors 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 all.

Understanding Dilution

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

Let's 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 £133/share.

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.

In 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.

There 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.