The board of directors of a company is responsible for determining the fair market value (FMV) of equity at the time of equity grants, taking into consideration any factors that may impact that determination. Because options are usually for common stock, the exercise price for options should usually be the FMV of your company's common stock.
Some factors that the Board may consider in determining the FMV may include the company's revenue history, liabilities, product/industry/market risk, cash situation, etc. Some people say that your "fair market value" should be whatever you could sell your stock for if someone were to buy the company as it stands today, but it is up to the board of the company to determine what to consider. They must make this consideration in good faith.
Your stock's FMV is usually NOT the same as your last financing valuation (unless you sold common stock). This is because an investor's valuation is typically either (i) for preferred stock, which holds different preferences than common stock and therefore is usually deemed to have a higher valuation than your common stock, or (ii) through a SAFE or Convertible Note with a valuation cap, which is NOT a reflection of the current FMV of your equity (in fact, SAFEs and convertible debt may actually contribute to help you determine a lower FMV price for common stock because those instruments would reduce what common stock will receive if a sale were to occur today).
Many boards elect to use a 409A valuation (a valuation provided by an independent third-party appraiser) to make that FMV determination. The reason for this is that under Section 409A of the US internal revenue code, directors can more safely rely on an equity valuation provided by an independent third party to ensure that equity and options are not undervalued at time of grant/issuance, thereby reducing potential director liability for undervaluing equity at time of grant.
That said, if your company is still in the early stages (pre-revenue), or has more liabilities than assets, then some boards make the determination that the FMV of their company's stock is deminimus/nominal and set it at whatever the par value is, choosing to forego the cost of a 409A. In contrast, issuing stock in a company that is worth something can lead to the stockholder needing to report and pay taxes on the value of the stock, which is why most companies are granting options instead of issuing stock directly once the company has innate value.
Because of this, it is highly recommended (some would say to treat it as a requirement), to do a 409A Valuation prior to making option grants.
If you are issuing stock directly instead of stock options, you don't need to satisfy ISO requirements, so the 409A is sometimes considered less important. However, it is still important to know the FMV of the stock because stockholders should either be (i) paying the FMV for the stock at the time of issuance, or (ii) reporting the value of the shares received as income to the IRS and paying taxes on that value. Again, if the FMV is nominal, it can be listed as the par value.
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