Interpolated Equity

Towards a fair, mathematically grounded approach to cash vs equity compensation at pre-IPO companies

Striking a fair balance between cash and equity compensation is a thorny issue for companies and employees alike. Even when companies offer prospective hires a range of cash salary and equity combinations, new employees face a huge information asymmetry risk. Furthermore, traditional equity structures result in needlessly complex compensation packages.

Here, I offer a radically different approach, Interpolated Equity (IE). Under IE, employees simply purchase company equity from their salary. These purchases are priced after the fact using fair-market, interpolated prices described below. IE is optimally fair to founders, employees, and investors while bringing far greater simplicity to mixed equity and cash compensation.

Also, I have built a rudimentary Google Spreadsheet to implement this model for readers to duplicate, extend, and play with on their own.


  1. Companies should minimize the impact of the inevitable information asymmetry between prospective hires and founders and management.
  2. Companies should be maximally transparent and not in any way contribute to distrust or lowered morale.
  3. As much a possible, employees should enjoy the same rate of return on their equity as founders and investors.
  4. Compensation packages should be comparable across different companies so that applicants can make an informed decision when choosing from multiple job offers.
  5. Equity programs should be flexible and handle situations like part-time commitments from founders at the beginning or anyone needing to take extended medical leave.


A typical job offer at a pre-IPO startup consists of two numbers: a yearly salary and an equity grant in the form of common stock or, for tax purposes with later employees, equity purchase options. At earlier startups, the grant will be a percentage and as startups progress towards IPO, it will often be a number of shares. Either way, the equity grant will usually have a vesting period, which in the current market is often three to four years with a one year cliff. At DOX we try to be employee-friendly so all of our grants are on a 3-year schedule with a 6-month cliff.

Often the company will give prospective hires a choice between three packages with varying mixtures of cash versus equity. Employees with a larger appetite for risk can opt for less cash/more equity, while employees with more immediate cash needs can opt for more cash/less equity.

There are multiple problems with this approach:

  1. Most founders, especially in earlier stage startups, really have no idea how much equity to grant. We read the Y-Combinator survey (pretending it applies to us), ask 2 or 3 friends who have no demonstrable expertise in the area, and then take a wild guess, all the while hoping that its enough to make the prospect happy and well incentivized while leaving room in the cap table to repeat the process with future hires. Paul Graham has attempted to formalize an upper bound on equity compensation, but the real rate which depends on market conditions which are impossible to determine and probability assumptions which are essentially wild guesses.
  2. The prospect has even less information than the founders. In most cases equity vs cash decisions are unalterable once made. Unfortunately, these decisions are often made when the prospect has little if any information on which to base them.
  3. The prospect must compare an annual income stream (the cash salary) to a pseudo one time grant of equity. The vesting schedule turns this into a sort of stream but its unclear what happens at the end of the period. Also, its a mispriced stream which assumes that the value of the company remains constant over the entire period. Generally, startups which are extant after 3 years are worth more than they were 3 years prior.
  4. Its very difficult for the prospect to compare offers across multiple startups which are at different stages and growing at different rates.

The reason that these issues are so difficult for startups compared to large, public companies, is that there isn’t a market mechanism that determines a fair market value of a starutp’s equity on a regular basis. But, we can use the little market activity there is to derive a fair market value.

The Interpolated Equity Solution, Detailed

Preliminaries — Constant Return Assumption

Interpolated Equity requires just one assumption about pre-IPO startups: the value of the equity grows at a constant rate of return between valuation events. Note that this does not mean that the value grows linearly but that it grows exponentially at a periodically compounded rate. However, even this assumption can be relaxed in extensions to the model which I will discuss at a later date.

The Assumption, In Formula Form

The Constant Rate Assumption, Formalized

This is a formalization of the statement above. The value of the company at time t is equal to the present value at time t of the value at time 0 plus the sum of the present values at time t of the total equity purchases by founders and employees over the period. The trick is to find the value of r which makes this equation hold. I have constructed a 4 employee model, which anyone is welcome to access and play with here.

The Consequences of the Constant Return Assumption

Once we derive the rate r which satisfies the assumption, we can determine implied market prices at any instant during the period in question. So, allocating equity now becomes much simpler. If a participant allocated $1000 of salary to equity in a given month, they get $1000 worth of shares in the company. Note that this model only refers to pre-money holdings at the valuation event at time t. Since these events are often outside investments


Note that compensation packages just got much simpler. Instead of a prospect needing to weigh cash, equity percentage, vesting terms, and founder preferred issues, they need only look at one number, cash, and can take comfort in knowing that they can allocate it in a fair, transparent manner as their particular situation demands.


Often times a company will start before a founder has left their employer. Perhaps one has quit and one is working part time. The full-time founder (FTF) needs to be compensated for their risk but its not fair for the as-yet part time founder (PTF) to have no stake in the company. Traditional equity splits make this difficult to manage. Under IE the solution is breathtakingly simple: pro-rate the part-time founder’s salary. Say the “standard” founder salary is $100,000, or roughly $8300 per month. Hypothetically, the part-time founder can choose to dedicate say 20 hours per week for one quarter wages, or about $2080 per month. Since the company will have no cash at this point, so the FTF will be “buying” $8300 of equity per month and the PTF will be “buying” $2080 of equity per month until going full time and reverting to the higher salary. By the laws of compounding interest, the FTF will be justly compensated for taking on more risk but the PTF will still be compensated for contributing to the company.

Further complicating the situation is that the founders may have put money into the company to pay for early costs. Traditional equity splits cannot elegantly handle the PTF putting in $20,000 with the FTF putting in $10,000 at inception. Under IE, this is also simple, just add those amounts to their unpriced purchases in the month they were made.


Transparency in compensation is a very important, controversial issue facing the startup and tech community. While, many people have strong feelings and disagreements on the issue, it is unarguable that a sizeable portion of the community does feel that there is unfairness in our hiring practices. While not a total solution, Interpolated Equity brings much needed transparency to the compensation process which can lend credence to these concerns where they are justified and mitigate them where they are not.

Tax Implications

To be honest, I am far from an expert in this area. At this stage, I am proposing this as an idealized economic model and to be frank, I am not exactly sure of how various jusridictions would treat IE grants.

Having said that, I believe that since the fair market value of each grant is, by definition of the model, what the participant paid for it, I believe that these would just be taxed as ordinary income. Any gains on these investments would be taxes as capital gains. So, if a participant’s total salary is $120,000 per year, the taxable, ordinary income is $120,000, independent of how much was allocated to equity and cash. Although this may cause cash flow issues, I do believe that it would be a fair assesment. Any realized gains would be calculated based on the interpolated price used to purchase the shares.

Other Issues

Minimum Equity Allocations: economics is often described as “assuming the absurd” and there is a bit of that at play in the baseline IE model. For example, one reason startups use equity in compensation just that they dont have any cash. So, under IE, companies may need to restrict packages to a minimum equity allocation. If a company believes a prospect’s market value is $120,000 per year but only has enough cash to offer $90,000, I beleive it is perfectly fine to make a restricted offer along the lines of: “We can offer you $120,000 under our IE but you must allocate at least $30,000 or more to equity per year, at least for the first 12 months”. This is fully supported by the model.

Vesting periods and minimum grants: IE allows for the elimination of vesting periods and I believe yields a much cleaner alternative. But, if someone works for a few months and then leaves, companies can end up with a polluted cap table with lots of small holders. I believe that rather than just taking away the equity that these employees worked for, vested or not, it is optimal to have a buyback clause that allows the company to “buy back” equity holdings, at the market price on a valuation event, if the total holding is below a certain size. I believe that this is far more fair to employees while preserving a the company’s interest in a clean cap table.

Pricing issues around preferred shares and liquidation preferences: On hacker news several commenters pointed out the flaw in using preferred equity grants to price common shares. That is a problem which is not directly addressed in this, initial, iteration of the model. This issue deserves more thorough treatment but as a temporary remedy, I’d offer up this solution: unbundle the liquidation preferences and other preferred terms from the underlying equity. Instead of an investor purchasing preferred shares, they would purchase common shares and separately purchase rights or swaps to synthetically realize the economic exposure of the preferences. Since the investor would be purchasing the synthetics at their theoretical market value, the increase in the company’s cash would equal the increase in its liabilities. Therefore, this transaction, theoretically, would not have any effect on the dilution or value of the equity held by any of the founders, employees, or investors.

Corner Cases

One issue that arises is what happens if a company using IE never has a valuation event. In other words, they never need to raise capital. The IE program should be structured so that if there is no valution event within some period, say 4 years, the company must undergo a 409a valuation and use that as the reference price.

Because IE, in a way, is just a transition function from one valuation state to the next, it is not limited to pre-funding companies. The model supports multiple rounds or valuation events which I will discuss in a future post.

Final Thoughts

This post is only just a starting point. IE raises operational and accounting that must be addressed. Also, integrating IE with an existing employee can be quite complex.

I would like to thank Michael Feng and Greg Weber for their feedback and help with this post.



In these examples, lets make the following assumptions:

  1. All founders and employees have a total package of $120,000 per year (so we have nice, round, monthly figures).

Each of these examples are saved as a separate, values-only worksheet in the Google Spreadsheet model.

Company A:

  1. Two founders both put in $10,000 at the beginning of the company.
  2. They work for 10 months at zero cash salary, contributing their full $10,000 per month to equity. After 10 months, they each allocate 50%, or $5,000, to equity.
  3. A first employee starts 6 months later and allocates 10% of income, or $1,000 per month to equity.
  4. A second employee starts 12 months later and also allocates 10% of income, or $1,000 per month to equity.
  5. The company raises a priced equity round 36 months later which gives the company a $5,000,000 pre-money valuation.

In this case, at month 36, before considering dilution from outside investment, the cap table is:

  1. Founders: 47.45% each
  2. First Employee: 3.30%
  3. Third Employee: 1.81%

Note that the risk of working for a startup in months 6 to 12 is generally much higher than months 12-18 and this justifies the larger package that the magic of compound interest gives to the first employee.

Company B:

Same conditions as Company A, but one founder is only part time for the first 6 months, earning a pro-rated, one-fifth salary, or $2,000 / month. Now, here is the cap table:

  1. Part Time Founder: 33.51%
  2. Full Time Founder: 60.48%
  3. First Employee: 3.94%
  4. Second Employee: 2.08%

Note that by working part time for six months, the founder avoided a large amount of personal risk and thus “spread” that surplus risk across the company. That founder ends up with less equity while the other participants are compensated for their higher risk.

Company C:

Same as company A, but lets say that an angel, who we will call Metatron for the sake of a great pop culture reference, puts in $50,000 at the inception of the company. Now here’s the cap table:

  1. The Angel Metatron: 20.08%
  2. Both Founders: 37.76% each
  3. First Employee: 2.80%
  4. Second Employee: 1.60%

It may seem unfair for Metatron to recieve such a large stake. But, this can be viewed another way, under this model, Metatron is getting exactly the stake that the $50,000 investment, in a company that literally had nothing, should get in an efficiently functioning market. Perhaps the real lesson is that the current market practice massively undercompensates angels for the enormous risk that they take on.

Company D:

Same as Company C, except now the Angel Metatron waited 6 months to make the angel investment. Here’s the new cap table:

  1. The Angel Metatron: 13.26%
  2. Both Founders: 41.05% each
  3. First Employee: 2.97%
  4. Second Employee: 1.67%

Here again we see the shift in risk from Metatron to the founders results in a significantly larger stake for the founders for their added risk. (note that in the model that I’ve put on google docs, I calculated these values by hacking it bit. Feel free to contact me for more explanation.