What is the ultimate tax model when you want to grant stock options to employees in Denmark?
The answer is found in section 7P (hereinafter “7P”) of the Danish Tax Assessment Act.
Note: In Denmark, "stock options" are usually called "warrants". A warrant is a right to subscribe for a newly issued share in a company.
7P does two things:
(1) It reduces the taxation of an employee from about 56% to 27/42%
(2) It only taxes if the employee realizes a gain on their shares
7P requires a specific process to implement. Among other things, a valuation of stock options must be performed when granting them.
So how is that valuation made?
In the following, I focus on private companies that are not publicly traded.
#1: Valuation of stock options vs. shares
A stock option is a right to buy a share sometime in the future.
When the recipient exercises a stock option, a new share of the company is issued. Technically, the recipient “subscribes” for a share. That share is called the underlying share. A stockoption is one instrument, while the underlying stock is another.
Is there a difference between the value of a stock option and the value of the underlying share? Many people intuitively think that there is no difference when they first think about valuing stock options.
Example of the logic:
If a company has raised capital from an investor at $14.5 per share recently, then stock options must also be worth $14.5, right? Not quite. It's a little more complicated.
In fact, a specific valuation of stock options must be made using a legally recognized valuation method. These methods take into account the market value of the underlying share, but also a number of other factors.
One factor is the advantage that the recipient has in being able to sit back and assess whether or not it is worthwhile to exercise stock options. If the business develops positively, the recipient can choose to take advantage. If not, they can simply choose to do nothing. Without having to pull money out of their pocket in the meantime.
#2: What does the law say?
7P tells us:
“The remuneration must be clearly identified”
“Remuneration” here means the market value of the stock options as determined using a recognized valuation methodology. Not the value of the underlying stock. Not the cash pay cut that the company may have agreed with the recipient.
We need to do a valuation with a recognised methodology to be able to use 7P. However, the wording of the law does not say anything about how that valuation should take place. Nor does it say what method we should use.
We're going to have to dig a little deeper.
A law doesn't just get passed. It typically a lot of deliberation from lawyers, industry professionals and politicians goes in advance. These considerations are collectively referred to as the “preparatory works” of a law. If we look in preparatory works for 7P, we find something interesting:
“Over time, the The Assessment and Taxation Council has approved several different methods for valuing stock options.”
The preparatory works continue:
“
[...]
In practice, the application of the Black-Scholes model is widely used in the valuation of stock options, even when the underlying shares are unlisted. The volatility has a significant impact on the value of stock options and cannot be directly read in the market.".
Black-Scholes is the first method mentioned by the preparatory works. We are also told that we can use Black-Scholes, even if we are dealing with unlisted companies. This is perhaps a little surprising seen from the outside. Why? Because Black-Scholes requires us to determine the volatility of the underlying stock, that is, the fluctuations in the share price over time.
But how can we determine the volatility if underlying the share is not publicly traded?
The preparatory works continue:
“
[...]
For unlisted companies, the volatility of shares of comparable listed companies can be used. Comparable listed companies mean companies within the same industry, for example. Companies in the same industry are subject to the same market conditions and are therefore likely to have the same value-creating assumptions, including profitability, growth and risk. Such companies are not necessarily at the same level in terms of profitability, growth and risk. These general criteria can therefore be advantageously emphasised in the selection of comparable companies'.
So the preparatory works continue want us to find a group of comparable listed companies and look at their volatility. Again, a bit surprising. Some professionals believe that it makes no sense at all to estimate the volatility of unlisted companies, especially in start-ups and other young companies. Possibly, but the preparatory works say it clearly: Black-Scholes can be used - and is being used in practice - also for unlisted companies.
Black-Scholes is the first method mentioned by the preparatory works, but not the only one:
“
[...]
For the valuation of stock options for shares not admitted to trading on a regulated market, the Assessment Board has established an indicative calculation model. Furthermore, the binomial model is used in practice, but it occurs significantly less frequently.”
In short, the formula of the Assessment Board is a simple method, which was established in 1992. The formula does not use volatility and is simple to use.
Preparatory works, continued (statement of the then Danish Minister for Taxation, dated 96/97):
“
[...]
The formula of the Assessment Board expresses a calculation model that can guide the estimation of the value of the asset, but the calculation model cannot simply be used unconsciously. On the contrary, it is necessary to consider whether the formula, taking into account the specific circumstances of the particular situation, can be assumed to lead to a correct valuation.”
Thus, we cannot automatically use a given valuation method without first assessing whether the method is correct. That assessment includes, among other things, the result of the method itself, which must be “correct”. The logical conclusion must be that if one method does not provide a correct valuation, we must find another method that does. We need to make an overall assessment.
Overall:
The preparatory works spend considerably more effort describing Black-Scholes than the Tax Council formula and the binomial model. That could suggest that we may need to see Black-Scholes as the primary method of valuing stock options- including for unlisted companies.
#3: What do the tax authorities say?
The tax authorities emphasise that it is not possible automatically to apply a given valuation method without further thought. One has to assess each case to determine which method is best suited.
Since the 90s, tax authorities have gradually tried to narrow the scope of the Tax Council's formula. The tax authorities themselves refer to the formula as the “Tax Council's indicative formula”. This indicates that one cannot blindly settle for using the formula without considering alternatives. At the same time, Black-Scholes is being brought more and more into play - including for unlisted companies.
An example is a decision from 2019 (SKM 2019.390.SR). A private equity fund had purchased a company and subsequently wanted establish a warrant programme. Should one use the Tax Council's formula or Black-Scholes to value warrants? Black-Scholes gave a valuation that was about twice as high compared to using the Tax Council's formula. Perhaps that was why the private equity fund argued for the application of the Tax Council's formula.
Why does valuation matter? The ruling does not mention it, but one reason could be the following:
7P allows for awarding warrants to employees for advantageous taxation. 7P has some percentage thresholds that determine how many warrants one can grant. Valuation therefore becomes crucial to the question of exactly how many warrants can be obtained to fit under 7P. If one operates close to the limits, one may have an incentive to argue for a valuation method which provides the lowest valuation per warrant.
What did the tax authorities say?
“The Danish Tax Agency is of the opinion that the Tax Council's indicative formula should not be used when calculating the value of the warrants in question, as it does not take into account, inter alia, volatility and asymmetric profit opportunities, see below. On the other hand, the Danish Tax Agency considers that the Black-Scholes model should be used in the present case.”
We can note that the Danish Tax Agency sees it as a problem that the Tax Council's formula does not include volatility and asymmetric profit opportunities. Perhaps we should see this as a general problem, perhaps only as a problem in the specific case.
Further:
“The Black-Scholes model is an internationally recognised method for calculating the value of options. One of the elements included in the Black Scholes model is the volatility of stocks. Volatility is a term for fluctuations in the value of an asset. Therefore, in tax law practice, the Black Scholes model is used preferentially for the valuation of stock options relating to shares admitted to trading on a regulated market, where the volatility (sensitivity to price fluctuations) of the shares can be quantified.
However, the Danish Tax Agency is of the opinion that with the available financial tools it is possible to calculate the volatility of a company such as the company in question. Thus, there are indices of volatilities in comparable industries in which the operating company under the holding company operates. For its calculation, the Danish Tax Agency has specifically used Damodaran's industrial index of option volatility.“
The Tax Agency mentions the availability of”indices of volatilities in comparable industries“.
Perhaps the Danish Tax Agency is indicating here that over the years it has become easier to find volatility data for comparable listed companies. It may speak in favor of an expanded use of Black-Scholes.
I myself have built a Python script which, using data from Yahoo Finance, can calculate the volatility of any group of comparable listed companies. Those types of tools have not always been so readily available. They make it considerably easier in practice to use Black-Scholes for unlisted companies.
#4: The Board of Equations Formula
The Tax Council's indicative formula for the valuation of stock options looks as follows:
H x L x R /100 = F
H = The trading value of the underlying share as a percentage of the exercise price
L = Maturity given in months
R = Discount account at the time of grant + four per cent reduced by 50 per cent, corresponding to the loan interest after tax stated per month
F = Value of a stock option as a percentage of the market price of a share
Let's take an example:
An unlisted company is considering issuing stock options to a group employees under 7P. The company is now considering how many stock options,
each employee can be granted.
Terms:
- Stock options mature (vests) over a period of four years
- Stock options can be exercised after four years if the employee has been employed throughout the entire period
- The market price per share is DKK 100.
- The exercise price per share is DKK 80, i.e. 80% of the market price of the underlying share
What value would stock options have when using the Tax Council's formula?
H = (100 kr/80 kr.) x 100 = 125
(Trading value of the underlying share as a percentage of the exercise price)
L = 4 x 12 = 48
(Maturity given in months)
R = (3.35% + 4% x 0.5)/12 = 0.4458333333
(The discount at the time of grant + four per cent reduced by 50 per cent, corresponding to the loan interest after tax given in months)
F = (125 x 48 x 0.4458333333)/100 = 26.75%
(A warrant's value as a percentage of the market price of a share)
Valuation per warrant: = 0.2675 x 100 = 26.75 kr.
Tax authorities have continuously stated that the formula is indicative only for the estimate of the value of warrants. At the same time, according to the authorities, the calculation model assumes a certain “naturally justified” correlation between the current market price of the underlying shares and the exercise price of the warrants.
This should probably be understood as follows: if the exercise price deviates too much from the current market price of the stock, you cannot use the formula. What's “too” much? I haven't looked at legal sources on that. However, indications can be found by testing the formula with different utilization rates. A very low exploitation price, e.g. nominal value of DKK 1, gives an unrealistically high value per warrant. It speaks to the fact that you can't use the formula in those cases. Conversely, an exercise price of, for example, 80 - 100% of the market value of the stock, typically gives better results. This suggests that the formula is more applicable when we work with utilization rates in that rental.
#5: Black-Scholes
The Black-Scholes formula looks as follows:
W = M x N(D1) - U x (e^-r x t) x N(D2)
W = Value of a warrant in NOK
M = Market price of the underlying share in NOK
U = Utilization price in NOK
r = The discount at the time of award
t = Maturity specified in years
N = Normal distribution function
σ = Volatility
D1 = (ln (M/U) + (r + σ^2/2) t)/(σx√t)
D2 = d1 - σ√T
e = Euler's Number ≈ 2.718281828
This version of the formula applies to so-called European call options, which can be exercised at some point in the future. At the same time, the formula does not take into account dividends, which may be paid during the term of the option.
Let's take the same example as above:
An unlisted company is considering issuing warrants to a group
employees under 7P. The company is now considering how many warrants,
each employee can be assigned.
Terms:
- Warrants mature (vests) over a period of four years
- Warrants can be exercised after four years if the employee has been employed throughout the entire period
- The market price per share is DKK 100.
- The exercise price per share is DKK 80, i.e. 80% of the market price of the underlying share
What value would warrants have using Black-Scholes?
M = 100 (Market price of the underlying share in NOK)
U = 80 (Utilization price in NOK)
r = 3.35% (The discount at the time of award)
t = 4 (Maturity given in years)
σ = 40% (Volatility as estimated using a comparable group of listed companies)
N (d1) = 0.8
N (d2) = 0.52
W = 43.86 kr.
Valuation per warrant = 43.86 kr.
Above, we saw that we get a valuation per warrant of DKK 26.75 when using
of the Board of Equations Guiding Formula. One would think that lowest possible
valuation will always be in the interests of the company and the beneficiaries. So that as many warrants as possible could be fit under 7P. However, this is not the case. The main thing is to minimize the uncertainty in the system.
#6: Binding Answer
Does the Tax Agency have to approve the valuation?
No, there is no requirement for approval of the valuation to use 7P. This lack of approval carries some risk. Could it be imagined that, in the long term, the tax authorities might question our specific use of 7P, including the valuation? It is not impossible, but there is a solution.
In fact, it is relatively simple to ask the Tax Agency for a so-called binding answer. Here you can ask about either warrants you have granted or are considering granting. For example, you can ask authorities to confirm or deny that a given valuation is correct. In autumn 2024, there is an estimated case processing time of about 6-8 months.
There are two options after asking for a binding answer:
You can either wait to issue warrants until you get a response.
The alternative is to issue warrants immediately and then await the response. If you do the latter: If the Swedish Tax Agency agrees with the valuation, the risk of future uncertainty has been eliminated. If Skat disagrees, one can adjust the program in order to meet the requirements of 7P. However, it requires that you have set up your program right to avoid tax problems. After that, you can choose either (1st) to send a new request for a binding reply, or (2nd) stick to adjusting using the guidelines one received in the first reply.
#7: Who does the valuation?
There is no requirement for any particular person or company to make the valuation. It is therefore not necessary to use, for example, a certified or registered accountant, economist, lawyer or lawyer. It is possible for the company to carry out the valuation itself, provided that you have the necessary skills internally. Alternatively, you can hire a specialist provider who is not necessarily an accountant or lawyer.
The crucial thing is to carry out a well-considered individual valuation of warrants based on the practice of the Tax Authorities and to carefully document the individual steps in the process.