While it's fine to look at opportunity costs, I'd suggest to separate them a bit more from costs for things that have to be paid during that year (health + long term care insurance).
First of all, to get a common basis for the comparison I'll use these numbers from the gross-net-salary calculator here for 73000 € annual employee's gross as they differ from OP's calculation.
month year
gross wage employee 6.083,33 € 73.000,00 €
taxes employee
Solidaritätszuschlag 78,67 € 944,04 €
church tax: 0,00 € 0,00 €
wage tax: 1.430,50 € 17.166,00 €
social insurance employee
pension: 565,75 € 6.789,00 €
unemployment insurance: 76,04 € 912,50 €
health insurance: 351,66 € 4.219,88 €
long term care insurance: 80,54 € 966,49 €
employee net wage 3.500,17 € 42.002,10 €
social insurance employer
pension: 565,75 € 6.789,00 €
unemployment insurance: 76,04 € 912,50 €
health insurance: 351,66 € 4.219,88 €
long term care insurance: 69,20 € 830,36 €
Sum costs employer: 7.145,98 € 85.751,74 €
Costs that need to be payed during that year
taxes: income < 9168 € => 0 € income tax
Nevertheless, the tax office may not believe that someone who starts full-time freelancing is not going to generate any income. So they may ask for advance tax. This will be payed back after the income tax declaration for the year is done, but nevertheless needs to be payed during the year in question.
Health + long term care insurance: Minimum contribution in the "volountary obligatory insurance" category is a bit more than 185 €/month, so 2232 €/year (cheapest category with no sick pay - but as there's no income, no income needs to be replaced).
However, as long as employment is the majority of income/work time, freelancing as a side business is covered by the insurance fees for the employment. For a freelancer who doesn't have any income, any job that pays > 450 €/month would cover that unsuccessful freelancing business as well. For 451 € monthly employee's gross, that would be ≈85 €/month, or 1017.48 €/year.
You figure 1200 € (100 €/month) for train tickets to interviews.
Now I am a freelancer and I hardly ever travel to customers without being reimbursed. Interviews/negotiations take place in phone/video conferences. Some budget for trade fairs and conferences may be needed, though.
- Does your unsuccessful freelancer really not have any other costs for their business?
No rent, no hardware, no software, no books, no tax advisor, no nothing?
Opportunity costs:
salary: IMHO it's going to be pretty hard to make more money in the very first year of freelancing than as employee (and remember, their gross freelancing income is the equivalent of the employer's gross of 86 k in the example!) as there's no customer base yet, tons of burocracy to be learned, ... Still, there should usually be some sales.
Here's a back of the envelope calculation. A year has ≈ 1760 working hours. Let's assume that your freelancer has an easy customer/business structure where they even as a beginner have only 1 unbillable hour of work per billable hour of work (optimistic assumption). That's 880 billable hours per year, and refers to years with no paticularly long time without projects. Assume further, our freelancer can place their services at 88 € / billable hour. That would be 77.5 k€ sales per year (after costs that are directy billed to the customer such as travel). Of this, all costs that are not directly billable to the client need to subtracted to get the gross income. To be better off than as employee, this gross income would roughly need to be larger than the employer's gross above (86 k€) plus some compensation for the risk of being out of project for a longer time. Here, even if there were basically no such costs that would require either hourly rate > 100 €/h at 880 billable hours or > 1000 billable hours at 88 €.
Both doable, but IMHO the estimates for the first year should be more conservative.
retirement/pension plan. Currently (2019), the (preliminary) average wage to get 1 pension "point" is 3242 €/month, so our employee gets 1.08 points in return for 13578 € annual contribution. Those 1.08 points would currently correspond to 34.58 €/month pension.
Now, for a freelancer who is not obligatory in the governmental pension system it is their own choice how to take care of their pension. Thus for the freelancer, the opportunity cost here is whatever it takes to get 34.58 €/month when they retire - which can be drastically lower than the governmental pension cass fees, but shouldn't be more* as they can do a volountary contribution to the governmental pension cass.
(A bit difficult to find in a quick online search, but some online tools suggest that a one-time payment of 4000 - 8500 € would lead to a Rürup pension in that order of magnitude. Rürup contracts behave rather similar to the governmental pension system but are capital based and have tons of choices, hence the spread. In any case, such a contract is to be had for quite a bit less than employer + employee contribution to the governmental pension cass for the same amount of pension).
Such a contract would probably not be the tool of choice for our freelancer in the described situation, though. *They'd rather consider putting money in such a contract or the governmental pension a bit later on when they can use the tax deduction or go for their own investments anyways.
What did I miss?
Someting is either not realistic at all in your scenario, or your freelancer is not a practical business person so should never have started this adventure in the first place.
Besides the lost opportunity to earn wage, what do they live off?
(This whole thing would look totally different if we knew they had reached the f*-you-state of wealth due to their previous 10 years of employment)
The peculiarities of the German social insurance system mean that unless you are really sure to generate a good income right from the beginning, so should not jump from 100 % employee to 100 % freelancer. It's much better to start freelancing as a part-time employee.
As you say in a comment, starting a full-sized freelancing business aside a full-time job is not going to work in the long run. But depending on the relations with your employer (who needs to know that you start freelancing), you can prepare your freelancing (do the burocracy) and negotiate your first freelancing jobs while still employed without a problem. Also for readers outside Germany: German employees have a right to downsize their day job to part-time (depending on size of employer's business and unless the employer can show "good reasons" against this).
Finally, getting a part-time job besides starting a freelancing business should not be too difficult for an IT person - that may not be as well paid as a full time position, but that opportunity cost is offset by this ensuring a certain income regardless of how the freelancing works out.
Plus, our hypothetical freelancer could go for part-time jobs that cover e.g. afternoon times that very few part-time employees are willing to cover.
What is your unsuccessful freelancer doing with their time?
- If they are completely unsuccessfully trying to find customers full time, they should stop to think much, much faster than after a whole year.
- OTOH, it is fine to say try out whether this works with spending, say, 1 or 2 days per week looking for customers and then as long as there is no billable work use the remaining time to reduce the opportunity costs in terms of lost salary:
- either work some flexible side job
- do DIY work that saves hiring someone else to do this (particularly if they are home owner)
- improve their professional skills. The latter would then mean that they may catch up with the lost opportunities when they look for employment again.
You are also missing that employers pay some insurances that the freelancer may want to have as well. E.g. Accident insurance and 3rd party liability insurance. (Without income, they won't be able to get occupational disablement insurance)
