In the present legal environment it's not possible for a country to exit just the Eurozone voluntarily, by itself. The only sure way is the complicated scenario in which a country would leave the EU and rejoin it without rejoining the Eurozone; it is so far out there that I doubt you can find any serious economic analysis of it. A few other scenarios have been posited in which all the EU member countries would essentially have to agree to it... but since they have given no indication they would do that for Greece, it's even more doubtful they would do it for Finland.
I actually voted to close this question as primarily opinion-based, but retracted since that is unfair given that I do answer it, even though with a "not really answerable" answer in many (and actually in the least unplausible, IMO) scenarios. It also turn out there is one paper, albeit not a deep analysis attempting to estimate this for Finland in particular. And given that a somewhat similar question about the costs of Brexit, wasn't closed... and that I answered a specific-Brexit-scenario question myself... I will answering this in more depth, to the extent that is possible based on publications I found.
Regarding euro-exit, for starters, you can read opinions/proposals like
In 2018, Columbia University economics professor and Nobel laureate Joseph Stiglitz, in the context of arguing that Italy faces "a choice [the country] shouldn’t have to make: between membership in the Eurozone and economic prosperity," remarked that "the challenge [of exit] will be to find a way to leave the Eurozone that minimizes the economic and political costs. A massive debt restructuring, carefully done, with special attention to the consequences for domestic financial institutions, will be essential. Without such a restructuring," Stiglitz argued, "the burden of euro denominated debt would soar, offsetting possibly a large part of the potential gains." He claimed that from "an economic perspective, the easiest thing to do would be for [the exiting country's] entities (governments, corporations and individuals) to simply redenominate debts from Euros into the new [national currency]" and then "enact a super-Chapter 11 bankruptcy law, providing expeditious recourse to debt restructuring to any entity for whom the new national currency presents severe economic problems."
But that's not really an answer that quantifies anything, like what would the blowback be if a EU member unilaterally did this.
Likewise, there are some off-the-cuff estimates, such as:
At the American Economic Association's annual meeting of 2015, Berkeley University economic historian Barry Eichengreen predicted that the withdrawal of a member state, such as Greece, from the Eurozone, would "set off [a] devastating turmoil in financial markets."
Actually this one offered a sort of quantification calling it "Lehman Brothers squared", but offered no deep analysis behind that "number".
For Italy, it turns out there is more serious attempt to quantify something. There's a 2017 paper by Bagnai et al.. It finds that if Italy exited the euro,
the Italian economy would recover its pre-crisis GDP level by 2020 i.e. five years before the year currently assumed by the IMF.
However, some of the caveats are that they assume the worst the EU could do in return is to impose
a retaliatory tariff on Italian products by core countries, equal to 5% for the first two years of the simulation sample
And another limitations is that they basically assume a fixed exchange rate for the new currency
In conceptual terms, our simulation experiments therefore amount to analysing the effects of realignment within a system of fixed exchange rates.
Frankly this seems a big limitation given that somewhat similar analyses on Greece have suggested its new currency would face fairly rapid devaluation.
And as it turns out, one of the handful of papers citing Bagnai... is one about Finland, Malinen et al. (2018). Its abstract concludes:
Although there is a way out of the euro for Finland and other member countries, exit would not be easy, nor would its short-term costs be known beforehand with any clear margin. We find the lack of a domestic payments system and uncertainty concerning the redenomination costs to be the biggest risks associated with the cost of Finland’s exit. Still, the costs of Finland’s exit need not be very large, around 10 billion euros in the best-case scenario, but we also acknowledge a very costly scenario for the exit.
The authors favor a unilateral exit after secret preparations. But in the draft one can find on SSRN, on page 11 the authors acknowledge that
Probably the biggest single uncertainty concerning the euro exit is the role that the exiting country would have in the EU after an exit, especially in the case of a unilateral withdrawal from the Eurozone.
And on p. 23
What remains unclear is whether the Eurozone authorities are willing and legally entitled to impose EU-related rather than Eurozone-specific hardships on an exiting country. If a country exiting the Eurozone also faced exclusion from the European Single Market, for instance, disincentives could become prohibitive. The European Court of Justice should in such cases be asked to assess whether such practices are legally allowed. The problem is that it may take years for the ECJ to reach a decision on this issue. In any case, present initiatives to develop a multi-speed EU may, under ideal scenarios, affect both the acceptability of exit and the need for retaliation.
On p. 35 it is revealed that in the optimistic scenario (the $10B euros one)
we assume that both ECB and EBA will provide Finnish monetary authorities the support they need and that Finland will be allowed to continue as a member of the EU.
As for the more pessimistic one(s)... they don't advance a figure.
Euro area authorities may be less than helpful in supporting the exit process. In the worst case, the ECB would even immediately stop euro clearing payments from Finland. Finland could also be cut off from SEPA, forcing Finland to rely completely on makeshift measures to run its payments system (see Section 3.1). The commission could even try to oust Finland from the EU, leading to major uncertainty, possibly large legal costs and (probably) to a political crisis in Finland and/or in the EU itself. Unfavorable derivative positions for exit could lead to unexpectedly large-scale losses for firms and banks with, e.g., need for substantial temporary financial support in the case of heavy depreciation of the NM. Finnish authorities could also fail on their preparations and/or on their efforts to achieve the trust of markets. Possible make-shift measures applied in banks could lead to failures of the payment systems causing additional hardship to the economy. These could lead to serious detrimental developments in, for example, Finland’s forex markets, domestic markets, trade and/or the balance of payments. We will not try to estimate these costs or their probability, as they are highly uncertain, but just to note that a much more costly scenario for Finland to exit the euro also exists.
Frankly, for the optimistic scenario the assumption of secret preparations doesn't quite square off with the assumption of complete support from the EU authorities. They do discuss the possibility of leaks (during the preparations) in the paper, but again that is not translated in quantitative terms. They do mention that if secrecy of preparations is not maintained, Finland may have to impose capital controls.
They estimate that 33% of the debts would have to be redenominated. On the plus side (from a realism perspective) they do take into account a depreciation of the new Finnish currency (NM) of 5-15% even in the optimistic scenario. But I find it strange the only effect of a depreciation considered is to actually reduce the cost of the exit, but reducing the value of the debts. The effects of the new currency depreciation on other aspects of the economy is not considered as an exit cost.
(As an aside, the journal in which this latter paper was published, The Economists' Voice "is a publishing forum for professional economists that seeks to fill the gap between op-ed pages of newspapers and scholarly journal articles." Also, I'm somewhat unsurprised that Stiglitz turns out to be an editor of this journal. The journal might contain other similar [Euro-exit] articles, because the topic has been of a fair bit of interest to Stiglitz; he wrote a [Euro-skeptical] book about.)