# Deducing purchasing power equivalent salaries under tax between two countries

I am trying to figure out how to compute the equivalent salary in a country `B` given a salary in a country `A` by taking into account purchasing power parity and tax rates in both countries. The computation I arrived at is the following, but I am not 100% confident that it is correct to do it this way:

Let `s_A` be the current salary in country `A`, with a tax rate of `t_A`. Let `e` be the exchange rate from `A` to `B`. Let the purchasing power factor between `A` and `B` be `p` (1 of `A`'s currency in `A` buys you `g` goods, while 1 of `A`'s currency after basic exchange rate conversion buys you `p` times `g` in `B`).

Given these numbers:

1. Determine net pay `n_A` after tax in country `A`:
• `n_A = s_A - (s_A * t_A)`.
2. Determine corresponding amount of money `m_B` in currency of country `B` through simple exchange rate.
• `m_B = n_A * e`
3. Determine amount of money `m_B'` in currency of country `B` that has the same purchasing power in `B` as `n_A` has in `A`.
• `m_B' = m_B + m_B * p`
4. Find amount `s_B` of salary in currency of `B` that yields `m_B'` after applying the correct tax according to the laws in `B`.

Example. Say we have a salary of 100,000 EUR per annum in Germany, and we want to know the corresponding relative salary in Norway. I follow the algorithm from above:

1. 100,000 EUR salary in GER after tax = 57,000 EUR due to 43% tax rate
2. 57,000 EUR = 581,400 NOK base exchange rate
3. 57,000 EUR in GER purchasing power = 581,400 NOK + (581,400 NOK * 24%) = 720,100 NOK in NO purchasing power since a Euro only has 76% of its purchasing power in Norway.
4. 720,100 NOK requires 1,050,000 NOK salary due to 33.4% tax rate

Hence, the equivalent relative salary for a 100,000 EUR salary in Germany would be a salary of 1,050,000 NOK in Norway.

Is this calculation valid?

• How are you determining purchasing power? Feb 22, 2022 at 1:42
• A note (that doesn't change your basic calculation, just the numbers): Income is usually taxed progressively, so e.g. the first 10k are taxed at 0% and e.g. only the amount above 60k is taxed at the highest rate. That way, the tax for 100k in germany turns out to be 27k, not 43k. Also, you may want to consider other "taxes" like health insurance. Feb 22, 2022 at 1:45
• @RobertLongson I googled it. I found several sources agreeing on roughly 75% for EUR relative to NOK. For example, this calculator: salaryconverter.nigelb.me Feb 22, 2022 at 7:39
• @Solarflare Good point about things like health insurance in general. In the example of GER and NO, these are part of the basic taxes though. But I think the income tax in Germany for a salary of 100K really does end up at 43K taxes. I used this calculator, and it was always correct so far for me personally: brutto-netto-rechner.info Feb 22, 2022 at 7:44
• Ok, the net income seems to turn out to be 57%, but it's not all taxes, just wanted to make sure you are not mixing things up. While health insurance is, depending on the country, arguably tax like (you pay a percentage and don't actually get more benefit if you pay more, and may or may not be able to opt out), payments for pensions (and maybe other social insurances), while reducing net income, is something you (at least in theory) get back later again/stay your own, so you may (or may not) want to treat them differently than pure tax, which is just gone. Feb 22, 2022 at 12:00