The question focuses on a personal philosophy rather than something objectively and universally correct. It's akin to pondering the meaning of (a timed chunk of) your life.
But I do want to raise some counterpoints here. I can't give you a universally correct answer, but I do want to show you other ways of looking at it, because your stance seems to heavily depend on your personal outlook.
For the answer's sake, I just want to define two concepts:
- Work - Something you get (reasonably) paid to do, but don't necessarily like doing.
- Fun/free time - Something you like doing and would (reasonably) pay to do (but not necessarily so)
Obviously, this distinction is going to be mentioned a lot.
Is it possible to put this into a rational formula or is it all irrational and emotional?
I wouldn't call it irrational, but it is personal and not objective.
Some people derive happiness from working/being efficient and therefore are able to work without needing to have fun to offset it. Other people don't like their job and thus need to also have fun to balance their life.
These two kinds of people will have a dramatically different attitude towards the value of personal time and what they are willing to spend to improve its quality.
However, taking this into account, how do you work out what your time is worth? [..] Can you explain your decision in a rational manner?
As an example, I can explain one of my rationales. When I buy a videogame (or any similar entertainment for that matter), I have agreed with myself that if I end up spending €1/hour or less, then I didn't make a bad financial decision.
This isn't a hard and fast rule (I've knowingly spent more for once-in-a-lifetime occasions), but it is something I use as a guideline when I'm contemplating spending on something that I'm not yet sure how much I'll enjoy it, or whether I'll regret spending that much money on it.
Why did I come to that number? I did the math. It was based on my income (after taxes and bills), free time, and savings plan. I factored in other costs (such as hardware costs) and figured out that at this rate, I would be having fun and accruing money faster than I'd spend, it so it's a net positive.
Now, five years down the line, I make more money, and I have less free time than I used to (such is life). Therefore, I can now afford to raise that limit to €3-5/hour, depending on how much free time I have.
In other words, the upper limit on cost/quality of my free time is directly correlated to my financial situation after unavoidables (taxes, bills, enforced savings).
Some people go "okay, well I get paid x per hour and that's how much my time is worth".
This is a very basic approximation. It's not wrong, but it is quite simplistic.
For one, if you're in a salaried position where overtime is not paid, this logic does not apply. You can't just spend X dollars on convenience and then use the won time to work extra and gain >X dollars.
The approximation is only relevant when you can work overtime at will, don't mind sacrificing some of your free time to your job, and when you also factor in any additional free time you will need to balance out the overtime you did.
Note: As a real life example, my FIL is able to work paid overtime pretty much at will, and this is exactly how he justifies making personal purchases that don't fit in his household budget.
But there's many flaws with this logic. Firstly, it implies that time and money are completely transferable. That's not true. Unless the opportunity cost of the drive is literally you would be late for work, that 15 minutes is probably not going to be used to create $20 worth of utility. Most of us with an extra 15 minutes would probably just waste it.
The underlying tone here seems to be that you are only valuing financial gains, and not emotional/recuperative gains from "wasting time". That is a very narrow perspective.
"Wasting time" may not net you any money, but that doesn't mean it's a waste of time. "Wasting time" implies that there was something better you could've done but needlessly avoided doing. If that's how you genuinely feel, sure, maybe go do something that doesn't feel like a waste of time.
But beware of the consequences of not letting yourself catch a break once in a while. When you overapply this and push yourself beyond your limits, it's going to have adverse effects.
The other thing is it makes our time incredibly valuable. Watching a movie costs like $40 - for someone on minimum wage. That's not including travel and ticket costs.
This argument again assumes that any free time is the needless avoidance of work time, which is a (in my opinion ridiculous) baseline. All work and no play makes Jack a dull boy, at least in my opinion.
Your statement is only correct if you genuinely think that the baseline of human life is to work every waking moment spent on non-essentials (such as eating or other bodily requirements).
And you may be right for some people. I personally know some people who can happily keep working all day with no need for free time. Seeing posts on SE also introduces me to other cultures where this pro-work attitude is still prevalent.
But, on the other side, every single one of these people I personally know (at least the ones I've known for more than a decade) has ended up with a severe long-term burnout because they overexerted themselves.
I'm not going to label anything as good or bad (it's a pointless discussion) but it is important to live your life sustainably, which means you need to avoid overexertion over extended periods.
Before you can decide on how much you spend on convenience/free time, you must first decide on your priorities. This is personal. A basic example of priorities would be:
- Saving up to $250/month
- Quality of life (free time, entertainment, luxury foods, activities, ...)
- Remaining savings
This is just a basic example. Do note that all bullet points inherently imply cost vs quality considerations. E.g. you wouldn't pay $1000 for an apple, even if food is your main priority.
After the priorities are decided, the math becomes relatively simple.
- Take your income
- Subtract all priorities higher than free time.
- Take an average cost into account for all things that are not fixed (e.g. groceries).
As a demo calculation:
$2500 monthly income
- $600 groceries
- $900 rent+bills
- $300 family/child care
- $250 savings
= $450 left
So you have a $450 "party fund".
Next, you need to consider how much time in a month you have to spend on leisure. Let's say that after the essentials (work, cooking, family care, ...) you average 3 free hours per day = 90 free hours per month.
You quickly realize that if you consistently drain your party fund during those 90 hours, you will average a spending of $5/hour or less.
Note that you or course don't have to spend it all, but because you already subtracted the minimum savings you want to keep each month, you have effectively agreed with yourself that you're allowed to spend the entire party fund if you have a valid reason to do so.
If you are able to fill your quality time at a lower cost (e.g. spending only $300 on free time in a month), and you find yourself wishing for more free time, then you can start evaluating whether spending $20 to convert two hours of busy time into free time is worth it to you.
I can't make that decision for you. But you can do the math yourself, based on your priorities and your evaluation of what benefit you derive from the convenience you pay for.
To summarize the most important points:
- If you can work overtime at will, and you love your job enough to not need to offset it with leisure time, and the convenience costs less than you can earn while working the same amount of time that the convenience saves you, then it makes sense to pay for the convenience and do your (financially more efficient) work instead.
- If you don't love your job and require X free time to balance your life after having worked Y hours, then you need to take this into account whenever you decide to work more. If you're considering working more to get some extra spending money, you need to count this as needing to invest X+Y (work + balanced free) time into it, not just work time.
- If you wish to have more free time, and have excess funds in your "party fund", then you can evaluate whether the financial cost of a convenience (which nets you a given amount of extra free time) is worth it to you. This is a quality vs quantity argument for your free time.
These are all just simplified examples to show you the variety of approaches/outlooks you can have on your work/personal life. Everyone's life is different, everyone has their own experiences, and everyone will have to adapt this philosophy to what matters to them.