Keeping butterflies in your house is a pretty huge return on investment, though a slow one. I'm going to stick with donation-based valuation because it leaves a lot of questions aside. A butterfly egg is worth 400, so for 400 currants you get to make 3200 currants over the course of six and two-thirds real days. It's 17.5 currants an hour for very minimal upkeep.
So singing lets you earn another 24 currants from that butterfly, but assuming you are already keeping your maximum number of butterflies around this delays the onset of the next butterfly by one hour and 12 minutes as well. In the end, if you run a tight ship you still make 17.5 currants per hour, you only delay the reinvestment in a new egg by just over an hour.
So instead of net earning, we would need to look at gross earning and expenditures to figure out how much singing is worth - even though at this point it is extremely obvious that it is worth next to nothing. You are earning 20 currants an hour from milks but losing 2.5 currants an hour from the amortized price of your egg. Singing does not affect your income, but saves you 1.2 hours of payments. So the currant value of singing to a butterfly is 3. Even if you are level 1 this is a bad return for your 10 energy.
In a world where you are a rational economic being you would only possibly be singing to butterflies if you want the xp. So the 3 currants could be seen as a bonus. The question of whether singing to butterflies is a good way to earn xp or not is something I'll leave for another time. At this time, the real question is how can we convert currants to xp to figure out how much our 3 currant bonus is worth.
Unfortunately there are a large number of ways to convert currants to xp and all of them are capped per day. Activating broccoli gives 80% of an xp per currant. Sno-Cones give around 55%. Donating to shrines gives only 20% but people still regard this as one of the top ways to earn xp. By the fact that people donate specifically for xp and the fact that people would donate more if they could, we can safely say that xp is worth at least five times as much as currants in the public evaluation. That would leave the currant bonus from singing to your butterflies being worth at most 0.6 xp before mood bonuses.
Given that this is completely meaningless, we could ask the question: how much would singing have to extend the life of a butterfly to make it worthwhile?
Singing at level 60 costs 286 energy. I typically use 0.8 for my energy:currants ratio, but since I'm talking donation currants, not cash currants, here, it is more appropriate to use a ratio of 1. After all, in order to turn those currants into energy I'd first have to liquidate the resource. In fact, since I know I'm talking about Butterfly Milk here, I could even use a ratio of 1.07 since we know milk only sells for 75% of list value due to rounding. But I'm going to set that aside since a good is a good and a currant is a currant.
So unless something is returning at least 1 donation currant value per energy I'm losing out. How much extra milk would give my 286 currants of value back? Since each milk takes 0.4 hours to produce and we're saving 2.5 currants an hour to produce them, each milk saves us 0.5 currants. So it would have to extend the life of the butterfly by 572 milks rather than 3.
Of course then I would only be able to sing to a butterfly every 9.5 real days without overloading it with milks that I would never collect.
Next week I'll look into how much xp you are getting from singing to butterflies to create a more complete approximation of the value of doing so. Without having done the math yet, I'm already pretty such that most of the value of singing to butterflies is tied up in "la!" I will also start experiments on how multiple milkers affect milk collection rate.
Until next time,