(or the subtle problem of using unit-less bonus factors)
I have observed some confusion about how to calculate the effect of the bonus provisions of the Power Ledger main sale. This article is an attempt to clarify the confusion.
As documented in Section 6 of the token generation paper, main sale participants are entitled to a bonus of 15% additional tokens
for purchases made in week 1, 10% additional tokens for purchases made in week 2, 5% additional tokens for purchases made in week 3 and 0% additional tokens for purchases made in week 4. In fact, since the token paper was published, Power Ledger has adjusted the bonuses for week 1 and week 2 purchases to be 25% and 15% respectively in the hope that doing so would jump start the main sale which has been lagging, at least in part, because of the poor performance of cryptocurrency markets in recent weeks.
What Does “Additional Tokens” Mean?
What does “additional tokens” mean? Does it mean that if you purchased USD 1000 tokens in week 1, you would be given an extra USD 250 worth of tokens? No, it does not mean that — there is no promise in the token paper to provide a bonus equivalent to 25% of the USD value of a week 1 purchase. The commitment in the token paper is simply to provide 15% (now 25%) additional tokens to week 1 buyers.
So what does “additional tokens” mean? It means additional to the number of tokens that a buyer would receive if making the same USD purchase in week 4, a week in which the buyer would receive no bonus.
Is The 25% Token Bonus Worth 25% Of The USD Contribution? Short answer: No
If a week 4 buyer buys USD 1000 “worth” of tokens and a week 1 buyer gets 25% more tokens than the week 4 buyer for the same outlay, doesn’t that mean that the week 1 buyer receives USD 1250 “worth” of tokens and hence is USD 250 better off?
No. The reason is the week 4 buyer spent USD 1000, but the tokens received are not “worth” USD 1000, but some smaller amount — the week 4 buyer will pay a premium to the main sale token price for his tokens and the week 1 buyer will receive a discount to the main sale price. Without knowing what the final contributions are (the main sale hasn’t finished yet), we can’t say what the week 1, week 4 or main sale price of the token is, but we do know that the week 1 price will be less than the main sale price which will be less than the week 4 price. In particular, we know that the week 4 price will be 1.25 * the week 1 price as shown by the following argument.
Why Does The Token Price Vary In Each Week Of The Main Sale?
If price(w1) and price(w4) are the prices paid by the week 1 and week 4 buyers, then the number of tokens received by the week 4 buyer for USD 1000 purchase is:
tokens(w4) = 1000/price(w4)
The number of tokens received by the week 1 buyer for the same outlay is 25% more than the number received by the week 4 buyer
tokens(w1) = 1000/price(w1) = 1.25 * tokens(w4) = 1250/price(w4)
price(w4) = 1.25 * price(w1)
What Is The Precise Value Of $1000 Purchase Made In Week 1? Answer: It isn’t known yet.
To work out the USD value of a USD 1000 purchase in week 1, one needs to multiply the number of tokens received, by the overall price of the tokens during the main sale:
value(w1) = tokens(w1) * main_sale_price = 1000 * main_sale_price / price(w1)
where: main_sale_price = total contributions / 140m tokens
Of course, until the main sale is over and we can total up all the contributions and divide by the number of main sale tokens, we can’t determine the actual USD value of a purchase made in week 1.
But what we can say is that the USD value of the week 1 bonus is determined by the ratio of main_sale_price to the week 1 price and the USD value of the bonus might be any number between 0% and 25% of the contributed USD value, depending on how all the contributions are distributed across the 4 weeks. The USD bonus value will only be close to 25% if almost everyone buys in week 4, whereas it will be closer to 0% if almost everyone buys in week 1.
It should be noted that only week 1 buyers are guaranteed to have a minimum bonus value of 0% of contributed funds. It is technically possible for week 2 buyers to receive a 15% token bonus, but actually lose USD dollar value w.r.t to their USD contribution because they end up paying a slight premium to the final main sale price for the tokens they purchase. Of course, this shouldn’t be concern to a buyer who believes the value of POWR will rise over the longer term but it may be of concern to buyers who intended to immediately dump their POWR in search of a quick profit.
Misleading Ways To Represent The 25% Bonus
While the statement:
A week 1 buyer who makes a USD 1000 token purchases receives the same number of tokens as a USD 1250 purchase made in week 4.
is technically true (if verbose), a statement like:
A week 1 buyer who makes a $1000 token purchase receives tokens worth $1250.
is very misleading since it implies that the USD value of the week 1 purchase instantly increases by USD 250 — it doesn’t. Unfortunately, the 2nd statement is easier to type, so it gets used even when it is highly misleading.
So, unfortunately, some people actually believe statements of the second kind and also that the mere existence of the bonus program increases the market value of the main sale by some percentage above its actual value, as expressed by the purchases made.
The problem arises, in part, because people are insisting on understanding the bonus as a percentage increase in purchase value. So for example, in:
week 1 bonus = purchase * 0.25
purchase is denominated in dollars and since 0.25 appears to have no units, the bonus must have units of dollars.
Some people realise that the bonus value calculated in this way is a value “used to calculate the bonus distribution” but some people literally believe that this artificial value is a real value some how magically gifted on the week 1 purchaser by the magic of the bonus scheme, even if it is pointed out that if the bonus factor was changed from 0.25 to 100, the bonus would be worth 100x the value of the purchases. When confronted with this absurdity, some people think that the absurdity lies in the use of an absurd value bonus factor 100, rather than the actually absurd conclusion that the bonus “value” represents a real USD value, rather than a calculation artifice.
Token Quotas — A Better Mental Model For Thinking About Token Bonus
So, let’s nip this absurdity in bud from the get go and assign useful units the value 0.25.
week 1 bonus = purchase * 0.25 tq/USD
Here, ‘tq’ stands for ‘token quota’.
When we do this, the bonus ends up with units of token quota and it is much harder to confuse “250 token quota” with “USD 250” since a token quota isn’t obviously equal to USD 1.
So what’s a token quota? A token quota is not an actual token, but the right to receive a portion of the main sale’s 140m tokens. The more USD the buyer purchases, the more token quotas the buyer receives and the earlier the purchaser buys, the greater the bonus the buyer receives. The buyer gets 1 tq per USD purchased, plus a bonus depending on which week the purchase is made: 0.25 tq for week 1, 0.15 tq for week 2, 0.05 tq for week 3 and nothing for week 4.
At the end of the sale, every buyer receives a portion of the tokens in proportion to the relative number of token quota they hold. So:
tokens allocated = (sum buyer’s token quota)/(sum all token quota) * # tokens
So what is a token quota worth?
value(token quota) = value(sum all token quota) / (sum all token quota)
value(sum all token quota) = value(sum all purchases)
value(token quota) = value(sum all purchases) / sum all token quota
Unless all the purchases are made in week 4, the sum of all purchases will be numerically less than then sum of all token quota which means that value of a token quota is necessarily less than 1 USD/tq.
This analysis has highlighted the confusion introduced with omitting the correct units in the bonus distribution calculations. The bonus adjusted USD dollars used in bonus calculations that denominate the bonus in USD are actually worth less than the USD surrendered by the buyer, however, unless this is made explicitly clear, the reader may confuse the bonus adjusted dollars with the unadjusted dollars and so think that a 25% token bonus means a 25% USD bonus — it doesn’t. By using the correct units with the bonus factor, it becomes much clearer that the bonus is best presented as a token quota which eventually becomes tokens when a buyer’s relative amount of token quota is multiplied by the number of tokens in the sale.
In conclusion, a simple mistake in omitting the correct units in bonus calculations can lead to a large amounts of confusion about what the true USD value of a token bonus is — use the correct units for the bonus factor and the confusion should disappear.
Appendix: An Example
The linked spreadsheet shows the weekly token price and bonus value calculations in tokens and USD for a hypothetical scenario. This should not be taken as a prediction of what will actually happen with the main sale. You can make a copy of the spreadsheet and edit it to experiment with different scenarios.
In the scenario presented, every buyer except the week 1 buyer loses a small USD amount w.r.t to their original contribution because the 25% additional token bonus received by the week 1 buyers reduces the volume weighted average price. These losses will be less severe if the relative number of contributions rises in later weeks.
Thanks For Reading!
If you are observing the chat forums associated with the Power Ledger token sale and see someone making these mistakes, feel free to send them a link to this article.
If you have a simpler way to express the same explanation, post a link in the comments.