# TempleDAO - Exploring The Pumpamentals

(Image by raccoon#0991)

This is a summary of some of the conversations around mechanics we've been having in the Discord.

### Contents
1. [Intrinsic Value & Price Ceiling](#intrinsic-value-&-price-ceiling)
2. [Runway](#Runway)
3. [Risk-Free Value](#Risk-Free-Value)
4. [Bank Runs](#Bank-Runs)
5. [The Code](#The-Code)

### Intrinsic Value & Price Ceiling
Many Templars have been speculating about the price of TEMPLE. Wen TEMPLE $100? Wen IV $2?

But the price of TEMPLE functions very differently from your average shitcoin–it can't just pump 10 or 100x. That wouldn't be very safe or sustainable, would it?

Luckily for us, we can build models that predict the growth of the IV based on treasury growth.

So let's look at some numbers. Let's say these are the current stats for TempleDAO (and as I'm writing this, these are the actual stats):
- **Treasury Value:** $149,047,354
- **Fully Diluted Supply:** 235,322,570
- **Circulating Supply:** 57,066,190
- **Intrinsic Value:** $0.633

Now let's see how the IV grows as more and more FRAX is sacrificed:

| Treasury Growth | Treasury % Growth | New IV | IV % Growth |
| --------------- | ----------------- | ------ | ----------- |
| $50m | 33.56% | $0.66 | 4.26% |
| $100m | 67.1% | $0.69 | 9.00% |
| $500m | 235.57% | $0.81 | 28.57% |
| $1B | 571.14% | $0.89 | 40.60% |
| $2B | 1242.28% | $0.99 | 56.40% |
| $10B | 6611.41% | $1.28 | 102.21% |
| $50B | 33,457% | $1.67 | 163.82% |
| $100B | 67,014% | $1.87 | 195.42% |
| $147B | 98,557% | $2.00 | 215.96% |

For the more visually-minded, here's a chart showing the same thing:

As you can see, the bigger the treasury grows, the less the intrinsic value goes up (technically speaking, intrinsic value increases logarithmically as the treasury grows).

Intuitively, why does this happen? Well, the more FRAX is sacrificed, the more TEMPLE is minted, which increases the amount of additional FRAX that must be sacrificed in order to further pump the IV. You'll see this type of dynamic in the other sections as well.

Importantly, this model assumes the treasury **only grows through FRAX sacrifices.** As Temple develops new sources of revenue, the IV will increase faster than what is shown here.

Now, how does this affect the price of TEMPLE? Well, as you know the TEMPLE price ceiling is pegged to a multiple of the intrinsic value (currently 6x), and so the price ceiling can only increase proportionally to intrinsic value.

Since we just saw that the IV will increase very slowly with treasury growth, we should expect the price ceiling to also go up very slowly. Sorry, Templars, your TEMPLE won't be worth $100 any time soon.

### Runway
At the time of writing, the runway is 122 days. This means the protocol can afford to distribute daily 0.7% yield (the current EPY) for 122 days without diluting the IV.

Having a sustainable runway is very important. At the very least, we want a runway that doesn't decrease. At best, we want a runway that's increasing over time (temporary decrease is fine and to be expected).

So how sustainable is the current runway? Let's see.

The runway depends on a few factors:
- The total supply
- the staked supply
- the EPY (daily yield)

I'm not going to run through the entire runway calculation here. Anyone who's curious can search through the discord for explanations or look through the code I provided below. If you can't be bothered to do that, don't worry. You can wait for my post on runway.

Anyway, let's see how our runway grows as the treasury grows (remember, the current runway is 122 days):

| Treasury Growth | Treasury % Growth | New Runway | Runway % Growth |
| --------------- | ----------------- | ------ | ----------- |
| $50m | 33.56% | 127 | 4.09% |
| $100m | 67.1% | 130 | 6.56% |
| $500m | 235.57% | 138 | 13.11% |
| $1B | 571.14% | 140 | 14.75% |
| $2B | 1242.28% | 142 | 16.39% |
| $10B | 6611.41% | 144 | 18.03% |
| $50B | 33,457% | 144 | 18.03% |
| $100B | 67,014% | 144 | 18.03% |
| $147B | 98,557% | 144 | 18.03% |

And once again, for the chartoooors:

As you can see, the runway eventually plateaus. The highest the runway can be given current protocol parameters, assuming the entire circulating supply remains staked, is roughly 145 days.

**Note:** this model assumes the entire circulating supply is staked, and that more FRAX is coming into the staking pool faster than staking rewards are being distributed.

The actual numbers you're seeing on the table show what the runway would be if the treasury grew by the given amount **tomorrow**. For example, If tomorrow suddenly 1 billion FRAX was sacrificed, then the runway would jump to 140 days.

### Risk-Free Value
Before we calculate the risk-free value (RFV), let's understand what it means and how it's different from intrinsic value (IV).

Each TEMPLE token is backed by some amount of FRAX,and the protocol guarantees that you can always sell your temple to it for this amount. We call this amount the IV.

But if you think about it, each TEMPLE token you own actually entitles you to more than just the IV.

The reason?

Staking rewards.

Let's imagine the worst case scenario for Temple: nobody wants to buy Temple anymore, all revenue stops coming into the treasury, and the price falls to the intrinsic value. What then?

Well, as bad as this sounds, we'd still be reliably getting our staking rewards. So in reality, the amount of money we'd get would actually be *more* than the IV in this worst case scenario. How much more? Let's do some quick mafs:

Our runway is currently 122 days, the IV is $0.633 and the daily yield rate is 0.7%.

So if I stake 1 TEMPLE, by the end of the runway, how much TEMPLE would I have?

$$ 1 \ \textrm{TEMPLE} \cdot 1.007^{122} = 2.342 \ \textrm{TEMPLE}$$

And since the IV is $0.633, the value of my holdings by the end of the runway would be $1.48.

In a sense, this is the RFV of each TEMPLE token, because you're 'guaranteed' (not really, because protocol parameters can be changed) this much FRAX if you can wait long enough to receive all the staking rewards.

There's also another definition of risk-free value. If Temple were to really just straight up fail, it would make sense for most/all of the treasury to go back to the TEMPLE holders.

So to get the RFV of each TEMPLE, we'd divide the treasury value by the circulating supply (all the TEMPLE not owned by the protocol). With the current metrics, this RFV works out to be

$$\$149,047,354 \ / \ 57,066,190 = $2.61$$

So there you have it, two different definitions of risk-free value for TEMPLE.

It's interesting to compare the RFV of Temple to other similar protocols like Olympus, etc.

The current **market-value per OHM** is ~$179, and the current RFV per OHM is ~$40.5. Since the current price of OHM is $792, it's a 4.42x multiple of the market-value, and a 19.5x multiple of the RFV.

In comparison, TEMPLE's price is a mere 2.57x multiple of its RFV in the worst case, and a 1.46x multiple of its RFV in the best case.

### Bank Runs
In the last section we discussed the meaning of risk-free value in the context of a worst case scenario, but we didn't fully explore what a worst case scenario would entail.

The main question that the discussion of bank runs brings up is: what actually happens when the price falls to IV?

If the price of drops to IV or below it, then something important is happening: people are burning their TEMPLE tokens in exchange for the IV.

This decreases the TEMPLE supply. And importantly, **it doesn't *uniformly* decrease the TEMPLE supply.**

It *only* decreases the circulating/staked supply. The amount of TEMPLE in the LP pool, staking rewards pool, bonus pool, and DAO pool stays the same.

What does this mean for the remaining faithful stakers?

More staking rewards (higher runway or EPY), and subsequently, higher risk-free value.

Let's work out the numbers for a specific scenario, using the same treasury stats as before:
- **Treasury Value:** $149,047,354
- **Fully Diluted Supply:** 235,322,570 TEMPLE
- **Circulating Supply:** 57,066,190 TEMPLE
- **Staking rewards pool:** 76,585,447 TEMPLE
- **Runway (assuming 0.7% EPY):** 122 days
- **Intrinsic Value:** $0.633

For simplicity, we'll assume the entire circulating supply is staked. For OHM, about 90% of the circulating supply is typically staked, so this isn't a horrible asumption.
Now, in our worst-case bank run scenario, TEMPLE price would drop to IV, or $0.633, and a big chunk of the circulating supply would be burned.

Let's say 30% of the circulating supply is sold for IV and burned in a day. I know this is unrealistic, but bear with me.

Then our circulating supply is now 39,946,333 TEMPLE, but our rewards pool hasn't shrunk at all, and our runway jumps to 153 days (check out my [other post on runway](https://hackmd.io/@bull4361/BynEUPW_K) to see how I calculated this)!

The RFV/TEMPLE would also jump to $1.85 from $1.48, or to $3.46 from $2.61, depending on your definition.

In reality, 30% of the circulating supply would never be burned in just one day, and so the effects of a bank run would be much less pronounced then what we see here. But the fundamental behaviour remains the same: the more TEMPLE is sold for IV, the higher the runway/staking rewards for faithful stakers.

### The Code

This is the code (python) I wrote to find the projections of IV and runway I shared above. You can look at the code yourself below, but I will summarize it here. All it really does is it starts with some initial stats about TempleDAO: the current value of the treasury (amount of FRAX in it), the current total supply, the current circulating supply, and the current EPY.

Then we choose how much treasury growth we want to project. So if we want to see what TempleDAO looks like after, say, 500m more FRAX has been sacrificed, we'd set treasury growth to `500_000_000`. There is also a variable called `average_sacrifice_val`. This is the average amount of FRAX sacrificed at a time. This matters for the simulation because many smaller sacrifices will increase the IV more than fewer large sacrifices.

Note that in this model, the treasury growth comes purely from FRAX sacrifices and not other revenue sources.

With all the initial conditions set, the simulation can run. This part's pretty straightforward.

We add the new FRAX sacrificed to the treasury.

We mint 83.3% of this sacrifice as new TEMPLE (the rest goes towards increasing IV), and we add 1/6th of the new TEMPLE minted to the circulating supply (because this is the amount immediately given to the sacrificer).

Finally, we calculate the new IV, and repeat this process until the target amount of FRAX has been sacrificed. Then we calculate the new runway and display the results.

Thanks for reading!
Twitter: [@bllu404](https://twitter.com/bllu404)

from math import floor, log

# Current stats - UPDATE these to the current ones in https://dune.xyz/ethpanda/TempleDAO 
initial_treasury_val = 144_222_153
initial_temple_supply = 228_912_361
initial_circulating_supply = 55_572_638
epy = 0.007

#DONT TOUCH
initial_iv = initial_treasury_val / initial_temple_supply
initial_runway = log((((initial_temple_supply - initial_circulating_supply) * 0.4375 + initial_circulating_supply) / initial_circulating_supply), 1 + epy)

# Growth stats - CHANGE these to whatever treasury growth you want to project.
treasury_growth = 10_000_000
average_sacrifice_val = 21_000
num_sacrifices = floor(treasury_growth / average_sacrifice_val)

#New variables to keep track of growing iv/supply/treasury
new_iv = initial_iv
new_supply = initial_temple_supply
new_treasury_val = initial_treasury_val
new_circulating_supply = initial_circulating_supply

for i in range(num_sacrifices):
    new_treasury_val += average_sacrifice_val
    new_supply += (1-(1/6)) * average_sacrifice_val / new_iv
    new_circulating_supply += (average_sacrifice_val / new_iv)/6
    new_iv = new_treasury_val / new_supply

new_runway = log((((new_supply - new_circulating_supply) * 0.4375 + new_circulating_supply) / new_circulating_supply), 1 + epy)

print("""
Initial Stats: 
- Initial Treasury: ${0:,.2f}
- Initial Supply: {1:,.0f}
- Initial Circulating Supply: {2:,.0f}
- Initial IV: ${3:.2f}
- Initial Runway: {4:,.2f}

Final Stats:
- New Treasury: ${5:,.2f}
- New Supply: {6:,.0f}
- New Circulating Supply: {7:,.0f}
- New IV: ${8:.2f}
- New Runway: {9:,.2f}
""".format(
    initial_treasury_val,
    initial_temple_supply,
    initial_circulating_supply,
    initial_iv,
    initial_runway,

    new_treasury_val,
    new_supply,
    new_circulating_supply,
    new_iv,
    new_runway
))