Understanding PPS (Price Per Share) Formula

The price per share formula is denoted by:

T=Vβˆ—PT = V * P

Where ’T’ is the amount of base asset tokens in the vault (strategy LP tokens), β€˜V ’is the total amount of 'Vault' tokens in circulation and P is the 'price' of those vault tokens.

At the start, P=1

Thus, V=T, the amount of base asset tokens inside the vault is equal to the amount of Vault Tokens.

By keeping track of the number of Vault Tokens in circulation, and the number of tokens inside the vault (which increase the longer they are held in the vault) the price can be calculated as follows:

PriceOfVaultToken=(TotalBaseAssetTokens)/(TotalVaultTokensOnCirculation)PriceOfVaultToken = (Total Base Asset Tokens)/ (Total Vault TokensOnCirculation)

Since the amount of Vault tokens is constant relative to the amount of underlying base asset tokens (which increase due to them being deployed in strategies, unless the strategies fail), the price will increase, and a depositor can burn their Vault Tokens to claim their initial deposit and profits.

NumberOfBaseTokensReceived=VaultTokensToBeBurnedβˆ—PriceNumberOfBaseTokensReceived = VaultTokensToBe Burned * Price
Example

  1. At time (i) (vault empty, and no Vault tokens minted) : Adam has 1000 USDC tokens and decides to invest them into a USDC/USDT dual sided LP vault.

    • He will be zapped in and the obtained amount of strategy LP tokens will be deposited into the vault. let’s say he obtained 1000 LP tokens from the ZAP. He will receive 1000 vault tokens as the price of the Vault token will be initialized to 1 with Adam’s deposit. Thus, the Vault is as follows: 1000 LP tokens / 1000 Vault tokens, giving a price of 1.

  1. At time (ii) (more strategy LP tokens have been generated through harvesting and compounding): The vault now has: 1050 LP tokens/ 1000 Vault Tokens, giving a price of 1.05

    • Sara adds 1000 USDC (which when zapped is equal to another 1000 LP tokens) and receives 952.38 vault tokens (because 1000 / 1.05), Thus the vault now has: 2050 LP tokens / 1952.38 Vault tokens, and still a price of 1.05

  1. At time (iii) (more strategy LP tokens have been generated through harvesting and compounding): The vault now has: 2100 LP tokens / 1952.38 Vault tokens, and a new price of 1.0756.

    • Adam burns 500 of his 1000 vault tokens and is entitled to 537.8 LP tokens back (500 * 1.0756). He can choose to receive the LP token or ZAP out into stable coins. The vault now contains: 1562.2 LP tokens / 1452.38 Vault Tokens, and still a price of 1.0756.

The formula to calculate the β€˜USD value of Investment’ in the vault would be:

π‘ˆsers𝑉𝑂𝐼=π‘π‘’π‘šπ‘π‘’π‘ŸOπ‘“π‘‰π‘Žπ‘’π‘™π‘‘Tπ‘œπ‘˜π‘’π‘›π‘ βˆ—π‘ƒπ‘Ÿπ‘–π‘π‘’Oπ‘“π‘‰π‘Žπ‘’π‘™π‘‘Tπ‘œπ‘˜π‘’π‘›π‘ βˆ—π‘ƒπ‘Ÿπ‘–π‘π‘’O𝑓𝐿𝑃Tπ‘œπ‘˜π‘’π‘›π‘ˆsers𝑉𝑂𝐼 = π‘π‘’π‘šπ‘π‘’π‘ŸO𝑓 π‘‰π‘Žπ‘’π‘™π‘‘Tπ‘œπ‘˜π‘’π‘›π‘  βˆ— π‘ƒπ‘Ÿπ‘–π‘π‘’Oπ‘“π‘‰π‘Žπ‘’π‘™π‘‘Tπ‘œπ‘˜π‘’π‘›π‘  βˆ— π‘ƒπ‘Ÿπ‘–π‘π‘’O𝑓𝐿𝑃Tπ‘œπ‘˜π‘’π‘›

This portion of the equation gives the number of LP tokens the user has in the vault:

π‘π‘’π‘šπ‘π‘’π‘ŸOπ‘“π‘‰π‘Žπ‘’π‘™π‘‘Tπ‘œπ‘˜π‘’π‘›π‘ βˆ—π‘ƒπ‘Ÿπ‘–π‘π‘’Oπ‘“π‘‰π‘Žπ‘’π‘™π‘‘Tπ‘œπ‘˜π‘’π‘›π‘ π‘π‘’π‘šπ‘π‘’π‘ŸOπ‘“π‘‰π‘Žπ‘’π‘™π‘‘Tπ‘œπ‘˜π‘’π‘›π‘  βˆ— π‘ƒπ‘Ÿπ‘–π‘π‘’Oπ‘“π‘‰π‘Žπ‘’π‘™π‘‘Tπ‘œπ‘˜π‘’π‘›π‘ 

Where the price of a pools underlying LP token:

PriceOfLPToken=USDValueOfLiquidityNumberOfLPTokensInirculationPriceOfLPToken = \frac{USDValueOfLiquidity}{NumberOfLPTokensInirculation}

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