# ⚗️NPV tokens and liquidity

Whether you are buying or selling future yield on Delorean, you interact with NPV tokens. These tokens are an intermediary between the protocol's discount formula and ETH. They are minted when you sell future yield and burned when you buy future yield. Liquidity providers let you convert between NPV tokens and ETH.

## Minting NPV tokens

NPV tokens are minted when you sell future yield. The number of NPV tokens minted depends is equal to the net present value of the future yield you are selling, given by the following formula:

Where:

*Daily Yield*is an estimated yield rate based on historical data*Number of Tokens*is how many tokens the user is locking*Discount Rate*is an immutable constant, representing the daily discount rate*n*is the number of days of yield sold by the user

The NPV tokens are minted when the user locks his tokens into escrow, committing future yield into an Delorean liquidity pool. The tokens have value because they can be used to withdraw future yield from the liquidity pool, as we'll see later.

To convert the NPV tokens into ETH, the user must take them to a swap protocol such as Uniswap v3 or Curve. Each market on Delorean has a directly integrated, recommended swap protocol.

Assuming the discount rate and daily yield estimate matches market sentiment, the price of NPV tokens should equal approximately 1 ETH. In this scenario, the user selling future yield can take his NPV tokens, and get exactly 1 ETH for each of them. We'll discuss later why the price of NPV tokens may drift, and how that plays out.

## Burning NPV tokens

NPV tokens are burned when you swap them to access future yield. You specify the number of NPV tokens you wish to burn, and the Delorean swap performs the burn operation and credits you with future yield worth that much in terms of net present value.

The nominal amount of yield you receive is variable. It depends on the payment rate into the Delorean pool. If payment happens earlier, the nominal amount will be lower. If payment happens later the nominal amount will be higher. Either way, the APY on the payments is the same.

As an example, observe that the following three charts show different payment schedules, but produce the same value when we apply the net present value formula:

The scenario on the left pays yield at a faster rate, and gives 5.2 ETH. The scenario on the right takes longer to repay, and therefore gives 5.6 ETH on that longer schedule.

Burning 5 NPV tokens creates a position that treats all three of these scenarios as equivalent.

## Providing liquidity between NPV tokens and ETH

Swaps between NPV tokens and ETH take place on token exchanges protocols like Uniswap. Liquidity providers create positions on these exchanges, and allow users to convert NPV tokens into ETH, and vice versa. This facilitates the sale and purchase of future yield on Delorean. Liquidity providers are compensated with transaction fees in the exchange protocol.

Assuming the discount rate and projected yield matches market expectations, an NPV token should be worth 1 ETH, or close to it. Liquidity providers can take advantage of this, and concentrate their liquidity around that price.

## NPV token price drift

NPV tokens are expected to be worth close to 1 ETH. This is the case when the discount rate and projected yield in the Delorean pool match the market's sentiment. If either of those variables are off, the price of an NPV token may drop below 1 ETH.

Price drops for NPV tokens are temporary, as long as the underlying continues to produce yield. As an example, consider this scenario: 500,000 GLP are locked in and 12 ETH net present value are sold. This mints 12 NPV tokens.

Suppose the market judges that GLP is risky, and doesn't believe the locked GLP will generate yield fast enough to justify a 1:1 price on NPV tokens:ETH. In this scenario, one of two things will happen. The first possibility is that the price of the NPV tokens drops until a buyer comes along. The second is that time passes, and the risk is reduced as some of the future ETH becomes present ETH.

The chart below shows the second scenario: some time has passed, and the locked GLP have generated 4 ETH.

The risk on this pool has been reduced, because 4 ETH is already on-hand. A buyer can purchase the 12 NPV tokens, and a third of his purchase is guaranteed. The ratio will continue to shift and reduce the risk until a buyer comes along.

In short, the passage of time creates an upward pressure on the value of NPV tokens.

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