Operator (APY > 10%)

APR Formula

$$APR = [\frac {(A + r*A * x)}{16} *\frac{365}{x+1}] * 100\%$$

A: Represents the profit on the first day

r: The proportion of recyclable funds, with a value range of [0,1]

x: Denotes number of days, with a range of [1,364]

r*A: represents the daily profit after the first day, assuming each subsequent day's earnings are r of the first day's

A + r*A * x: represents the total profit over x+1 days

\frac{365}{x+1}: represents the number of such profit cycles within 365 days

16: denotes 16 sBTC in principal

How to calculate A

1. Revenue

   1. Deposit Revenue

      1. Fee rate> 8: 660 sats per Deposit transaction

      2. Fee rate < 8: 330 sats per Deposit transaction

   2. Withdrawal Revenue:

      1. 0.15% of advanced payment amount

      2. 1000 × Feerate: Real-time Bitcoin network fee rate

2. Expenditure

   1. Fund Recovery Cost

      1. Maximum Claim+Happy Take transaction size:

         1. 586 vbytes + 420 vbytes = 1006 × Feerate

      2. Minimum Claim+Happy Take transaction size:

         1. 300 vbytes + 420 vbytes = 720 × Feerate

Define:

a The number of deposit transactions

b The number of withdrawal transactions

v The volume of withdrawal requests

f_p The average feerate of withdrawal requests

f_{ch} The average fee cost of claim transaction and happy take transaction Then, we calculate

$$A = (660 * a + b * 1000 * f_p + v * 0.0015) - b*f_{ch}$$

Why do yields (A) decrease in subsequent days?

On Day 1, the Operator's principal remains 100% available, resulting in the highest yield rate on this initial day. From Day 2 onward, only redeemed funds become recyclable for reuse. We assume an average daily capital recovery rate of 10%, which is then redeployed (note: compound interest effects are excluded from this calculation due to multiple yield-impacting factors, hence APY computation is not considered here).

The 10% figure is a hypothetical value, with the actual ratio being influenced by multiple factors:

1. Bitcoin Network Congestion

   1. High congestion may reduce the Operator's capital recovery rate to near 0%

   2. Under low-congestion conditions, 100% recovery becomes achievable

2. Fee Rates of Claim & Happy Take Transactions

   1. If the Operator's preset fee rate (determined during the deposit phase and immutable) falls below current network rates:

      1. Recovery requires waiting until network fees drop to the preset level

3. User-Specified Fee Rates

   1. Operators typically select recovery fee rates ≤ users' specified rates to avoid losses

   2. When user-specified rates are significantly below current network fees:

      1. Recovery timelines extend proportionally

APR Trend Chart

Since the Operator cannot initiate the next round of services only after 100% of the funds have been recovered, a dynamic fund recovery process is a more reasonable method for calculating the Operator's APR. We selected several different sets of values to demonstrate the changing trend of the Operator's APR.

A = 0.2， r = 0.1 and r = 0.05

The yellow line represents a daily recovery rate of r = 0.05, corresponding to an ultimate annualized yield of APR = 24%. The green line represents a daily recovery rate of r = 0.1, corresponding to an ultimate annualized yield of APR = 46.75%.

A = 0.2, r = 0 and r = 1

We present the APR yields under two extreme scenarios, which determine the upper and lower bounds of the Operator's APR. The yellow line represents a daily recovery rate of r = 0, corresponding to an ultimate annualized yield of APR = 1.25%. The grey line represents a daily recovery rate of r = 1, corresponding to an ultimate annualized yield of APR = 456.25%.

APR > 5%, r = ？

Considering that most real-world BTC annual yields are below 5%, we calculate the required recovery rate r for which APR > 5%.

According to calculations, when A = 0.2 and r = 0.009, the Operator's APR = 5.345%. This requirement is highly achievable in practice. With an initial principal of 15 BTC, a daily refund of just 0.135 BTC (15×0.009) from Day 2 onward would suffice to maintain an APR above 5%.