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Debt Obligations - Narrative (Details)
3 Months Ended 9 Months Ended
Mar. 29, 2024
shares
Feb. 01, 2023
USD ($)
$ / shares
shares
Jan. 27, 2021
USD ($)
debtInstrument
Mar. 31, 2024
shares
Sep. 30, 2024
USD ($)
Dec. 31, 2023
USD ($)
Jun. 02, 2023
USD ($)
Debt Instrument [Line Items]              
Unamortized discount         $ 623,000 $ 815,000  
Debt instrument, post-transaction from exercise of warrant   1.00%          
Common Stock              
Debt Instrument [Line Items]              
Exercise of warrant, net (in shares) | shares 324,955     324,955      
CF Global Credit, LP              
Debt Instrument [Line Items]              
Issuance of warrant (in shares) | shares   325,457          
Exercise price of warrants (in dollars per share) | $ / shares   $ 0.01          
Term   7 years          
Secured Debt              
Debt Instrument [Line Items]              
Proceeds from issuance of debt   $ 10,000,000.0          
Unamortized discount   200,000          
Net cash proceeds   8,500,000          
Debt issuance costs   $ 1,300,000          
Promissory Notes              
Debt Instrument [Line Items]              
Number of instruments (in instruments) | debtInstrument     2        
Secured Debt              
Debt Instrument [Line Items]              
Exercise price of warrants (in dollars per share) | $ / shares   $ 0.01          
Debt instrument, covenant loan to value ratio   0.40          
Secured Debt | Arq Limited              
Debt Instrument [Line Items]              
Unamortized discount   $ 300,000          
Face amount   10,000,000.0          
Estimated fair value   $ 9,700,000          
Periodic payment, principal     $ 100,000        
Debt instrument, fee amount             $ 50,000
Debt instrument, collateral amount             $ 700,000
Indebtedness to net worth ratio         4    
Debt instrument, annual increase         20.00%    
Equity percentage         1.25    
Secured Debt | Arq Limited | Promissory Note A              
Debt Instrument [Line Items]              
Face amount     8,000,000.0        
Secured Debt | Arq Limited | Promissory Note B              
Debt Instrument [Line Items]              
Face amount     $ 2,000,000.0        
Secured Debt | Between 1 And 36 Moths              
Debt Instrument [Line Items]              
Debt instrument, prepayment premium   2.00%          
Secured Debt | Between 37 Months And Maturity Date              
Debt Instrument [Line Items]              
Debt instrument, prepayment premium   1.00%          
Secured Debt | Adjusted Term SOFR for an Interest Period of One Month in Effect on the Third U.S. Government Securities Business Day              
Debt Instrument [Line Items]              
Debt instrument, prepayment premium   2.00%          
Secured Debt | Fiscal Year 2024              
Debt Instrument [Line Items]              
Debt covenant, minimum annual Revenue requirement   $ 85,000,000          
Debt covenant, minimum consolidated EBITDA requirement   3,000,000          
Secured Debt | Fiscal Year 2025 and Thereafter              
Debt Instrument [Line Items]              
Debt covenant, minimum annual Revenue requirement   100,000,000          
Debt covenant, minimum consolidated EBITDA requirement   16,000,000          
Secured Debt | Through January 2026 | Arq Limited              
Debt Instrument [Line Items]              
Interest rate, stated percentage     6.00%        
Secured Debt | Penalty Year 2024 | Arq Limited              
Debt Instrument [Line Items]              
Prepayment penalty, percentage         3.00%    
Secured Debt | Penalty Year 2025 | Arq Limited              
Debt Instrument [Line Items]              
Prepayment penalty, percentage         2.00%    
Secured Debt | Penalty Year 2026 | Arq Limited              
Debt Instrument [Line Items]              
Prepayment penalty, percentage         1.00%    
Secured Debt | Beginning March 31, 2023              
Debt Instrument [Line Items]              
Debt covenant, minimum cash balance requirement   $ 5,000,000          
Secured Debt | SOFR              
Debt Instrument [Line Items]              
Debt instrument, floor rate percentage   1.00%          
Debt instrument, cap rate percentage   2.00%          
Debt instrument, percent of paid in cash   9.00%          
Debt instrument, percent of paid in kind   5.00%          
Secured Debt | SOFR | Adjusted Term SOFR for an Interest Period of One Month in Effect on the Third U.S. Government Securities Business Day              
Debt Instrument [Line Items]              
Debt instrument, interest rate   14.00%          
Secured Debt | Base Rate              
Debt Instrument [Line Items]              
Debt instrument, percent of paid in cash   8.00%          
Secured Debt | Prime Rate | After January 2026 | Arq Limited              
Debt Instrument [Line Items]              
Interest rate, stated percentage     2.75%