Ratio wise R.A. and Final Bills payment amount calculations using Excel

Ratio-wise RA & Final Bills Payment Calculator

Grand Received (Total Fund)

Total Demand ₹0.00

Final Bills (100%) ₹0.00

RA Bills Demand ₹0.00

Available for RA ₹0.00

Sr.	Work Name	Work Cost (₹)	Demand / Pending (₹)	Bill Stage	Payment Allocated (₹)	Action

Detailed Step-by-Step Calculation Breakdown

Note: Final stage bills receive 100% full payment to close completed works. Remaining funds are distributed proportionately among RA bills.

Equitable Distribution of Infrastructure Funds: Ratio-Wise Bill Payment Methodology

1. Executive Summary & Problem Statement

In public works and commercial civil engineering projects, managing contractor bill disbursements during periods of limited fund allocation presents a significant operational challenge. When funds received from government grants or project owners are insufficient to clear all pending contractor demands, applying funds arbitrarily can cause friction and project delays.

Core Principles of Funds Allocation:

• Priority Clearance: Works marked as Final Stage are paid at 100% of their demand to clear liabilities, release security deposits, and officially close completed contracts.
• Proportional Distribution: Remaining funds are distributed across active Running Account (RA) bills using a uniform ratio to maintain project velocity without favoring specific contractors.

2. Mathematical Formulation

Let the total received grant be G, total pending demands be D, and individual demand for work i be D_i.

Step 1: Total Demand Breakdown

The total demand is the sum of all pending final and RA bills:

D_Total = Σ D_i
D_Final = Σ D_i (where Stage = 'Final')
D_RA = D_Total - D_Final

Step 2: Available Funds for Running Bills

Final bills receive 100% payment priority. The remaining fund for allocation among RA bills is:

G_RA = G - D_Final

Step 3: Proportional Allocation Ratio (R)

The uniform payment ratio applied to all pending RA bills is calculated as:

R = G_RA / D_RA

Step 4: Individual Payment Allocation (P_i)

If Stage = 'Final' ➔ P_i = D_i (100% Payment)
If Stage = 'RA' ➔ P_i = D_i × R

3. Solved Numerical Example

Consider a division office that has received a grant of ₹900.00 Lakhs against five pending bills totaling ₹1,113.50 Lakhs.

Input Data Summary

Sr.	Work Name	Contract Cost (₹)	Demand / Bill Amount (₹)	Bill Stage
1	Work A	550.00	275.00	RA
2	Work B	592.00	296.00	RA
3	Work C	160.00	80.00	Final
4	Work D	748.00	374.00	RA
5	Work E	177.00	88.50	Final

Step-by-Step Calculation Procedure

Step 1: Compute Summary Totals

• Total Expected Demand (D_Total): 275 + 296 + 80 + 374 + 88.50 = ₹1,113.50 Lakhs
• Total Final Bill Demands (D_Final): Work C (80.00) + Work E (88.50) = ₹168.50 Lakhs
• Total RA Bill Demands (D_RA): 1,113.50 - 168.50 = ₹945.00 Lakhs

Step 2: Reserve Priority Funds for Final Bills

Deduct full final bill payments from total available funds (G = ₹900.00 Lakhs):
• Available Balance for RA Bills (G_RA): 900.00 - 168.50 = ₹731.50 Lakhs

Step 3: Determine Allocation Ratio for RA Bills

Compute the proportional factor for active running account bills:
• Proportional Ratio (R): 731.50 / 945.00 = 0.774074 (or 77.41%)

Step 4: Compute Individual Allocations

• Work A (RA): ₹275.00 × 0.774074 = ₹212.87 Lakhs
• Work B (RA): ₹296.00 × 0.774074 = ₹229.13 Lakhs
• Work C (Final): Paid 100% = ₹80.00 Lakhs
• Work D (RA): ₹374.00 × 0.774074 = ₹289.50 Lakhs
• Work E (Final): Paid 100% = ₹88.50 Lakhs

4. Final Distribution Results Table

Sr.	Work Name	Demand (₹)	Stage	Proportion / Formula	Payment Allocated (₹)
1	Work A	275.00	RA	275.00 × 77.41%	212.87
2	Work B	296.00	RA	296.00 × 77.41%	229.13
3	Work C	80.00	Final	Full Demand (100%)	80.00
4	Work D	374.00	RA	374.00 × 77.41%	289.50
5	Work E	88.50	Final	Full Demand (100%)	88.50
Grand Total		₹1,113.50	-	Disbursement Total	₹900.00

5. Key Takeaways & Conclusion

By segregating final bills from running bills, public engineering departments ensure that completed works are administratively closed without unnecessary delay. Distributing the residual grant proportionally across RA bills ensures that all ongoing projects receive financial assistance relative to their scale and progress, preventing project stalling while preserving complete financial audit integrity.

Yogendra Gopal Borse

Civil Engineer | Assistant Engineer Grade-I, Maharashtra PWD

B.Tech (Civil) from VJTI Mumbai. Experienced in bridge design, road works, estimation, project monitoring and digital engineering tools. Creator of YogiPWD – practical technical resources for civil engineers.

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