Financial Modeling
Fixed-Declining Balance Depreciation (DB Rate, Partial First-Year & Final Stub)
Compute exact fixed-declining balance depreciation rates rounded to 3 decimal places, prorate partial first-year months, and close out final stub periods cleanly.
How fixed-declining balance differs from double-declining balance
Unlike DDB (which applies a fixed multiple such as 2 / Life regardless of salvage value), the fixed-declining balance method solves directly for the constant annual percentage rate r = ROUND(1 - (Salvage / Cost) ^ (1 / Life), 3) that decays Cost down to Salvage over Life full years.
When an asset enters service mid-year with Months_Y1 active months (default 12), Year 1 charges Cost * r * Months_Y1 / 12, intermediate years t = 2..Life charge (Cost - Prior_Accumulated) * r, and the spill-over stub year Life + 1 charges (Cost - Prior_Accumulated) * r * (12 - Months_Y1) / 12.
| Period | Formula Logic (Cost=100,000, Salvage=12,960, Life=4, Months=6) | Rate r | Period Expense |
|---|---|---|---|
| Fixed Rate r | ROUND(1 - (Salvage / Cost) ^ (1 / Life), 3) | 0.400 | — |
| Year 1 (6 mo) | ROUND(Cost * r * Months / 12, 2) | 0.400 | 20,000 |
| Year 2 (12 mo) | ROUND((Cost - Y1) * r, 2) | 0.400 | 32,000 |
| Year 3 (12 mo) | ROUND((Cost - Y1 - Y2) * r, 2) | 0.400 | 19,200 |
| Year 4 (12 mo) | ROUND((Cost - Y1 - Y2 - Y3) * r, 2) | 0.400 | 11,520 |
| Year 5 (6 mo stub) | ROUND((Cost - Sum(Y1:Y4)) * r * (12 - Months) / 12, 2) | 0.400 | 3,456 |
3-Decimal Fixed-Declining Rate & Partial Year-1 Charge
Rounding the implied decay rate to 3 decimal places matches Excel's native DB convention before multiplying by cost and the first-year month fraction.
=ROUND(B2 * ROUND(1 - (B3 / B2) ^ (1 / B4), 3) * B5 / 12, 2)Subsequent Full-Year & Final-Stub Charges
Each full intermediate year multiplies remaining opening book value by r, while period Life + 1 prorates by (12 - Months_Y1) / 12 whenever Months_Y1 < 12.
=ROUND((B2 - SUM($E$2:E2)) * $B$6, 2)Try the example
Use the original values or change them to test your understanding.