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Capital Recovery Calculator

Calculate the equal periodic payment needed to recover a present sum over time using the capital recovery factor formula.

Investment Parameters

$
%
$

Periodic Capital Recovery (Annual)

$14,902.95

10 payments over 10 years at 8.0% annual rate

Capital Recovery Factor (CRF)

0.14903

Periodic multiplier: 14.903%

Annual Equivalent Cost

$14,902.95

Equivalent annual uniform cost of capital

Total Capital Recovered

$149,029.49

Sum of 10 periodic payments

Total Cost of Capital (Interest)

$49,029.49

Financing charges above net capital

Sinking Fund Factor (SFF)

0.06903

Factor to accumulate target future sum

Net Depreciable Outlay

$100,000.00

Initial outlay ($100,000.00) minus salvage ($0.00)

Capital Outlay & Financing Cost Breakdown

Total Inflows$149,029.49
  • Net Principal Recovered$100,000.0067.1%
  • Cost of Capital (Interest)$49,029.4932.9%

How Capital Recovery is Calculated

Mathematical derivation of periodic annuity payment from present capital and discount rate.

  1. Determine Total Periods and Periodic Rate

    i=rm=8%1=8.0000%i = \frac{r}{m} = \frac{8\%}{1} = 8.0000\%

    With 10 years and annual compounding, the investment covers 10 total periods at a periodic rate of 8.0000% per period.

  2. Calculate Capital Recovery Factor (CRF)

    CRF(i,N)=i(1+i)N(1+i)N−1=0.0800(1+0.0800)10(1+0.0800)10−1=0.14903\text{CRF}(i, N) = \frac{i(1 + i)^N}{(1 + i)^N - 1} = \frac{0.0800(1 + 0.0800)^{10}}{(1 + 0.0800)^{10} - 1} = 0.14903

    The capital recovery factor converts present value into an equivalent series of equal periodic payments.

  3. Calculate Periodic Capital Recovery Payment

    A=P×CRF=$100,000.00×0.14903=$14,902.95A = P \times \text{CRF} = \$100,000.00 \times 0.14903 = \$14,902.95

    Using the standard capital recovery formula accounting for salvage value $S = $0.00:

  4. Compute Cumulative Payments & Financing Cost

    Over 10 periods, total recovered cash flows equal $149,029.49, representing $100,000.00 net capital and $49,029.49 total financing cost.

Capital Recovery Schedule

Period-by-period breakdown of principal recovery, interest cost, and remaining unrecovered capital.

PeriodPayment (A)Principal RecoveredInterest / ReturnRemaining Balance
Period 1$14,902.95$6,902.95$8,000.00$93,097.05
Period 2$14,902.95$7,455.18$7,447.76$85,641.87
Period 3$14,902.95$8,051.60$6,851.35$77,590.27
Period 4$14,902.95$8,695.73$6,207.22$68,894.54
Period 5$14,902.95$9,391.39$5,511.56$59,503.15
Period 6$14,902.95$10,142.70$4,760.25$49,360.46
Period 7$14,902.95$10,954.11$3,948.84$38,406.34
Period 8$14,902.95$11,830.44$3,072.51$26,575.90
Period 9$14,902.95$12,776.88$2,126.07$13,799.03
Period 10$14,902.95$13,799.03$1,103.92$0.00
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What is Capital Recovery and the Capital Recovery Factor?

In engineering economics, corporate finance, and capital budgeting, capital recovery represents the equal periodic payment or cash flow required to recover an initial capital investment over its useful operational life at a specified rate of return. When a business purchases industrial machinery, installs commercial solar infrastructure, or invests in corporate vehicle fleets, the asset must generate sufficient periodic returns to pay back both the initial principal outlay and the opportunity cost of capital (interest or discount rate).

The core mathematical mechanism driving this analysis is the Capital Recovery Factor (CRF). The CRF is a financial ratio that converts a present lump-sum expenditure into an equivalent uniform series of annual or periodic cash flows. If you are analyzing overall capital deployment on the corporate balance sheet, you can evaluate your company baseline with our capital employed calculator or track balance-sheet asset wear over time with our accumulated depreciation calculator.

The Capital Recovery Factor (CRF) Formula

The standard formula for the Capital Recovery Factor computes the ratio of a constant periodic annuity ($A$) to the present value ($P$) over $N$ compounding periods at periodic interest rate $i$:

CRF(i,N)=i(1+i)N(1+i)N−1\text{CRF}(i, N) = \frac{i(1 + i)^N}{(1 + i)^N - 1}

Where:

  • i: Periodic interest rate or Minimum Attractive Rate of Return (MARR), expressed as a decimal ($r / m$).
  • N: Total number of payment compounding periods ($n \times m$, where $n$ is years and $m$ is compounding frequency).
  • P: Initial present value or capital expenditure outlay.
  • A: Equal periodic capital recovery payment or required annuity cash flow.

When there is no residual salvage value at the end of the asset useful life ($S = 0$), the periodic payment is calculated directly by multiplying the initial investment by the CRF:

A=P×CRF(i,N)=P×[i(1+i)N(1+i)N−1]A = P \times \text{CRF}(i, N) = P \times \left[ \frac{i(1 + i)^N}{(1 + i)^N - 1} \right]

This formula is mathematically identical to the standard loan installment equation used to amortize commercial term debts. If you are comparing debt financing alternatives, explore our business loan calculator or generate a detailed payment breakdown using our amortization calculator.

Accounting for Salvage Value in Capital Recovery

Many capital assets retain substantial residual value at the end of their operational lifespan, such as heavy construction equipment or corporate transport vehicles sold on secondary markets. In engineering economics, capital recovery with salvage value ($S$) represents the net equivalent uniform annual cost of owning and operating the asset.

There are two standard, mathematically equivalent methods to compute capital recovery with salvage value:

Method 1: Sinking Fund Deduction Method

In this approach, the annual equivalent cost of the full initial investment is computed using the CRF, and the annual equivalent benefit of the future salvage value is subtracted using the Sinking Fund Factor (SFF):

CR=P×CRF(i,N)−S×SFF(i,N)\text{CR} = P \times \text{CRF}(i, N) - S \times \text{SFF}(i, N)

Where the Sinking Fund Factor is given by:

SFF(i,N)=i(1+i)N−1=CRF(i,N)−i\text{SFF}(i, N) = \frac{i}{(1 + i)^N - 1} = \text{CRF}(i, N) - i

Method 2: Net Depreciable Capital Plus Return on Salvage

Because CRF equals SFF plus the periodic rate (CRF = SFF + i), substituting this identity yields the most widely used engineering economy formula:

CR=(P−S)×CRF(i,N)+S×i\text{CR} = (P - S) \times \text{CRF}(i, N) + S \times i

Under this intuitive formula, (P - S) × CRF represents the annual payment needed to fully recover the depreciated capital outlay, while S × i accounts for the ongoing annual cost of capital tied up in the salvage value throughout the asset lifespan. To compare all six discrete engineering economics multipliers, use our compounding discount calculator, or to model regular income payouts from structured capital funds, see our annuity payout calculator.

Step-by-Step Worked Example

Suppose a manufacturing company evaluates an automated packaging line with the following investment parameters:

  • Initial Purchase and Installation Cost (P): $100,000
  • Annual Discount Rate / MARR (r): 8.0% (i = 0.08)
  • Useful Economic Lifespan (n): 10 years (N = 10)
  • Estimated Salvage Value at Year 10 (S): $10,000
  • Payment Frequency: Annual (m = 1)

Step 1: Compute the Capital Recovery Factor (CRF)

CRF(0.08,10)=0.08(1+0.08)10(1+0.08)10−1=0.08×2.1589251.158925=0.1490295\text{CRF}(0.08, 10) = \frac{0.08(1 + 0.08)^{10}}{(1 + 0.08)^{10} - 1} = \frac{0.08 \times 2.158925}{1.158925} = 0.1490295

Step 2: Calculate the Annual Capital Recovery Cost (A)

Applying the formula with net depreciable capital (P - S = $90,000):

A=($100,000−$10,000)×0.1490295+($10,000×0.08)A = (\$100{,}000 - \$10{,}000) \times 0.1490295 + (\$10{,}000 \times 0.08)
A=$13,412.65+$800.00=$14,212.65 per yearA = \$13{,}412.65 + \$800.00 = \$14{,}212.65 \text{ per year}

Step 3: Analyze Total Recovered Capital and Financing Cost

Over the 10-year period:

  • Total Annual Inflows / Payments Recovered: $14,212.65 × 10 = $142,126.54
  • Total Value Recovered Including Salvage: $142,126.54 + $10,000 = $152,126.54
  • Total Cost of Capital (Interest Charges): $152,126.54 - $100,000 = $52,126.54

To evaluate corporate borrowing charges after corporate tax deductions, you can assess net borrowing costs with our after-tax cost of debt calculator or evaluate periodic compounding conversions using our annuity calculator.

Applications of Capital Recovery in Financial Decision Making

Application AreaPrimary GoalDecision Rule
Annual Worth (AW) AnalysisCompare projects with unequal lifespansSelect the project with the highest positive Annual Worth
Equipment ReplacementDetermine optimal economic replacement lifeReplace asset when annual operating costs exceed capital recovery
Levelized Cost of Energy (LCOE)Annualize power plant construction outlaysDivide annualized capital recovery by annual megawatt-hour output
Lease vs. Buy DecisionsCompare outright purchase against lease ratesLease if annual lease cost is less than annual capital recovery plus maintenance

Frequently asked questions

What is the difference between Capital Recovery Factor (CRF) and Sinking Fund Factor (SFF)?
The Capital Recovery Factor converts a present lump-sum value into an equal periodic annuity payment. The Sinking Fund Factor calculates the periodic deposit required to accumulate a specific future lump-sum target. Mathematically, CRF equals SFF plus the periodic interest rate (CRF = SFF + i).
How does the Capital Recovery Factor change when interest rate is zero?
When the interest rate is 0%, money has no time value. In this case, the CRF simplifies to 1 / N, and the periodic capital recovery payment is simply the net capital expenditure divided equally by the number of periods: (P - S) / N.
Why is Capital Recovery important for Levelized Cost of Energy (LCOE)?
Renewable energy projects such as wind farms and solar installations require large upfront capital expenditures with low variable operating costs. Energy economists multiply the initial overnight capital cost by the CRF to calculate the annual capital charge, which is then divided by expected annual electricity generation to compute the cost per kilowatt-hour.
What happens to the Capital Recovery Factor as the tenure approaches infinity?
As the number of periods (N) approaches infinity, the Capital Recovery Factor approaches the periodic interest rate (i). In this perpetual scenario, the periodic payment represents pure interest (perpetuity), because the principal is never amortized.
How do inflation and tax depreciation affect capital recovery in practice?
In comprehensive engineering economics evaluations, analysts adjust the discount rate to account for inflation (using the real interest rate) and incorporate tax shields generated by MACRS or straight-line depreciation to determine after-tax annual capital recovery costs.

Resources and references

The formulas and methods in this calculator were checked against these independent sources.