Recover capital and cover operation
Capital recovery is the equivalent annual cost of owning capital, accounting for terminal salvage and the required return on unrecovered investment.
Period 0: −$10,000.00. This is the time-zero cash flow. Periods use the payment interval stated in the model.
Salvage is $2,000.00 received at the end of year 4. EAC is a positive cost magnitude.
Capital recovery accounts for both the return OF capital and the required return ON capital.
Cash-flow dates and signs are part of the answer. Model values retain precision; displays round money to cents. Illustrative assumptions exclude taxes and inflation unless stated.
What the model means
Let initial investment I, salvage S at N, operating cost E per year. CR=I(A/P)−S(A/F). The identity A/P−A/F=i leads to CR=(I−S)(A/P)+Si, or CR=(I−S)(A/F)+Ii.
Build the calculation
Annual cost is EAC=CR+E. With annual revenue R, net annual worth is AW=R−E−CR. A lower EAC is economically preferred only when alternatives deliver equivalent required service over a justified study horizon. The capital equivalent CE is the present equivalent of ownership capital costs, I−S(P/F,i,N). Multiplying CE by A/P yields capital recovery.
Set up. Calculate. Explain.
Rebuild the starting scenario
First cost: 10000 $; Salvage fraction: 0.2 fraction of first cost; Annual operating cost: 500 $/year; Interest rate: 10 % per year; Number of years: 4 years. Calculate the equivalent annual cost including operation.
Setup hint
Capital recovery accounts for both the return OF capital and the required return ON capital.
Open the visual solution
- Capital recovery accounts for both the return OF capital and the required return ON capital.
- Annualize the first cost and subtract annualized terminal salvage.
- Equivalent identity: CR=(I−S)(A/P)+Si. Add operating cost; a net-revenue AW would subtract this cost.
Period 0: −$10,000.00. This is the time-zero cash flow. Periods use the payment interval stated in the model.
Salvage is $2,000.00 received at the end of year 4. EAC is a positive cost magnitude.
Capital recovery accounts for both the return OF capital and the required return ON capital.
Cash-flow dates and signs are part of the answer. Model values retain precision; displays round money to cents. Illustrative assumptions exclude taxes and inflation unless stated.
Checks allow 0.1% numerical rounding (minimum $0.05 or 0.001 in the stated nonmonetary unit). Interpolated factors and rates are approximations; keep table precision consistent.
Transfer the idea to a new scenario
First cost is $18,000, salvage is 20% of first cost at year 6, operation costs $1,200/year, i=8%. Find EAC.
Setup hint
Capital recovery accounts for both the return OF capital and the required return ON capital.
Open the visual solution
- Capital recovery accounts for both the return OF capital and the required return ON capital.
- Annualize the first cost and subtract annualized terminal salvage.
- Equivalent identity: CR=(I−S)(A/P)+Si. Add operating cost; a net-revenue AW would subtract this cost.
Period 0: −$18,000.00. This is the time-zero cash flow. Periods use the payment interval stated in the model.
Salvage is $3,600.00 received at the end of year 6. EAC is a positive cost magnitude.
Capital recovery accounts for both the return OF capital and the required return ON capital.
Cash-flow dates and signs are part of the answer. Model values retain precision; displays round money to cents. Illustrative assumptions exclude taxes and inflation unless stated.
Checks allow 0.1% numerical rounding (minimum $0.05 or 0.001 in the stated nonmonetary unit). Interpolated factors and rates are approximations; keep table precision consistent.
Why does salvage appear with a minus sign in capital recovery cost?
Can you defend your setup?
Can you place each amount on the timeline, match the interest period, calculate the equivalent quantity, and state the decision or limitation?
Completion is saved on this browser.