Calculate capitalized cost, initial cost, annual maintenance cost, or interest rate from any three values in a perpetuity model with ongoing maintenance.
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Capitalized Cost Formula
The capitalized cost model used here treats annual maintenance cost as a perpetual annual cost. The main formula is:
- CC = capitalized cost, in dollars
- IC = initial cost, in dollars
- MC = annual maintenance cost, in dollars per year
- R = annual interest rate, as a percent
To solve for initial cost:
To solve for annual maintenance cost:
To solve for interest rate:
The calculator lets you enter any three values and solves for the fourth. If you leave capitalized cost blank, it adds the initial cost to the present value of an indefinite maintenance cost. If you leave initial cost blank, it subtracts the capitalized maintenance amount from the capitalized cost. If you leave annual maintenance cost blank, it finds the yearly cost implied by the difference between capitalized cost and initial cost. If you leave interest rate blank, it finds the rate that makes the given maintenance cost match the difference between capitalized cost and initial cost.
Interest Rate Factors for Capitalizing Annual Maintenance
The factor below shows how many dollars of capitalized cost are created by each $1 of annual maintenance cost.
| Interest Rate | Capitalization Factor, 1 / (R / 100) | Capitalized Value of $1,000/year |
|---|---|---|
| 2% | 50.00 | $50,000 |
| 3% | 33.33 | $33,333 |
| 5% | 20.00 | $20,000 |
| 8% | 12.50 | $12,500 |
| 10% | 10.00 | $10,000 |
Typical Input Checks
| Input Situation | What It Means |
|---|---|
| Interest rate is greater than 0 | The standard perpetuity formula can be used. |
| Capitalized cost is greater than initial cost | The difference represents the capitalized value of future maintenance. |
| Capitalized cost equals initial cost | This usually implies zero annual maintenance cost in this model. |
| Capitalized cost is less than initial cost | The inputs usually imply a negative maintenance cost, so the values should be checked. |
Example Problems
Example 1: Calculate capitalized cost
Suppose the initial cost is $80,000, annual maintenance is $3,000, and the interest rate is 6%.
The capitalized cost is $130,000.
Example 2: Calculate annual maintenance cost
Suppose the capitalized cost is $250,000, the initial cost is $150,000, and the interest rate is 5%.
The annual maintenance cost is $5,000 per year.
FAQ
What is capitalized cost?
Capitalized cost is the total present cost of an asset when you include both the initial cost and the present value of ongoing annual costs. In this calculator, the ongoing annual maintenance cost is assumed to continue indefinitely.
Why does a lower interest rate increase capitalized cost?
A lower interest rate makes future annual costs worth more in present-value terms. For example, $1,000 per year capitalized at 5% is $20,000, but the same $1,000 per year capitalized at 2% is $50,000.
Can the interest rate be zero?
For a nonzero annual maintenance cost, the interest rate must be greater than 0 because the perpetuity formula divides by the interest rate. If the annual maintenance cost is $0, then the capitalized cost equals the initial cost in this model.
