Capitalized Cost Analysis 

Many public sector projects such as bridges, dams, highways and toll roads, railroads, and hydroelectric and other power generation facilities have very long expected useful lives. A perpetual or infinite life is the effective planning horizon. Permanent endowments for charitable organizations and universities also have perpetual lives. The economic worth of these types of projects or endowments is evaluated using the present worth of the cash flows.

The formula to calculate CC is derived from the PW relation P/A ( P/A , i %, n ), where n = ∞  time periods. Take the equation for P using the P/A factor and divide the numerator and denominator by (1 + i )ⁿ to obtain

As n approaches ∞, the bracketed term becomes 1/i . We replace the symbols P and PW with CC as a reminder that this is a capitalized cost equivalence. Since the A value can also be termed AW for annual worth, the capitalized cost formula is simply

Solving for A or AW, the amount of new money that is generated each year by a capitalization of an amount CC is

This is the same as the calculation A/P( i) for an infinite number of time periods. Equation (5-2) can be explained by considering the time value of money. If $20,000 is invested now (this is the capitalization) at 10% per year, the maximum amount of money that can be withdrawn at the end of every year for eternity is $2000, which is the interest accumulated each year. This leaves the original $20,000 to earn interest so that another $2000 will be accumulated the next year. The cash flows (costs, revenues, and savings) in a capitalized cost calculation are usually of two types: recurring, also called periodic, and nonrecurring. An annual operating cost of $50,000 and a rework cost estimated at $40,000 every 12 years are examples of recurring cash flows. Examples of nonrecurring cash flows are the initial investment amount in year 0 and one-time cash flow estimates at future times, for example, $500,000 in fees 2 years hence.

The procedure to determine the CC for an infinite sequence of cash flows is as follows:

1.      Draw a cash flow diagram showing all nonrecurring (one-time) cash flows and at least two cycles of all recurring (periodic) cash flows.

2.      Find the present worth of all nonrecurring amounts. This is their CC value.

3.      Find the A value through one life cycle of all recurring amounts. (This is the same value in all succeeding life cycles) Add this to all other uniform amounts (A) occurring in years 1 through infinity. The result is the total equivalent uniform annual worth (AW).

4.      Divide the AW obtained in step 3 by the interest rate i to obtain a CC value. This is an application of Equation (4-1).

5.      Add the CC values obtained in steps 2 and 4.

Drawing the cash flow diagram (step 1) is more important in CC calculations than elsewhere, because it helps separate nonrecurring and recurring amounts. In step 5 the present worths of all component cash flows have been obtained; the total capitalized cost is simply their sum.

The Haverty County Transportation Authority (HCTA) has just installed new software to charge and track toll fees. The director wants to know the total equivalent cost of all future costs incurred to purchase the software system. If the new system will be used for the indefinite future, find the equivalent cost:

a-      now, a CC value,

b-      for each year hereafter, an AW value.

The system has an installed cost of $150,000 and an additional cost of $50,000 after 10 years. The annual software maintenance contract cost is $5000 for the first 4 years and $8000 thereafter. In addition, there is expected to be a recurring major upgrade cost of $15,000 every 13 years. Assume that i = 5% per year for county funds.

a-      The five-step procedure to fi nd CC now is applied.

1.      Draw a cash flow diagram for two cycles Figure (4–3).

2.      Find the present worth of the nonrecurring costs of $150,000 now and $50,000 in year 10 at i = 5%. Label this CC₁

Figure (4-3): Cash flows for two cycles of recurring costs and all nonrecurring amounts, Example (4-4)

3.      And 4 .Convert the $15,000 recurring cost to an A value over the first cycle of 13 years, and find the capitalized cost CC₂ at 5% per year using Equation (4-1).

There are several ways to convert the annual software maintenance cost series to A and CC values. A straightforward method is to, first, consider the $−5000 an A series with a capitalized cost of

Second, convert the step-up maintenance cost series of $−3000 to a capitalized cost CC₄ in year 4, and find the present worth in year 0. (Refer to Figure (4–4) for cash flow timings.)

5.      The total capitalized cost CC_T for Haverty County Transportation Authority is the sum of the four component CC values.

b-      Equation (4-2) determines the AW value forever.

Correctly interpreted, this means Haverty County officials have committed the equivalent of $17,350 forever to operate and maintain the toll management software.