Capitalized Costs

Engineering Economics · FE Reference Handbook section

Engineering Economics

1 formulas

10 exam-style examples

~47 min

All Engineering Economics lectures

Handbook notes for this section

Definitions and conditions exactly as the handbook states them.

Capitalized costs are present worth values using an assumed perpetual period of time.

Core formulas for this FE topic

Definitions, applicability, units, assumptions and worked examples for each relation.

Worked exam-style examples

The four ways this section is written on the real exam — thoughts first, then equations, then substitution.

Example 1

Capitalized cost of a perpetual public works asset — Capitalized Costs

A bridge deck costs $407,000 to build and $20,000 per year to maintain forever. At 5.0% interest, determine the capitalized cost.

Given

First cost = $407,000
A = $20,000/yr
$i = 5.0%$

Find

Capitalized cost of the asset

Start with the thinking

Capitalized cost is the present worth of a cash flow that continues indefinitely.
For a perpetuity P = A/i, so a lower interest rate raises the capitalized cost sharply.

Step-by-step solution

Formula
$CC = First cost + A/i$
Perpetuity term — A/i = $20,000/0.050 = $400,000
Substituting — CC = $407,000 + $400,000
Evaluate — CC = $807,000

Answer:

Capitalized cost ≈ $807,000

Why the other options are there

$408,000 (multiplied instead of divided)
$400,000 (omitted the first cost)

Reference: FE Reference Handbook — Engineering Economics → Capitalized Costs

Example 2

Capitalized cost of a perpetual public works asset — Capitalized Costs (2)

A bridge deck costs $611,000 to build and $33,000 per year to maintain forever. At 8.0% interest, determine the capitalized cost.

Given

First cost = $611,000
A = $33,000/yr
$i = 8.0%$

Find

Capitalized cost of the asset

Start with the thinking

Capitalized cost is the present worth of a cash flow that continues indefinitely.
For a perpetuity P = A/i, so a lower interest rate raises the capitalized cost sharply.

Step-by-step solution

Formula
$CC = First cost + A/i$
Perpetuity term — A/i = $33,000/0.080 = $412,500
Substituting — CC = $611,000 + $412,500
Evaluate — CC = $1,023,500

Answer:

Capitalized cost ≈ $1,023,500

Why the other options are there

$613,640 (multiplied instead of divided)
$412,500 (omitted the first cost)

Reference: FE Reference Handbook — Engineering Economics → Capitalized Costs

Example 3

Capitalized cost of a perpetual public works asset — Capitalized Costs (3)

A bridge deck costs $622,000 to build and $12,000 per year to maintain forever. At 5.5% interest, determine the capitalized cost.

Given

First cost = $622,000
A = $12,000/yr
$i = 5.5%$

Find

Capitalized cost of the asset

Start with the thinking

Capitalized cost is the present worth of a cash flow that continues indefinitely.
For a perpetuity P = A/i, so a lower interest rate raises the capitalized cost sharply.

Step-by-step solution

Formula
$CC = First cost + A/i$
Perpetuity term — A/i = $12,000/0.055 = $218,182
Substituting — CC = $622,000 + $218,182
Evaluate — CC = $840,182

Answer:

Capitalized cost ≈ $840,182

Why the other options are there

$622,660 (multiplied instead of divided)
$218,182 (omitted the first cost)

Reference: FE Reference Handbook — Engineering Economics → Capitalized Costs

Example 4

Capitalized cost of a perpetual public works asset — Capitalized Costs (4)

A bridge deck costs $629,000 to build and $43,000 per year to maintain forever. At 7.0% interest, determine the capitalized cost.

Given

First cost = $629,000
A = $43,000/yr
$i = 7.0%$

Find

Capitalized cost of the asset

Start with the thinking

Capitalized cost is the present worth of a cash flow that continues indefinitely.
For a perpetuity P = A/i, so a lower interest rate raises the capitalized cost sharply.

Step-by-step solution

Formula
$CC = First cost + A/i$
Perpetuity term — A/i = $43,000/0.070 = $614,286
Substituting — CC = $629,000 + $614,286
Evaluate — CC = $1,243,286

Answer:

Capitalized cost ≈ $1,243,286

Why the other options are there

$632,010 (multiplied instead of divided)
$614,286 (omitted the first cost)

Reference: FE Reference Handbook — Engineering Economics → Capitalized Costs

Example 5

Capitalized cost of a perpetual public works asset — Capitalized Costs (5)

A bridge deck costs $496,000 to build and $45,000 per year to maintain forever. At 9.5% interest, determine the capitalized cost.

Given

First cost = $496,000
A = $45,000/yr
$i = 9.5%$

Find

Capitalized cost of the asset

Start with the thinking

Capitalized cost is the present worth of a cash flow that continues indefinitely.
For a perpetuity P = A/i, so a lower interest rate raises the capitalized cost sharply.

Step-by-step solution

Formula
$CC = First cost + A/i$
Perpetuity term — A/i = $45,000/0.095 = $473,684
Substituting — CC = $496,000 + $473,684
Evaluate — CC = $969,684

Answer:

Capitalized cost ≈ $969,684

Why the other options are there

$500,275 (multiplied instead of divided)
$473,684 (omitted the first cost)

Reference: FE Reference Handbook — Engineering Economics → Capitalized Costs

Example 6

Capitalized cost of a perpetual public works asset — Capitalized Costs (6)

A bridge deck costs $212,000 to build and $10,000 per year to maintain forever. At 8.5% interest, determine the capitalized cost.

Given

First cost = $212,000
A = $10,000/yr
$i = 8.5%$

Find

Capitalized cost of the asset

Start with the thinking

Capitalized cost is the present worth of a cash flow that continues indefinitely.
For a perpetuity P = A/i, so a lower interest rate raises the capitalized cost sharply.

Step-by-step solution

Formula
$CC = First cost + A/i$
Perpetuity term — A/i = $10,000/0.085 = $117,647
Substituting — CC = $212,000 + $117,647
Evaluate — CC = $329,647

Answer:

Capitalized cost ≈ $329,647

Why the other options are there

$212,850 (multiplied instead of divided)
$117,647 (omitted the first cost)

Reference: FE Reference Handbook — Engineering Economics → Capitalized Costs

Example 7

Capitalized cost of a perpetual public works asset — Capitalized Costs (7)

A bridge deck costs $817,000 to build and $19,000 per year to maintain forever. At 6.5% interest, determine the capitalized cost.

Given

First cost = $817,000
A = $19,000/yr
$i = 6.5%$

Find

Capitalized cost of the asset

Start with the thinking

Capitalized cost is the present worth of a cash flow that continues indefinitely.
For a perpetuity P = A/i, so a lower interest rate raises the capitalized cost sharply.

Step-by-step solution

Formula
$CC = First cost + A/i$
Perpetuity term — A/i = $19,000/0.065 = $292,308
Substituting — CC = $817,000 + $292,308
Evaluate — CC = $1,109,308

Answer:

Capitalized cost ≈ $1,109,308

Why the other options are there

$818,235 (multiplied instead of divided)
$292,308 (omitted the first cost)

Reference: FE Reference Handbook — Engineering Economics → Capitalized Costs

Example 8

Capitalized cost of a perpetual public works asset — Capitalized Costs (8)

A bridge deck costs $286,000 to build and $28,000 per year to maintain forever. At 5.5% interest, determine the capitalized cost.

Given

First cost = $286,000
A = $28,000/yr
$i = 5.5%$

Find

Capitalized cost of the asset

Start with the thinking

Capitalized cost is the present worth of a cash flow that continues indefinitely.
For a perpetuity P = A/i, so a lower interest rate raises the capitalized cost sharply.

Step-by-step solution

Formula
$CC = First cost + A/i$
Perpetuity term — A/i = $28,000/0.055 = $509,091
Substituting — CC = $286,000 + $509,091
Evaluate — CC = $795,091

Answer:

Capitalized cost ≈ $795,091

Why the other options are there

$287,540 (multiplied instead of divided)
$509,091 (omitted the first cost)

Reference: FE Reference Handbook — Engineering Economics → Capitalized Costs

Example 9

Capitalized cost of a perpetual public works asset — Capitalized Costs (9)

A bridge deck costs $642,000 to build and $24,000 per year to maintain forever. At 9.5% interest, determine the capitalized cost.

Given

First cost = $642,000
A = $24,000/yr
$i = 9.5%$

Find

Capitalized cost of the asset

Start with the thinking

Capitalized cost is the present worth of a cash flow that continues indefinitely.
For a perpetuity P = A/i, so a lower interest rate raises the capitalized cost sharply.

Step-by-step solution

Formula
$CC = First cost + A/i$
Perpetuity term — A/i = $24,000/0.095 = $252,632
Substituting — CC = $642,000 + $252,632
Evaluate — CC = $894,632

Answer:

Capitalized cost ≈ $894,632

Why the other options are there

$644,280 (multiplied instead of divided)
$252,632 (omitted the first cost)

Reference: FE Reference Handbook — Engineering Economics → Capitalized Costs

Example 10

Capitalized cost of a perpetual public works asset — Capitalized Costs (10)

A bridge deck costs $655,000 to build and $8,000 per year to maintain forever. At 7.5% interest, determine the capitalized cost.

Given

First cost = $655,000
A = $8,000/yr
$i = 7.5%$

Find

Capitalized cost of the asset

Start with the thinking

Capitalized cost is the present worth of a cash flow that continues indefinitely.
For a perpetuity P = A/i, so a lower interest rate raises the capitalized cost sharply.

Step-by-step solution

Formula
$CC = First cost + A/i$
Perpetuity term — A/i = $8,000/0.075 = $106,667
Substituting — CC = $655,000 + $106,667
Evaluate — CC = $761,667

Answer:

Capitalized cost ≈ $761,667

Why the other options are there

$655,600 (multiplied instead of divided)
$106,667 (omitted the first cost)

Reference: FE Reference Handbook — Engineering Economics → Capitalized Costs