Lecture 8: Depreciation and Income Taxes

I. The Fundamental Concepts of Depreciation

A. Defining Depreciation

Depreciation is a fundamental concept in engineering economic analysis, primarily utilized in calculating income taxes.

It is essential to distinguish depreciation from physical deterioration or obsolescence.

Depreciation, in an accounting context, represents an expense recorded over time to reflect the loss of value of a business asset.

B. Depreciation as a Book Cost

Depreciation falls under the category of book costs.

  1. Nature of Book Costs: Book costs are financial effects resulting from past decisions recorded in a firm’s accounting records. They represent the expense paid for a specific business asset being “written off” over a number of periods.
  2. Cash Flow Rule: Ordinary book costs, including depreciation expense itself, do not represent an actual cash flow (transaction of dollars from one party to another) and are therefore generally excluded from before-tax engineering economic analysis.
  3. Exception: The primary exception is that depreciation significantly impacts the cash flow related to tax payments, which are cash flows and must be included in after-tax analyses.

C. Types of Depreciable Property

Engineers must distinguish various types of depreciable property and differentiate depreciation expenses from other business operating expenses.

II. Calculating Depreciation Schedules

Depreciation calculations are necessary to systematically reduce the book value of an asset over its useful or recovery life.

A. Historical Depreciation Methods

While modern tax law often mandates specific accelerated methods, classic methods help illustrate the core concept:

  • Straight-Line (SL) Depreciation: Provides a constant annual depreciation expense.
  • Sum-of-the-Years’-Digits (SOYD) Depreciation: Provides an accelerated rate of depreciation.
  • Double Declining Balance (DDB) Depreciation: Provides an accelerated rate of depreciation, usually requiring a switch to Straight-Line later in the asset’s life to maximize write-offs.

B. Modified Accelerated Cost Recovery System (MACRS)

For taxation purposes in the United States, the Modified Accelerated Cost Recovery System (MACRS) is the mandated approach used for calculating allowable depreciation charges.

  1. Key Elements: MACRS requires identifying three primary factors based on the asset type:
    • Cost Basis: The initial amount used for depreciation calculation.
    • Property Class/Recovery Period: Defines the number of years over which the asset must be depreciated (e.g., 3-year, 5-year, 7-year class).
    • Applicable Depreciation Percentage: Determined by the recovery period and specific tables provided by tax authorities.
  2. MACRS Example Percentages (5-Year Property):
    • Year 1: 20.00%
    • Year 2: 32.00%
    • Year 3: 19.20%
    • Year 4: 11.52%
    • Year 5: 11.52%
    • Year 6: 5.76% (Note: This 6th-year expense is due to the half-year convention applied in the first year).
  3. Bonus Depreciation: The framework of MACRS often includes Bonus Depreciation rules, which allow a business to deduct a substantial portion (sometimes 100%) of the asset’s cost basis in the year it is placed in service.

C. Asset Disposal

Full accounting for depreciation requires managing the tax implications of disposing of a business asset, which can lead to capital gains, capital losses, or depreciation recapture.

III. Understanding the Framework of Income Taxes

Income taxes represent a significant disbursement that affects the economic viability of projects, particularly in the private sector for corporations.

A. Corporate Tax Rate

The tax rate used in economic analysis is typically the incremental tax rate, which is the rate applied to the last dollar of taxable income earned.

It is often necessary to combine state and federal tax rates to determine the appropriate composite incremental tax rate for calculations.

B. Rate of Return Relationship (Nondepreciable Assets)

For investment alternatives involving nondepreciable assets, the after-tax rate of return (\(i_{at}\)) is nominally related to the before-tax rate of return (\(i_{bt}\)) and the tax rate (\(T\)):

\[i_{at} = i_{bt} (1 - T)\]

IV. Analyzing Projects on an After-Tax Basis

The introduction of income taxes requires a systematic method for modeling project finances, centered on the calculation of After-Tax Cash Flows (ATCF).

A. Developing After-Tax Cash Flows (ATCF)

The calculation process starts with the project’s Before-Tax Cash Flow (BTCF).

  1. Before-Tax Cash Flow (BTCF): This initial flow typically includes:
    • Revenues or Receipts
    • Operating Expenses (Disbursements)
    • Initial Capital Expenditures
    • Final Salvage/Disposal Value
  2. Taxable Income (TI): The amount upon which taxes are levied. TI is calculated by adjusting the operating income (or BTCF excluding initial and disposal costs) for non-cash expenses like depreciation and cash expenses like interest payments. \[TI = (Revenues - Operating Expenses) - Depreciation - Interest Payments\]
  3. Taxes Due: Calculated by multiplying the Taxable Income by the applicable corporate incremental tax rate (\(T\)). If TI is negative, the resulting tax is negative, representing a tax shield or tax savings.
  4. After-Tax Cash Flow (ATCF): The final cash flow sequence used for analysis. \[ATCF = BTCF - Taxes\]

B. After-Tax Analysis

Once the ATCF stream is determined, the project can be analyzed using standard measures of merit:

  • After-Tax Present Worth (PW)
  • After-Tax Equivalent Uniform Annual Worth (EUAW)
  • After-Tax Internal Rate of Return (IRR)
  • After-Tax Payback Period

These measures are crucial for comparing investment alternatives accurately, as taxes often affect alternatives dissimilarly.