## Depreciation and Taxes

##### Methods of Calculating Depreciation

**Learning Objectives:**

- Apply straight line method of depreciation.
- Calculate depreciation using reducing balance method.
- Calculate depreciation using sum of digits method.
- Perform calculations using Accelerated Cost Recovery System (ACRS).
- Apply MACRS method of depreciation.

**Straight Line Depreciation Method**

Straight line method depreciates cost evenly through out the useful life of the fixed asset. Straight line depreciation is calculated as follows:

\[\mathrm{Depreciation \ per\ annum = \dfrac{(Cost - Residual\ Value)}{ Useful \ Life}}\]
\[ D_{j} =\dfrac{C - S_{n}}{n}\]
C= Cost of Purchase

S$_n$ = Salvage value after n years

n = no. of years

**Reducing Balance Depreciation Method**

Reducing Balance Method charges depreciation at a higher rate in the earlier years of an asset. The amount of depreciation reduces as the life of the asset progresses. Depreciation under reducing balance method may be calculated as follows:

$\mathrm{Depreciation\ per\ annum}$ = $\mathrm{(Net \ Book \ Value \ - Residual\ Value) \times Rate \%}$

Where Net Book Value is the asset's net value at the start of an accounting period. It is calculated by deducting the accumulated (total) depreciation from the cost of the fixed asset.

Residual Value is the estimated scrap value at the end of the useful life of the asset. As the residual value is expected to be recovered at the end of an asset's useful life, there is no need to charge the portion of cost equaling the residual value.

Rate of depreciation is defined according to the estimated pattern of an asset's use over its life term.

**Sum of the Years' Digits Depreciation Method**

Sum of the years' digits depreciation method, like reducing balance method, is a type of accelerated depreciation technique that allocates higher depreciation expense in the earlier years of an asset's useful life.

Calculation of depreciation under this method can be summarized in the following 4 steps:

Step 1: Calculate the sum of the years' digits in an asset's useful life

For an asset having a useful life of 4 years, the sum of the years' digits will be calculated as follows:

Sum of years' digits = 4 + 3 + 2 + 1 = 10

Step 2: Calculate the depreciable amount

Depreciable amount, as with all depreciation methods, is equal to:

Asset's cost of acquisition or construction including any subsequent capital expenditure

Less: Estimated residual value or scrap value at the end of the asset's useful life

Step 3: Calculate the un-depreciated useful life

Un-depreciated useful life is equal to the number of years in the asset's useful life that have not yet been subjected to depreciation.

Hence, for an asset that has a useful life of 4 years, the un-depreciated useful life to be used in calculating depreciation shall be 4 years in the first year of depreciation, 3 years in the second year and so on.

Step 4: Calculate depreciation using the sum of years' digits \& un-depreciated useful life

Depreciation using the sum of the years' digits method can be calculated using the following formula:

Depreciation Expense = Un-depreciated useful life (Step 3) x Depreciable Amount (Step 2)
Sum of the years' digits (Step 1)

**ACRS and MACRS Depreciation Methods**

In ACRS system, D$_j$ = (Factor) * C and this factor is according to the table given in the table on page 115 of NCEES FE Reference Handbook.

**Solved Example: 9194-01**

Which method of depreciation is suitable for finding depreciation of a building that has a life of 100 years?

A. Constant percentage method

B. Straight-line method

C. Sinking fund method

D. Quantity survey method

Correct Answer: **B**

**Solved Example: 9194-02**

Diminishing method of depreciation provides:

A. More depreciation in initial years

B. Equal amount of depreciation every year

C. More depreciation in later years

D. Depreciation amount changes in every 2 year

Correct Answer: **A**

##### Recapture

**Solved Example: 9188-01**

Which of the following statements is correct?

A. Over a project’s life, a typical business will generate a greater amount of total project cash flows (undiscounted) if a faster depreciation method is adopted.

B. No matter which depreciation method you adopt, total tax obligations over a project’s life remain unchanged.

C. Depreciation recapture equals cost basis minus an asset’s book value at the time of disposal, that is, if the salvage value is less than the asset’s cost basis.

D. Cash flows normally include depreciation expenses since they represent a cost of doing business.

Correct Answer: **B**

##### Depreciation Terminology

**Learning Objectives:**

- Understand the concept of depreciation
- Understand basic terms of asset depreciation.
- Comprehend methods of calculating depreciation charges
- Identify the factors to be considered when choosing a depreciation method
- Determine the impact on profits by using different depreciation methods.

The term

**Depreciation**is used for long-lived tangible assets.The term

**Depletion**is used for natural resources.The term

**Amortization**is used for intangible assets.

Information needed in order to calculate depreciation:

Depreciable base = original cost – salvage value.

Estimated service (useful) life versus physical life.

Depreciation method:**

Activity based—units of use or production.

Straight-line—based on calendar time.

Accelerated—Sum of Years’ Digits or declining-balance.

Special—group and composite, retirement and replacement, hybrid, combination, other.

** All take the same total depreciation over an asset’s useful life.

**Solved Example: 17-5-01**

What is Amortization?

A. Accounting techniques are used to periodically lower the book value of a loan.

B. Notable reduction in the utility of an inventory item or fixed asset.

C. Accrual accounting technique used to allocate the cost of extracting natural resources

D. The loss in the physical efficiency of an asset as it ages.

Correct Answer: **A**

**Solved Example: 17-5-02**

What is Scrap Value?

A. The combined cost of purchase and installation of an asset can be depreciated minus its salvage value

B. The worth of a physical asset's components when the asset itself is deemed no longer usable

C. Represents the value of a company according to the stock market

D. The estimated resale value of an asset at the end of its useful life

Correct Answer: **B**

**Solved Example: 17-5-03**

What is Depreciable Value?

A. The combined cost of purchase and installation of an asset can be depreciated minus its salvage value.

B. The worth of a physical asset's components when the asset itself is deemed no longer usable.

C. Represents the value of a company according to the stock market.

D. The estimated resale value of an asset at the end of its useful life.

Correct Answer: **A**

##### After-Tax Cash Flow

**Solved Example: 9261-01**

Which parameter is NOT considered in the cash flow statement?

A. Trading activities

B. Operating activities

C. Financing activities

D. Investing activities

Correct Answer: **A**