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### Taxes and Depreciation

If you make some money, the government takes part of it

Taxable Income

- We pay taxes as individuals on our taxable income.

Computation of Personal Income Taxes

- The tax rate is graduated to tax the rich more than the poor. In 2000, the tax rates for a single individual were:

Corporation’s Taxable Income

- A corporation pays taxes on its Before Tax Income

Computation of a Corporation’s Taxes

- The corporate rate is also graduated. In 1996:

Taxes on Profit

- The owners of a company are taxed twice on its profits
- Dividends come from the company’s after tax income
- Stock holders must pay personal income tax on dividend receipts as ordinary income
- Stock holders must pay the tax on profits made because of growth in stock price as capital gains

Economic Analysis considering Taxes

- How do we do an economic analysis considering the effects of taxes?

Example 1: Should we invest?

- New Machine:
- Investment = $11,000
- Tax Life (N) and Actual Life (n) = 5 years
- Tax Salvage(SV) and Actual Salvage (MV) = $1,000
- Income = $4,000 per year
- Operating Expenses = $1,000 per year
- 40% Tax Rate
- After Tax MARR = 9%

Method 1: Straight Line Depreciation

- P is the investment,
- N is the tax life, and
- SV is the tax salvage
- The depreciation amount is the same each year.
- The depreciation in year k is: (P - SV)/N.
- The book value at year N is to be equal to SV.
- The book value decreases linearly.

Example 1: ROR

- After-tax NPW

= -11000 + 2600 (P/A, 0.09, 5) + 1000 (P/F, 0.09, 5)

= -236

- Before-tax ROR = 13.34%
- After-tax ROR = 8.20%

What is Depreciation?

- Decline in value to the owner.
- Decline in resale value.
- Decline in value due to wear and tear (deterioration).
- Decline in value due to obsolescence.
- An amount deducted from income before computing taxes

Why do we compute depreciation?

- Reduces net profit before taxes
- Decreases taxes
- Increases the cash flow after taxes

ATCF = Depreciation + Net Income after taxes

- To maximize net present worth of cash flows, we would like to make depreciation as large as possible!

How do you compute Depreciation?

- It is computed separately for each asset
- It depends on the age of the asset
- It depends on the Initial Cost of the asset (P)
- It depends (sometimes) on the Tax Salvage of the Asset (SV)
- It depends on the Tax Life of the asset (N)

Definitions of Depreciation and Book Value

- The Depreciation in year k is Dk
- The Book Value is the Initial Cost (P) minus the Accumulated Depreciation
- BVk = P - (D1 + D2 + … + Dk)

Different Depreciation Methods

- So-called historical or classical methods
- Straight Line
- Sum of the Years Digits
- Declining Balance
- Current method mandated by the government
- Modified Accelerated Capital Recovery System (MACRS) - GDS and ADS

Method 2: SYD

- The Sum of Years Digits (SYD) method is d based on

SYD = 1 + 2 + … + N = (N)(N+1)/2

- The depreciation in year k is

(N - k + 1)/SYD multiplied by (P - S)

- This is an accelerated depreciation method.

Economic Analysis for SYD Depreciation

- After-tax NPW

= -11000 + 3133 (P/A, 0.09, 5) – 266.67 (P/G, 0.09, 5)

+ 1000 (P/F, 0.09, 5)

= -58.77

- Before-tax ROR = 13.34%
- After-tax ROR = 8.79%

Method 3: The Declining Balance method

- A rate (a fraction) must be specified
- The depreciation in year k is rate*(book value at beginning of that year)
- Double Declining Balance (DDB) means the rate of depreciation is two times the straight-line rate.
- In other words, for the DDB, the rate = 2(1/N)
- This is an accelerated depreciation method.

Example 1 DDB Depreciation

This type of income is called “Gain on disposal”

This type of tax is called “Recapture”

Economic Analysis for DDB Depreciation

- After tax NPW

= -11000 + 3560(P/F, 0.09, 1) + 2856(P/F, .09, 2) +

… + 942(P/F, .09, 5)

= 24.01

- Before-tax ROR = 13.34%
- After-tax ROR = 9.09%

Switching from the Declining Balance method to the Straight Line method

- One can switch to the straight line method
- to reduce the Book Value to zero
- or to reach some specified salvage value
- The best place to switch is when the straight line depreciation is greater than the declining balance depreciation

Conclusions

- All previous analysis methods described work with tax considerations
- Use after tax cash flows and after tax MARR for analysis
- Depreciation of investments is required in analysis
- The method of depreciation may affect the decision

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