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

Who gets it? Who pays it? What is it used for?

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.

For the Straight Line Method

Example 1: After Tax Analysis

Example 1: ROR After-tax NPW = (P/A, 0.09, 5) (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 D k The Book Value is the Initial Cost (P) minus the Accumulated Depreciation –BV k = P - (D 1 + D 2 + … + D k )

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 = … + 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.

SYD Method

Example 1 with SYD Depreciation

Economic Analysis for SYD Depreciation After-tax NPW = (P/A, 0.09, 5) – (P/G, 0.09, 5) (P/F, 0.09, 5) = 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.

For the Declining Balance 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 = (P/F, 0.09, 1) (P/F,.09, 2) + … + 942(P/F,.09, 5) = Before-tax ROR = 13.34% After-tax ROR = 9.09%

Example 1 Comparison

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