# CHAPTER 6-II AFTER-TAX ECONOMIC ANALYSIS. Learning Objectives Terminology and Rates Before- and After-Tax Analysis Taxes and Depreciation Depreciation.

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CHAPTER 6-II AFTER-TAX ECONOMIC ANALYSIS

Learning Objectives Terminology and Rates Before- and After-Tax Analysis Taxes and Depreciation Depreciation Recapture and Capital Gains After-Tax Analysis

Important Terms Gross Income –Total income for the tax year from all revenue-producing functions of the enterprise. Income Tax –The total amount of money transferred from the enterprise to the various taxing agencies for a given tax year Operating Expenses –All costs associated with doing business for the tax year Taxable Income –Calculated amount of money for a specified time period from which the tax liability is determined

Net Profit After Tax (NPAT) For Federal corporate income tax T is represented by a series of tax rates The applicable tax rate depends upon the total amount of TI. Taxes owed equals: –Taxes = (taxable income) x (applicable rate) = t (R k -E k -d k ) Amount of money remaining each year when income taxes are subtracted from taxable income – NIAT = (R k -E k -d k ) – t (R k -E k -d k )= (1-t) (R k -E k -d k ) Net profits (if positive) represent funds that are the claim of the owners of the firm NIAT can be: –“Saved” by the firm, –Reinvested within the firm, –Paid out as dividends to the stockholders, –Some combination of paying dividends and reinvesting

Federal Corporate Tax Rates Corporate Tax Rates: –No one single rate; –Series of “graduated” rates; –TI is partitioned into up to 8 brackets of taxable income –A tax rate is then applied to each bracket of taxable income and then summed across all applicable brackets. See Table 6-5 for the 8 bracket rates –Assume TI = \$200,000. 1 st \$50,000 (0.15) = \$7,500 (\$150,000 left) Next \$25,000 (0.25) = \$6,250 (\$125,000 left) Next \$25,000 (0.34) = \$8,500 (\$100,000 left) Tax all monies between \$100,000 to \$335,000 at 34% Last \$100,000 (0.34) = \$34,000

Marginal Tax Rates Each bracket rate is termed a “marginal” rate –The first \$50,000 of TI is taxed at the bracket rate of 15% –Any additional TI over \$50,000 flows into the next bracket –The next \$25,000 or part thereof, is taxed at the marginal bracket rate of 25% –Each additional \$ that moves a firm into a higher bracket is taxed at the higher bracket’s tax rate Total Tax: Add the bracket tax amounts –\$7,500+6,250+8,500+34,000= \$56,250 Tax as a % of TI: 56,250/\$200,000 = 28.13%

State and Federal Most states have a state and local corporate tax structure Firms must pay: –Federal corporate taxes, and possibly –State corporate taxes, and even –County or city income taxes. If this is the case, apply a combined tax rate –t = state rate + (1 – state rate) (Federal Rate) State income taxes are deductible expenses for federal income tax purposes

Personal vs. Corporate Individuals must apply the various standard or itemized deductions permitted by current law. Corporations deduct actual cash-flow expenses Individuals have to file as either: –Single, –Married, –Head of household Individual Tax Rates: Similar bracket design with 5 brackets; 15%, 28%, 31%, 36%, 39.6%

CFBT and CFAT CFBT: –Actual real cash flows associated with an investment BEFORE any income tax considerations Next, CFBT will be defined as: gross income –expenses CFBT=R k -E k CFAT for a given time period is defined as: –CFAT k = CFBT k –T k =(R k -E k )- t(R k -E k -d k )=(1-t)(R k -E k )+ td k –CFAT k = NIAT k + td k Focus on (R k -E k -d k ) –For some time periods this term could be negative –Operating “loss,” which can generate a “negative” tax –Let the sign take care of itself!

Two or More Depreciation Plans For depreciation plans over the same recovery period, and targeting the same salvage value: –The total taxes saved are equal for all depreciation models; –The present worth of taxes saved is always less for accelerated depreciation methods Criteria to be used –Minimize the PW at some i% over n time periods of the tax; –Maximize the PW at some i% over n time periods of the taxes saved If the firm is profitable and the TI amount is > 0, then: –Using a depreciation plan that writes off more of the asset in the early years –Which can be reinvested at or above the firm’s MARR!

Capital Gain and Capital Loss Firms sell or dispose of assets from time to time –Assets that are disposed do have a book value (Could be + or“0”) Depreciation Recapture (Gain 0n Sale) is defined as: –DR = Selling Price – Current Book Value; Capital Gain is defined as: –CG = Selling Price – First Cost –Certain Assets will gain value over time and could be sold for more than what was originally paid for them. – This will generate a tax liability and tax will have to be paid! A capital loss occurs when an asset is sold for less than its current book value. –Could generate a tax savings since the “loss” could be tax deductible within certain rules.

Four Possibilities The asset is sold for a price > BV t –SP > BV t generates a tax liability The asset is sold for a price = BV t –SP = BV t no tax liability generated The asset is sold for a price < BV t –SP < BV t generates a tax savings The asset is sold for a price > Original basis (B)

Disposal Example An asset was purchased for \$10,000, 3 years ago Assume the current BV for tax purposes is \$3,000 Suppose three different hypothetical selling prices T=34% Assume (SP = \$4,000)> (BV = \$3,000) ; DR=1000 –Tax=1,000 (0.34) = \$340;NCF sale = \$1,000 – 340 = \$660 Assume SP = \$3,000 –No tax implications!; NCF Sale = \$3,000 Assume SP = \$2,000; loss on disposal= -1000 –Tax: (-1,000)(0.34) = -\$340.00; form of a negative tax! Assume SP = \$12,000 and B = \$10,000 –Two Components to deal with: (SP – B) = 12,000 – 10,000 = \$2,000 Gain amount (T=0.28) B – BV Time of Sale = \$10,000 - \$3,000 = \$7,000 (T=0.34)

Disposal During the Recovery Period Under current Federal tax law: Any depreciable asset that is disposed of during the recovery period requires: –Only ½ year of the normal depreciation is permitted in the year of disposal –The beginning of year book value is reduced by the ½ year of recovery to establish the BV for tax purposes

Example Assume an asset is in its 4th year of recovery and is sold –Assume the beginning of year book value is \$5,000 –Assume the 4th year’s depreciation charge – if not disposed – would be \$2,000 –Only ½ year of recovery is permitted for year 4 or ½ (2,000) = \$1,000 –The book value for tax purposes is BV 3 = \$5,000 (BOY) –Less the \$1,000 of permitted recovery due to the half-year rule on disposal, or \$4,000. SP, is now compared to the \$4,000 BV at the time of sale to determine if there is any recaptured depreciation Expand the TI expression to accommodate depreciation recapture amounts (TI = R k -E k -d k +DR + CG – CL)

After-Tax Cash Flow Evaluation The economic desirability of the cash flow can be determined using PW, FW, AW, ROR,... Single Project: –PW or AW > 0 at i% or, –IROR > MARR Two or More Alternatives: –Select the alternative with the largest PW or AW value at the i% rate –If using IROR, must apply the incremental analysis approach Some firms may set a before-tax discount rate – MARR BT For after-tax analysis –MARR After-Tax = MARR Before Tax (1-t)

Before-Tax MARR ( Before Tax MARR ) [ ( 1- effective income tax rate ) ] = After Tax MARR After-tax MARR Before-tax MARR = ------------------------- ( 1 - effective tax rate ) ( 1 - effective tax rate ) If the asset is non-depreciable and there are no gains or losses on disposal, tax credits, or other types of deductions involved this approximation in the equation above is exactIf the asset is non-depreciable and there are no gains or losses on disposal, tax credits, or other types of deductions involved this approximation in the equation above is exact ~ ~ ~ ~ -

ATCF Calculations A tabular approach is suggested See Figure 6-5 and Example 16.16 Best performed with a spreadsheet model Depreciation amounts can be calculated in another spreadsheet and copied (values only) into the ATCF worksheet User inputs besides the CF values are the discount rate and the tax rate

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