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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

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chapter 6 ii

CHAPTER 6-II

AFTER-TAX ECONOMIC ANALYSIS

learning objectives
Learning Objectives
  • Terminology and Rates
  • Before- and After-Tax Analysis
  • Taxes and Depreciation
  • Depreciation Recapture and Capital Gains
  • After-Tax Analysis
important terms
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
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 (Rk-Ek-dk)
  • Amount of money remaining each year when income taxes are subtracted from taxable income
    • NIAT = (Rk-Ek-dk) – t (Rk-Ek-dk)= (1-t) (Rk-Ek-dk)
  • 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
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.
      • 1st $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
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
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
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 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=Rk-Ek
  • CFAT for a given time period is defined as:
    • CFATk = CFBTk –Tk=(Rk-Ek)- t(Rk-Ek-dk)=(1-t)(Rk-Ek)+ tdk
    • CFATk = NIATk + tdk
  • Focus on (Rk-Ek-dk)
    • 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
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
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
Four Possibilities
  • The asset is sold for a price > BVt
    • SP > BVt generates a tax liability
  • The asset is sold for a price = BVt
    • SP = BVt no tax liability generated
  • The asset is sold for a price < BVt
    • SP < BVt generates a tax savings
  • The asset is sold for a price > Original basis (B)
disposal example
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;NCFsale = $1,000 – 340 = $660
  • Assume SP = $3,000
    • No tax implications!; NCFSale = $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 – BVTime of Sale= $10,000 - $3,000 = $7,000 (T=0.34)
disposal during the recovery period
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
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 BV3 = $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 = Rk-Ek-dk +DR + CG – CL)
after tax cash flow evaluation
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 – MARRBT
  • For after-tax analysis
    • MARRAfter-Tax = MARRBefore Tax(1-t)
slide17

Before-Tax MARR

  • ( Before Tax MARR ) [ ( 1- effective income tax rate ) ] = After Tax MARR
  • After-tax MARR
  • Before-tax MARR = -------------------------
  • ( 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 exact

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atcf calculations
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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