CHAPTER 6-II

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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

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 (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
• Corporate Tax Rates:
• No one single rate;
• 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
• 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,
• 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=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
• 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 > 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
• 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
• 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 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
• 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)

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
• 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