0. Analisa Ekonomi After-Tax

Principles of Engineering Economic Analysis, 5th edition

Bab 10Bab 10

Setelah-PajakEconomiAnalisa


Teknik Analisa Economi 1. Identidikasi alternatip investasi 2. Tetapkan planning horizon 3. Tentukan discount rate 4. Estimasi cash flows 5. Bandingkan antar alternatip 6. Lakukan Analisa Tambahan 7. Pilih investasi yang diinginkan


Pesan Utama #1Lakukan analisa setelah-

pajak/after-tax, jangan analisa sebelum-pajak/beore-tax,

kecuali dalam situasi tidak umum.


Corporate Income Tax Rates for Tax Years Beginning January 1, 1993 and Beyond


Selama hukum pajak penghasilan berbeda dengan buku, pelajari sistem hukum perpajakan di

Indonesia


Contoh 10.1A small business is forecasting a taxable income of $50,000 for the year. The owner is considering making an investment that will increase taxable income by $45,000. If the investment is pursued and the anticipated return occurs, what will be the magnitude of the increase in income taxes caused by the new investment? What would be the magnitude of the increase in income taxes if the company forecasts a taxable income of $400,000 for the year?


Contoh 10.1 (Lanjutan)

With a “base” taxable income of $50,000, the federal income tax will be 0.15($50,000), or $7500. The income tax for a taxable income of $95,000 will be $13,750 + 0.34($20,000) = $20,550.

With a “base” taxable income of $400,000, the federal income tax will be $113,900 + 0.34($65,000) = $136,000 or 34% of $400,000. Because every dollar of the additional $45,000 in taxable income will be taxed at 34%, the increase in taxable income will be 0.34($45,000) = $15,300 for a total tax of $151,300.


• effective tax rate = income tax divided by taxable income;

• incremental tax rate = average rate charged to incremental investment; and

• marginal tax rate = tax rate that applies to the last dollar included in taxable income.


Fiscal Year 2007 Effective Tax Rates

CompanyEffective Tax Rate Company

Effective Tax Rate

ABB 27.0% Federal Express 37.3%

Abbott Laboratories 19.3% Harley-Davidson 35.5%

BP 37.0% Hewlett-Packard 20.8%

Canon 33.2% Home Depot 36.4%

Caterpillar 30.0% Intel 23.9%

Coca-Cola 24.0% J.B. Hunt Transport Services 34.4%

ConocoPhillips 48.9% Motorola 26.0%

Eli Lilly 23.8% Wal-Mart 33.6%


Contoh 10.2

For Example 10.1, the effective tax rate, when “base” taxable income is $50,000 and an additional $45,000 in taxable income will occur, is

$20,550/($50,000 + $45,000), or 21.63%.

The incremental tax rate is

($20,550 - $7500)/$45,000, or 29%.

The marginal tax rate is 34%.


In performing engineering economic analyses, use

the marginal tax rate.




LetBTCF = before-tax cash flowDWO = depreciation write-off, allowance or chargeTI = taxable incomestr = state income tax rateftr = federal income tax rateitr = income tax rateT = income taxATCF = after-tax cash flow


ATCF = BTCF(1 - itr) + itr(DWO)

itr = str + ftr(1 - str)

If ftr = 35% and str = 7%, then

itr = 0.07 + 0.35(0.93)

itr = 0.3955 or 39.55%


Analisa After-Tax

Alternatip Single


Contoh 10.3

A $500,000 investment in a surface mount placement machine produces after-tax net revenue of $92,500/yr for 10 years, at which time the SMP machine has a salvage value of $50,000. Based on a 40% income tax rate, a 10% ATMARR, & SLN depreciation, what will be the ATPW, ATFW, ATAW, ATIRR, and ATERR for the SMP investment? What will be the BTCF, BTPW, BTFW, BTAW, BTIRR, and BTERR if the BTMARR is 0.10/(1.0 – 0.4) = 16.667%?


BT & AT Analysis of the SMP Investment with SLNEOY BTCF DWO TI T ATCF

0 -$500,000.00 -$500,000.001 $124,166.67 $45,000.00 $79,166.67 $31,666.67 $92,500.002 $124,166.67 $45,000.00 $79,166.67 $31,666.67 $92,500.003 $124,166.67 $45,000.00 $79,166.67 $31,666.67 $92,500.004 $124,166.67 $45,000.00 $79,166.67 $31,666.67 $92,500.005 $124,166.67 $45,000.00 $79,166.67 $31,666.67 $92,500.006 $124,166.67 $45,000.00 $79,166.67 $31,666.67 $92,500.007 $124,166.67 $45,000.00 $79,166.67 $31,666.67 $92,500.008 $124,166.67 $45,000.00 $79,166.67 $31,666.67 $92,500.009 $124,166.67 $45,000.00 $79,166.67 $31,666.67 $92,500.00

10 $174,166.67 $45,000.00 $79,166.67 $31,666.67 $142,500.00MARRBT = 16.667% MARRAT = 10%

PW BT = $96,229.49 PW AT = $87,649.62

FW BT = $449,547.99 FW AT = $227,340.55

AW BT = $20,406.41 AW AT = $14,264.57

IRR BT = 21.64% IRR AT = 13.80%

ERR BT = 18.74% ERR AT = 11.79%


Example 10.4

A $500,000 investment in a surface mount placement machine produces before-tax net revenue of $124,166.67/yr for 10 years, at which time the SMP machine has a salvage value of $50,000. Based on a 40% income tax rate, a 10% ATMARR, & 5-yr MACRS depreciation, what will be the ATPW, ATFW, ATAW, ATIRR, and ATERR for the SMP investment?


AT Analysis of the SMP Investment with MACRS

EOY BTCF DWO TI T ATCF0 -$500,000.00 -$500,000.001 $124,166.67 $100,000.00 $24,166.67 $9,666.67 $114,500.002 $124,166.67 $160,000.00 -$35,833.33 -$14,333.33 $138,500.003 $124,166.67 $96,000.00 $28,166.67 $11,266.67 $112,900.004 $124,166.67 $57,600.00 $66,566.67 $26,626.67 $97,540.005 $124,166.67 $57,600.00 $66,566.67 $26,626.67 $97,540.006 $124,166.67 $28,800.00 $95,366.67 $38,146.67 $86,020.007 $124,166.67 $0.00 $124,166.67 $49,666.67 $74,500.008 $124,166.67 $0.00 $124,166.67 $49,666.67 $74,500.009 $124,166.67 $0.00 $124,166.67 $49,666.67 $74,500.00

10 $174,166.67 $0.00 $174,166.67 $69,666.67 $104,500.00PW AT = $123,988.64

FW AT = $321,594.61

AW AT = $20,178.58

IRR AT = 16.12%

ERR AT = 12.46%


SMP Investment

Measure of Economic Worth With SLN With MACRS

PWAT $87,649.62 $123,988.64FWAT $227,340.55 $321,594.61

AWAT $14,264.57 $20,178.58

IRRAT 13.80% 16.12%

ERRAT 11.79% 12.46%


Main Message #2In general, the faster an

investment is depreciated, the greater

its after-tax present worth.


Example 10.5

A $500,000 investment in a surface mount placement machine produces BTCF of $124,166.67/yr for 10 years, at which time the SMP machine is sold for $50,000. If DDB depreciation is used, based on a 40% income tax rate, a 10% ATMARR, & 5-yr MACRS depreciation, what will be the ATPW, ATFW, ATAW, ATIRR, and ATERR for the SMP investment?


TIn = BTCFn(incl Fn) - DWOn - Bn

Taxable income in the year of property disposal (EOY = n) is equal to the before-tax cash flow in the year of property disposal, including salvage value realized, less the depreciation write-off in the year of property disposal, less the book value at the time of property disposal.

Recall, if depreciable property is disposed of before the end of the recovery period, when using MACRS depreciation, a half-year allowance (in the case of personal property) or mid-month allowance (in the case of real property) is permitted in the year of disposal.


AT Analysis of the SMP Investment with DDBEOY BTCF DWO TI T ATCF

0 -$500,000.00 -$500,000.001 $124,166.67 $100,000.00 $24,166.67 $9,666.67 $114,500.002 $124,166.67 $80,000.00 $44,166.67 $17,666.67 $106,500.003 $124,166.67 $64,000.00 $60,166.67 $24,066.67 $100,100.004 $124,166.67 $51,200.00 $72,966.67 $29,186.67 $94,980.005 $124,166.67 $40,960.00 $83,206.67 $33,282.67 $90,884.006 $124,166.67 $32,768.00 $91,398.67 $36,559.47 $87,607.207 $124,166.67 $26,214.40 $97,952.27 $39,180.91 $84,985.768 $124,166.67 $20,971.52 $103,195.15 $41,278.06 $82,888.619 $124,166.67 $16,777.22 $107,389.45 $42,955.78 $81,210.89

10 $174,166.67 $13,421.77 $107,057.81 $42,823.12 $131,343.55B 10 = $53,687.09

PW AT = $105,429.72

FW AT = $273,457.54

AW AT = $17,158.20

IRR AT = 14.88%

ERR AT = 12.12%


Example 10.6

A $500,000 investment is made in a consulting study that produces BTCF of $124,166.67/yr for 10 years, plus an additional $50,000 in the 10th year. Based on a 40% income tax rate and a 10% ATMARR, what will be the ATPW, ATFW, ATAW, ATIRR, and ATERR for the investment in the consultant?


AT Analysis of a $500,000 Investment in a ConsultantEOY BTCF TI T ATCF

0 -$500,000.00 -$500,000.00 -$200,000.00 -$300,000.001 $124,166.67 $124,166.67 $49,666.67 $74,500.002 $124,166.67 $124,166.67 $49,666.67 $74,500.003 $124,166.67 $124,166.67 $49,666.67 $74,500.004 $124,166.67 $124,166.67 $49,666.67 $74,500.005 $124,166.67 $124,166.67 $49,666.67 $74,500.006 $124,166.67 $124,166.67 $49,666.67 $74,500.007 $124,166.67 $124,166.67 $49,666.67 $74,500.008 $124,166.67 $124,166.67 $49,666.67 $74,500.009 $124,166.67 $124,166.67 $49,666.67 $74,500.0010 $174,166.67 $174,166.67 $69,666.67 $104,500.00

PW AT = $169,336.56

FW AT = $439,215.43

AW AT = $27,558.75

IRR AT = 21.64%

ERR AT = 15.03%


Expensing vs Capitalizing

Measure of Economic Worth Expensing Capitalizing

PWAT $169,336.56 $123,988.64FWAT $439,215.43 $321,594.61

AWAT $27,558.75 $20,178.58

IRRAT 21.64% 16.12%

ERRAT 15.03% 12.46%


After-Tax Analysis

Multiple Alternatives


Example 10.7

Recall the two design alternatives for the Scream Machine considered previously. Now, we perform an after-tax analysis, based on: design A having an initial investment of $300,000 and producing before-tax net annual revenue of $71,666.67; and design B having an initial investment of $450,000 and producing before-tax net annual revenue of $103,333.33. Based on a 40% income tax rate, a 10% ATMARR, and 7-yr MACRS depreciation, perform an after-tax comparison of the two alternatives.


AT Analysis of the Scream Machine Design AlternativesEOY BTCF(A) DWO(A) TI(A) T(A) ATCF(A)

0 -$300,000.00 -$300,000.001 $71,666.67 $42,870.00 $28,796.67 $11,518.67 $60,148.002 $71,666.67 $73,470.00 -$1,803.33 -$721.33 $72,388.003 $71,666.67 $52,470.00 $19,196.67 $7,678.67 $63,988.004 $71,666.67 $37,470.00 $34,196.67 $13,678.67 $57,988.005 $71,666.67 $26,790.00 $44,876.67 $17,950.67 $53,716.006 $71,666.67 $26,760.00 $44,906.67 $17,962.67 $53,704.007 $71,666.67 $26,790.00 $44,876.67 $17,950.67 $53,716.008 $71,666.67 $13,380.00 $58,286.67 $23,314.67 $48,352.009 $71,666.67 $0.00 $71,666.67 $28,666.67 $43,000.0010 $71,666.67 $0.00 $71,666.67 $28,666.67 $43,000.00

PW(A) = $50,790.36EOY BTCF(B) DWO(B) TI(B) T(B) ATCF(B)

0 -$450,000.00 -$450,000.001 $103,333.33 $64,305.00 $39,028.33 $15,611.33 $87,722.002 $103,333.33 $110,205.00 -$6,871.67 -$2,748.67 $106,082.003 $103,333.33 $78,705.00 $24,628.33 $9,851.33 $93,482.004 $103,333.33 $56,205.00 $47,128.33 $18,851.33 $84,482.005 $103,333.33 $40,185.00 $63,148.33 $25,259.33 $78,074.006 $103,333.33 $40,140.00 $63,193.33 $25,277.33 $78,056.007 $103,333.33 $40,185.00 $63,148.33 $25,259.33 $78,074.008 $103,333.33 $20,070.00 $83,263.33 $33,305.33 $70,028.009 $103,333.33 $0.00 $103,333.33 $41,333.33 $62,000.0010 $103,333.33 $0.00 $103,333.33 $41,333.33 $62,000.00

PW(B) = $60,824.10


Example 10.8

In the previous example, suppose alternative A qualifies as 3-yr property and alternative B qualifies as 7-yr property. Based on a 40% income tax rate and a 10% ATMARR, perform an after-tax comparison of the two alternatives.


AT Analysis of Alternatives with Different Property ClassesEOY BTCF(A) DWO(A) TI(A) T(A) ATCF(A)

0 -$300,000.00 -$300,000.001 $71,666.67 $99,990.00 -$28,323.33 -$11,329.33 $82,996.002 $71,666.67 $133,350.00 -$61,683.33 -$24,673.33 $96,340.003 $71,666.67 $44,430.00 $27,236.67 $10,894.67 $60,772.004 $71,666.67 $22,230.00 $49,436.67 $19,774.67 $51,892.005 $71,666.67 $0.00 $71,666.67 $28,666.67 $43,000.006 $71,666.67 $0.00 $71,666.67 $28,666.67 $43,000.007 $71,666.67 $0.00 $71,666.67 $28,666.67 $43,000.008 $71,666.67 $0.00 $71,666.67 $28,666.67 $43,000.009 $71,666.67 $0.00 $71,666.67 $28,666.67 $43,000.00

10 $71,666.67 $0.00 $71,666.67 $28,666.67 $43,000.00PW(A) = $64,084.76

EOY BTCF(B) DWO(B) TI(B) T(B) ATCF(B)0 -$450,000.00 -$450,000.001 $103,333.33 $64,305.00 $39,028.33 $15,611.33 $87,722.002 $103,333.33 $110,205.00 -$6,871.67 -$2,748.67 $106,082.003 $103,333.33 $78,705.00 $24,628.33 $9,851.33 $93,482.004 $103,333.33 $56,205.00 $47,128.33 $18,851.33 $84,482.005 $103,333.33 $40,185.00 $63,148.33 $25,259.33 $78,074.006 $103,333.33 $40,140.00 $63,193.33 $25,277.33 $78,056.007 $103,333.33 $40,185.00 $63,148.33 $25,259.33 $78,074.008 $103,333.33 $20,070.00 $83,263.33 $33,305.33 $70,028.009 $103,333.33 $0.00 $103,333.33 $41,333.33 $62,000.00

10 $103,333.33 $0.00 $103,333.33 $41,333.33 $62,000.00PW(B) = $60,824.10


Example 10.9

A distribution center is considering using a robot to perform palletizing. The robot has an initial cost of $125,000; its annual O&M cost is $500; it qualifies as 3-yr property; and it has a $25,000 salvage value after 5 yrs. Alternatively, 2 people can perform the palletizing at an annual cost of $50,000. Using a 5-yr planning horizon, a 40% tax rate, a 10% ATMARR, and an AW analysis, should the robot be purchased?


AT Analysis of Robotic versus Manual Palletizing

Since labor cost can be expensed in the year in which it occurs, the ATEUAC of manually palletizing is $50,000(0.60) = $30,000

As shown below, the EUAC of robotic palletizing is $19,840.63. Therefore, the robot is justified economically.

EOY BTCF DWO TI T ATCF0 -$125,000.00 -$125,000.001 -$500.00 $41,662.50 -$42,162.50 -$16,865.00 $16,365.002 -$500.00 $55,562.50 -$56,062.50 -$22,425.00 $21,925.003 -$500.00 $18,512.50 -$19,012.50 -$7,605.00 $7,105.004 -$500.00 $9,262.50 -$9,762.50 -$3,905.00 $3,405.005 $24,500.00 $0.00 $24,500.00 $9,800.00 $14,700.00

AW = -$19,840.63


Example 10.10

Acme Brick is considering adding 5 lift trucks to its fleet. It can either purchase or lease the trucks. If purchased, each truck has a first cost of $18,000; annual O&M costs of $3750; and a salvage value of $3000. Lift trucks qualify as 3-yr property.

If the lift trucks are leased, beginning-of-year payments of $5900/truck, plus operating costs of $1800/truck, will be incurred.

Using a 5-yr planning horizon, a 40% tax rate, a 10% ATMARR, and an AW analysis, should the trucks be purchased or leased?


AT Analysis of Purchasing versus Leasing Lift Trucks

EOY BTCF(P) DWO(P) TI(P) T(P) ATCF(P)0 -$90,000.00 -$90,000.001 -$18,750.00 $29,997.00 -$48,747.00 -$19,498.80 $748.802 -$18,750.00 $40,005.00 -$58,755.00 -$23,502.00 $4,752.003 -$18,750.00 $13,329.00 -$32,079.00 -$12,831.60 -$5,918.404 -$18,750.00 $6,669.00 -$25,419.00 -$10,167.60 -$8,582.405 -$3,750.00 $0.00 -$3,750.00 -$1,500.00 -$2,250.00

PW(P) = -$140,045.81 PW(P) = -$96,486.74EOY BTCF(L) DWO(L) TI(L) T(L) ATCF(L)

0 -$29,500.00 -$29,500.00 -$11,800.00 -$17,700.001 -$38,500.00 $0.00 -$38,500.00 -$15,400.00 -$23,100.002 -$38,500.00 $0.00 -$38,500.00 -$15,400.00 -$23,100.003 -$38,500.00 $0.00 -$38,500.00 -$15,400.00 -$23,100.004 -$38,500.00 $0.00 -$38,500.00 -$15,400.00 -$23,100.005 -$9,000.00 $0.00 -$9,000.00 -$3,600.00 -$5,400.00

PW(L) = -$132,783.18 PW(L) = -$90,926.87

Lease the lift trucks!


After-Tax Analysis

Borrowing Investment Capital


ATCF = BT&LCF(1 - itr) - LCF + itr(DWO + IPMT)

After-tax cash flow equals before-tax-and-loan cash flow times one minus the income tax rate, less the loan cash flow, plus the product of the income tax rate and the sum of the depreciation write-off and the interest payment made on the loan.


TIn = BT&LCFn(incl Fn) - IPMTn – DWOn - Bn

Taxable income in the year of property disposal equals before-tax-and-loan cash flow in the year of property disposal, including salvage value realized, less the interest payment made in the year of property disposal, less depreciation write-off in the year of property disposal, less the book value at the time of disposal.


Four Loan Repayment Plans1. Pay interest each period, but make no

principal payment until the end of the loan period

2. Make equal end-of-period principal payments and pay interest each period on the unpaid balance at the beginning of the period

3. Make equal end-of-period payments over the loan period

4. Make no payment until the end of the loan period


Because interest can be deducted from taxable income, the effective after-tax interest rate paid on borrowed funds is

ieff = i(1 - itr)

Similarly, ATMARR = BTMARR(1 – itr)

With an interest rate of 12%, an income tax rate of 40%, and an ATMARR of 10%, since the BTMARR = 0.10/0.60, or 16.667%, it costs less to borrow the money than to use internal funds.

If the interest rate on the loan is greater than the BTMARR, then one should borrow as little as possible and repay the principal as quickly as possible. Likewise, if the interest rate is less than the BTMARR, then one should borrow as much as possible and delay repaying the principal as long as possible.


Example 10.11

Now, we apply the four loan repayment methods to the SMP investment. We assume $300,000 is borrowed at 12% annual compound interest and repaid in 10 yrs.

We will use a 10-yr planning horizon, a 40% tax rate, a 10% ATMARR, and a PW analysis to determine the preferred borrowing method.


2 roots: -18.62% and 41.54%


income tax rate = 40%EOY BT&LCF PPMT IPMT DWO TI Tax ATCF

0 -$500,000.00 -$300,000.00 -$200,000.001 $124,166.67 $30,000.00 $36,000.00 $100,000.00 -$11,833.33 -$4,733.33 $62,900.002 $124,166.67 $30,000.00 $32,400.00 $160,000.00 -$68,233.33 -$27,293.33 $89,060.003 $124,166.67 $30,000.00 $28,800.00 $96,000.00 -$633.33 -$253.33 $65,620.004 $124,166.67 $30,000.00 $25,200.00 $57,600.00 $41,366.67 $16,546.67 $52,420.005 $124,166.67 $30,000.00 $21,600.00 $57,600.00 $44,966.67 $17,986.67 $54,580.006 $124,166.67 $30,000.00 $18,000.00 $28,800.00 $77,366.67 $30,946.67 $45,220.007 $124,166.67 $30,000.00 $14,400.00 $0.00 $109,766.67 $43,906.67 $35,860.008 $124,166.67 $30,000.00 $10,800.00 $0.00 $113,366.67 $45,346.67 $38,020.009 $124,166.67 $30,000.00 $7,200.00 $0.00 $116,966.67 $46,786.67 $40,180.0010 $174,166.67 $30,000.00 $3,600.00 $0.00 $170,566.67 $68,226.67 $72,340.00

PW AT = $156,374.28

FW AT = $405,594.61

AW AT = $25,449.19

IRR AT = 28.51%

ERR AT = 16.54%

After-Tax Analysis of SMP Investment with $300,000 Borrowed & Repaid Using Method 2


After-Tax Analysis of SMP Investment with $300,000 Borrowed & Repaid Using Method 3

MARR = 10% interest rate = 12%income tax rate = 40%

EOY BT&LCF PPMT IPMT DWO TI Tax ATCF0 -$500,000.00 -$300,000.00 -$200,000.001 $124,166.67 $17,095.25 $36,000.00 $100,000.00 -$11,833.33 -$4,733.33 $75,804.752 $124,166.67 $19,146.68 $33,948.57 $160,000.00 -$69,781.90 -$27,912.76 $98,984.183 $124,166.67 $21,444.28 $31,650.97 $96,000.00 -$3,484.30 -$1,393.72 $72,465.144 $124,166.67 $24,017.59 $29,077.65 $57,600.00 $37,489.02 $14,995.61 $56,075.815 $124,166.67 $26,899.71 $26,195.54 $57,600.00 $40,371.13 $16,148.45 $54,922.976 $124,166.67 $30,127.67 $22,967.58 $28,800.00 $72,399.09 $28,959.64 $42,111.787 $124,166.67 $33,742.99 $19,352.26 $0.00 $104,814.41 $41,925.76 $29,145.668 $124,166.67 $37,792.15 $15,303.10 $0.00 $108,863.57 $43,545.43 $27,525.999 $124,166.67 $42,327.21 $10,768.04 $0.00 $113,398.63 $45,359.45 $25,711.97

10 $174,166.67 $47,406.47 $5,688.78 $0.00 $168,477.89 $67,391.16 $53,680.26

PW AT = $160,734.89

FW AT = $416,904.92

AW AT = $26,158.86

IRR AT = 31.65%

ERR AT = 16.68%


2 roots: -3.65% and 53.49%



ATPW maximized @ 9.328% MARR


Method 1 is preferred

(Given the results, it is anticipated that ATPW will increase with increased

borrowing. Let’s see what happens if we borrow 100% of the capital needed to acquire the SMP machine and repay

using Method 1.)





SMP Investment

Measure 0% Debt* 60% Debt* 100% Debt*of Worth Capitalizing Capitalizing Capitalizing

PWAT $123,988.64 $175,603.01 $210,012.58

FWAT $321,594.61 $455,468.98 $544,718.55

AWAT $20,178.58 $28,578.58 $34,178.58

* Financed at 12% annual compound interest rate, repaying loan over a 10-year period using repayment method 1 (interest only loan)


How much can the interest rate increase and it still be profitable to borrow money? We will find that it depends on the repayment method used. With a MARR of 10%, as long as the interest rate paid on borrowed capital is less than 10%/(1 - 0.40), or 16.667%, there is a repayment method for which it is economical to borrow investment capital.

Let’s see what the effect is of borrowing $500,000 at an interest rate of 16.667%, using all four repayment methods.


ATPW for a $500,000 Loan with an Interest Rate Equal to MARR/(1 – itr).MARR = 10% interest rate = 16.667%

income tax rate = 40%EOY BT&LCF PPMT IPMT DWO TI Tax ATCF

0 -$500,000.00 -$500,000.00 $0.001 $124,166.67 $0.00 $83,333.33 $100,000.00 -$59,166.66 -$23,666.67 $64,500.002 $124,166.67 $0.00 $83,333.33 $160,000.00 -$119,166.66 -$47,666.67 $88,500.003 $124,166.67 $0.00 $83,333.33 $96,000.00 -$55,166.66 -$22,066.67 $62,900.004 $124,166.67 $0.00 $83,333.33 $57,600.00 -$16,766.66 -$6,706.67 $47,540.005 $124,166.67 $0.00 $83,333.33 $57,600.00 -$16,766.66 -$6,706.67 $47,540.006 $124,166.67 $0.00 $83,333.33 $28,800.00 $12,033.34 $4,813.33 $36,020.007 $124,166.67 $0.00 $83,333.33 $0.00 $40,833.34 $16,333.33 $24,500.008 $124,166.67 $0.00 $83,333.33 $0.00 $40,833.34 $16,333.33 $24,500.009 $124,166.67 $0.00 $83,333.33 $0.00 $40,833.34 $16,333.33 $24,500.0010 $174,166.67 $500,000.00 $83,333.33 $0.00 $90,833.34 $36,333.33 -$445,500.00

PW = $123,988.640 -$500,000.00 -$500,000.00 $0.001 $124,166.67 $50,000.00 $83,333.33 $100,000.00 -$59,166.66 -$23,666.67 $14,500.002 $124,166.67 $50,000.00 $75,000.00 $160,000.00 -$110,833.33 -$44,333.33 $43,500.003 $124,166.67 $50,000.00 $66,666.67 $96,000.00 -$38,500.00 -$15,400.00 $22,900.004 $124,166.67 $50,000.00 $58,333.33 $57,600.00 $8,233.34 $3,293.33 $12,540.005 $124,166.67 $50,000.00 $50,000.00 $57,600.00 $16,566.67 $6,626.67 $17,540.006 $124,166.67 $50,000.00 $41,666.67 $28,800.00 $53,700.00 $21,480.00 $11,020.007 $124,166.67 $50,000.00 $33,333.33 $0.00 $90,833.34 $36,333.33 $4,500.008 $124,166.67 $50,000.00 $25,000.00 $0.00 $99,166.67 $39,666.67 $9,500.009 $124,166.67 $50,000.00 $16,666.67 $0.00 $107,500.00 $43,000.00 $14,500.0010 $174,166.67 $50,000.00 $8,333.33 $0.00 $165,833.34 $66,333.33 $49,500.00

PW = $123,988.640 -$500,000.00 -$500,000.00 $0.001 $124,166.67 $22,696.59 $83,333.33 $100,000.00 -$59,166.66 -$23,666.67 $41,803.422 $124,166.67 $26,479.35 $79,550.57 $160,000.00 -$115,383.90 -$46,153.56 $64,290.313 $124,166.67 $30,892.58 $75,137.34 $96,000.00 -$46,970.67 -$18,788.27 $36,925.024 $124,166.67 $36,041.34 $69,988.58 $57,600.00 -$3,421.91 -$1,368.76 $19,505.525 $124,166.67 $42,048.23 $63,981.69 $57,600.00 $2,584.98 $1,033.99 $17,102.766 $124,166.67 $49,056.27 $56,973.65 $28,800.00 $38,393.02 $15,357.21 $2,779.547 $124,166.67 $57,232.31 $48,797.61 $0.00 $75,369.06 $30,147.62 -$12,010.878 $124,166.67 $66,771.03 $39,258.89 $0.00 $84,907.78 $33,963.11 -$15,826.369 $124,166.67 $77,899.53 $28,130.39 $0.00 $96,036.28 $38,414.51 -$20,277.7610 $174,166.67 $90,882.79 $15,147.13 $0.00 $159,019.54 $63,607.82 $4,528.94

PW = $123,988.640 -$500,000.00 -$500,000.00 $0.001 $124,166.67 $0.00 $0.00 $100,000.00 $24,166.67 $9,666.67 $114,500.002 $124,166.67 $0.00 $0.00 $160,000.00 -$35,833.33 -$14,333.33 $138,500.003 $124,166.67 $0.00 $0.00 $96,000.00 $28,166.67 $11,266.67 $112,900.004 $124,166.67 $0.00 $0.00 $57,600.00 $66,566.67 $26,626.67 $97,540.005 $124,166.67 $0.00 $0.00 $57,600.00 $66,566.67 $26,626.67 $97,540.006 $124,166.67 $0.00 $0.00 $28,800.00 $95,366.67 $38,146.67 $86,020.007 $124,166.67 $0.00 $0.00 $0.00 $124,166.67 $49,666.67 $74,500.008 $124,166.67 $0.00 $0.00 $0.00 $124,166.67 $49,666.67 $74,500.009 $124,166.67 $0.00 $0.00 $0.00 $124,166.67 $49,666.67 $74,500.0010 $174,166.67 $500,000.00 $1,835,812.08 $0.00 -$1,661,645.41 -$664,658.17 -$1,496,987.25

PW = $6,545.98


Notice, the after-tax present worth equals $123,988.64 for Methods 1, 2, and 3, but $6,545.98 for Method 4. In fact, the ATPW for Methods 1, 2, and 3 is identical to that obtained when no money is borrowed (see Example 10.4). Hence, for interest rates less than MARR/(1 - itr), it pays to borrow money, as long as Method 1, 2, or 3 is used.


Example 10.12

A small business borrows $100,000 at 15% compounded annually and repays the loan over a 5-yr period. Its income tax rate is 40%. If the business has a 10% ATMARR, using an ATPW analysis, which repayment method is preferred? How does the preference change for various interest rates?


After-Tax Analysis of Four Methods of Repaying a $100,000 LoanEOY PPMT IPMT TI T ATCF

0 -$100,000.00 $100,000.001 $0.00 $15,000.00 -$15,000.00 -$6,000.00 -$9,000.002 $0.00 $15,000.00 -$15,000.00 -$6,000.00 -$9,000.003 $0.00 $15,000.00 -$15,000.00 -$6,000.00 -$9,000.004 $0.00 $15,000.00 -$15,000.00 -$6,000.00 -$9,000.005 $100,000.00 $15,000.00 -$15,000.00 -$6,000.00 -$109,000.00

ATPW = $3,790.79

0 -$100,000.00 $100,000.001 $20,000.00 $15,000.00 -$15,000.00 -$6,000.00 -$29,000.002 $20,000.00 $12,000.00 -$12,000.00 -$4,800.00 -$27,200.003 $20,000.00 $9,000.00 -$9,000.00 -$3,600.00 -$25,400.004 $20,000.00 $6,000.00 -$6,000.00 -$2,400.00 -$23,600.005 $20,000.00 $3,000.00 -$3,000.00 -$1,200.00 -$21,800.00

ATPW = $2,418.43

0 $100,000.00 $100,000.001 $14,831.56 $15,000.00 -$15,000.00 -$6,000.00 -$23,831.562 $17,056.29 $12,775.27 -$12,775.27 -$5,110.11 -$24,721.453 $19,614.73 $10,216.82 -$10,216.82 -$4,086.73 -$25,744.834 $22,556.94 $7,274.61 -$7,274.61 -$2,909.85 -$26,921.715 $25,940.48 $3,891.07 -$3,891.07 -$1,556.43 -$28,275.13

ATPW = $2,617.01

0 $100,000.00 $100,000.001 $0.00 $0.00 $0.00 $0.00 $0.002 $0.00 $0.00 $0.00 $0.00 $0.003 $0.00 $0.00 $0.00 $0.00 $0.004 $0.00 $0.00 $0.00 $0.00 $0.005 $100,000.00 $101,135.72 -$101,135.72 -$40,454.29 -$160,681.43

ATPW = $229.47


-$20,000

-$10,000

$0

$10,000

$20,000

$30,000

$40,000

0% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 16% 17% 18% 19% 20%

Interest Rate on Borrowed Capital

Method 1 Method 2 Method 3 Method 4

ATMARR /(1 - itr ) = 16.667%

ATMARR= 10%

Method 4 is best Method 1 is best Method 2 is best if borrowing is

required

ATPW for the $100,000 Loan for Each of Four Repayment Methods


Example 10.13

Recall Example 3.8, which involved choosing a mortgage for a house purchase. Three alternative mortgages were considered: 30-yr conventional; 30-yr ARM; and a 30-yr balloon (interest only) loan. The ARM was eliminated due to risk considerations.

If the professional couple is in a 33% income tax bracket and their ATMARR is 6.5% per annum compounded monthly, which mortgage is preferred?

ATPWballoon =PV(0.065/12,60,0.67*1848.48)

+PV(0.065/12,60,,350000*1.01753+7500)

= -$326,264.30


ATPW for the 30-Year Conventional LoanMonth BTLCF IPMT TI T ATLCF Month BTLCF IPMT TI T ATLCF

1 -$2,338.87 $2,039.04 -$2,039.04 -$672.88 -$1,665.98 31 -$2,338.87 $1,984.42 -$1,984.42 -$654.86 -$1,684.012 -$2,338.87 $2,037.37 -$2,037.37 -$672.33 -$1,666.54 32 -$2,338.87 $1,982.43 -$1,982.43 -$654.20 -$1,684.673 -$2,338.87 $2,035.69 -$2,035.69 -$671.78 -$1,667.09 33 -$2,338.87 $1,980.42 -$1,980.42 -$653.54 -$1,685.334 -$2,338.87 $2,034.00 -$2,034.00 -$671.22 -$1,667.65 34 -$2,338.87 $1,978.41 -$1,978.41 -$652.88 -$1,685.995 -$2,338.87 $2,032.29 -$2,032.29 -$670.66 -$1,668.21 35 -$2,338.87 $1,976.39 -$1,976.39 -$652.21 -$1,686.666 -$2,338.87 $2,030.58 -$2,030.58 -$670.09 -$1,668.77 36 -$2,338.87 $1,974.35 -$1,974.35 -$651.54 -$1,687.337 -$2,338.87 $2,028.86 -$2,028.86 -$669.52 -$1,669.34 37 -$2,338.87 $1,972.30 -$1,972.30 -$650.86 -$1,688.018 -$2,338.87 $2,027.13 -$2,027.13 -$668.95 -$1,669.91 38 -$2,338.87 $1,970.24 -$1,970.24 -$650.18 -$1,688.699 -$2,338.87 $2,025.39 -$2,025.39 -$668.38 -$1,670.49 39 -$2,338.87 $1,968.17 -$1,968.17 -$649.50 -$1,689.37

10 -$2,338.87 $2,023.64 -$2,023.64 -$667.80 -$1,671.07 40 -$2,338.87 $1,966.08 -$1,966.08 -$648.81 -$1,690.0611 -$2,338.87 $2,021.88 -$2,021.88 -$667.22 -$1,671.65 41 -$2,338.87 $1,963.99 -$1,963.99 -$648.12 -$1,690.7512 -$2,338.87 $2,020.11 -$2,020.11 -$666.64 -$1,672.23 42 -$2,338.87 $1,961.88 -$1,961.88 -$647.42 -$1,691.4513 -$2,338.87 $2,018.33 -$2,018.33 -$666.05 -$1,672.82 43 -$2,338.87 $1,959.75 -$1,959.75 -$646.72 -$1,692.1514 -$2,338.87 $2,016.53 -$2,016.53 -$665.46 -$1,673.41 44 -$2,338.87 $1,957.62 -$1,957.62 -$646.01 -$1,692.8515 -$2,338.87 $2,014.73 -$2,014.73 -$664.86 -$1,674.01 45 -$2,338.87 $1,955.47 -$1,955.47 -$645.31 -$1,693.5616 -$2,338.87 $2,012.92 -$2,012.92 -$664.26 -$1,674.60 46 -$2,338.87 $1,953.32 -$1,953.32 -$644.59 -$1,694.2717 -$2,338.87 $2,011.09 -$2,011.09 -$663.66 -$1,675.21 47 -$2,338.87 $1,951.14 -$1,951.14 -$643.88 -$1,694.9918 -$2,338.87 $2,009.26 -$2,009.26 -$663.06 -$1,675.81 48 -$2,338.87 $1,948.96 -$1,948.96 -$643.16 -$1,695.7119 -$2,338.87 $2,007.41 -$2,007.41 -$662.45 -$1,676.42 49 -$2,338.87 $1,946.76 -$1,946.76 -$642.43 -$1,696.4420 -$2,338.87 $2,005.56 -$2,005.56 -$661.83 -$1,677.03 50 -$2,338.87 $1,944.55 -$1,944.55 -$641.70 -$1,697.1721 -$2,338.87 $2,003.69 -$2,003.69 -$661.22 -$1,677.65 51 -$2,338.87 $1,942.33 -$1,942.33 -$640.97 -$1,697.9022 -$2,338.87 $2,001.81 -$2,001.81 -$660.60 -$1,678.27 52 -$2,338.87 $1,940.10 -$1,940.10 -$640.23 -$1,698.6423 -$2,338.87 $1,999.93 -$1,999.93 -$659.98 -$1,678.89 53 -$2,338.87 $1,937.85 -$1,937.85 -$639.49 -$1,699.3824 -$2,338.87 $1,998.03 -$1,998.03 -$659.35 -$1,679.52 54 -$2,338.87 $1,935.59 -$1,935.59 -$638.74 -$1,700.1225 -$2,338.87 $1,996.12 -$1,996.12 -$658.72 -$1,680.15 55 -$2,338.87 $1,933.31 -$1,933.31 -$637.99 -$1,700.8826 -$2,338.87 $1,994.19 -$1,994.19 -$658.08 -$1,680.78 56 -$2,338.87 $1,931.02 -$1,931.02 -$637.24 -$1,701.6327 -$2,338.87 $1,992.26 -$1,992.26 -$657.45 -$1,681.42 57 -$2,338.87 $1,928.72 -$1,928.72 -$636.48 -$1,702.3928 -$2,338.87 $1,990.32 -$1,990.32 -$656.80 -$1,682.06 58 -$2,338.87 $1,926.41 -$1,926.41 -$635.71 -$1,703.1529 -$2,338.87 $1,988.36 -$1,988.36 -$656.16 -$1,682.71 59 -$2,338.87 $1,924.08 -$1,924.08 -$634.95 -$1,703.9230 -$2,338.87 $1,986.39 -$1,986.39 -$655.51 -$1,683.36 60 -$333,258.00 $1,921.74 -$1,921.74 -$634.17 -$332,623.83

BTPW = -$314,972.87 ATPW = -$325,333.87

30-yr conventional loan is preferred; decision is reversed!


How Much Money Should You Borrow?• The simple answer is “no more than you can

repay.”• Considering the four repayment methods,

except for Method 4, ATPW increases as the percent of the investment capital borrowed increases so long as the interest rate paid is less than the ATMARR divided by one minus the income tax rate.

• Method 4 achieves a negative ATPW for interest rates less than ATMARR/(1-itr), as the following example illustrates.


ExampleA company invests $100,000 and receives $268,418.33 after 5 years. The ATMARR for the business is 10%. The firm pays income taxes at a marginal rate of 40%. If investment capital is borrowed, an annual compound interest rate of 12% must be paid.

Determine which repayment method is best if

a) $20,000 is borrowed?

b) $40,000 is borrowed?

c) $60,000 is borrowed?

d) $80,000 is borrowed?

e) $100,000 is borrowed?


ATMARR = 10% interest rate = 12%income tax rate = 40% % borrowed = 40%

Method EOY BT&LCF PPMT IPMT TI Tax ATCF1 0 -$100,000.00 -$40,000.00 -$60,000.00

1 $0.00 $0.00 $4,800.00 -$4,800.00 -$1,920.00 -$2,880.002 $0.00 $0.00 $4,800.00 -$4,800.00 -$1,920.00 -$2,880.003 $0.00 $0.00 $4,800.00 -$4,800.00 -$1,920.00 -$2,880.004 $0.00 $0.00 $4,800.00 -$4,800.00 -$1,920.00 -$2,880.005 $268,418.33 $40,000.00 $4,800.00 $263,618.33 $105,447.33 $118,171.00

PW = $4,245.68Method EOY PPMT IPMT TI Tax ATCF

2 0 -$100,000.00 -$40,000.00 -$60,000.001 $0.00 $8,000.00 $4,800.00 -$4,800.00 -$1,920.00 -$10,880.002 $0.00 $8,000.00 $3,840.00 -$3,840.00 -$1,536.00 -$10,304.003 $0.00 $8,000.00 $2,880.00 -$2,880.00 -$1,152.00 -$9,728.004 $0.00 $8,000.00 $1,920.00 -$1,920.00 -$768.00 -$9,152.005 $268,418.33 $8,000.00 $960.00 $267,458.33 $106,983.33 $152,475.00


3 0 -$100,000.00 -$40,000.00 -$60,000.001 $0.00 $6,296.39 $4,800.00 -$4,800.00 -$1,920.00 -$9,176.392 $0.00 $7,051.96 $4,044.43 -$4,044.43 -$1,617.77 -$9,478.623 $0.00 $7,898.19 $3,198.20 -$3,198.20 -$1,279.28 -$9,817.114 $0.00 $8,845.97 $2,250.42 -$2,250.42 -$900.17 -$10,196.225 $268,418.33 $9,907.49 $1,188.90 $267,229.43 $106,891.77 $150,430.17


4 0 -$100,000.00 -$40,000.00 -$60,000.001 $0.00 $0.00 $0.00 $0.00 $0.00 $0.002 $0.00 $0.00 $0.00 $0.00 $0.00 $0.003 $0.00 $0.00 $0.00 $0.00 $0.00 $0.004 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00

10 $268,418.33 $40,000.00 $30,493.67 $237,924.67 $95,169.87 $102,754.80PW = $3,802.65


Sensitivity of ATPW to % Capital Borrowed, Interest Rate Paid & Payment Method


Sensitivity of ATPW to % Capital Borrowed, Interest Rate Paid & Payment Method

M4 ATPW = $0 with 15.07% interest rate


Sensitivity of ATPW to % Capital Borrowed, Interest Rate & Payment Method



M4 ATPW = $0 with 15.07% interest rate




In 1958, two Nobel-prize winning economists, Franco Modigliani and Merton Miller, published an investment theory that a firm should focus on maximizing corporate wealth and not worry about debt-to-equity ratios. Their theorem stated that, under certain conditions, the value of a firm is unaffected by how the firm is financed. The theorem’s basic premise is that corporate wealth is maximized by minimizing income taxes paid.


Main Message #3It is profitable to borrow

investment capital as long as the interest rate is less than the ATMARR divided by one minus the income

tax rate.


Additional Tax Considerations

Investment Tax Credit


Investment Tax CreditInvestment Tax Credit Comes and goes; began in 1962 Repealed in 1985 when max tax rate

was decreased from 46% to 34% If ITC returns, will probably vary

somewhat from our example Last version: 10% tax credit in Yr 1;

reduce cost basis 5%


Example 10.14

For the SMP machine, suppose a 10% investment tax credit is available. The cost basis is reduced by 5%; hence, the cost basis is $475,000. What are the measures of economic worth, given the 10% investment tax credit and using a 10% ATMARR?


Applying the Investment Tax Credit to the SMP Investment

EOY BTCF DWO TI T ITC ATCF0 -$500,000.00 -$500,000.001 $124,166.67 $95,000.00 $29,166.67 $11,666.67 $50,000.00 $162,500.002 $124,166.67 $152,000.00 -$27,833.33 -$11,133.33 $0.00 $135,300.003 $124,166.67 $91,200.00 $32,966.67 $13,186.67 $0.00 $110,980.004 $124,166.67 $54,720.00 $69,446.67 $27,778.67 $0.00 $96,388.005 $124,166.67 $54,720.00 $69,446.67 $27,778.67 $0.00 $96,388.006 $124,166.67 $27,360.00 $96,806.67 $38,722.67 $0.00 $85,444.007 $124,166.67 $0.00 $124,166.67 $49,666.67 $0.00 $74,500.008 $124,166.67 $0.00 $124,166.67 $49,666.67 $0.00 $74,500.009 $124,166.67 $0.00 $124,166.67 $49,666.67 $0.00 $74,500.00

10 $174,166.67 $0.00 $174,166.67 $69,666.67 $0.00 $104,500.00PW = $161,710.59FW = $419,435.61AW = $26,317.65IRR = 18.39%

ERR = 13.13%

=0.95*500000*0.32


Additional Tax Considerations

Section 179 Expense Deduction


Section 179 Expense DeductionSection 179 Expense Deduction

Designed for small businesses, Section 179 expense deduction allows taxpayers to elect, in the year certain tangible property is placed in service, to treat the cost as an expense rather than a capital expenditure. Up to $250,000 can be deducted; the balance becomes the cost basis for depreciation. (The amount deducted is reduced by the amount the aggregate cost of qualifying property exceeds $800,000.)


Section 179 Expense Deduction

Let $K = aggregate cost of qualifying property

D179 = Section 179 expense deduction

If $K < $250,000, then D179 = $K

If $250,000 < $K < $800,000, then D179 = $250,000

If $800,000 < $K < $1,050,000, then D179 = $1,050,000 - $K

Example

If $K = a) $200,000, b) $500,000, c) $850,000, d) $1,200,000, then D179 = a) $200,000, b) $250,000, c) $200,000, d) $0


Example 10.15

Assume two $500,000 SMP machines are the only assets purchased and placed in service during the tax year. Since the $1,000,000 investment exceeds the $800,000 cap, the cost basis is reduced by $1,050,000 - $1,000,000, or $50,000. What are the measures of economic worth, given the Section 179 expense deduction?


Applying the Section 179 Expense Deduction to the SMP Investment

BTCFSection 179 Deduction DWO TI T ATCF

-$1,000,000.00 -$1,000,000.00$248,333.34 $50,000.00 $190,000.00 $8,333.34 $3,333.34 $245,000.00$248,333.34 $0.00 $304,000.00 -$55,666.66 -$22,266.66 $270,600.00$248,333.34 $0.00 $182,400.00 $65,933.34 $26,373.34 $221,960.00$248,333.34 $0.00 $109,440.00 $138,893.34 $55,557.34 $192,776.00$248,333.34 $0.00 $109,440.00 $138,893.34 $55,557.34 $192,776.00$248,333.34 $0.00 $54,720.00 $193,613.34 $77,445.34 $170,888.00$248,333.34 $0.00 $0.00 $248,333.34 $99,333.34 $149,000.00$248,333.34 $0.00 $0.00 $248,333.34 $99,333.34 $149,000.00$248,333.34 $0.00 $0.00 $248,333.34 $99,333.34 $149,000.00$298,333.34 $0.00 $0.00 $298,333.34 $119,333.34 $179,000.00

PW = $239,127.60FW = $620,235.41AW = $38,916.92IRR = 16.02%

ERR = 12.38%

=(1000000-50000)*0.32


Reminder!Reminder!When using MACRS-GDS for property

years that include a half-year* depreciation the first year and a half-

year depreciation the last year, we assume a half-year depreciation charge occurs regardless of when, during the year, the acquisition or disposal of the

asset occurs

* The same principle applies when using property classes with a mid-month convention


Timing of the1st Year DWO• In general, the engineering economy

literature assumes the investment occurs at the end of year zero and the first depreciation charge is taken during the first year, or at the end of year one.

• In practice, companies typically take the first year’s depreciation charge in the year in which the investment is made.

• The following example illustrates the impact of delaying the depreciation charge one year


Example 10.16

Recall the two design alternatives for The Scream Machine considered previously. Now, we perform an after-tax analysis, based on: design A having an initial investment of $300,000 and producing before-tax net annual revenue of $71,666.67; and design B having an initial investment of $450,000 and producing before-tax net annual revenue of $103,333.33. Based on a 40% income tax rate, a 10% ATMARR, and 7-yr MACRS depreciation, perform an after-tax comparison of the two alternatives when the first year DWO occurs at the end of zero.


Recall, with 1st DWO @ EOY = 1, ATPW(A) = $37,951.10 and ATPW(B) = $41,565.37, a $3614.18 incremental difference. Here, with 1st DWO @ EOY = 0, ATPW(A) = $59,447.76 and ATPW(B) = $73,810.19, a $14,362.43 incremental difference.

EOY BTCF(A) DWO(A) TI(A) T(A) ATCF(A)0 -$300,000.00 $42,870.00 -$42,870.00 -$17,148.00 -$282,852.001 $71,666.67 $73,470.00 -$1,803.33 -$721.33 $72,388.002 $71,666.67 $52,470.00 $19,196.67 $7,678.67 $63,988.003 $71,666.67 $37,470.00 $34,196.67 $13,678.67 $57,988.004 $71,666.67 $26,790.00 $44,876.67 $17,950.67 $53,716.005 $71,666.67 $26,760.00 $44,906.67 $17,962.67 $53,704.006 $71,666.67 $26,790.00 $44,876.67 $17,950.67 $53,716.007 $71,666.67 $13,380.00 $58,286.67 $23,314.67 $48,352.008 $71,666.67 $0.00 $71,666.67 $28,666.67 $43,000.009 $71,666.67 $0.00 $71,666.67 $28,666.67 $43,000.0010 $71,666.67 $0.00 $71,666.67 $28,666.67 $43,000.00

PW(A) = $59,447.76EOY BTCF(B) DWO(B) TI(B) T(B) ATCF(B)

0 -$450,000.00 $64,305.00 -$64,305.00 -$25,722.00 -$424,278.001 $103,333.33 $110,205.00 -$6,871.67 -$2,748.67 $106,082.002 $103,333.33 $78,705.00 $24,628.33 $9,851.33 $93,482.003 $103,333.33 $56,205.00 $47,128.33 $18,851.33 $84,482.004 $103,333.33 $40,185.00 $63,148.33 $25,259.33 $78,074.005 $103,333.33 $40,140.00 $63,193.33 $25,277.33 $78,056.006 $103,333.33 $40,185.00 $63,148.33 $25,259.33 $78,074.007 $103,333.33 $20,070.00 $83,263.33 $33,305.33 $70,028.008 $103,333.33 $0.00 $103,333.33 $41,333.33 $62,000.009 $103,333.33 $0.00 $103,333.33 $41,333.33 $62,000.0010 $103,333.33 $0.00 $103,333.33 $41,333.33 $62,000.00

PW(B) = $73,810.19


What We Learned in Chapter 101. Income tax rates and regulations change rapidly2. The definitions of effective income tax rate, incremental income tax rate, and marginal income tax rate3. Marginal income tax rates should be used in performing engineering economic analyses4. Consult an expert in income taxes if income taxes will play a major role in determining the economic

viability of an investment5. Straight-line depreciation is the most commonly used depreciation method in financial reporting6. The modified accelerated cost recovery system (MACRS) is the depreciation method allowed by the

U.S. Internal Revenue Service in performing income tax calculations7. If an investment can be expensed, the after-tax cost equals the product of the investment and one

minus the income tax rate8. If borrowed capital is used to fund an investment, each dollar of interest paid costs 60 cents after-taxes

if the income tax rate is 40%9. Every dollar of depreciation increases ATCF by the product of the income tax rate and the depreciation

allowance (see Equation 10.4.)10. When borrowing investment capital at interest rates less than the minimum attractive rate of return,

delay repaying principal and interest as long as possible, i.e., use Method 411. When borrowing investment capital at an interest rate greater than the minimum attractive rate of return,

but less than the minimum attractive rate of return divided by one minus the income tax rate, delay paying principal as long as possible, i.e., use Method 1

12. When the interest rate is greater than the minimum attractive rate of return divided by one minus the income tax rate, avoid borrowing investment capital; if borrowed capital is required, then repay as much of the principal as possible as quickly as possible, i.e., Method 2

13. Income tax considerations can change the recommendation regarding the investment to be made14. Research has shown that a firm’s cost of capital is not significantly influenced by its debt-to-equity ratio

and 15. Nobel Prizes in economics were awarded to two researchers who developed a theorem to the effect that

corporate wealth is maximized by minimizing income taxes paid


Pit Stop #10—It’s Been A Taxing Experience1. True or False: If an investment cannot be justified economically using a

before-tax analysis, it cannot be justified using an after-tax analysis. 2. True or False: After-tax present worth will be greater when using MACRS

than it will be when using SLN. 3. True or False: The faster an asset is depreciated, the greater will be its after-

tax present worth. 4. True or False: If money can be borrowed for 20% compounded annually and

the marginal income tax rate is 40%, then it will be profitable to borrow the investment capital if your after-tax MARR is greater than 12%.

5. True or False: If the same amount of money is invested in something that can be expensed as in something that must be depreciated (and both provide the same annual returns) then, to maximize after-tax present worth, you should choose the investment that can be depreciated.

6. True or False: If investment capital is borrowed, the income tax rate equals 40%, the after-tax MARR is 12%, and the loan rate is 15%, then it is best to repay the loan using Method 1.



9. True or False: The investment tax credit is not in force, currently. 10. True or False: Section 179 Expense Reduction is not in force, currently.


Pit Stop #10—It’s Been A Taxing Experience1. True or False: If an investment cannot be justified economically using a

before-tax analysis, it cannot be justified using an after-tax analysis. False2. True or False: After-tax present worth will be greater when using MACRS

than it will be when using SLN. True3. True or False: The faster an asset is depreciated, the greater will be its after-

tax present worth. True4. True or False: If money can be borrowed for 20% compounded annually and

the marginal income tax rate is 40%, then it will be profitable to borrow the investment capital if your after-tax MARR is greater than 12%. True

5. True or False: If the same amount of money is invested in something that can be expensed as in something that must be depreciated (and both provide the same annual returns) then, to maximize after-tax present worth, you should choose the investment that can be depreciated. False

6. True or False: If investment capital is borrowed, the income tax rate equals 40%, the after-tax MARR is 12%, and the loan rate is 15%, then it is best to repay the loan using Method 1. True



9. True or False: The investment tax credit is not in force, currently. True10. True or False: Section 179 Expense Reduction is not in force, currently.

False

0. Analisa Ekonomi After-Tax

Documents

pit stop 10its

aftertax present

engineering

minimum attractive

tax cash flow

tax net revenue

yr planning

tax present