ENGINEERING ECONOMIC ENHANCED EBOOK
ENGINEERING ECONOMIC ENHANCED EBOOK
14th Edition
ISBN: 9780190931940
Author: NEWNAN
Publisher: OXF
Question
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Chapter 12, Problem 39P
To determine

The present worth of the first 4 year of after tax cash flow from the barge.

Expert Solution & Answer
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Answer to Problem 39P

The present worth of the first 4 year of after tax cash flow from the barge is $5815022.

Explanation of Solution

Given:

Cost of the barge is $13.2million.

Expected income from the barge is $7.5million for the first year.

Growth in income is $1million per year.

Expenses for the first year is $2.6million.

Growth in expenses is $400,000 per year.

The tax rate is 38%.

MARR is 12%.

Concept used:

Write the equation for the base book value.

(Basebookvalue)nthyear=[(Bookvalue) ( n1 ) thyear(( MACRSrate)× ( Bookvalue ) ( n1 ) th year)]

Write the formula to calculate the taxable income.

TI=BTCFDI

Here, the taxable income is TI, the depreciation is DI and the before tax cash flow is BTCF.

Write the formula to calculate the taxable amount.

TAX=0.38×TI

Here, the taxable amount is TAX.

Write the formula to calculate the after tax cash flow.

ATCF=TAX+BTCF

Here, the after tax cash flow is ATCF.

Calculation:

The projected revenue for the first year is $7,500,000.

The revenue of the project is growing $1,000,000 for each year.

Calculate the project revenue for second year.

Revenue2nd=Revenue1st+$1000000=$7500000+$1000000=$8500000

Calculate the project revenue for third year.

Revenue3rd=Revenue2nd+$1000000=$8500000+$1000000=$9500000

Calculate the project revenue for fourth year.

Revenue4th=Revenue3rd+$1000000=$9500000+$1000000=$10500000

The operating and maintenance cost for first year is $2,600,000.

The expenses of operating and maintenance cost is increasing by $400,000 for each year.

Calculate the operating and maintenance cost for second year.

(Operating and Maintenance cost)2nd=[( Operating and Maintenance cost) 1 st +$400000]=$2600000+$400000=$3000000

Calculate the operating and maintenance cost for third year.

(Operating and Maintenance cost)3rd=[( Operating and Maintenance cost) 2 nd +$400000]=$3000000+$400000=$3400000

Calculate the operating and maintenance cost for fourth year.

(Operating and Maintenance cost)4th=[( Operating and Maintenance cost) 3 rd +$400000]=$3400000+$400000=$3800000

Calculate the net revenue as shown in table below.

Year Projected revenue (a) Operating and maintenance cost (b) Net revenue (ab)
1 $7500000 $2600000 $4900000
2 $8500000 $3000000 $5500000
3 $9500000 $3400000 $6100000
4 $10500000 $3800000 $6700000

Calculate the book value by using MACRS percentage rate as shown in table below.

Year MACR rate (a) Base book value (b) Depreciation charge (a×b) Net book value b(a×b)
1 10% $13200000 $1320000 $11880000
2 18% $11880000 $2138400 $9741600
3 14.40% $9741600 $1402790.4 $8338809.6
4 11.52 $8338809.6 $960630.9 $7378178.7

Calculate the gain on the salvage value as shown below.

Gain=(ExpectedsalvagevalueNetbookvalueafter3year)

Substitute $0 for expected salvage value and $7378178.7 for net book value.

Gain=($0$7378178.7)=$7378178.7

Calculate the tax effect as shown below.

Taxeffect=Gain×Taxrate

Substitute $7378178.7 for Gain and 38% for Tax rate.

Taxeffect=$7378178.7×0.38=$2803707.9

Calculate the net salvage value after fourth year as shown below.

Netsalvagevalue=ExpectedsalvagevalueTaxeffect

Substitute $0 for expected salvage value and $2803707.9 for tax effect.

Netsalvagevalue=$0($2803707.9)=$2803707.9

Take before tax cash flow for the first year is $4900000.

Calculate the taxable income for the first year.

Taxableincome=Beforetaxcashflowdepreciation

Substitute $4900000 for before tax cash flow and $1320000 for depreciation.

Taxableincome=$4900000$1320000=$3580000

Calculate income tax for first year as shown below.

Incometax=38%oftaxableincome

Substitute $3580000 for taxable income.

Incometax=0.38×$3580000=$1360400

Calculate the after tax cash flow for the first year as shown below.

Aftertaxcashflow=Beforetaxcashflow+Incometax

Substitute $4900000 for before tax cash flow and $1360400 for income tax.

Aftertaxcashflow=$4900000+$1360400=$6260400

Calculate the after tax cash flow as shown in table below for all the subsequent years.

Year BTCF Depreciation Taxable income Income tax ATCF
0 $13200000 $13200000
1 $4900000 $1320000 $3580000 $1360400 $6260400
2 $5500000 $2138400 $3361600 $1277408 $6777408
3 $6100000 $1402790.4 $4697210 $1784939.65 $7884939.65
4 $6700000 $960630.9 $5739369 $2180960.26 $8880960.26

Write the equation for present worth factor of annuity (PW).

PW=D+A(PA,i,n)+F(PF,i,n)=D+A( ( 1+i ) n1i ( 1+i ) n)+F(1 ( 1+i ) n)

Here, the present worth is PW, initial payment is D, present value of money is P, interest rate is i, the after tax cash flow is A, the net salvage amount is F, and the number of year is n.

Substitute $13200000 for D, $6260400 for A, 12% for i, 4years for n and $0 for F.

PW=($13200000+$6260400( ( 1+0.12 ) 4 1 0.12 ( 1+0.12 ) 4 )+$0( 1 ( 1+0.12 ) 4 ))=($13200000+$6260400(3.037))=($13200000+$19015022)=$5815022.

Conclusion:

Therefore, the present worth of the first 4 year of after tax cash flow is, $5815022.

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