Engineering Economic Analysis
Engineering Economic Analysis
13th Edition
ISBN: 9780190296902
Author: Donald G. Newnan, Ted G. Eschenbach, Jerome P. Lavelle
Publisher: Oxford University Press
Question
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Chapter 13, Problem 53P
To determine

The after-tax annual costs and compare and decide whether Machine A should be retained or replaced by Machine B.

Expert Solution & Answer
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Answer to Problem 53P

The machineAshould be retained.

Explanation of Solution

Given for Machine A :

Cost of machine A is $54000.

The overhauled cost of Machine A is $9000.

Life of Machine A is 12 years.

Tax expense is $9000.

Selling price of Machine is $30000.

Salvage value after 12years is zero.

Cost of machine B is $42000.

Life of Machine B is 12 years.`

Combined tax rate is 40%.

Concept used:

Write the formula to calculate the taxable income.

TI=DIBTCF ...... (I)

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=TI×(0.40) ...... (II)

Here, the taxable amount is TAX.

Write the formula to calculate the after tax cash flow.

ATCF=TAXBTCF ...... (III)

Here, the after tax cash flow is ATCF.

Calculation:

Calculate the book value of the Machine A.

Bookvalue=Cost(Depreciationtilldate)=$54000912($540000)=$13500

Calculate Recaptured depreciation if the machine is sold.

Recaptured Depreciation=$30000$13500=$16500

Calculate the annual depreciation of machine by using straight line depreciation.

Depreciation=BSN ...... (IV)

Here, cost of machine is B, salvage value is S, and number of year is, N.

Calculate the annual depreciation of machine A.

Substitute $54000 for B, 0 for S, and 12 years for N in Equation (IV).

Depreciation=$54000012=$4500

Calculate the annual depreciation of machine B.

Substitute $42000 for B, 0 for S, and 12 years for N in Equation (IV).

Depreciation=$42000012=$3500

Calculate the after-tax cash flow as shown in table below.

Year BTCF Depreciation(DI) Taxable income(TI) Income tax(TAX) ATCF
0 $30000 $16500 $6600 $23400
1 $0 $4500 $4500 $1800 $1800
2 $0 $4500 $4500 $1800 $1800
3 $0 $4500 $4500 $1800 $1800
412 $0 $0 $0 $0

Here, calculate the taxable income, income tax and after tax cash flow from Equations (I), (II) and (III) respectively.

If machine A were sold the year 0 entries would be as shown below.

Year BTCF Depreciation(DI) Taxable income(TI) Income tax(TAX) ATCF
0 $30000 $16500 $6600 $23400

If machine A is kept, the entries are just the reverse.

Calculate the after-tax annual cost.

after-tax annual cost=[$23400$1800(PA,10%,3)](AP,10%,12) ...... (V)

Write the equation for factor (AP,i%,n).

(AP,i%,n)=[i(1+i)n(1+i)n1] ...... (VI)

Here, annual cost is A, present worth is P, rate of interest is i, and number of year is n.

Calculate the factor (AP,10%,12)

Substitute 10% i, and 12 years for n in Equation (VI).

(AP,10%,12)=[0.10( 1+0.10)12( 1+0.10)121]=0.1468

Calculate the factor (PA,10%,3)

(PA,i%,n)=[(1+i)n1i(1+i)n] ...... (VII)

Substitute 10% i, and 3 years for n in Equation (VII).

(PA,10%,3)=[( 1+0.10)310.10( 1+0.10)3]=2.487

Substitute 0.1468 for (AP,10%,12), and 2.487 for (PA,10%,3) in Equation (V).

After-tax Annual cost=[$23400$1800×2.487]0.1468=$2778

The cash flow in year 0 reflects the loss of income after Recaptured Depreciation tax from not selling Machine A. this is the preferred way to handle the current market value of the defender.

Calculate the after-tax cash flow for Machine B as shown in table below.

Year BTCF Depreciation Taxable income Income tax ATCF
0 $42000 $42000
112 $2500 $3500 $1100 $400 $2900

Calculate the after-tax Annual cost.

after-tax Annual cost=[$4200000(AP,10%,12)$2900] ...... (VIII)

Substitute 0.1468 for (AP,10%,12) in Equation (VIII).

After-tax Annual cost=[$4200000×0.1468$2900]=$3266.

Conclusion:

The after-tax annual cost of B is more than the A. Hence, keep machine A.

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