ENGINEERING ECONOMIC ENHANCED EBOOK
ENGINEERING ECONOMIC ENHANCED EBOOK
14th Edition
ISBN: 9780190931940
Author: NEWNAN
Publisher: OXF
Question
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Chapter 12, Problem 17P
To determine

(a)

The after tax rate of return for the investment.

Expert Solution
Check Mark

Answer to Problem 17P

The internal rate if return is 7.72%.

Explanation of Solution

Given:

The cost of installing a machine is $200,000.

The useful life is 20 years.

Salvage value is $50000.

Per month income is $2500.

Per month expenses is $200.

Interest rate is 38%.

Concept used:

Write the expression for straight line depreciation.

SLN Depreciation=BSN ....... (I)

Here, cost of installing is B, useful life in years is N and salvage value is S.

Write the expression for taxable income.

Taxable income (c)=ab ....... (II)

Here, before tax cash flow is a and depreciation is b.

Write the expression for income tax.

Income tax(d)=[(c)×0.40] ....... (III)

Here, taxable income is c.

Write the expression for after tax cash flow.

After tax cash flow (e)=a+d ....... (IV)

Write the expression for after tax rate of return.

P=[F1(P/F,i,n)+F2(P/F,i,n)+F3(P/F,i,n)+F4(P/F,i,n)+F5(P/F,i,n)] ....... (V)

Here, the present value of the annuity is P, future value of the series is F, interest rate is i and number of periods is n.

Write the expression for rate of return by linear interpolation.

IRR=i%low+(i%highi%low)[FlowPFlowFhigh] ....... (VI)

Here, the internal rate of return is IRR, lower interest rate is i%low, higher interest rate is i%high, factor of lower interest rate is Flow, factor of higher interest rate is Fhigh,

If after-tax IRR is less than expected, then the investment is not considered.

If after-tax IRR is greater than expected, then the investment is considered.

Calculation:

Calculate the depreciation of the machine.

Substitute $200,000 for B, $50000 for S and 20 for N in Equation (I).

SLN Depreciation=$200,0000$5000020=$7500

The depreciation charged in the machine would be $7500.

Calculate the before tax cash flow.

Net income=incomeexpenses=$2500$200=$2300/month

BTCF=$2300/month(12 month1 year)=$27600/year

Here, the before tax cash flow is BTCF.

Calculate the taxable income.

Substitute $27600 for a and $7500 for b in Equation (II).

Taxable income (c)=$27600$7500=$20100

Calculate the income tax.

Substitute $20100 for c in Equation (III).

Income tax(d)=[($14,000)×0.38]=$7638

Calculate the after tax cash flow.

Substitute $7638 for d and $27600 for a in Equation (IV).

After tax cash flow (e)=$27600+($7638)=$19962

The table for computation of the after tax rate of return for investment is shown below.

(a) (b) (c) (d) (e)
Year Before tax cash flow Depreciation Taxable Income (ab) Income tax [(c)×0.40] After tax cash flow
0 $200,000 $200,000
1 $27600 $7500 $20100 $7638 $19962
2 $27600 $7500 $20100 $7638 $19962
3 $27600 $7500 $20100 $7638 $19962
4 $27600 $7500 $20100 $7638 $19962
5 $27600 $7500 $20100 $7638 $19962
6 $27600 $7500 $20100 $7638 $19962
7 $27600 $7500 $20100 $7638 $19962
8 $27600 $7500 $20100 $7638 $19962
9 $27600 $7500 $20100 $7638 $19962
10 $27600 $7500 $20100 $7638 $19962
11 $27600 $7500 $20100 $7638 $19962
12 $27600 $7500 $20100 $7638 $19962
13 $27600 $7500 $20100 $7638 $19962
14 $27600 $7500 $20100 $7638 $19962
15 $27600 $7500 $20100 $7638 $19962
16 $27600 $7500 $20100 $7638 $19962
17 $27600 $7500 $20100 $7638 $19962
18 $27600 $7500 $20100 $7638 $19962
19 $27600 $7500 $20100 $7638 $19962
20 $50000 $50000

Table (1)

Calculate the after tax rate of return.

Substitute $200,000 for P, $19962 for F in Equation (V).

$200,000=[$19962( P/F,i,1)+$19962( P/F,i,2)+......+$19962( P/F,i,20)]10.02i(1+i)20(1+i)20+1=0

Solve the equation for i.

i=7.72%

The internal rate if return is 7.72%.

Conclusion:

The internal rate if return is 7.72%.

To determine

(b)

The after tax rate of return for the investment.

Expert Solution
Check Mark

Answer to Problem 17P

The internal rate if return is 7.72%.

Explanation of Solution

Given:

The cost of installing a machine is $200,000.

The useful life is 20 years.

Salvage value is $50000.

The market price is $150000

Per month income is $2500.

Per month expenses is $200.

Interest rate is 38%.

Calculation:

Calculate the depreciation of the machine.

Substitute $200,000 for B, $50000 for S and 20 for N in Equation (I).

SLNDepreciation=$200,0000$5000020=$7500

The depreciation charged in the machine would be $7500.

Calculate the before tax cash flow.

Net income=incomeexpenses=$2500$200=$2300/month

BTCF=$2300/month(12 month1 year)=$27600/year

Calculate the taxable income.

Substitute $27600 for a and $7500 for b in Equation (II).

Taxable income (c)=$27600$7500=$20100

Calculate the income tax.

Substitute $20100 for c in Equation (III).

Income tax(d)=[($14,000)×0.38]=$7638

Calculate the after tax cash flow.

Substitute $7638 for d and $27600 for a in Equation (IV).

After tax cash flow (e)=$27600+($7638)=$19962

The table for computation of the after tax rate of return for investment is shown below.

(a) (b) (c) (d) (e)
Year Before tax cash flow Depreciation Taxable Income (ab) Income tax [(c)×0.40] After tax cash flow
0 $200,000 $200,000
1 $27600 $7500 $20100 $7638 $19962
2 $27600 $7500 $20100 $7638 $19962
3 $27600 $7500 $20100 $7638 $19962
4 $27600 $7500 $20100 $7638 $19962
5 $27600 $7500 $20100 $7638 $19962
6 $27600 $7500 $20100 $7638 $19962
7 $27600 $7500 $20100 $7638 $19962
8 $27600 $7500 $20100 $7638 $19962
9 $27600 $7500 $20100 $7638 $19962
10 $27600 $7500 $20100 $7638 $19962
11 $27600 $7500 $20100 $7638 $19962
12 $27600 $7500 $20100 $7638 $19962
13 $27600 $7500 $20100 $7638 $19962
14 $27600 $7500 $20100 $7638 $19962
15 $27600 $7500 $20100 $7638 $19962
16 $27600 $7500 $20100 $7638 $19962
17 $27600 $7500 $20100 $7638 $19962
18 $27600 $7500 $20100 $7638 $19962
19 $27600 $7500 $20100 $7638 $19962
20 $150000 $100000 $38000 $112000

Table (1)

Calculate the after tax rate of return.

Substitute $200,000 for P, $19962 for F in Equation (V).

$200,000=[$19962( P/F,i,1)+$19962( P/F,i,2)+......+$19962( P/F,i,20)]10.02i(1+i)20(1+i)20+1=0 ....... (VI)

Solve the equation for i

i=7.72%

The internal rate if return is 7.72%.

Conclusion:

The internal rate if return is 7.72%.

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