ENGINEERING ECO ANALYSIS W/STUDY GUIDE
ENGINEERING ECO ANALYSIS W/STUDY GUIDE
13th Edition
ISBN: 9780190693053
Author: NEWNAN
Publisher: Oxford University Press
Question
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Chapter 12, Problem 23P
To determine

(a)

The after tax rate of return.

Expert Solution
Check Mark

Answer to Problem 23P

The after tax rate of return is 18.46%.

Explanation of Solution

Concept used:

Write the expression for depreciation.

D=2n×BVt1 ......(I)

Here, book value is BV and useful life is n.

Write the expression for taxable income.

(Taxable income)t=BTCFtDt ......(II)

Here, before tax cash flow is BTCF.

Write the expression for income tax.

(Tax)t=(Taxable income)t×tax rate ......(III)

Write the expression for after tax cash flow.

(ATCF)t=BTCFtTaxt ......(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)+F6(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, 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, .

Calculation:

Calculate depreciation.

Substitute $80,000 for BVt1, 4 for n and 1 for t in Equation (I).

D1=24×$80,000=$40,000

Substitute $40,000 for BVt1, 4 for n and 2 for t in Equation (I).

D2=24×$40,000=$20,000

Substitute $20,000 for BVt1, 4 for n and 3 for t in Equation (I).

D3=24×$20,000=$10,000

Substitute $10,000 for BVt1, 4 for n and 4 for t in Equation (I).

D4=24×$10,000=$5,000

Calculate taxable income.

Substitute $30,000 for BTCF, $40,000 for D1 and 1 for t in Equation (II).

(Taxable income)1=$30,000$40,000=$10,000

Substitute $30000 for BTCF, $20,000 for D2 and 2 for t in Equation (II).

(Taxable income)2=$30,000$20,000=$10,000

Substitute $35000 for BTCF, $10,000 for D3 and 3 for t in Equation (II).

(Taxable income)3=$35,000$10,000=$25,000

Substitute $40000 for BTCF, $5,000 for D4 and 4 for t in Equation (II).

(Taxable income)4=$40,000$5,000=$35,500

Substitute $10,000 for BTCF, 0 for D5 and 5 for t in Equation (II).

(Taxable income)5=$10,0000=$10,000

Substitute $10,000 for BTCF, 0 for D6 and 6 for t in Equation (II).

(Taxable income)6=$10,0000=$10,000

Calculate income tax.

Substitute $10,000 for taxable income, 0.46 for tax rate and 1 for t in Equation (III).

(Tax)1=$10,000×0.46=$4,600

Substitute $10,000 for taxable income, 0.46 for tax rate and 2 for t in Equation (III).

(Tax)2=$10,000×0.46=$4,600

Substitute $25,000 for taxable income, 0.46 for tax rate and 3 for t in Equation (III).

(Tax)3=$25,000×0.46=$11,500

Substitute $35,500 for taxable income, 0.46 for tax rate and 4 for t in Equation (III).

(Tax)4=$35,500×0.46=$16,330

Substitute $10000 for taxable income, 0.46 for tax rate and 5 for t in Equation (III).

(Tax)5=$10000×0.46=$4600

Substitute $10000 for taxable income, 0.46 for tax rate and 6 for t in Equation (III).

(Tax)6=$10000×0.46=$4600

Calculate after tax cash flow.

Substitute $30000 for BTCF, $4,600 and 1 for t for tax in Equation (IV).

(ATCF)1=$30,000($4,600)=$34,600

Substitute $30000 for BTCF, $2300 and 2 for t for tax in Equation (IV).

(ATCF)2=$30,000$4,600=$25,400

Substitute $35000 for BTCF, $11,500 and 3 for t for tax in Equation (IV).

(ATCF)3=$35,000$11,500=$23,500

Substitute $40000 for BTCF, $16,330 and 4 for t for tax in Equation (IV).

(ATCF)4=$40000$16,330=$23,670

Substitute $10000 for BTCF, $4600 and 5 for t for tax in Equation (IV).

(ATCF)5=$10000$4600=5400

Substitute $10000 for BTCF, $4600 and 6 for t tax in Equation (IV).

(ATCF)6=$10000$4600+$6250=$11650

The table for the calculated values is shown below.

Year Before Tax Cash Flow Depreciation Taxable Income Tax After Tax Cash Flow
0 $100000 $80000
1 $30000 $40,000 $10000 $4600 $34600
2 $30000 $20,000 $10000 $4600 $25400
3 $35000 $10,000 $25000 $11500 $23500
4 $40000 $5,000 $35500 $16330 $23670
5 $10000 0 $10000 $4600 $5400
6 $10000 0 $10000 $4600 $11650

Table (1)

Calculate the after tax rate of return.

Substitute $80000 for P, $34600 for F1, $25400 for F2, $23500 for F3, $23670 for F4, $5400 for F5, $11650 for F6 in Equation (V).

$80,000=[$34,600( P/F,i,1)+$25,400( P/F,i,2)+$23,500( P/F,i,3)+$23,670( P/F,i,4)+$5,400( P/F,i,5)+$11,650( P/F,i,6)] ......(VII)

Consider the table and apply trial and error method equalizing the equation (VII).

Determine an interest rate which equalizes left hand side and right hand side of Equation (VII).

Substitute the tabular values into the right hand side of the equation (VII).

The table for values close to the left hand side of the equation (VII) is shown below.

Interest rate Value
18% $80751.38
19% $79126.31

Table (2)

Calculate the rate of return by linear interpolation.

Substitute $80000 for P, 18% for i%low, 19% for i%high, $80751.38 for Flow and $79126.31 for Fhigh in Equation (VI).

IRR=18%+(19%18%)[$80751.38$80000$80751.38$79126.31]=18%+1%[$751.35$1625.04]=0.18+0.01×0.46=18.46%.

Conclusion:

Thus, the internal rate if return is 18.46%.

To determine

(b)

The reason for the difference in the rate of return obtained in part (a) and the rate of return obtained in Problem 12-22.

Expert Solution
Check Mark

Answer to Problem 23P

Interest is deductible so it reduces the tax liability and the after tax cash flow of the loan. Therefore there the rate of return obtained in part (a) is different from the rate of return obtained in Problem 12-22.

Explanation of Solution

In the previous problem the total purchasing amount of the tools was $100,000 so tax was deducted on this amount. In this problem the purchasing amount was same but the corporation paid $20,000 and only $80,000 was borrowed. There is difference in the interest rate because the interest is deductible that reduces the tax liability. It also reduces the after tax cash flow of the loan.

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Chapter 12 Solutions

ENGINEERING ECO ANALYSIS W/STUDY GUIDE

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