ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN: 9780190931919
Author: NEWNAN
Publisher: Oxford University Press
Question
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Chapter 14, Problem 85P
To determine

The better alternative.

Expert Solution & Answer
Check Mark

Answer to Problem 85P

The alternative B should be preferred.

Explanation of Solution

Given:

Year A B
0 $420 $300
1 $200 $150
2 $200 $150
3 $200 $150

MARR is 8%.

Combined income tax rate is 38%.

Calculation:

Calculate the Straight line depreciation value.

D=BSN         ...... (I)

Here, book value is B, salvage value is S and useful life is N.

Substitute $420 for B, 0 for S and 3 years for N in Equation (I).

D=$420$03=$140

Calculate the IRR forAlternative A.

Year Cash flow in Year 0 dollars (a) Cash flow in actual dollars (b)(a×(1+0.05)n) Straight line depreciation (c) Taxable income (d)(bc) Incometax (e)(d×38%) After tax cash flow(Actual dollars) (f)(be) After tax cash flow(in year zero dollars) (g)(f(1+0.05)n)
0 $420 $420 $420 $420
1 $200 $210 $140 $70 $26.6 $183.4 $174.67
2 $200 $220.5 $140 $80.5 $30.59 $189.91 $172.25
3 $200 $231.5 $140 $91.5 $34.77 $196.73 $170
IRR 11.22%

Calculate the IRR.

A=ATCF(1+i)n         ...... (II)

Here, initial cash flow is A, after tax cash flow is ATCF and rate of return is IRR.

Substitute $420 for A and calculate the value of i in Equation (II).

$420=174.67(1+i)1+172.5(1+i)2+170(1+i)3i=11.22%

Calculate the IRR for Alternative B.

Calculate the Straight line depreciation value.

Substitute $300 for B, 0 for S and 3 years for N in Equation (I).

D=$300$03=$100

Year Cash flow in Year 0 dollars (a) Cash flow in actual dollars (b)(a×(1+0.05)n) Straight line depreciation (c) Taxable income (d)(bc) Incometax (e)(d×38%) After tax cash flow(Actual dollars) (f)(be) After tax cash flow(in year zero dollars) (g)(f(1+0.05)n)
0 $300 $300 $300 $300
1 $150 $157.5 $100 $57.5 $21.85 $135.65 $129.2
2 $150 $165.4 $100 $65.4 $24.85 $140.55 $127.48
3 $150 $173.6 $100 $73.6 $27.97 $145.63 $125.8
IRR 13.88%

Calculate the IRR.

Substitute $300 for A and calculate the value of i in Equation (II).

$300=$129.2(1+i)+$127.48(1+i)2+$125.48(1+i)3i=13.22%

Thus, IRR of Alternative B is more.

Conclusion:

The alternative B should be preferred.

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Chapter 14 Solutions

ENGR.ECONOMIC ANALYSIS

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