ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN: 9780190931919
Author: NEWNAN
Publisher: Oxford University Press
Question
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Chapter 14, Problem 81P
To determine

If the device should be purchased or not.

Expert Solution & Answer
Check Mark

Answer to Problem 81P

The device should be purchased.

Explanation of Solution

Given:

Purchase amount is $10000.

MACRS 5 year depreciation.

Net Benefit is $2500 at the end of year 1.

Increase in benefit per year is $1250.

Inflation rate is 10%.

Combined interest rate is 40%.

After tax rate of return is 15%.

Calculation:

Make the table to calculate the MARCS 5 year depreciation.

Year BTCF (a) MACR rate (b) Depreciation (c)[(BTCF0d n1)×bn] Cumulative depreciation (d)
0 $10000
1 $2500 20% $2000 $2000
2 $3750 32% $2560 $4560
3 $5000 19% $1033.6 $5593.6
4 $6250 11.52% $507.62 $6101.22
5 $7500 11.52% $449.14 $6550.36
6 $8750 5.76% $198.7 $6749.06

Draw the table to calculate the after tax cash flow.

Year BTCF (a) Depreciation (b) TaxableIncome (c)(a)(b) Income taxes (d)(c×0.4) ATCF (e)(a+d)
0 $10000 $10000
1 $2500 $2000 $500 $200 $2300
2 $3750 $2560 $1190 $476 $3274
3 $5000 $1033.6 $3966.4 $1586.4 $3413.6
4 $6250 $507.62 $5742.38 $2297.12 $3952.88
5 $7500 $449.14 $7050.86 $2820 $4680
6 $8750 $198.7 $8551.3 $3420.52 $5329.48

Make the table to compute the required data.

Year ATCF (a) ATCF Year 0 (b)(a×1.07n)
0 $10000 $10000
1 $2300 $2149.5
2 $3274 $2860
3 $3413.6 $2786.5
4 $3952.88 $3015.63
5 $4680 $3336.77
6 $5329.48 $3551.25

Calculate after tax rate of return.

P=A1(1+i)1+A2(1+i)2+A3(1+i)3+A4(1+i)4+A5(1+i)5+A6(1+i)6 ...... (I)

Here, the after tax cash flow for year 1 is A1, for year 2 is A2, for year 3 is A3, for year 4 is A4, for year 5 is A5, for year 6 is A6 and the after tax rate of return is i.

Substitute, $10000 for P

$2149.5 for A1, $2860 for A2, $2786.5 for A3, $3015.63 for A4, $3336.77 for A5 and $3551.25 for A6 in Equation (I).

$10000=$2149.5(1+i)1+$2860(1+i)2+$2786.5(1+i)3+$3015.63(1+i)4+$3336.77(1+i)5+$3551.25(1+i)6

Solve for the value of i.

i=0.1764i=0.1764×100%i=17.64%.

Conclusion:

Since the after tax rate of return is greater than 15%.

Hence, the device should be purchased.

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