Engineering Economy
Engineering Economy
8th Edition
ISBN: 9780073523439
Author: Leland T Blank Professor Emeritus, Anthony Tarquin
Publisher: McGraw-Hill Education
Question
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Chapter 16.A, Problem 13P

(a):

To determine

Calculate the recovery rate.

(a):

Expert Solution
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Explanation of Solution

Straight line recovery rate (RRSL1) for Year 1 can be calculated as follows:

RRSL1=0.5×1n=0.5×13=0.167

Thus, the recovery rate for Year 1 is 0.167.

Straight line recovery rate (RRSL2) for Year 2 can be calculated as follows:

RRSL2=1n=×13=0.333

Thus, the recovery rate for Year 2 is 0.333.

Straight line recovery rate (RRSL3) for Year 3 can be calculated as follows:

RRSL3=1n=×13=0.333

Thus, the recovery rate for Year 3 is 0.333.

The straight line recovery rate (RRSL4) for Year 4 can be calculated as follows:

RRSL4=0.5×1n=0.5×13=0.167

Thus, the recovery rate for Year 4 is 0.167.

(b):

To determine

Calculate the present worth.

(b):

Expert Solution
Check Mark

Explanation of Solution

The book value is $80,000. MACRS recovery rate for Year 1 (RR1) is 33.33%, Year 2 (RR20 is 44.5%, Year 3 (RR3) is 14.81%, and Year 4 (RR4) is 7.41%. Interest rate (i) is 15%.

The present worth of the MACRS (PWMACRS) depreciation can be calculated as follows:

PWMACRS=(RR1×B(1+i)1)+(RR2×B(1+i)2)+(RR3×B(1+i)3)+(RR4×B(1+i)4)=(0.3333×80,000(1+0.15)1)+(0.4445×80,000(1+0.15)1)+(0.1481×80,000(1+0.15)3)+(0.0741×80,000(1+0.15)1)=(26,6641.15)+(35,5601.3225)+(11,8481.520875)+(5,9281.74901)=61,253

Thus, the present worth of the depreciation that is calculated by MACRS is $61,253.

The present worth of the SL (PWSL) depreciation can be calculated as follows:

PWSL=(RRSL1×B(1+i)1)+(RRSL2×B(1+i)2)+(RRSL3×B(1+i)3)+(RRSL4×B(1+i)4)=(0.167×80,000(1+0.15)1)+(0.333×80,000(1+0.15)1)+(0.333×80,000(1+0.15)3)+(0.167×80,000(1+0.15)1)=(13,3601.15)+(26,6401.3225)+(26,6401.520875)+(13,3601.74901)=56,915

Thus, the present worth of the depreciation that is calculated by the SL method is $56,915.

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