EBK ENGINEERING ECONOMY
EBK ENGINEERING ECONOMY
8th Edition
ISBN: 8220103675437
Author: Blank
Publisher: YUZU
Question
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Chapter 13, Problem 32P

(a):

To determine

Calculate the payback period.

(a):

Expert Solution
Check Mark

Explanation of Solution

Investment (C) is $245,000. Expense (AE) is $38,000 per year. Income (AI) is $92,000. MARR (i) is 15%. Salvage value (SV) is 15% of the first cost.

Payback period (n) can be calculated as follows:

(AIAE)((1+i)n1i(1+i)n)+SV(1+i)n=C(92,00038,000)((1+0.15)n10.15(1+0.15)n)+0.15×245,000(1+0.15)n=245,00054,000((1+0.15)n10.15(1+0.15)n)+36,750(1+i)n=245,00054,000((1+0.15)n10.15(1+0.15)n)+36,750(1+i)n=245,000

Substitute n as 7 by trial and error method to verify the time period in the above calculation.

54,000((1+0.15)710.15(1+0.15)7)+36,750(1+0.15)7=245,00054,000(2.660010.15(2.6600))+36,7502.6600=245,00054,000(1.66000.399)+36,7502.6600=245,00054,000(4.1604)+13,815.79=245,000224,661.6+13,815.79=245,000210,845.81<245,000

Since the calculated present value of the cost is less than the initial cost, increase the payback period to 8.

54,000((1+0.15)810.15(1+0.15)8)+36,750(1+0.15)8=245,00054,000(3.0590210.15(3.05902))+36,7503.05902=245,00054,000(2.059020.45885)+12,013.65=245,00054,000×4.4873+12,013.65=245,000242,314.2+12,013.65=245,000230,300.55245,000

Since the calculated value is nearly equal to the initial cost, it is verified that the payback period is 8 years.

(b):

To determine

Calculate the payback period using spreadsheet.

(b):

Expert Solution
Check Mark

Explanation of Solution

The spreadsheet function for payback period is given below:

= NPER(15%,54000,-245000,0.15*245000)

The above function gives the value of 7.4 years.

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