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 14, Problem 27P
To determine

Calculate the present worth.

Expert Solution & Answer
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Explanation of Solution

The cash flow in Year 0 (CF0) is -$10,000 and in Year 1 (CF1) is $2,000. From Year 2 to 4 is $5000. The time period (n) is 3.

The market rate (MR) is 20%. The inflation rate (f) is 5%.

The interest rate (if) can be calculated as follows:

MR=i+f+i×f0.2=i+0.05+i×0.051.05i=0.20.05i=0.151.05=0.1429

The interest rate is 14.29%.

The present worth (PW) without considering the inflation can be calculated as follows:

PW=CF0+CF1(1(1+MR)1)+CF2((1+MR)n1MR(1+MR)n)(1(1+MR)1)=10,000+2,000(1(1+0.2)1)+5,000((1+0.2)310.2(1+0.2)3)(1(1+0.2)1)=10,000+2,000(0.8333)+5,000(2.1065)(0.8333)=10,000+1,666.6+8,776.73=443.33

The present worth is $443.33.

The present worth (PW) with considering the inflation can be calculated as follows:

PW=CF0+(CF1(1+f)1(1+i)1)+(CF2(1+f)2(1+i)2)+(CF3(1+f)3(1+i)3)+(CF4(1+f)4(1+i)4)=(10,000+(2,000(1+0.05)1(1+0.1429)1)+(5,0000(1+0.05)2(1+0.1429)2)+(5,0000(1+0.05)3(1+0.1429)3)+(5,000(1+0.05)4(1+0.1429)4))=(10,000+(2,0001.2)+(5,00001.4401)+(5,00001.7282)+(5,0002.0739))=(10,000+1,666.67+3,471.98+2,893.18+2,410.92)=442.75

The present worth is $442.75.

The present worth can be calculated using a spreadsheet as follows:

Engineering Economy, Chapter 14, Problem 27P

The present worth (CV) of individual cash flow can be found using a spreadsheet function as follows:

= $B7/(1 + $B$2)^$A7

The above function is for calculating the present value of the cash flow in Year 2.

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