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 4, Problem 61P
To determine

Calculate the present, future, and equivalent annual value.

Expert Solution & Answer
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Explanation of Solution

Equivalent cash flow (CF1) from year 1 to 5 is -$100. Time period 1 (n1) is 5. Interest rate 1 (i1) is 14%. Equivalent cash flow (CF2) from year 6 to 8 is -$160. Interest rate 2 (i2) is 10%. Time period 2 (n2) is 3.

Present value (P) can be calculated as follows:

P=CF1((1+i1)n11i1(1+i1)n1)+CF2((1+i2)n21(1+i2)n2i2)(1(1+i1)n1)=100((1+0.14)51(1+0.14)50.14)+(160)((1+0.1)310.1(1+0.1)3)(1(1+0.14)5)=100(1.92541510.14(1.925415))+(160)(1.33110.1(1.331))(11.925145)=100(0.9254150.269558)+(160)(0.3310.1331)(0.5194)=100(3.4331)+(160)(2.4869)(0.5194)=343.31206.67=549.98

Present value is -$549.98.

Future value (F) can be calculated as follows:

F=CF1((1+i1)n11i1)(1+i2)n2+CF2((1+i2)n21i2)=100((1+0.14)510.14)(1+0.1)3+(160)((1+0.1)310.1)=100(1.92541510.14)(1.331)+(160)(1.33110.1)=100(0.9254150.14)(1.331)+(160)(0.3310.1)=100(6.6101)(1.331)+(160)(3.31)=879.8529.6=1,409.4

Future value is -$1,409.4.

Equivalent annual value (A) can be calculated as follows:

F=A((1+i1)n11i1)(1+i2)n2+A((1+i2)n21i2)1,409.4=A((1+0.14)510.14)(1+0.1)3+A((1+0.1)310.1)1,409.4=A(1.92541510.14)(1.331)+A(1.33110.1)1,409.4=A(0.9254150.14)(1.331)+A(0.3310.1)1,409.4=A(6.6101)(1.331)+A(3.31)1,409.4=8.798A+3.31A12.108A=1,409.4A=1,409.412.108=116.4

Equivalent annual value is -$116.4.

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Chapter 4 Solutions

Engineering Economy

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