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 3, Problem 2CS
To determine

Calculate the equivalent annual value.

Expert Solution & Answer
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Explanation of Solution

Table 1 shows the cash flow of two projects that described the case as follows:

YearLandPark
14,000,000 
23,000,000 
32,250,000 
41,265,000550,000
5949,219650,000
6 750,000

Interest rate is 7%. CFLn indicates the cash flow of project land in the year n. CFLP indicates the cash flow of Project Park in the year n. Time period (n) for this calculation is 3 years. Revenue collected from bond (B) is $3,000,000.

The equivalent annual value (A) for each in 2 years can be calculated as follows:

A=(CFL0+CFL1(1+i)1+CFL2(1+i)2+CFL3(1+i)3+CFL4(1+i)4+CFL5(1+i)5+CFP4(1+i)4+CFP5(1+i)5+CFP6(1+i)6B)(1+i)n(i(1+i)n(1+i)n1)=(4,000,000+3,000,000(1+0.07)1+2,250,000(1+0.07)2+1,678,000(1+0.07)3+1,265,625(1+0.07)4+949,219(1+0.07)5+550,000(1+0.07)4+650,000(1+0.07)5+750,000(1+0.07)63,000,000)(1+0.07)3(0.07(1+0.07)3(1+0.07)31)

=(4,000,000+3,000,0001.07+2,250,0001.1449+1,678,0001.225043+1,265,6251.310796+949,2191.402552+550,0001.310796+650,0001.402552+750,0001.500733,000,000)(1.225043)(0.07(1.225043)1.2250431)=(4,000,000+2,803,738.3178+1,965,237.1386+1,369,747.8374+965,539.2601+676,779.8984+419,592.3698+463,440.9277+499,756.7853,000,000)(1.225043)(0.085753010.225043)=10,163,832.534(1.225043)(0.381052)=4,744,528.71

The equivalent annual value is $4,744,528.71.

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