EBK ENGINEERING FUNDAMENTALS: AN INTROD
EBK ENGINEERING FUNDAMENTALS: AN INTROD
5th Edition
ISBN: 9780100543409
Author: MOAVENI
Publisher: YUZU
Question
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Chapter 20, Problem 17P
To determine

Find the equivalent annual worth of the cash flow diagram.

Expert Solution & Answer
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Answer to Problem 17P

The equivalent annual worth of the cash flow diagram is $3868.37.

Explanation of Solution

Given data:

The normal interest rate (i) is 8%.

Formula used:

Formula to calculate the annual worth for the given cash flow diagram is,

AW=[$5000(PA,i,n)(AP,i,n)$2000(PA,i,n)(PF,i,n)(AP,i,n)+$8000(PF,i,n)(AP,i,n)+$5000(AF,i,n)] (1)

Here,

F is the future cost,

P is the present cost,

A is the uniform series payment,

i is the normal interest rate, and

n is the number of years.

Refer the Problem 20.17 Figure in the textbook, the equation (1) is rewritten with respect to the given number of years is,

AW=[$5000(PA,i,6)(AP,i,10)$2000(PA,i,3)(PF,i,4)(AP,i,10)+$8000(PF,i,8)(AP,i,10)+$5000(AF,i,10)] (2)

Formula to calculate the present cost for the given uniform series payment is,

(PA,i,n)=[(1+i)n1i(1+i)n] (3)

Formula to calculate the uniform series payment for the given present cost is,

(AP,i,n)=[i(1+i)n(1+i)n1] (4)

Formula to calculate the present cost for the given future cost is,

(PF,i,n)=[1(1+i)n] (5)

Formula to calculate the uniform series payment for the given future cost is,

(AF,i,n)=[i(1+i)n1] (6)

Calculation:

To calculate the equivalent annual worth of the cash flow diagram:

Substitute 8% for i, and 6 for n in equation (3) to find (PA,i,6).

(PA,i,6)=[(1+(8%))61(8%)(1+(8%))6]=[(1+0.08)610.08(1+0.08)6]=4.623

Substitute 8% for i, and 10 for n in equation (4) to find (AP,i,10).

(AP,i,10)=[(8%)(1+(8%))10(1+(8%))101]=[0.08(1+0.08)10(1+0.08)101]=0.149

Substitute 8% for i, and 3 for n in equation (3) to find (PA,i,3).

(PA,i,3)=[(1+(8%))31(8%)(1+(8%))3]

(PA,i,3)=[(1+0.08)310.08(1+0.08)3]=2.577

Substitute 8% for i, and 4 for n in equation (5) to find (PF,i,4).

(PF,i,4)=[1(1+(8%))4]=[1(1+0.08)4]=0.735

Substitute 8% for i, and 8 for n in equation (5) to find (PF,i,8).

(PF,i,8)=[1(1+(8%))8]=[1(1+0.08)8]=0.540

Substitute 8% for i, and 10 for n in equation (6) to find (AF,i,10).

(AF,i,10)=[(8%)(1+(8%))101]=[0.08(1+0.08)101]=0.069

Substitute 4.623 for (PA,i,6), 0.149 for (AP,i,10), 2.577 for (PA,i,3), 0.735 for (PF,i,4), 0.540 for (PF,i,8), and 0.069 for (AF,i,10) in equation (2) to find AW.

AW=[$5000(4.623)(0.149)$2000(2.577)(0.735)(0.149)+$8000(0.540)(0.149)+$5000(0.069)]=$3868.37

Therefore, the equivalent annual worth of the cash flow diagram is $3868.37.

Conclusion:

Thus, the equivalent annual worth of the cash flow diagram is $3868.37.

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