EBK ENGINEERING ECONOMY
EBK ENGINEERING ECONOMY
8th Edition
ISBN: 8220103675437
Author: Blank
Publisher: YUZU
Question
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Chapter 12, Problem 31P

(a):

To determine

Calculate the internal rate of return (ir).

(a):

Expert Solution
Check Mark

Explanation of Solution

Table 1 shows the project cash flow:

Table 1

AlternateXYZAB
Initial cost (FC) -30,000-15,000-45,000-70,000-40,000
NCF9,000-4,90011,10019,00010,000
Life time (n)1010101010

MARR (i) is 15%.

The internal rate of return can be calculated using the following formula:

FC=NCF((1+ir)n1ir(1+ir)n)        (1)

The internal rate of return (ir) can be calculated using the following formula:

30,000=9,000((1+ir)101ir(1+ir)10)

Substitute ir as 0.27 by trial and error method in the above calculation.   

30,000=9,000((1+0.27)1010.27(1+0.27)10)30,000=9,000(10.915310.27(10.9153))30,000=9,000(9.91532.9471)30,000=9,000(3.3644)30,000<30,279.6

The calculated value is greater than the initial cost. Thus, increase the ir value to 0.273.

30,000=9,000((1+0.273)1010.273(1+0.273)10)30,000=9,000(11.175910.273(11.1759))30,000=9,000(10.17593.05102)30,000=9,000(3.3352)30,00030,016.8

Since the calculated value is equal to the initial cost, the value of ir is confirmed as 27.3%.

Table 2 shows the internal rate of return value for different alternatives that are obtained using Equation (1). The alternates are raked based on the internal rate of return as follows:

Table 2

Alternateir
Y30.4%
X27.3%
A24%
B21.4%
Z21%

Since there is an investment limit, alternates Y, X, and A can be selected.

The internal rate of return can be calculated using the spreadsheet as follows:

EBK ENGINEERING ECONOMY, Chapter 12, Problem 31P , additional homework tip  1

(b):

To determine

The overall rate of return (ROR).

(b):

Expert Solution
Check Mark

Explanation of Solution

After investing in alternate Y, X, and A, the remaining money (RM) is $15,000(120,000115,000). The overall rate of return can be calculated as follows:

ROR=(FCY×irY)+(FCX×irX)+(FCA×irA)+(RM×i)FCY+FCXFCA+RM=(15,000×0.304)+(30,000×0.273)+(70,000×0.24)+(5,000×0.15)15,000+30,000+70,000+5,000=4,560+8,190+16,800+750120,000=0.2525

The overall rate of return is 25.25%.

The overall rate of return can be calculated using the spreadsheet as follows:

EBK ENGINEERING ECONOMY, Chapter 12, Problem 31P , additional homework tip  2

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