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ENG106
HW#5
Winter, 2006
Problem 1
Knowns:
(Read the problem statement)
Two M.E. alternatives (A and B) with two years needs
Constant-dollar cash flows with B-A incremental analysis as below:
EOY
A
B
B-A
0
-$30,000
-$40,000
-$10,000
1
$20,000
$43,000
$23,000
2
$18,200
$5,000
-$13,200
Find:
(a)
Comment on your co-worker's statement.
(b)
Over what range of MARR, would you recommentd the selection of machine B?
Solution:
(a)
Whenever you need to make a rate of return comparison of M.E. alternatives,
you must perform an incremental analysis.
(b)
Perform incremental analysis on B-A.
Check if increment B-A is pure or mixed by finding an i* and then calculating PB(i*):
EOY
Flow
PB(i*)
i*:
10% =IRR(flow0:flow2)
0
-$10,000
-$10,000
1
$23,000
$12,000
=(PB at EOY 0)*(1+i*)+flow1
2
-$13,200
$0
From the project balance we see that this is a mixed investment and
conclude that IRR is not equal to i*.
We then compute the project balance (PB) at the end of each year as follows:
PB(IRR, MARR)
0
= -$10, 000
PB(IRR, MARR)
1
= -$10, 000(1+IRR) + $23,000 = $13,000 - $10,000 IRR
PB(IRR, MARR)
2
= ($13, 000 - $10,000 IRR)(1+MARR) - $13,200 = $0
Rearranging terms in PB(IRR, MARR)
2
gives an expression for IRR as a function of MARR:
IRR = 1.3 -1.32 / (1+MARR)
This is plotted in Fig. 1, from which we conclude that project B will be accepted
if 10%<MARR<20% which is the range over which IRR for B-A >MARR
Figure 1. IRR vs. MARR
6%
8%
10%
12%
14%
16%
18%
20%
22%
6%
8%
10%
12%
14%
16%
18%
20%
22%
24%
MARR
IRR
IRR
MARR