8-28 A firm is considering three mutually exclusive alter- natives as part of a
ID: 2510409 • Letter: 8
Question
8-28 A firm is considering three mutually exclusive alter- natives as part of a production improvement pro- gram. The alternatives are as follows: Installed cost Uniform annual benefit Useful life, in years $10,000 $15,000 $20,000 1,890 20 1,625 10 1,625 20 For each alternative, the salvage value at the end of useful life is zero. At the end of 10 years, Alt. A could be replaced by another A with identical cost and benefits. (a) Construct a choice table for interest rates from 0% to 100%. (b) The MARR is 6%. If the analysis period is 20 years, which alternative should be selected?Explanation / Answer
ANSWER:
Year
Cash Flow - Plan A
Cash Flow - Plan B
Plan B Rather than Plan A
Cash Flow - Plan C
Plan C rather than Plan B
0
-10,000
-15,000
-5,000
-20,000
-5,0000
1-10
+1,625
1,625
0
+1,890
+265
10
-10,000
0
+10,000
0
0
11-20
+1,625
+1,625
0
+1,890
+265
ROR
10%*
8.8%
7.2%**
7%
0.6%***
*The calculation is done for a 10-year period:
$10,000 = $1,625 (P/A, i%, 10)
i=10%
The second 10-year period has the similar return.
?
**The calculation is as below:
$5,000 = $10,000 (P/F, i%, 10)
(P/F, i%, 10) = $5,000/$10,000 = 0.5
i = 7.2%
?
***The calculation is as below:
$5,000 = $265 (P/A, i%, 20)
i = 0.6%
?
The above table reflects two different sets of computations.
?
1. The rate of return for each Plan is calculated as below:
PLAN
ROR
A
10%
B
8.80%
C
7%
2. Performing two incremental analyses are
Increment
Rate of Return
Plan B – Plan A
7.2%
A desirable increment. Retain Plan B and reject Plan A.
Plan C – Plan B
0.6%
An undesirable increment. Retain Plan B and reject Plan C.
Conclusion: Choose Plan B.
Year
Cash Flow - Plan A
Cash Flow - Plan B
Plan B Rather than Plan A
Cash Flow - Plan C
Plan C rather than Plan B
0
-10,000
-15,000
-5,000
-20,000
-5,0000
1-10
+1,625
1,625
0
+1,890
+265
10
-10,000
0
+10,000
0
0
11-20
+1,625
+1,625
0
+1,890
+265
ROR
10%*
8.8%
7.2%**
7%
0.6%***
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