Two investment opportunities are as follows: A B First cost $150 $100 Uniform an
ID: 1191603 • Letter: T
Question
Two investment opportunities are as follows:
A B
First cost $150 $100
Uniform annual benefit 25 22.25
End-of-useful-life salvage value 20 0
Useful life, in years 15 10
________________________________________________
At the end of 10 years, Alt. B is not replaced. Thus, the comparison is 15 years of A versus 10 years of B. If the MARR is 10%, which alternative should be selected.
Explanation / Answer
The incremental cash flow for whole period is 15 years in our case. we always subtract the lower initial cost from the higher initial cost. The cash flows are as follows:
Year
A
B
A-B
0
-150
-100
-50
1
25
22.25
2.75
2
25
22.25
2.75
3
25
22.25
2.75
4
25
22.25
2.75
5
25
22.25
2.75
6
25
22.25
2.75
7
25
22.25
2.75
8
25
22.25
2.75
9
25
22.25
2.75
10
25
22.25
2.75
11
25
0
25
12
25
0
25
13
25
0
25
14
25
0
25
15
45
0
45
Now, the incremental cash flow (i.e., A-B) tells us that if A which is the expensive alternative with initial cost as 150 was bought instead of B
Paying $50 extra now, it would give a savings $2.75 for the each first 10 years, plus $25 for the each oh last 4 years, and $45 at the 15th year.
Now we can find out how much interest this additional expense $50 is giving us.
we will equate the NPB and NPC of the (A-B) cash flow.
50 = 2.75(P/A,i,10)+25(P/A,i,4)(P/F,i,10)+45(P/F,i,15)
Try different i values and find the value of i at which the right hand side becomes 50.
If you can prove the i is more than the MARR that will also do.
Now their MARR = 10%, and the additional cost is generating 11.46% interest. So the conclusion is go for the higher initial cost alternative or select Alt. A
Year
A
B
A-B
0
-150
-100
-50
1
25
22.25
2.75
2
25
22.25
2.75
3
25
22.25
2.75
4
25
22.25
2.75
5
25
22.25
2.75
6
25
22.25
2.75
7
25
22.25
2.75
8
25
22.25
2.75
9
25
22.25
2.75
10
25
22.25
2.75
11
25
0
25
12
25
0
25
13
25
0
25
14
25
0
25
15
45
0
45
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