The question is incomplete because the two mutually exclusive alternatives details were not given in the question.
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Question:
Two mutually exclusive alternatives are being considered for the environmental protection equipment at a petroleum refinery. one of these alternatives must be selected. the estimated cash flows for each alternative are as follows:
ALTERNATIVE A:
capital investment= $20,000
annual expenses= $5,500
market value at end of useful life= $1,000
useful life= 5 years
ALTERNATIVE B:
capital investment= $38,000
annual expenses= $4,000
market value at end of useful life= $4,200
useful life= 10 years
a) Which environmental protection equipment alternative should be selected? the firms MARR is 20% per year. assume the equipment will be needed indefinitely
b) Assume the study period is shortened to five years. the market value of alternative B after five years is estimated to be $15,000. which alternative would you recommend
Answer / Explanation:
First, we need to identify the budget line:
The budget line shows the various combination of goods that can be brought by the consumer with the given income. The slope of the budget line is the ratio of two goods prices. It has a negative slope.
Now, to calculate for the present value, we have,
(a) Alternative A = -20,000 - 5500/(
1
+
0.20
)
² - 5500/(
1
+
0.20
)
³ -5500/(
1
+
0.20
)
⁴ - 5500/(
1
+
0.20
)
⁵ + 1000/(
1
+
0.20
)
⁵
= −
36046.49
Alternative B = -38,000 - 4000/ (
1
+
0.20
) - 4000/ (
1
+
0.20
)² - 4000/ (
1
+
0.20
)³ - 4000/ (
1
+
0.20
)⁴ - 4000/ (
1
+
0.20
)⁵ - 4000/ (
1
+
0.20
)⁶ - 4000/ (
1
+
0.20
)⁷ - 4000/ (
1
+
0.20
)⁸ - 4000/ (
1
+
0.20
)⁹
= −
54091.56
Going forward to calculate the annual worth, we have,
Alternative A = NPV / PVIFA ( 20%, 5 years)
−
36046.49 / 2.9906
= −
$
12053.26
Alternative B = NPV / PVIFA ( 20%, 5 years)
−
54091.56 / 4.1925
=
−
$
12901.98
It should be noted that Alternative A should be chosen as it has lower annual cost.
(b) Present Value:
Alternative B = -38000 - 4000/ (
1
+
0.20
) - 4000/ (
1
+
0.20
)² - 4000/ (
1
+
0.20
)³ - 4000/ (
1
+
0.20
)⁴ - 15000/ (
1
+
0.20
)⁵
= - 43934.28
Annual Worth for Alternative B therefore is
= -43934.28 / 29906
= − $
14690.79
It should be noted that Alternative A should be chosen as it has lower annual cost.
