Annual costs of 3 different systems is provided below (the negative number impli
ID: 2427946 • Letter: A
Question
Annual costs of 3 different systems is provided below (the negative number implies a cost). If the MARR is 8%, which system is the most economical of the three? Provide numerical justification.
n
System A
System B
System C
0
0
-$2,000,000
-$4,000,000
1
-$9,000,000
-$3,800,000
-$1,900,000
2
-$9,000,000
-$3,800,000
-$1,900,000
3
-$9,000,000
-$3,800,000
-$1,900,000
4
-$9,000,000
-$3,800,000
-$1,900,000
5
-$9,000,000
-$3,800,000
-$1,900,000
6
-$9,000,000
-$3,800,000
-$1,900,000
7
-$9,000,000
-$3,800,000
-$1,900,000
8
-$9,000,000
-$3,800,000
-$1,900,000
n
System A
System B
System C
0
0
-$2,000,000
-$4,000,000
1
-$9,000,000
-$3,800,000
-$1,900,000
2
-$9,000,000
-$3,800,000
-$1,900,000
3
-$9,000,000
-$3,800,000
-$1,900,000
4
-$9,000,000
-$3,800,000
-$1,900,000
5
-$9,000,000
-$3,800,000
-$1,900,000
6
-$9,000,000
-$3,800,000
-$1,900,000
7
-$9,000,000
-$3,800,000
-$1,900,000
8
-$9,000,000
-$3,800,000
-$1,900,000
Explanation / Answer
SYSTEM A
PRESENT VALUE OF THE TOTAL COST
= -$9000000 * PVIFA 8%, 8PERIODS
= -$9000000 * 5.7466
= -$51719400
SYSTEM B
PRESENT VALUE OF THE TOTAL COST
= -$2000000 * PVIF8%,1PERIOD + (-$3800000 * PVIFA 8%, 7PERIODS )
= -$2000000 * 0.9259 + (-$3800000 * 5.2046)
= -$1851800 - $19777480
= -$21629280
SYSTEM C
PRESENT VALUE OF THE TOTAL COST
= -$4000000 * PVIF8%,1PERIOD + (-$1900000 * PVIFA 8%, 7PERIODS )
= -$4000000 * 0.9259 + (-$1900000 * 5.2046)
= -$3703600 - $9888740
= -$13592340
SYSTEM C IS MORE ECONOMICAL BECAUSE THE PRESENT VALUE OF THE FUTURE CASH COST IS LESS THAN COMPARING TO THE OTHER TWO SYSTEM.
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