Consider the following alternatives: Year Alternative A Alternative B Alternative C 0 -$400.00 -$500.00 $0.00 1...
Consider the following alternatives:
|
Year |
Alternative A |
Alternative B |
Alternative C |
|
0 |
-$400.00 |
-$500.00 |
$0.00 |
|
1 |
$163.00 |
$193.00 |
$0.00 |
|
2 |
$163.00 |
$193.00 |
$0.00 |
|
3 |
$163.00 |
$193.00 |
$0.00 |
|
4 |
$163.00 |
$193.00 |
$0.00 |
Given the following MARR rates, which alternative should be selected:
a) 6%
b) 9%
c) 10%
d) 15%
Homework Answers
To see which alternative is preferable, we will calculate their present values
Present value = Future value/(1+Interest rate)^time
So for year 0 present value will be the same
For year 1 alternative A at 6% interest rate
= 163/(1+6%)^1
= $153.77
For the second year
= 163/(1+6%)^2
= $145.07
And same for Alternative B at different interest rates
At 9% interest rate, Alternative B
= 193/(1+9%)^1
= $177.06
Alternative C is do nothing, which will be preferred if the present value of both of them is negative.
The following tales will show the present value of both alternative
| Year | Alternative A | PV | Alternative B | PV |
| 0 | -$400 | -$400.00 | -$500 | -$500.00 |
| 1 | $163 | $153.77 | $193 | $182.08 |
| 2 | $163 | $145.07 | $193 | $171.77 |
| 3 | $163 | $136.86 | $193 | $162.05 |
| 4 | $163 | $129.11 | $193 | $152.87 |
| Total | $164.81 | $168.77 |
Aletrnative B is preferrable
b) At interest rate of 9%
| Year | Alternative A | PV | Alternative B | PV |
| 0 | -$400 | -$400.00 | -$500 | -$500.00 |
| 1 | $163 | $149.54 | $193 | $177.06 |
| 2 | $163 | $137.19 | $193 | $162.44 |
| 3 | $163 | $125.87 | $193 | $149.03 |
| 4 | $163 | $115.47 | $193 | $136.73 |
| Total | $128.07 | $125.27 |
Alternative A will be preferred.
c) At interest rate of 10%
| Year | Alternative A | PV | Alternative B | PV |
| 0 | -$400 | -$400.00 | -$500 | -$500.00 |
| 1 | $163 | $148.18 | $193 | $175.45 |
| 2 | $163 | $134.71 | $193 | $159.50 |
| 3 | $163 | $122.46 | $193 | $145.00 |
| 4 | $163 | $111.33 | $193 | $131.82 |
| Total | $116.69 | $111.78 |
Alternative A will be preferred.
d) At interest rate of 15%
| Year | Alternative A | PV | Alternative B | PV |
| 0 | -$400 | -$400.00 | -$500 | -$500.00 |
| 1 | $163 | $141.74 | $193 | $167.83 |
| 2 | $163 | $123.25 | $193 | $145.94 |
| 3 | $163 | $107.18 | $193 | $126.90 |
| 4 | $163 | $93.20 | $193 | $110.35 |
| Total | $65.36 | $51.01 |
Alternative A will be prferred.
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