Economic Life The Scampini Supplies Company recently purchased a new delivery tr
ID: 2743102 • Letter: E
Question
Economic Life
The Scampini Supplies Company recently purchased a new delivery truck. The new truck cost $22,500, and it is expected to generate net after-tax operating cash flows, including depreciation, of $6,250 per year. The truck has a 5-year expected life. The expected salvage values after tax adjustments for the truck are given below. The company's cost of capital is 12%.
Year
Annual Operating Cash Flow
Salvage Value
0
-$22,500
$22,500
1
6,250
17,500
2
6,250
14,000
3
6,250
11,000
4
6,250
5,000
5
6,250
0
What is the optimal number of years to operate the truck?
Would the introduction of salvage values, in addition to operating cash flows, ever reduce the expected NPV and/or IRR of a project?
I. Yes. Salvage possibilities could only lower NPV and IRR.
II. Salvage possibilities would have no effect on NPV and IRR.
III. No. Salvage possibilities could only raise NPV and IRR.
Year
Annual Operating Cash Flow
Salvage Value
0
-$22,500
$22,500
1
6,250
17,500
2
6,250
14,000
3
6,250
11,000
4
6,250
5,000
5
6,250
0
Explanation / Answer
Scenario 1, sell the truck after one year of service
The NPV of this scenario would be calculated as:
NPV = ($6,250 + $17,500 ) / 1.12 - $22,500
NPV = $ -1,294.64
The IRR would be such that:
0 = ( $6,250 + $17,500 ) / R - $22,500
.: R = ( $6250 + $17,500 ) / $22,500
R = 1.0556
The IRR is 5.56%
Scenario 2, abandon the vehicle after two years:
NPV = $6,250 / 1.12 + ( $6,250 + $14,000 ) / 1.12^2 - $22,500
NPV = $ -776.47
The IRR is such that the following is satisfied:
0 = $6,250 / R + ( $6,250 + $14,000 ) / R^2 - $22,500
.:
Using the quadratic equation
R = 2 * ( $6,250 + $14,000 ) / ( - $6,250 +/- sqrt( $6,250^2 - 4 * ( $6,250 + $14,000 ) * ( - $22,500 ) ) )
R = 1.0977 or -0.8199
We can disqualify -0.8199 as non-sensical and say that the IRR is 9.77%
Scenario 3, abandon truck after three years:
NPV = $6,250 / 1.12 + $6,250 / 1.12^2 + ( $6,250 + $11,000 ) / 1.12^3 - $22,500
NPV = $341.03
The IRR satisfies the equation:
0 = $6,250 / R + $6,250 / R^2 + ( $6,250 + $11,000 ) / R^3 - $22,500
by numerical methods we have:
R = 1.1274
The IRR is 12.74%
Scenario 4, abandon truck after 4 years:
NPV = $6,250 / 1.12 + $6,250 / 1.12^2 + 6,250 / 1.12^3 + ( $6,250 + $5,000 ) / 1.12^4 - $22,500
NPV = $ -338.98
IRR = 11.35%
Scenario 5, abandon truck after 5 years
NPV = $6,250 / 1.12 + $6,250 / 1.12^2 + 6,250 / 1.12^3 + 6,250 / 1.12^4 + 6,250 / 1.12^5 - $22,500
NPV = $29.85
IRR = 12.05%
The truck's optimal economic life is three years giving you an internal rate of return of 12.74% and an NPV of $341.03.
The cash flows and salvage values by definition determines the NPV and IRR of a project.
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