Economic Life - The Scampini Supplies Company recently purchased a new delivery

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 after-tax operating cash flows, including depreciation of $6,250 per year. The truck has a 5 year expected life. The company'safter tax adjustments for the truck are below and cost of capital is 10%.

Year 0 : Operating Cash Flow = -$22,500, Salvage value = $22,500

Years 1-5 Annual Operating Cahs Flows = $6,250; Salvage Value: Year 1 = 17,500, year 2 = 14,000, year 3 = 11,000, year 4 = 5,000 and year 5 = 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?

Explanation / Answer

You basically have five scenarios as to when to abandon the truck.

Scenario 1, sell the truck after one year of service

The NPV of this scenario would be calculated as:
NPV = ($6,250 + $17,500 ) / 1.10 - $22,500
NPV = -909.09

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 / 1.10 + ( $6,250 + $14,000 ) / 1.10^2 - $22,500
NPV = -82.64

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 / 1.10 + $6,250 / 1.10^2 + ( $6,250 + $11,000 ) / 1.10^3 - $22,500
NPV = $1,307.29

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 = $726.73

IRR = 11.35%

Scenario 5, abandon truck after 5 years

NPV = $1,192.42

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 $1,307.29.

The cash flows and salvage values by definition determines the NPV and IRR of a project.

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