A contractor has to choose one of the following alternatives in performing earth

Question

A contractor has to choose one of the following alternatives in performing earthmoving contracts: A. Buy a truck for $35,000. Salvage value is expected to be $8,000 at the end of its 7-year depreciable life. Maintenance is $2,500 per year. Daily operating expenses are $200. B. Hire a similar unit for $550 per day Based on a 10% after tax-rate of return, how many days per year must the truck be used to justify the purchace? base calculations on straight line depreciation and a 40% income tax rate. Answer should be 30 days...

Explanation / Answer

Let t be the number of days for which the truck is used.

Calculate annual worth of investment A:

Yearly costs = 2500 + 200t
Yearly depreciation = 7000
Yearly before tax cash flow = 2500 + 200t + 7000 = -(9500 + 200t)
Yearly tax = -0.4(9500 + 200t) = -3800 - 80t

Yearly after tax cash flow = -(9500+200t) - (-3800 - 80t) = -9500 - 200t + 3800 + 80t = -5700 - 120t

AW = -35000(A/P,10%,7) - 5700 - 120t + (8000 - 40% of 8000) (A/F,10%,7)
      = -35000(0.2056) - 5700 - 120t + 4800(0.1054)
      = -12391 - 120t

Calculate the AW of investment B:

Yearly cash flow = -550t

The investment A is justified if

-12391 - 120t > -550t
-12391 > -430t
430t > 12391
t > 28.79

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