New diesel locomotives will cost a railroad $600,000 each and can be depreciated

Question

  New diesel locomotives will cost a railroad $600,000 each and can be depreciated straight-line over their five-year life. Using a diesel instead of a coal-fired steam locomotive will save $12,000 annually in operating expenses. Railroads have a required rate of return of 10 percent and a tax rate of 40 percent.

a.         What is the maximum price a railroad would be willing to pay for a coal-fired steam locomotive? (Hint: Set up the cash flows for a coal-fired locomotive at a price of P, including depreciation, and then compare them to the incremental cash flows associated with a diesel costing $600,000.)

b.         Will your answer to (a) change if the railroad has enormous tax-loss carryforwards that put it in a zero taxpaying position for the foreseeable future?   

Explanation / Answer

a. We need to find incremental cash flow due to diesel locomotive, as shown below -

This cash flow needs to be discounted to get NPV of cash flow due to diesel locomotive. This is as per below table -

NPV = $227,447 - THis is the amount in excess that can be paid to diesel locomotive compared to coal fired loco. Thus, maximum price that could be paid for coal fired loco is = 600,000 - 227,447 = $372,553

b. In case the effective tax rate for the company is 0% over next 5 years, then we cannot assume any tax benefit for diesel loco. Thus, effective cash flow benefit is restricted to $12000 annually. Now the NPV of cash flow becomes $45,489 as shown in table below -

Now the maximum price that can be paid to coal-fired locomotive increases to $554,511 (=$600,000 - $45,489)

Savings due to diesel locomotive Amount Formula Operating expenses 12000 Saving in taxes 48000 =(600000/5)*40% Total cash flow 60000

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