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Study Guide to Accompany Principles of Corp. Finance (10th Edition)

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Problem

Magna Charter has been asked to operate a Beaver bush plane for a mining company exploring north and west of Fort Liard. Magna will have a firm one-year contract with the mining company and expects that the contract will be renewed for the five-year duration of the exploration program. If the mining company renews at year 1, it will commit to use the plane for four more years.

Magna Charter has the following choices.

• Buy the plane for $500,000.

• Take a one-year operating lease for the plane. The lease rate is $118,000, paid in advance.

• Arrange a five-year, noncancelable financial lease at a rate of $75,000 per year, paid in advance.

These are net leases: all operating costs are absorbed by Magna Charter.

How would you advise Agnes Magna, the charter company’s CEO? For simplicity assume five- year, straight-line depreciation for tax purposes. The company’s tax rate is 35%. The weighted- average cost of capital for the bush-plane business is 14%, but Magna can borrow at 9%. The expected inflation rate is 4%.

Ms. Magna thinks the plane will be worth $300,000 after five years. But if the contract with the mining company is not renewed (there is a 20% probability of this outcome at year 1), the plane will have to be sold on short notice for $400,000.

If Magna Charter takes the five-year financial lease and the mining company cancels at year 1, Magna can sublet the plane, that is, rent it out to another user.

Make additional assumptions as necessary.

Step-by-step solution

Consider first the choice between buying and a five-year financial lease. Ignoring salvage value, the incremental cash flows from leasing are shown in the following table:

  t = 0    t = 1 t = 2 t = 3 t = 4 t

Buy: 0.80 probability that contract will be renewed for 5 years    

Initial cost of plane 500.00          

Depreciation tax shield   -35.00 -35.00 -35.00 -35.00 -35.0

Lease payment -75.00 -75.00 -75.00 -75.00 -75.00  

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Lease payment tax shield 26.25 26.25 26.25 26.25 26.25  

Total cash flow 451.25  -83.75  -83.75  -83.75  -83.75  -35.0

       

Buy: 0.20 probability that contract will not be renewed      

Initial cost of plane 500.00          

Depreciation tax shield   -35.00        

Lease payment -75.00          

Lease payment tax shield 26.25          

Total cash flow 451.25 -35.00        

             

Expected cash flow 451.25 -74.00 -67.00 -67.00 -67.00 -28.0

PV(at 5.85%) 451.25 -69.91 -59.80 -56.49 -53.37 -21.0

Total PV(at 5.85%) = $190.60          

We have discounted these cash flows at the firm’s after-tax borrowing rate:

0.65 × 0.09 = 0.0585 = 5.85%

The table above shows an apparent net advantage to leasing of $190.61. However, if Magna buys the plane, it receives the salvage value. There is an 80% probability that the plane will be kept for five years and then sold for $300 (less taxes) and there is a 20% probability that the plane will be sold for $400 in one year. Discounting the expected cash flows at the company cost of capital (these are risky flows) gives:

The net gain to a financial lease is: $190.60 – $151.20 = $39.40

(Note that the above calculations assume that, if the contract is not renewed, Magna can, with certainty, charge the same rent on the plane that it is paying, and thereby zero-out all subsequent lease payments. This is an optimistic assumption.)

The after-tax cost of the operating lease for the first year is:

0.65 × $118 = $76.70

Assume that a five-year old plane is as productive as a new plane, and that plane prices increase at the inflation rate (i.e., 4% per year). Then the expected payment on an operating lease will also increase by 4% per year. Since there is an 80% probability that the plane will be leased for five years, and a 20% probability that it will be leased for only one year, the expected cash flows for the operating lease are as shown in the table below:

  t = 0    t = 1 t = 2 t = 3 t = 4 t

Lease: 0.80 probability that contract will be renewed for 5 years    

After-tax lease payment -76.70 -79.77 -82.96 -86.28 -89.73 0.

       

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Lease: 0.20 probability that contract will not be renewed      

After-tax lease payment -76.70          

             

Expected cash flow -76.70 -63.82 -66.37 -69.02 -71.78 0.

PV(at 14%) -76.70 -55.97 -51.07 -46.59 -42.50 0.

Total PV(at 14%) = $-272.84          

These cash flows are risky and depend on the demand for light aircraft. Therefore, we discount these cash flows at the company cost of capital (i.e., 14%). The present value of these payments is greater than the present value of the safe lease payments from the financial lease, so it appears that the financial lease is the lower cost alternative. Notice, however, our assumption about future operating lease costs. If old planes are less productive than new ones, the lessor would not be able to increase lease charges by 4% per year.

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Chapter 25, Problem 22

Magna Charter has been asked to operate a Beaver bush plane for a mining company exploring north and west of Fort Liard. Magna...

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