Question

Lewis Securities Inc. has decided to acquire a new market data and quotation system for its Richmond home office. The system receives current market prices and other information from several online data services and then either displays the information on a screen or stores it for later retrieval by the firm’s brokers. The system also permits customers to call up current quotes on terminals in the lobby. The equipment costs $1,000,000 and, if it were purchased, Lewis could obtain a term loan for the full purchase price at a 10% interest rate. Although the equipment has a 6-year useful life, it is classified as a special-purpose computer and therefore falls into
the MACRS 3-year class. If the system were purchased, a 4-year maintenance contract could be obtained at a cost of $20,000 per year, payable at the beginning of each year. The equipment would be sold after 4 years, and the best estimate of its residual value is $200,000. However, because real-time display system technology is changing rapidly, the actual residual value is uncertain. As an alternative to the borrow-and-buy plan, the equipment manufacturer informed Lewis that Consolidated Leasing would be willing to write a 4-year guideline lease on the equipment, including maintenance, for payments of $260,000 at the beginning of eachyear. Lewis’s marginal federal-plus-state tax rate is 25%. You have been asked to analyze the lease-versus-purchase decision and, in the process, to answer the following questions.

b. (1) What is the present value of owning the equipment? (Hint: Set up a time line that shows the net cash flows over the period t 5 0 to t 5 4, and then find the PV of
these net cash flows, or the PV of owning.)

(2) What is the discount rate for the cash flows of owning?

c. What is Lewis’s present value of leasing the equipment? (Hint: Again, construct a
time line.)

d. What is the net advantage to leasing (NAL)? Does your analysis indicate that Lewis
should buy or lease the equipment? Explain.

e. Now assume that the equipment’s residual value could be as low as $0 or as high as
$400,000, but $200,000 is the expected value. Because the residual value is riskier
than the other relevant cash flows, this differential risk should be incorporated into
the analysis. Describe how this could be accomplished. (No calculations are necessary,
but explain how you would modify the analysis if calculations were required.)
What effect would the residual value’s increased uncertainty have on Lewis’ leaseversus-
purchase decision?

f. The lessee compares the present value of owning the equipment with the present
value of leasing it. Now put yourself in the lessor’s shoes. In a few sentences, how
should you analyze the decision to write or not to write the lease?

Answer 1

b.

            1.         To develop the cost of owning, we begin by constructing the depreciation schedule:  depreciable basis = $1,000,000.

                                                   MACRS           Depreciation         End-Of-Year

                                  Year            Rate                   Expense            Book Value

                                     1              0.3333                  $  333,300            $666,700

                                     2              0.4445                      444,500              222,200

                                     3              0.1481                      148,100                74,100

                                     4              0.0741                        74,100                         0

                                                     1.0000                 $1,000,000

Cost Of Owning Time Line:

1Depreciation is a tax-deductible expense, so it produces a tax savings of t(depreciation).  For example, the savings in year 1 is 0.4($333,300) = $133,320.

2Each  maintenance  expense  is  $20,000, but  it  is  tax  deductible, so  the  after-tax  flow is (1 - t)$20,000 = $12,000.

3The ending book value is $0, so taxes must be paid on the full $200,000 salvage (residual) value.

PV cost of owning (@6%) = $591,793.

2.         The proper discount rate depends on (1) the riskiness of the cash flow stream and (2) the general level of interest rates.  The loan payments and the maintenance costs are fixed by contract, hence are not at all risky.  The depreciation deductions are also “locked in,” but the tax rate could change.  Thus, depreciation cash flows (tax savings) are not totally certain, but they are relatively certain.  Only the residual value is highly uncertain.  On balance, and in relation to cash flows associated with such activities as capital budgeting, we conclude that the cash flows in the time line are relatively safe, so they should be discounted at a relatively low rate.  In fact, they have about the same degree of riskiness as the firm’s debt cash flows (which also have some tax rate risk, and which are also contractual in nature).   Therefore, we conclude that leasing has about the same impact on the firm’s financial risk as debt financing, so the appropriate discount rate is Lewis’s cost of debt.  (Note:  the larger the residual value in relation to the other flows, the less justifiable is this statement.)  Further, since the cash flows are stated on an after-tax basis, the rate should be the after-tax cost of debt.  Lewis’s before-tax debt cost is 10 percent, and since the firm is in the 40 percent tax bracket, its after-tax cost is 10.0%(1 - 0.40) = 6.0%.  Therefore, we use 6 percent as the discount rate.

When we have been engaged as consultants on lease-versus-buy decisions, the proper discount rate is often discussed.  We know of no way to specify exactly how to adjust for the salvage (residual) value risk.  Therefore, what we have been doing is running the analysis on a spreadsheet model and making a data table where the dependent variable is the NAL as calculated below and the independent variable is the discount rate.  Then, we produce a graph which shows the range of discount rates over which the NAL is positive.  This usually heads off problems over the proper discount rate.

c.     If Lewis leased the equipment, its only cash flows would be the after-tax lease payments:

1Each lease payment is $260,000, but this is deductible, so the after-tax cost of the lease is (1 - t)($260,000) = $156,000.

PV cost of leasing (@6%) = $572,990.

d.         The net advantage to leasing (NAL) is $18,751:

            NAL= PV Cost Of Owning - PV Cost Of Leasing

                        = $591,793 - $572,990 = $18,803.

The NAL is positive, which indicates that the PV cost of owning is greater.  Therefore, leasing is less expensive than borrowing and buying, so Lewis should lease the equipment rather than purchase it.

e.         First, note that the residual value in a lease analysis will be shown either in the “cost of owning section” or in the “cost of leasing” section, depending on whether or not the company plans to continue using the leased asset at the expiration of the basic lease.   If the lessee plans to continue using the equipment, then it will have to be purchased when the lease expires, and in this case the residual value appears as a cost in the leasing cost section.  However, if the lessee plans not to continue using the equipment, then the residual value will not be shown in the leasing section--rather, it will be shown as an inflow in the cost of owning section.  In Lewis’s case, the asset will not be needed at the expiration of the lease, so the residual is shown as an inflow in the owning section.  In this situation, we account for increased risk by increasing the rate used to discount the residual value cash flow, resulting in a lower present value of the residual cash flow.  This leads to a higher cost of owning, so the greater the risk of the residual value, the higher the cost of owning, and the more attractive leasing becomes.

Note, though, that the situation would be different if Lewis planned to lease and then exercise a fair market value purchase option in order to continue using the equipment.  Then the residual would be shown as a cost in the leasing section, and its higher risk would be reflected by discounting it at a lower rate.  In that situation the riskiness of the residual would penalize rather than help the lease.

In the case at hand, the lessor, not the lessee, will own the asset at the end of the lease, so the lessor bears the residual value risk. In effect, the lease transaction passes the risk associated with the residual value from the lessee/user to the lessor.  Of course, the lessor recognizes this, and as a result, assets with highly uncertain residual values will carry higher lease payments than assets with relatively certain residual values.  However, the most successful leasing companies have developed expertise in renovating and disposing of used equipment, and this gives them an advantage over most lessees in reducing residual value risks.

Further, leasing companies usually deal with a wide array of assets, so residual value estimates that are too high on one asset may be offset by estimates that are too low on another.

f.          The lessor should view “writing” the lease as an investment, so the lessor should compare the return on the lease with returns available on alternative investments of similar risk.