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Lease or Buy?

Based on our discussion thus far, Ms. Smart`s analysis comes down to this: if Tasha Corp. leases instead of buying, it saves $10,000 today because it avoids having to pay for the machine, but it must give up $2,330 per year for the next five years in exchange. We now must decide whether getting $10,000 today and then paying back $2,330 per year is a good idea.

A PRELIMINARY ANALYSIS

Suppose Tasha were to borrow $10,000 today and promise to make aftertax payments of $2,330 per year for the next five years. This is essentially what Tasha will be doing if it leases instead of buying. What interest rate would Tasha be paying on this ¬loan ­? Note that we need to find the unknown rate for a five-year annuity with payments of $2,330 per year and a present value of $10,000. It is easy to verify that the rate is 5.317 percent.

Suppose Tasha were to borrow $10,000 today and promise to make aftertax payments of $2,330 per year for the next five years. This is essentially what Tasha will be doing if it leases instead of buying. What interest rate would Tasha be paying on this ¬loan ­? Note that we need to find the unknown rate for a five-year annuity with payments of $2,330 per year and a present value of $10,000. It is easy to verify that the rate is 5.317 percent.

The cash flows for our hypothetical loan are identical to the cash flows from leasing instead of buying, and what we have illustrated is that when Tasha leases the machine, it effectively arranges financing at an aftertax rate of 5.317 percent. Whether this is a good deal or not depends on what rate Tasha would pay if it simply borrowed the money. For example, suppose Tasha can arrange a five-year loan with its bank at a rate of 7.57575 percent. Should Tasha sign the lease or should it go with the bank? Because Tasha is in a 34 percent tax bracket, the aftertax interest rate would be 7.57575 _ (1 _ .34) = 5 percent. This is less than the 5.317 percent implicit aftertax rate on the lease. In this particular case, Tasha would be better off borrowing the money because it would get a better rate.

We have seen that Tasha should buy rather than lease. The steps in our analysis can be summarized as follows:

1. Calculate the incremental aftertax cash flows from leasing instead of buying.

2. Use these cash flows to calculate the implicit aftertax interest rate on the lease.

3. Compare this rate to the company`s aftertax borrowing cost and choose the cheaper source of financing.

The most important thing to note from our discussion thus far is that in evaluating a lease, the relevant rate for the comparison is the company`s aftertax borrowing rate. The fundamental reason is that the alternative to leasing is long- term borrowing, so the aftertax interest rate on such borrowing is the relevant benchmark.

THREE POTENTIAL PITFALLS

There are three potential problems with the implicit rate that we calculated on the lease. First of all, we can interpret this rate as the internal rate of return, or IRR, on the decision to lease rather than buy, but doing so can be confusing. To see why, notice that the IRR from leasing is 5.317 percent, which is greater than Tasha`s aftertax borrowing cost

of 5 percent. Normally, the higher the IRR, the better, but we decided that leasing was a bad idea here. The reason is that the cash flows are not conventional; the first cash flow is positive and the rest are negative, which is just the opposite of the conventional case. With this cash flow pattern, the IRR represents the rate we pay, not the rate we get, so the lower the IRR, the better.

A second, and related, potential pitfall has to do with the fact that we calculated the advantage of leasing instead of buying. We could have done just the opposite and come up with the advantage of buying instead of leasing. If we did this, the cash flows would be the same, but the signs would be reversed. The IRR would be the same. Now, however, the cash flows would be conventional, so we could interpret the 5.317 percent IRR as saying that borrowing and buying is better.

The third potential problem is that our implicit rate is based on the net cash flows of leasing instead of buying. There is another rate that is sometimes calculated, which isbased solely on the lease payments. If we wanted to, we could note that the lease provides $10,000 in financing and requires five payments of $2,500 each. It would be tempting to then determine an implicit rate based on these numbers, but the resulting rate would not be meaningful for making lease versus buy decisions, and it should not be confused with the implicit return on leasing instead of borrowing and buying.

Perhaps because of these potential sources of confusion, the IRR approach we have outlined thus far is not as widely used as the NPV-based approach that we describe next.