Neighborhood Savings Bank is considering leasing $100,000 worth of computer equi

Question

Neighborhood Savings Bank is considering leasing $100,000 worth of computer equipment. A 4 year lease would require payments in advance of $22,000 per year. The bank does not currently pay income taxes and does not expect to have to pay income taxes in the foreseeable future. If the bank purchased the computer equipment, it would depreciate the equipment on a straight-line basis down to an estimated salvage value of $20,000 at the end of the 4th year. The banks cost of secured debt is 14%, and its cost of capital is 20%. Calculate the net advantage to leasing.

Explanation / Answer

the Bank's cost of capital is 20%, then you should use that rate, not 14%. I'll do it both ways, just for comparison purposes.

Financing the purchase price of 100,000 over 4 yrs at 14% would require payments of 30,106. At 20%, payments would be 32,191.

But let's just compare the Present Value of the Lease vs a Purchase, at 14% and 20%.

Under the Lease, payments of 22,000 are due on the first day of each year. That's an Annuity Due, not an Ordinary Annuity.

The Present Value of an Annuity Due of 22,000, 4 payments, at 14%, is 73,076.
The PV at 20% is 68,343.

The Present Value of the equipment is 100,000 less the PV of its salvage value.
The PV of 20,000 at 14% is 11,842; at 20% it's 9,645.

The NPV of a purchase is 88,158 or 90,355 vs the PV of a Lease of 73,076 or 68,343.

So either way, leasing is better than buying.

But interestingly, your approach would have been correct (at 14%), but for the use of an Ordinary Annuity instead of an Annuity Due.
There is no such thing as the NPV of a lease, just the PV of the lease payments - 68,343.

The PV of a purchase of 100,000 is 100,000, adjusted only by the PV of the 20,000 salvage value.   

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