Question

A machine that costs $280,000 would be depreciated using the straightline method by a leasing firm over a period of 3 years. Both the book value and the market value would be zero at the end of the 3 years. Both the lessor and the lessee have a tax rate of 21 percent. What is the NPV of the lease relative to the purchase to the lessor if the applicable pretax cost of borrowing is 7 percent and the lease payments are set at $102,100 annually for 3 years?

Answer 1

Assuming that the machine is purchased using a fully amortising loan, we need to build a loan schedule to compute loan repayment and interest costs. To begin with, first we need to determine annual repayments using PMT function in excel. Foormula will be =PMT(7%,3,280000,0,0). Loan schedule:

Year	Opening Principal	Total Repayment	Interest	Principal Repayment	Closing Principal
1	$           280,000	$               106,694	$             19,600	$          87,094	$                 192,906
2	$           192,906	$               106,694	$             13,503	$          93,191	$                   99,714
3	$              99,714	$               106,694	$               6,980	$          99,714	$                            (0)

After that we have to compute cash outflows under purchase option:

Year	1	2	3
Loan Repayment (1)	$           106,694	$               106,694	$           106,694
Depreciation (2)	$              93,333	$                  93,333	$             93,333
Interest (3)	$              19,600	$                  13,503	$               6,980
Total Tax Deductions (2+3)	$           112,933	$               106,837	$           100,313
Tax Shield @ 21% (4)	$              23,716	$                  22,436	$             21,066
Net Cash outflow (1-4)	$              82,978	$                  84,259	$             85,629

PV of purchase	$221,043.33 (=NPV(0.07,B13:D13)
PV of lease	$267,942.67 (=PV(0.07,3,-102100,0,0)
Difference	($46,899.33)

Thus, purchasing is a better option than leasing.