Question

You work for a nuclear research laboratory that is contemplating leasing a diagnostic scanner (leasing is a common practice with expensive, high-tech equipment). The scanner costs $5,400,000 and would be depreciated straight-line to zero over four years. Because of radiation contamination, it will actually be completely valueless in four years. You can lease it for $1,540,000 per year for four years. Assume that the tax rate is 25 percent. You can borrow at 6 percent before taxes.

Calculate the NAL. (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Should you lease or buy?

Answer 1

Cost of buying =   -5400000      
Annual lease payment=   -1540000      
After tax lease payment = 1540000*(1-25%)=   -1155000      
Borrowing rate is cost of capital that is 6% or 0.06. After tax rate (i) = 0.06*(1-25%)   0.045      
Time (n)=   4      
          
Present value of Lease payment=    Annual lease cost * (1- (1/(1+r)^n))/r      
-1155000*(1-(1/((1+0.045)^4)))/0.045          
-4143592.181          
          
Depreciation tax benefit per year = Cost of asset/no of years* tax rate          
5400000/4*25%=   337500      
Present value of tax benefit of depreciation =          
337500*(1-(1/((1+0.045)^4)))/0.045          
1210789.923          
Total cost of buying = cost of machine + tax benefit of depreciation          
-5400000+1210789.92=   -4189210.077      
Net advantage to leasing = Present value of lease cost - Present value of buying Cost           
-4143592.181   -(   -4189210.077   )
45617.89584          
          
So Net advantage to Lease is    $45,617.90   

It is positive. So we should lease it