Question

You work for a nuclear research laboratory that is contemplating leasing a diagnostic scanner (leasing is a very common practice with expensive, high-tech equipment). The scanner costs $5,400,000, and it would be depreciated straight-line to zero over five years. Because of radiation contamination, it actually will be completely valueless in five years. You can borrow at 8 percent before taxes. Your company does not anticipate paying taxes for the next several years, but the leasing company has a tax rate of 24 percent. Over what range of lease payments will the lease be profitable for both parties? (Do not round intermediate calculations. Enter your answers from lowest to highest rounded to 2 decimal places, e.g., 32.16.)

Answer is complete but not entirely correct.

Total payment range

$1,349,843.32 selected answer incorrect

to

$1,352,464.87 selected answer correct

Answer 1

Cost of scanner = $5,400,000

Life = 5 years

Depreciation = 5,400,000/5 = $1,080,000

Taxes = 24%

Tax savings on depreciation = 0.24 * $1,080,000 = $259,200

Borrowing rate before tax = 8%

PVIFA(8%,5) = [1- (1+ 0.08)^-5]/0.08 = 3.992710037

Cost per annum = 5,400,000 / 3.992710037 = $1,352,464.855

Borrowing rate after tax = 8(1-0.24) = 6.08%

PVIFA(6.08,5) = [1- (1+ 0.0608)^-5]/0.0608 = 4.203212105

Present value of tax savings = $259,000 * PVIFA(6.08,5)

= $259,200 *4.203212105 = $1,088,631.935

Net cost to lessor = cost of scanner – Present value of tax savings

= $5,400,000 - $1,088,631.935= $4,311,368.065

Lease payment for annum after tax = $4,311,368.065/ 4.203212105= $1,025,731.74

Lease payment before tax = 1025731.74/ (1- 0.24) = $1,349,647.026

Total payment range is $1,349,647.026 to $1,352,464.855