Question

Green Corporation is considering leasing a new equipment. The lease lasts for 8 years. The lease calls for 8 payments of $225,000 per year with the first payment occurring immediately. The equipment would cost $1,480,000 to buy and would be straight-line depreciated to a zero salvage value over 8 years. The actual salvage value is negligible because of technological obsolescence. The firm can borrow at a rate of 6%. The corporate tax rate is 25%. The corporate tax rate is 25%. What is the NPV of the lease relative to the purchase?

		$17,412.66
		$11,796.99
		-$8,564.23
		-$12,194.86
		$8,649.72

Answer 1

Year	0	1 to 7	8
Cash inflow in not purchasing   the equipment	1,480,000	0	0
After tax lease payment	-168,750	-168,750	0
Depreciation tax shield	0	-46,250	-46,250
Total annual cash flow	1,311,250	-215,000	-46,250
PV factor (6% (1- 0.25))=4.5%	1	5.89270094023	0.70318512692
Present value =	1,311,250	- 1,266,930.70	- 32,522.31

Total NPV =$(1,311,250 - 1,266,930.70 - 32,522.31)

=$11,796.99

Working notes :

1.After tax lease payment=Lease payment×(1−tax rate)

=225,000×(1−0.25)

=225,000 × 0.75

=$168,750

2. Depreciation tax shield= Machine cost/Useful life × tax rate

=1,480,000/8 × 0.25

=185,000 × 0.25

=$46,250

Since the firm forgo in purchasing an equipment, then the machine cost would result into cash inflow, while the potential depreciation tax shield would be consider as a cash outflow.

Note ÷

The Present value factor for 1 to 7 years is sum of present value factor from 1 year to 7 year . The sum of present value factor is taken because the cash flows are same. So for ease of calculation, sum has been taken at once for calculation.

Present value for 7 years are as follows ÷

year 1=(1+ 0.045)¹ = 0.95693779904

year 2=(1+ 0.045)²=0.91572995123

year 3=(1+0.045)³=0.87629660404

year 4=(1+0.045)⁴=0.83856134357

year 5=(1+0.045)⁵ =0.80245104647

year 6=(1+0.045)⁶=0.76789573824

year 7=(1+0.045)⁷ =0.73482845764

Total 5.89270094023