Question

The Smith & Jones Company is considering either the purchase or lease of a new machine details as follows:                                                                                    

                Purchase Cost of new machine                                                 $97,000                

                Annual Maintenance Costs payable at start of year               $10,000

                                                Only payable if machine is purchased.                                 

                Machine Useful Life  5 years                                                 

Salvage Value at end of 5th year                                         $8,000   (taxed at 30%)                                 

Alternatively the machine can be leased with lease payments covering all capital and operating costs details as follows.               

                Annual Lease Payment                 $29,200 payable at the start of the year

                Term of lease                                                    5 years                                                 

Cash savings associated with the acquisition of the machine are expected to be $50,000 per annum.

Other details:

                Company's Cost of Capital                                            8%                                                                         

                Corporate Tax Rate                                                     30%                                                                       

  Required:   

Should the Company LEASE the Equipment? Please show the formular. Thanks

Answer 1

Computation of PV of cash outflows:

In case of purchase of machinery -

Particulars \ Year	0	1	2	3	4	5
Initial Cost	$97,000	--	--	--	--	--
Add: Cost of maintenance	$10,000	$10,000	$10,000	$10,000	$10,000	--
Less: Depreciation Tax Shield	--	($5,340)	($5,340)	($5,340)	($5,340)	($5,340)
Less: Post-tax Salvage Value	--	--	--	--	--	($2,400)
Net Cash outflow	$107,000	$4,660	$4,660	$4,660	$4,660	($7,740)
PVIF @ 8%	1.0000	0.9259	0.8573	0.7938	0.7350	0.6806
PV of Cash outflow	$107,000	$4,314.69	$3,995.09	$3,699.15	$3,425.14	($5,267.8)

The total cash outflow from purchase of machinery is $117,136.27

Working Notes:

Computation of Depreciation Tax shield:

Depreciation p.a. (assuming Straight Line method of depreciation)

= (Cost of machinery - Salvage Value) / Useful life of the asset

= ($97,000 - $8,000) / 5

= $17,800

Depreciation tax shield = Depreciation * Tax Rate

= $17,800 * 30%

= $5,340

Computation of Post-tax Salvage Value:

Post Tax Salvage Value = Salvage value * (1 - tax rate)

= $8,000 * (1 - 30%)

= $8,000 * (1 - 0.30)

= $5,340

Computation of Cash outflow from Lease:

PV of cash outflow from lease = PV of post-tax lease rental

Post tax lease rental = $29,200 * (1 - 0.30)

= $20,440

PV of post-tax lease rental = $20,440 * PVIFA (8%, 5)

[where PVIFA is PV inflation factor of annuity]

= $20,440 * 3.9927

= $81,610

Working Notes:

Computation of PVIFA (8%, 5)

PVIFA (8%, 5) = (1 / 1.08) + (1 / (1.08)²) + .... + (1 / (1.08)⁵)

By solving we get, PVIFA (8%, 5) = 3.9927 (approx)

Conclusion:

Comparing the PV of cash outflows under the 2 options i.e., $117,136 (being PV of cash outflow of Purchase) vs $81,610 (being PV of cash outflow of Leasing), the company should go for leasing since the cash outflow is comparatively less