Question

The Wildcat Oil Company is trying to decide whether to lease or buy a new computer-assisted drilling system for its oil exploration business. Management has decided that it must use the system to stay competitive; it will provide $3.2 million in annual pretax cost savings. The system costs $9.9 million and will be depreciated straight-line to zero over its five-year life, after which it will be worthless. Wildcat's tax rate is 24 percent and the firm can borrow at 8 percent. Lambert Leasing Company has offered to lease the drilling equipment to Wildcat for payments of $2,130,000 per year. Lambert's policy is to require its lessees to make payments at the start of the year. What is the NAL for Wildcat? (Do not round intermediate calculations and enter your answer in dollars, not millions of dollars, rounded to 2 decimal places, e.g., 1,234,567.89.) What is the maximum lease payment that would be acceptable to Wildcat? (Do not round intermediate calculations and enter your answer in dollars, not millions of dollars, rounded to 2 decimal places, e.g., 1,234,567.89.

Answer 1

Computation of Present Value of Costs in lease option

S.no	Particulars	Amount
A	Lease rent p.a	$2,130,000
B	Tax shield @ 24% on A	$511,200.00
C	Lease rent ( Net of Tax)( A-B)	$1,618,800.00

Since lease payments commences at the start of the year, we have to use the Present value of the Annuity due formula

Present value of Annuity due = C * [{ 1-( 1+i)^-n}/i] ( 1+i)

Here C = Cash flow per period

I = Rate of interest

n = No.of years

PV of Annuity due= C * [{ 1-( 1+i)^-n}/i] ( 1+i)

= $ 1618800[ { 1-( 1+0.08)^-5 } / 0.08] ( 1+0.08)

= $ 1618800[ { 1-( 1.08)^-5} /0.08]( 1.08)

= $ 1618800[ { 1-0.6806}/0.08] ( 1.08)

= $ 1618800[ 0.3194/0.08] ( 1.08)

= $ 1618800[ 3.9925] ( 1.08)

= $6980103.72

Hence Present value cost of lease option is $ 6980103.72

Computation of Present value cost of Buy option

Depreciation = ( Cost of Computer - Salvage value ) / Useful life

= ( $ 9900000-0) /5

= $ 1980000

Computation of Present value of Taxshield on Depreciation

Tax shield on Depreciation = $ 1980000* Tax rate

= $ 1980000*0.24

= $ 475200

Year	Tax shield on Depreciation	Disc @ 8%	Discounted Tax shield
1	$475,200	0.9259	$440,000.0000
2	$475,200	0.8573	$407,407.4074
3	$475,200	0.7938	$377,229.0809
4	$475,200	0.7350	$349,286.1860
5	$475,200	0.6806	$323,413.1352
	Total		$1,897,335.8096

S.No	Particulars	Amount
A	Initial Cost	$9,900,000
B	PV of Tax shield on Depreciation	$1,897,335.8096
C	Net Cost incurred( A-B)	$8,002,664.19

NAL = PV of cost incurred in Buying option - PV of Cost in lease option

= $ 8002664.19-$ 6980103.72

= $ 1022560.47

Computation of Maximum lease paymnet

The maximum lease we can incurr is the amount at which Present value of the After tax lease payments is equal to PV of Cost in Buying option.

Let the lease payment be X

X ( 1-Tax rate) PVAF ( 8%,5) = $ 8002664.19

X( 1-0.24) 4.3121 = $ 8002664.19

X ( 0.76) = $ 8002664.19/4.3121

X( 0.76) = $ 1855862.3849.

X = $ 1855862.3849/0.76

X = $ 2441924.191

Hence the Maximum lease we can afford is $ 2441924.191

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