Question

A corporation is considering purchasing a machine that has an 8-year life and will save the firm $3,825 per year in net operating costs. The machine would be depreciated on a straight-line basis to a zero salvage value. The firm has a 21% tax rate and a 14% p.a. required rate of return on this project.

a. If the machine costs $22,000, should it be purchased?

b. If the machine can be leased for $3,400 per year payable at the end of each year, should the firm buy the machine or lease it?

c. If the machine costs $8,500, what is the maximum lease payment the firm would be willing to pay if it was to consider a leasing alternative?

Answer 1

a) Depreciation per yer under the buy option

= Purchase price / No of years

= 22000/8

= 2750

Tax saving of dereciation = 2750 * 21%

= 577.5

Total saving under buy otpion = 3825 + 577.5 = 4402.5

Year	Cash flow	PVF @ 14%	PVCF
0	(22,000)	1	(22,000)
1	4402.5	0.8772	3,862
2	4402.5	0.7695	3,388
3	4402.5	0.6750	2,972
4	4402.5	0.5921	2,607
5	4402.5	0.5194	2,287
6	4402.5	0.4556	2,006
7	4402.5	0.3996	1,759
8	4402.5	0.3506	1,543
	NPV		(1,577)

Since the PV of cash inflows is less than PV of cash out flow it is advisable not to change the asset.

b) If the company took the machine on lease then net cost to the company

There will tax shield on the lease payments = 3400 * 21% = 714

The same will not be considered as cost. the net cost to the company is 3400-714 = 2686

Year	Cash Outflow	PVF @ 14%	PVCF
1	2686	0.8772	2,356
2	2686	0.7695	2,067
3	2686	0.6750	1,813
4	2686	0.5921	1,590
5	2686	0.5194	1,395
6	2686	0.4556	1,224
7	2686	0.3996	1,073
8	2686	0.3506	942
	Total		12,460

if we purchase machine today we have to pay 22000. For the leasing today cash out flow is 12460. Hence go for the leasing

C)

Particulars	Amount
Purchase Cost	$                  8,500.00
Salvage Value	$                               -
Depreciable Amount	$                  8,500.00
Useful life	8
Dep per anum (8500/8)	$                  1,062.50
Tax rate	21.00%
Disc Rate	14.00%
Tax shield on Dep (1062.5*21%)	$                      223.13
PVAF(r%,n )	4.6389
PV of Tax Shield on Dep (223.13 * 4.6389)	$                  1,035.05

Particulars	Amount
Purchase Cost	$                   8,500.00
PV of Tax Shield on Dep	$                   1,035.05
After Tax Salvage Value	$                                -
Amount to be recovered through Lease	$                   7,464.95

Lease rental:
Let X be the Lease rent.
Particulars	Amount
Rent	X
Tax Rate	21%
After Tax Lease Rent	0.79X
No. of Years	8
Disc Rate	14.00%
PVAF( 14 %, 8 )	4.6389
Total Lease Rentals	4.6389X
Thus $ 7464.95 = 4.6389X
X = $ 7464.95 / 4.6389
X = $ 1609.22 The maximum lease the firm is willing to pay is 1609.22
Thus Lease Rental per anum is $ 1609.22

please let me know if any assistance is required