Question

Question 3: Your company is considering the acquisition of a computer system for $22,000 for a five-year project. You may either buy the computer with borrowed money at 8%, with a single repayment at the end of 5 years, or lease it with yearly payments of $7500, $6500, $5500, $4500, and $3500 at the end of years 1 through 5. The salvage value is $2000, and the expected yearly benefits are $6000. Your corporate income tax rate is 50%, depreciation is by double declining balance, and discount rate is 8%.
a) Should you buy or lease?

b) Does your answer change if your discount rate is 5%? What if it is 15%?

Answer 1

a) To evaluate the option in between lease and purchase we need to evaluate the present worth of both option and which has least present cost is opted.

Option Purchase

Tax Benefit is calculate on the depreciation.

Depreciation Rate = 2 x (1/ Estimated useful life)

= 2 * ( 1/ 5)

= 40%

Depreciation Schedule
Year	Book Value	Depreciation %	Depreciation expense	Accumulated Depreciation	Book Value Year End
1	$22000	40	$8800	8800	13200
2	$13200	40	$5280	14080	7920
3	$7920	40	$3168	17248	4572
4	$4752	40	$1901	19149	2851
5	$2851	40	$1140	20289	1711

Net present value of outflow in purchase option

Present value in purchase agreement
Year	Tax benefit on depreciation	Repayment of Borrowed money	After tax Salvage benefit	Total cash flow	After tax Discount factor ( 4%)	Present value
1	4400			4400	0.925	4070
2	2640			2640	0.889	2346.96
3	1584			1584	0.855	1354.32
4	950.5			950.5	0.822	781.311
5	570	26400	144.5	-25685.5	0.790	-20291.5
Net Outflow						-11739

After tax discount rate = Discount rate ( 1- tax rate) = 8 ( 1- .50) = 4%

After tax expense = Expense ( 1- tax rate)

Total repayment of Borrowed money= (After tax interest for 5 years + Principal amount)

[(22000 * 8%) ( 1- .50)] * 5 + 22000

4400 + 22000

= 26400

After tax salvage value = (Salvage value - Book value at the year end 5) (1 - tax rate)

( 2000 - 1711) ( 1- .50 ) = $144.5 at the year end 5

Tax benefit on depreciation = (Depreciation expense * 50%)

Net present value of cash outflow under lease option

Year	Lease payments	After tax payments	After tax Present value factor	Present value
1	7500	3750	0.925	3468.75
2	6500	3250	0.889	2889.25
3	5500	2750	0.855	2351.25
4	4500	2250	0.822	1849.5
5	3500	1750	0.790	1382.5
Net outflow				11941.25

Net outflow under purchase option = $11793.00

Net outflow under lease option = $ 11941.25

DECISION: Company should Buy the computer system.

b) If discount rate is 5 % then present value under both options.

after

Present value in purchase agreement
Year	Tax benefit on depreciation	Repayment of Borrowed money	After tax Salvage benefit	Total cash flow	After tax Discount factor ( 2.5%)	Present value
1	4400			4400	0.976	4294.4
2	2640			2640	0.952	2513.28
3	1584			1584	0.929	1471.536
4	950.5			950.5	0.906	861.153
5	570	26400	144.5	-25685.5	0.884	-22706
Net Outflow						13565.6

Present value in lease
Year	Lease payments	After tax payments	After tax Present value factor	Present value
1	7500	3750	0.976	3660
2	6500	3250	0.952	3094
3	5500	2750	0.929	2554.75
4	4500	2250	0.906	2038.5
5	3500	1750	0.884	1547
Net outflow				12894.25

Decision: Lease option should be opted Since outflow is less under lease option.

If discount rate is 15% then present value under both options.

Present value in purchase agreement
Year	Tax benefit on depreciation	Repayment of Borrowed money	After tax Salvage benefit	Total cash flow	After tax Discount fator (7.5%)	Present value
1	4400			4400	0.930	4092
2	2640			2640	0.865	2283.6
3	1584			1584	0.805	1275.12
4	950.5			950.5	0.749	711.9245
5	570	26400	144.5	-25685.5	0.697	-17902.8
Net Outflow						9540.15

Present value in lease
Year	Lease payments	After tax payments	After tax Present value factor (7.5%)	Present value
1	7500	3750	0.930	3487.5
2	6500	3250	0.865	2811.25
3	5500	2750	0.805	2213.75
4	4500	2250	0.749	1685.25
5	3500	1750	0.697	1219.75
Net outflow				11417.5

Decision: Company should opted for purchase of computer equipment. Since it has lower present value outflow.