Question

Sadik Industries must install $1 million of new machinery in its Texas plant. It can obtain a 6-year bank loan for 100% of the cost at a 14% interest rate with equal payments at the end of each year. Sadik's tax rate is 34%. The equipment falls in the MACRS 3-year class. Alternatively, a Texas investment banking firm that represents a group of investors can arrange a guideline lease calling for payments of $320,000 at the end of each year for 3 years. Under the proposed lease terms, the Sadik must pay for insurance, property taxes, and maintenance. Sadik must use the equipment if it is to continue in business, so it will almost certainly want to acquire the property at the end of the lease. If it does, then under the lease terms it can purchase the machinery at its fair market value at Year 3. The best estimate of this market value is $200,000, but it could be much higher or lower under certain circumstances. If purchased at Year 3, the used equipment would fall into the MACRS 3-year class. Sadik would actually be able to make the purchase on the last day of the year (i.e. slightly before year 3), so Sadik would get to take the first depreciation expense at Year 3(the remaining depreciation expenses would be from Year 4 through Year 6). On the time line, Sadik would show the cost of purchasing the used equipment at Year 3 and its depreciation expenses starting at Year 3. To assist management in making the proper lease-versus-buy decision, you are asked to answer the following questions: a. What is the net advantage of leasing? Should Sadik take the lease? b. Consider the $200,000 estimate residual value. How high could the residual value get before the net advantage of leasing falls to zero?

Answer 1

a)	NAL OF LEASING:
1)	NPV OF BUYING:
	Annual installments of the loan = 1000000*0.14*1.14^6/(1.14^6-1) =	257157
	Interest rate for discounting = 14*(1-34%) =	9.24%
		0	1	2	3	4	5	6
	Beginning balance of loan		1000000	882843	749284	597027	423454	225580
	Interest at 14%		140000	123598	104900	83584	59283	31581
	Total		1140000	1006441	854184	680611	482737	257161
	Installment		257157	257157	257157	257157	257157	257161
	Ending balance		882843	749284	597027	423454	225580	0
	Depreciation under MACRS		333300	444500	148100	74100
	Cash flows of buying:
	Principal repayment		-117157	-133559	-152257	-173573	-197874	-225580
	After tax interest [Interest * (1-34%)]		-92400	-81575	-69234	-55165	-39127	-20844
	Tax shield on depreciation		113322	151130	50354	25194	0	0
	After tax cash flows from buying		-96235	-64004	-171137	-203545	-237001	-246423
	PVIF at 9.24% [PVIF = 1/1.0924^n]		0.91542	0.83799	0.76711	0.70222	0.64282	0.58845
	PV at 9.24%		-88095	-53634	-131280	-142933	-152349	-145008
	NPV of buying	-713300
2)	NPV OF LEASING:
	After tax lease payments = 320000*(1-34%) =		-211200	-211200	-211200	0	0	0
	Purchase of the leased asset				-200000
	Depreciation tax shield on the leased asset acquired				22664	30226	10071	5039
	After tax cash flows from leasing		-211200	-211200	-388536	30226	10071	5039
	PVIF at 9.24% [PVIF = 1/1.0924^n]		0.91542	0.83799	0.76711	0.70222	0.64282	0.58845
	PV at 9.24%		-193336	-176983	-298048	21225	6474	2965
	NPV of leasing	-637702
3)	NAL OF LEASING = -637702-(-713300) =	75598
	DECISION:
	As the NAL is positive, Sadiq should take the lease.
b)	If the NAL is to be zero, the residual value at t3 should be increased such that the PV of the increase in price-the PV of tax shields on the addl depreciation
	should be 0.
	If x is the increase in residual value:
	PV of increase in residual value = x*0.76711
	The PV of depreciation tax shield will be x*0.34*(0.3333*.76711+0.4445*0.70222+0.1481*0.64282+0.0741*0.58845) = x*0.24025
	So 75598 = x*(0.76711-0.24025)
	x = 75598/(0.76711-0.24025) =	143488
	The increase in price should be $143488.
	That is the residual value should be 200000+143488 =	343488
	for NAL to be 0.