Question

 

Omni Enterprises is considering whether to borrow funds and purchase an asset or to lease the asset under an operating lease arrangement. If it purchases the asset, the cost will be $10,000. It can borrow funds for four years at 12 percent interest. The asset will qualify for a 25 percent CCA. Assume a tax rate of 35 percent.

The other alternative is to sign two operating leases, one with payments of $2,600 for the first two years and the other with payments of $4,600 for the last two years. In your analysis, round all values to the nearest dollar. The leases would be treated as operating leases. If the objective is to minimize the present value of after-tax costs, which alternative should be selected?

Answer 1

Cash flows of lease (after tax)

Determining periodic cash flows in case of leasing is easy. Most leases involve periodic fixed payments and an optional one-time terminal payment. They may also involve payment of insurance, etc. associated with the asset which also need to be accounted for. These payments have associated tax shield, i.e. they are allowed as deduction from the company’s taxable income which results in a decrease in net tax liability of the company.

Periodic after-tax cash flows of lease = (maintenance costs + lease rentals) * (1 – tax rate)

Terminal after-tax cash flows = periodic after-tax cash flows + amount paid at purchase the asset

	Year 1	Year 2	Year 3	Year 4
Maintenance cost	0	0	0	0
Lease rentals	2600	2600	4600	4600
Tax shield @ 35%	910	910	1610	1610
Net Cash flow	1690	1690	2990	2990

Cash flows of purchase (after tax)

The most significant component of cash outflows in case of purchase of asset is the payment for cost of the asset. If the company uses its own funds, the total cost is assumed to be paid at the time 0, however, if the company obtains a loan to finance the purchase, the loan repayment and associated tax shield on interest shall appear in all the periods of the lease analysis.

Other cash flows include the tax shield on depreciation, any potential savings, maintenances costs, insurance, etc. associated with the purchase and use of the asset.

Once we know the after-tax cash flows under both the alternatives, we just need to find present values for each option using the company’s after-tax cost of debt and choosing the option that has lower present value of cash outflows.

Annual cash flows of purchasing have three components: the loan amount to be repaid in each period, the maintenance costs to be borne each year, the tax shields associated with maintenance costs, depreciation expense and interest expense. The following table summarizes the calculation of cash flows under this alternative.

Period (Years)		1	2	3	4
Loan repayment	A	3,292	3,292	3,292	3,292
Maintenance costs	B	0	0	0	0
Depreciation	D	2,500	2,500	2,500	2,500
Interest expense	I	1,200	949	668	353
Total tax deductions	T = B+D+I	3,700	3,449	3,168	2,853
Tax shield @ 35%	t = 0.35×T	1,295	1,207	1,109	998
Net cash flows	N = A+B–t	1,997	2,085	2,184	2,294

Annual loan repayment is based on present value calculation; it is the amount paid at the end of each year for 5 years that would write off the loan completely. It is calculated using the following MS Excel function: PMT (12%,4,-10000).

Interest expense are calculated in the following debt amortization table:

Period	Opening	Total	Interest	Principal	Closing
	Principal	Repayment		Repayment	Principal
0	10,000	-	-	-	10,000
1	10,000	3,292	1,200	2,092	7,908
2	7,908	3,292	949	2,343	5,564
3	5,564	3,292	668	2,625	2,940
4	2,940	3,292	353	2,940	0

It is necessary to prepare amortization table because tax laws do not allow deduction of total loan amount, instead only interest expense is allowed as deduction.

Depreciation is calculated at 25% straight line basis

Tax shield is subtracted from loan repayments and maintenance costs while calculating the net cash outflows because tax shield represents a cash inflow which arises due to tax deductibility of the expenses.

Comparison of PV of outflow

Now, we have to calculate the present value of cash outflows under both the options using the after-tax cost of debt which is 7.8% (12% * (1-35%))

Present value of leasing at 7.8% = $7,623

Present value of purchasing at 7.8% = $7,089

Since Purchasing with loan has a lower present value of cash outflows, it should be the preferred option.

Working: Present Value calculation:

The calculation of PV is as per below formula:

CF1	+	CF2	+	CF3	+	CF4
( 1 + r )1		( 1 + r )2		( 1 + r )3		( 1 + r )4

Where,
   r is the internal rate of return;
   CF₁ is the period year one net cash outflow;
   CF₂ is the period year two net cash outflow;
   CF₃ is the period year three net cash outflow;
   CF₄ is the period year four net cash outflow;

		Year 0	Year 1	Year 1	Year 1	Year 1
Lease	Total cash flow	$0	$1,690	$1,690	$2,990	$2,990
	Discount rate at 7.8%	1	1.078	1.078	1.078	1.078
		PV(C0)	PV(C1)	PV(C2)	PV(C3)	PV(C4)
		$0	$1,568	$1,454	$2,387	$2,214
	PV of outflow	$7,623
Purchase	Total cash flow	$0	1,997	2,085	2,184	2,294
		PV(C0)	PV(C1)	PV(C2)	PV(C3)	PV(C4)
		$0	$1,853	$1,794	$1,743	$1,699
	PV of outflow	$7,089