Question

Assume that you are examining a lease versus buy analysis and you suddenly realize that the residual value is considered to be more risky than the rest of the cash flows. Then, which of the following is correct?

	A.	If the residual value were included as an outflow (a negative cash flow), the increased risk would be reflected by applying a lower discount rate to the residual value cash flow.
	B.	The discount rate applied to the cash flows is irrelevant of the riskiness of the cash flows.
	C.	The discount rate applied to the residual value inflow (a positive cash flow) should be decreased to account for the increased risk.
	D.	The before-tax cost of debt should be used as the discount rate, instead of the after-tax cost of debt.
	E.	The discount rate applied to the residual value outflow (a negative cash flow) should be increased to account for the increased risk.

Answer 1

Lets understand a little about both leasing ans buying.

Leasing is  a contractual arrangement in which a company (the lessee) obtains an asset from another company (the lessor) against periodic payments of lease rentals. It may typically also involve an option to transfer the ownership of the asset to the lessee at the end of the lease.

Buying the asset involves purchase of the asset with company’s own funds or arranging a loan to finance the purchase.

In finding out whether leasing is better than buying, we need to find out the periodic cash flows under both the options and discount them using the after-tax cost of debt to see where does the present value of the cost of leasing stands as compared to the present value of the cost of buying. The alternative with lower present value of cash outflows is selected.

After-tax cash flows of lease:

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

After-tax cash flows of purchase

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.

In the question above the residual value is more risky compared to the other cash flows.

"D" is not correct we always use the after tax cost of debt for discounting to account for the tax sheild and avoiding double conting of tax.

"C"& "E" is incorrect as residual value is a negetive cash flow in case of lease and positive in case of buying

"A" is not correct as to show increased risk the discount rate should be increased

"B" is the correct answer as the after tax cost of debt is used for discounting purpose for both lease and buy. The discount rate applied if to calculate the NPV of both options