# Lease Versus Purchase Paper

**Question description**

Using the problem and answer highlight in yellow answer this question:

Discuss the application of time value of money concepts used in evaluating lease versus purchase decisions

Management has decided to acquire a new asset that costs $200,000. The estimated economic life of the asset is five years, but the firm wants the use of the asset only for three years. If the firm purchases the asset, it anticipates selling it at the end of three years for $50,000.

The firm may lease the asset for $55,000 a year paid at the end of each year. The lease does not include maintenance. It is estimated that annual maintenance initially will be $5,000 (paid at the end of the year), but that cost will increase by $1,000 each year as the asset ages.

The firm could purchase the asset with a five-year loan of $200,000. The loan will be retired in five payments of $40,000 unless the equipment is sold, in which case the loan must be paid off at closing of the sale. The interest rate is 10 percent and is paid at the end of each year on the balance owed. The annual interest payment is provided below.

If the firm does purchase the asset, it will enter into a maintenance agreement with the manufacturer that costs $5,000 a year. The annual depreciation expense is provided below. The firm’s tax bracket is 40 percent.

Based on the above information, should the firm borrow and purchase or should the firm lease?

To help answer the question, fill in the following tables. (It is not necessary to have an entry in every blank.)

Cash Outflows/Inflows Associated with Leasing Year 1 2 3 4 5 Lease payments Maintenance Total tax-deductible expenses Tax savings After-tax net cash outflow from leasing

Cash Outflows/Inflows Associated with Owning Year 1 2 3 4 5 Maintenance Depreciation 40,000 60,000 40,000 30,000 20,000 Interest 20,000 16,000 12,000 8,000 4,000 Principal Repayment Total tax-deductible expences Tax savings Sale of equipment After-tax inflow from sale of equipment After-tax net cash outflow from owning

## Answer

Since the present value of the cash outflows from owning exceed the present value of the cash outflows from leasing, leasing is preferred.
Present value of the cost of leasing (using the 10 percent interest rate): $36,000(0.909) + $36,600(0.826) + $37,200(0.751) = $90,892
Present value of the cost of leasing (using the 10 percent interest rate): $39,000(0.909) + 28,600(0.826) + 56,200(0.751) = $101,281 Since the asset is sold at the end of the third year, there are no entries for years 4 and 5 even though the expected life of the asset is five years. The $80,000 balance of the loan must be repaid when the asset is sold. The asset is sold for $50,000 but its book value is $60,000. The book value is the $200,000 cost minus the sum of the amount of depreciation during the first three years ($40,000 + $60,000 + $40,000). Since the asset is sold for $50,000, the firm has a $10,000 loss ($50,000 – $60,000). The $10,000 loss produces a $4,000 tax savings ($10,000 × 0.4). The net cash inflow from the sale is $50,000 + $4,000 = $54,000. The cash outflow at the end of the third year is maintenance ($5,000) plus interest ($12,000) plus principal repayment ($120,000) minus the tax savings ($26,800) plus the after-tax proceeds from the sale ($54,000). That is $5,000 + $12,000 + $120,000 – $26,800 – $54,000 = $56,200. |

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