Question

Solving for unknown lease payment

Benning Manufacturing Company is negotiating with a customer for the lease of a large machine manufactured by Benning. The machine has a cash price of $800,000. Benning wants to be reimbursed for financing the machine at an 8% annual interest rate.

Required:

1.  Determine the required lease payment if the lease agreement calls for 10 equal annual payments beginning immediately.

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2.  Determine the required lease payment if the first of 10 annual payments will be made one year from the date of the agreement.

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3.  Determine the required lease payment if the first of 10 annual payments will be made immediately and Benning will be able to sell the machine to another customer for $50,000 at the end of the 10-year lease.

Answer 1

1. Calculation of lease payment:

[1 + (1 (1 + 0.08)¹)] + [1 (1+0.08)²] +. . . . . . . [1(1+0.08)⁹]

In the case we should look in the table of present value of annuity due:

Lease payment =$110,390

2. Calculation of lease payment:

[(1(1+0.08)¹)] + [1(1+0.08)²] +. . . . . . . [1(1+0.08)¹⁰]

Lease payment = $119,225

3. Calculation of lease payment:

[1 + (1 (1 + 0.08)¹)] + [1 (1 + 0.08)²] +. . . . . . . [1 (1 + 0.08)⁹]

Present value of scrap: $50,000 × 0.463 = $23,150

Total lease cost = $800,000 – $23,150

= $776,850

Annual Lease payment = $107,196