Question

Sandra Morris is presently leasing a small business computer from Eller Office Equipment Company. The lease requires 10 annual payments of $11,000 at the end of each year and provides the lessor (Eller) with an 11% return on its investment. You may use the following 11% interest factors:
9 Periods 10 Periods 11 Periods
Future Value of 1 1.999 2.15892 2.33164
Present Value of 1 0.50025 0.46319 0.42888
Future Value of Ordinary Annuity of 1 12.48756 14.48656 16.64549
Present Value of Ordinary Annuity of 1 6.24689 6.71008 7.13896
Present Value of an Annuity Due of 1 6.74664 7.24689 7.71008

Required:
a. Assuming the computer has a ten-year life and will have no salvage value at the expiration of the lease, what was the original cost of the computer to Eller? SHOW YOUR WORK.
b. What amount would each payment be if the ten annual payments are to be made at the beginning of each period? SHOW YOUR WORK.

Answer 1

Answer: a. $73,810.88

b. $10,185.18

Explanation:

a. The payments of $11,000 are constant so this can be considered an Annuity.

The cost of the Computer is it's present value which is,

Present Value of Annuity = Annuity Payment * Present Value Interest Factor of Annuity, 11%, 10 periods

= 11,000 * 6.71008 (Payment is made at the end of the year so this is an Ordinary Annuity)

= $73,810.88

b. When an Annuity is instead paid at the beginning of the period it is considered to be an Annuity due.

The formula is the same but for the figures ,

Present Value of Annuity Due = Annuity * Present Value Interest Factor of an Annuity Due, 11% , 10 periods

73,810.88 = Annuity * 7.24689

Annuity = 73,810.88/7.24689

= $10,185.18