Question

PROB 1. —Present value of an ordinary annuity due.

Jill Morris is planning to purchase an array of small business equipments from Eller Office Equipment Company. He expects to generate an income of $4,000 at the end of each year for the next 10 years from the use of these equipments. The market rate of interest for small equipment loans is 8%. The following 8% interest factors are given to you.

​9 Periods​10 Periods​11 Periods

Future Value of 1​1.99900​2.15892​2.33164

Present Value of 1​.50025​.46319​.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 Annuity Due of 1​6.74664​7.24689​7.71008

Instructions

(a)​Assuming the equipments have a ten-year life and will have no salvage value at the expiration of the period of life what would be the maximum price he would be willing to pay for the equipments now?

(b)​What amount would he be willing to pay if the annual inflows of cash could be received at the beginning of each year?

Answer 1

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a) Assuming the equipments have a ten-year life and will have no salvage value at the expiration of the period of life what would be the maximum price he would be willing to pay for the equipments now? Present Cash Present Factor @ Value of Flow 8% Year Cash flow (A) (B) (A*B) 0.925925926 1 4000 1.08 3,704 0.85733882 4000 2 1.1664 3,429 4000 1.259712 3,175 0.793832241 4000 1.360489 4000 1.469328 4 0.735029853 2,940 2,722 2,521 5 0.680583197 0.630169627 4000 1.586874 4000 1.713824 6 7 0.583490395 2,334 1.85093 0.540268885 2,161 8 4000 0.500248967 4000 1.999005 4000 2.158925 9 2,001 10 0.463193488 1,853 Maximum price that would be paid is the Present Value of Allcash flow 26,840 b) What amount would he be willing to pay if the annual inflows of cash could be received at the beginning of each year? Present Cash Present Factor @ Value of Flow 8% Year Cash flow (A) (B) (A*B) 4,000 In this amount would be received at staring of year one. So present value factor would be one 4000 1 1 0.925925926 2 4000 1.08 3,704 3,429 3 4000 1.1664 0.85733882 0.793832241 4000 1.259712 3,175 4000 1.360489 5 0.735029853 2,940 4000 1.469328 4000 1.586874 2,722 6 0.680583197 7 0.630169627 2,521 0.583490395 4000 1.713824 4000 1.85093 4000 1.999005 Maximum price that would be paid is the Present 2,334 9 0.540268885 2,161 10 0.500248967 2,001 Value of All cash flow 24,988 Please note that I have not utilised the Present value factor provided in the question as they are not clearly visible. Else I have calcuated the present value on my own @ 8%