Question

Anderson Manufacturing​ Co., a small fabricator of​ plastics, needs to purchase an extrusion molding machine for ​$110,000 Kersey will borrow money from a bank at an interest rate of 8​% over five years. Anderson expects its product sales to be slow during the first​ year, but to increase subsequently at an annual rate of 10​%. Anderson therefore arranges with the bank to pay off the loan on a​ "balloon scale," which results in the lowest payment at the end of the first year and each subsequent payment being just 10​% over the previous one. Determine the five annual payments.

Period (N) Payment

1 $

2 $

3 $

4 $

5 $

Answer 1

Purchase Price of Machine = $110,000

To be repayable at interest rate of 8% in 5 years

First year repayment = “X”, that increases by 10% every year

Calculate the five annual payments.

Putting the formula for geometric gradient cash flows

P = A1 [1 – (1+g) ^N (1+i) ^–N ÷ i-g], where g = 10% and i=8%

$110,000 = A1 [1 – (1+0.10) ⁵ (1+0.08) ^–5 ÷ 0.08 – 0.10]

$110,000 = A1 (4.8043)

A1 = $110,000 ÷ 4.8043

A1 = 22896

First year cash flow = 22896

Second year cash flow = 22896 + 10% of 22896 = 25,185.6

Third year cash flow = 25,185.6 + 10% of 25,185.6 = 27,704.16

Fourth year cash flow = 27,704.16 + 10$ of 27,704.16 = 30,474.57

Fifth year cash flow = 30,474.57 + 10% of 30,474.57 = 33,522