Question

Accusoft Systems is offering small business owners a software package that keeps track of many accounting functions from bank transactions to sales invoices. The site license will cost $50,000 to install and will require a fee of $6000 every 3 months. If your company can save $13,500 every quarter and have the security of managing its books in-house, how long will it take for you to recover the investment at an interest rate of 12% per quarter?

The time taken to recover the investment is determined to be ............ quarters.

Answer 1

Discounted payback period (DPBP) is the year when the project's cumulative discounted cash flow is zero.

Quarterly net cash flow ($) = Quarterly savings - Quarterly fee = 13,500 - 6,000 = 7,500

Quarter	Cash flow ($)	PV Factor @12%	Discounted Cash Flow ($)	Cumulative Discounted Cash Flow ($)
0	-50,000	1.0000	-50,000	-50,000
1	7,500	0.8929	6,696	-43,304
2	7,500	0.7972	5,979	-37,325
3	7,500	0.7118	5,338	-31,986
4	7,500	0.6355	4,766	-27,220
5	7,500	0.5674	4,256	-22,964
6	7,500	0.5066	3,800	-19,164
7	7,500	0.4523	3,393	-15,772
8	7,500	0.4039	3,029	-12,743
9	7,500	0.3606	2,705	-10,038
10	7,500	0.3220	2,415	-7,623
11	7,500	0.2875	2,156	-5,467
12	7,500	0.2567	1,925	-3,542
13	7,500	0.2292	1,719	-1,823
14	7,500	0.2046	1,535	-289
15	7,500	0.1827	1,370	1,081

DPBP lies between quarters 14 and 15.

DPBP = 14 + (Absolute value of cumulative discounted cash flow, quarter 14 / Discounted cash flow, quarter 15)

= 14 + (289 / 1,370)

= 14 + 0.21

= 14.21 quarters