Question

The Hospital needs to purchase a new CDI system for use with the current hospital EHR.

One firm (Firm A) requires an up-front payment of $250,000 and an annual maintenance payment of $25,000 at the time the contract is signed. Thereafter, maintenance payments of $30,000 are due at the beginning of each anniversary year for a total of 5 maintenance payments (including the initial payment made at time of purchase).   

The other firm (Firm B) requires an up-front payment of $325,000 and an annual maintenance payment of $5,000 at the time the contract is signed. Thereafter, maintenance payments of $7,000 are due at the beginning of each anniversary year for a total of 5 maintenance payments (including the initial payment made at time of purchase).

Installation, other initial set up and equipment costs, will be $60,000 for either product. Both vendors quoted on-site training for staff will cost $5,000 and occur at the time of implementation. No ongoing training costs were noted in either proposal because the $5,000 includes “training a trainer.”

At the end of the third year, you are required to pay an additional fee for a system and equipment upgrade effective the first of the fourth year. The additional fee is $60,000. Each vendor offers a webinar to train staff on the new upgraded features and the fee is $650. The fee is payable along with the upgrade fee.

The new system will improve operations in the department and is estimated to help the hospital's case mix index and could generated an extra $120,000 over each of the next 5 years. The CFO states that he can earn 5% interest on the hospital’s funds. He will not consider any project that yields less than a 20% return. Cost Accounting states the useful life of this acquisition is 5 years, and there is no residual value after 5 years.

Calculate the payback of each option (use the actual numbers not the present values.)

My best guess:

Payback period= Cost of project/ annual cash flow

$520650/120,000=4.33

Answer 1

Firm A

Cash Out Flows
Initial Cash Out Flow
Upfront payment	250000
Maintenance Payment	25000
Initial Installation	60000
Training	5000
Subsequent Cash Out Flows
End of 3rd yr or starting of 4Th year	60000
Training	650
Total Cash out Flow	400650

Particulars	1	2	3	4	5
Additional Income	120000	120000	120000	120000	120000
Yearly Maintenance Payment	-30000	-30000	-30000	-30000	-30000
Opportunity forgone (Interest Income)	-1416.666667	-1416.666667	-1416.666667	-1669.375	-1669.375
	(340000*5%/12)	(340000*5%/12)	(340000*5%/12)	400650*5%/12	400650*5%/12
Net Cash Flow from Operation	88583.33333	88583.33333	88583.33333	88330.625	88330.625
Cummulative Net Cash Inflow	88583.33333	177166.6667	265750	354080.625	442411.25

Payback Period = 400650/88330.63
PBP =4.53
Alternate way to solve (This method can be used when there are uneven cash inflows)
Payback period = 4 yrs + (400650-354080.60)/88330.63
Pay back period = 4.53 years
i.e 4 years and 6 months and 11 Days	Appx
12*.53	6.36	6months
30*.36	10.8	Days

Firm B
Particulars	1	2	3	4	5
Additional Income	120000.00	120000.00	120000.00	120000.00	120000.00
Yearly Maintenance Payment	-7000.00	-7000.00	-7000.00	-7000.00	-7000.00
Opportunity forgone (Interest Income)	-1645.83	-1645.83	-1645.83	-1898.54	-1898.54
	(395000*5%/12)	(395000*5%/12)	(395000*5%/12)	455650*5%/12	455650*5%/12
Net Cash Flow from Operation	111354.17	111354.17	111354.17	111101.46	111101.46
Cummulative Net Cash Inflow	111354.17	222708.33	334062.50	445163.96	556265.42
Cash outflows other than operating expenses are 455650.
Which being recovered in 5th year
Approximately Payback period is as follows:
Pay Back Period =455650/111101.46
4.10
Payback Period is 4.10 years
Cash Out Flows
Initial Cash Out Flow
Upfront payment	325000
Maintenance Payment	5000
Initial Installation	60000
Training	5000	395000
Subsequent Cash Out Flows
End of 3rd yr or starting of 4Th year	60000
Training	650	60650
Total Cash out Flow	455650