Question

Supposing, you run a healthcare services and you are planning on providing a new testing service to your clients. For this, you need to buy a new equipment that costs $40,000, which should be paid by monthly installments within 12 months. Your projected clients are only 50 per month.

1) Do a What-if analysis on pricing for each client per service versus Monthly-payments
2) Identify the range of the solution.
3) Discuss on the objective of this problem.
4) What are the constraints?

Answer 1

a.   Let’s suppose the new equipment cost $40,000 for the Health care services is paid back in equal 12 monthly installments at an assumed rate of 6%, compounded monthly.
Total payments that are made can be calculated as:
C = P [(1+R/12)^nx12 – 1],
Where,
‘C’ is the Monthly payments, ‘P’ Initial amount, ‘R’ is the rate of interest and ‘n’ no. of years
= $40,000 (1+0.06/12)^1x12 – 1 = $ 3,667.20
Interest for successive months = $600 for 1st month, $553.99 for 2nd month and so on:
Quarter Payment   Principal Paid   Interest Paid   Remaining Balance
1.   $ 3,667.20   $ 3,067.20   $ 600.00   $ 36,932.80
2.   $ 3,667.20   $ 3,113.21   $ 553.99   $ 33,819.59
3.   $ 3,667.20   $ 3,159.91   $ 507.29   $ 30,659.68
4.   $ 3,667.20   $ 3,207.30   $ 459.90   $ 27,452.38
5.   $ 3,667.20   $ 3,255.41   $ 411.79   $ 24,196.97
6.   $ 3,667.20   $ 3,304.25   $ 362.95   $ 20,892.72
7.   $ 3,667.20   $ 3,353.81   $ 313.39   $ 17,538.91
8.   $ 3,667.20   $ 3,404.12   $ 263.08   $ 14,134.79
9.   $ 3,667.20   $ 3,455.18   $ 212.02   $ 10,679.61
10.   $ 3,667.20   $ 3,507.01   $ 160.19   $ 7,172.60
11.   $ 3,667.20   $ 3,559.61   $ 107.59   $ 3,612.99
12.   $ 3,667.18   $ 3,612.99   $ 54.19   $ 0
Totals   $ 44,006.38   $ 40,000.00   $ 4,006.38  
Total amount to be repaid = $44,006.38
Now in order to square off the value of borrowed money, the Health services should at least charge its patients/customers with $ 3,667.20 on an average per month.
b.   Range of solution includes the two possible situations, where the Health services squares off the monthly payments with the chargeable on patients and keeping a profit margin of at least 20%:
Since 50 customers/patients visit the health center on monthly basis, each patient should be charged with an amount at least:
= $3,667.20/50 = $73.344
To have a minimum standard margin or a profit of 20%, the health services should charge:
=$3,667.20x0.20+$3,667.20x0.20/50 = $4400.44/50 = $88.02 each patient.
c.   Objective of the problem involves the capacity assessment - cost estimation of the additional funds bought and the minimum return to pay the off the borrowed funds with a considerable leverage for the operations.
d.   The constraints involve the capacity assessment in terms of revenue estimation with respect to the additional capital employed in the form of borrowed funds. Additionally, the existing customer turnover rate and the price estimation, which may or may not fall in the standard market prices range.