a) To calculate the average time each patient spends within the facility, we can use Little’s Law, which states that the average number of customers in a system is equal to the average arrival rate multiplied by the average time spent in the system.
Given:
Average arrival rate (λ) = 20 patients per hour
Average number of customers in the facility (L) = 14 patients
Using Little’s Law:
L = λ * W
14 = 20 * W
W = 14 / 20
W = 0.7 hours
Therefore, on average, each patient spends 0.7 hours (or 42 minutes) within the facility.
b) To determine the present value of the total cost for each leasing option, we need to calculate the present value of each cash flow and then sum them up.
Option A:
Deposit: $70,000 (refundable after the lease period)
Monthly payment: $60,000 for 36 months
Using an interest rate of 10% per year, we can calculate the present value of each cash flow:
Deposit: $70,000
Monthly payment: $60,000 for 36 months at a monthly interest rate of 10%/12
Present value of deposit:
PV(deposit) = $70,000 / (1 + 10%)^0 = $70,000
Present value of monthly payments:
PV(monthly payments) = $60,000 * [(1 – (1 + 10%)^-36) / (10%/12)] = ?
Option B:
Three annual payments: $700,000 each at the beginning of year 1, 2, and 3
Using an interest rate of 10% per year, we can calculate the present value of each cash flow:
First payment: $700,000
Second payment: $700,000 / (1 + 10%)^1
Third payment: $700,000 / (1 + 10%)^2
Present value of first payment:
PV(first payment) = $700,000 / (1 + 10%)^0 = $700,000
Present value of second payment:
PV(second payment) = $700,000 / (1 + 10%)^1 = ?
Present value of third payment:
PV(third payment) = $700,000 / (1 + 10%)^2 = ?
To calculate the present value of the total cost for each option, we sum up the present values of all cash flows:
Total present value for Option A: PV(deposit) + PV(monthly payments)
Total present value for Option B: PV(first payment) + PV(second payment) + PV(third payment)
Compare the total present values for both options. The option with the lower total present value is the better option.
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