Provide Detailed Descriptions And Show All Calculations Used ✓ Solved
Provide Detailed Descriptions And Show All Calculations Used To Arrive
Provide detailed descriptions and show all calculations used to arrive at solutions for the following questions: Community Hospital has annual net patient revenues of $150 million. At the present time, payments received by the hospital are not deposited for six days on average. The hospital is exploring a lockbox arrangement that promises to cut the six days to one day. If these funds released by the lockbox arrangement can be invested at 8 percent, what will the annual savings be? Assume the bank fee will be $2,000 per month. St. Luke’s Convalescent Center has $200,000 in surplus funds that it wishes to invest in marketable securities. If transaction costs to buy and sell the securities are $2,200 and the securities will be held for three months, what required annual yield must be earned before the investment makes economic sense? Your firm is considering the following three alternative bank loans for $1,000,000: 10 percent loan paid at year end with no compensating balance 9 percent loan paid at year end with a 20 percent compensating balance 6 percent loan that is discounted with a 20 percent compensating balance requirement Assume that you would normally not carry any bank balance that would meet the 20 percent compensating balance requirement. What is the rate of annual interest on each loan? An important source of temporary cash is trade credit, which does not actually bring in cash, but instead slows its outflow. Vendors often provide discounts for early payment. What is the formula to determine the effective interest rate if the discount is not utilized?
Sample Paper For Above instruction
Introduction
Effective management of cash flows is vital for healthcare institutions and businesses alike, impacting operational efficiency and profitability. This paper presents detailed calculations and comprehensive explanations for various financial scenarios, including hospital payment timing, investment yields, loan interest rates, and trade credit discounts. Each case provides insights into optimizing cash management strategies and financial decision-making.
Case 1: Hospital Lockbox Arrangement Savings
Community Hospital, with annual net patient revenues of $150 million, faces delayed deposit cycles, averaging six days. The hospital's objective is to reduce this to one day via a lockbox arrangement, thereby improving cash flow. To quantify the financial benefit, we compute the interest savings from faster access to funds and deduct bank fees.
Step 1: Daily Revenue Calculation
Annual revenue = $150 million
Number of days in a year = 365
Daily revenue = $150,000,000 / 365 ≈ $410,958.90
Step 2: Cash Flow Difference Due to Reduced Days
Current delay: 6 days
Proposed delay: 1 day
Difference: 5 days
Incremental available funds = Daily revenue × 5 days ≈ $410,958.90 × 5 ≈ $2,054,794.49
Step 3: Interest Earnings from Investments
Interest rate = 8% per annum
Annual interest on the incremental funds = $2,054,794.49 × 8% ≈ $164,383.56
Step 4: Deduct Bank Fees
Bank fee per month = $2,000
Annual bank fee = $2,000 × 12 = $24,000
Step 5: Net Savings
Net annual savings = Interest earnings – Bank fees = $164,383.56 – $24,000 ≈ $140,383.56
Conclusion:
Implementing the lockbox reduces the collection delay and yields approximately $140,384 annually after accounting for bank fees, emphasizing significant cash flow improvements.
Case 2: Investment Yield Required for Surplus Funds
St. Luke’s Convalescent Center intends to invest $200,000 in securities for three months. Transaction costs amount to $2,200, and they seek a minimum annual yield for the investment to be worthwhile.
Step 1: Total Investment and Transaction Costs
Investment amount = $200,000
Transaction costs = $2,200
Step 2: Effective Funds Invested
Since transaction costs are paid upfront, net amount invested = $200,000 – $2,200 = $197,800
Step 3: Holding Period Returns
Holding period = 3 months = 0.25 years
Step 4: Calculation of Required Yield
Let r be the annual yield needed. The total return over three months must cover transaction costs and provide a positive yield.
Total return over 3 months = net gain = (investment amount × r × 0.25) – transaction costs
Set the break-even condition:
\[
(200,000 × r × 0.25) ≥ 2,200
\]
\[
r ≥ \frac{2,200}{200,000 × 0.25} = \frac{2,200}{50,000} = 0.044
\]
Thus, the minimum annual yield r ≈ 4.4%.
Step 5: Adjusting for transaction costs
Considering the actual invested funds after costs, the required annual yield is approximately 4.4%.
Conclusion:
The investment must earn at least 4.4% per year to offset transaction costs within three months, making investment profitable.
Case 3: Comparison of Bank Loans and Effective Interest Rates
Three loan options are considered: a 10% loan with no balance requirement, a 9% loan with a 20% compensating balance, and a 6% discount loan with a 20% compensating balance. The goal is to determine each loan's effective interest rate.
Loan 1: 10% Annual Interest, No Balance Requirement
Interest rate = 10% straightforward, as no compensating balance or discounts apply.
Loan 2: 9% with 20% Compensating Balance
- Borrowed amount = $1,000,000
- Compensating balance = 20% × $1,000,000 = $200,000
- Usable funds = $1,000,000 – $200,000 = $800,000
Interest paid annually = 9% of $1,000,000 = $90,000
Effective interest rate:
\[
\text{Interest} / \text{Usable funds} = 90,000 / 800,000 = 11.25\%
\]
Loan 3: Discount Loan with 20% Compensating Balance
- Discount rate = 6%
- Discount amount = 20% × $1,000,000 = $200,000
- Loan proceeds = $1,000,000 – $200,000 = $800,000
Interest (discount) paid = 6% of $1,000,000 = $60,000
Effective interest rate:
\[
\text{Interest} / \text{Proceeds} = 60,000 / 800,000 = 7.5\%
\]
Summary:
- Loan 1: 10%
- Loan 2: 11.25%
- Loan 3: 7.5%
Conclusion:
The discount loan with a 20% compensating balance yields the lowest effective interest rate at 7.5%, making it the most economical among the options considered.
Case 4: Effective Interest Rate Without Discount Utilization
Trade credit discounts influence cash management. When a discount is offered for early payment, but the discount is not utilized, understanding the effective interest rate is critical.
Formula:
\[
\text{Effective interest rate} = \frac{\text{Discount %}}{1 – \text{Discount %}} \times \frac{360}{\text{Days beyond discount period}}
\]
Where:
- Discount % is the trade discount offered
- Days beyond the discount period is the number of days late compared to the early payment deadline
Example:
If a 2% discount is offered for payments within 10 days, and payment is delayed to 30 days, the effective interest rate lost by not taking the discount is:
\[
\frac{0.02}{1 – 0.02} \times \frac{360}{30 – 10} = \frac{0.02}{0.98} \times 18 ≈ 0.0204 \times 18 ≈ 0.3672 \text{ or } 36.72\%
\]
Conclusion:
This formula helps determine the true cost of not availing early payment discounts, guiding firms to decide whether to pay early or wait.
Conclusion
Effective cash management involves strategic decisions regarding collection processes, investment opportunities, loan choices, and trade credit utilization. By meticulously calculating potential savings, yields, and interest rates, organizations can optimize their financial performance. Implementing lockbox arrangements, evaluating investment returns, comparing loan options, and understanding trade credit implications are essential practices for sound financial management in healthcare and broader business contexts.
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