Provide Detailed Descriptions And Show All Calculatio 436402
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 be the annual savings? 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?
Paper For Above instruction
Introduction
Effective cash management and financing decisions are critical for healthcare organizations and firms alike, impacting liquidity, profitability, and operational efficiency. This paper provides detailed calculations and explanations for multiple scenarios: the potential annual savings from a lockbox arrangement at Community Hospital, the economic viability of investing surplus funds at St. Luke’s Convalescent Center, the true cost of various bank loans considering compensating balances, and the calculation of effective interest rates on early payment discounts offered by vendors. Each scenario underscores core financial principles pertinent to healthcare finance and corporate treasury management.
Community Hospital and Lockbox Arrangements
Community Hospital's annual net patient revenues amount to $150 million. Currently, payments are delayed by six days, which ties up significant working capital and potential investment earnings. The hospital is considering a lockbox service that would reduce this delay to just one day, thereby accelerating cash receipts.
The first step involves calculating the amount of funds currently tied up due to the six-day delay:
\[
\text{Funds tied up} = \frac{\text{Annual revenues}}{365} \times \text{Number of days delayed}
\]
So,
\[
= \frac{\$150,000,000}{365} \times 6 \approx \$2,465,753
\]
This is the approximate daily inflow:
\[
\frac{\$150,000,000}{365} = \$410,959
\]
The reduction from six days to one day frees:
\[
= \$410,959 \times (6 - 1) = \$410,959 \times 5 = \$2,054,795
\]
Assuming the funds are invested at an 8% annual rate, the annual interest earned on this freed-up amount is:
\[
\text{Interest} = \text{Amount} \times \text{Interest rate}
\]
\[
= \$2,054,795 \times 0.08 \approx \$164,384
\]
However, the hospital incurs a bank fee of $2,000 per month, totaling:
\[
= \$2,000 \times 12 = \$24,000
\]
The net annual savings are thus:
\[
\text{Interest savings} - \text{Bank fees} = \$164,384 - \$24,000 \approx \$140,384
\]
This simplifies to the hospital saving approximately $140,384 annually through the lockbox arrangement after considering investment earnings and fees.
Investment Decision for St. Luke’s Convalescent Center
St. Luke’s has surplus funds of $200,000 and seeks to determine the minimum annual yield necessary for the investment to be economically justified, considering transaction costs and the short hold period of three months.
The total cost to purchase and sell securities is $2,200, and securities are held for three months (a quarter of a year). The return must compensate for these transaction costs and provide an attractive annual yield.
The equation for the minimum required yield (\(i_{annual}\)) is derived from:
\[
\text{Net gain} \geq \text{Transaction costs}
\]
Expressed as:
\[
\text{Investment} \times \text{Holding period yield} - \text{Transaction costs} \geq 0
\]
The holding period yield (HPY) for three months:
\[
\text{HPY} = \frac{\text{Future value} - \text{Initial investment}}{\text{Initial investment}}
\]
Annualized, the yield is:
\[
i_{annual} = \left(1 + \frac{\text{Interest for 3 months}}{\text{Principal}}\right)^4 - 1
\]
The net gain over three months, after transaction costs, must be positive:
\[
\text{Principal} \times \text{Quarterly yield} - 2,200 \geq 0
\]
Assuming minimal gain, the quarterly yield \(i_q\):
\[
200,000 \times i_q - 2,200 \geq 0 \Rightarrow i_q \geq \frac{2,200}{200,000} = 0.011 \text{ or } 1.1\%
\]
The annual yield:
\[
i_{annual} = (1 + i_q)^4 - 1 = (1 + 0.011)^4 - 1 \approx 1.0455 - 1 = 0.0455 \text{ or } 4.55\%
\]
Thus, the minimum annual yield must be approximately 4.55% for the investment to be justified.
Comparative Analysis of Bank Loans
Three different loan options are considered for $1,000,000:
1. 10% Loan, No Compensating Balance
Annual interest:
\[
= \$1,000,000 \times 10\% = \$100,000
\]
Interest rate:
\[
= \frac{\$100,000}{\$1,000,000} = 10\%
\]
2. 9% Loan with 20% Compensating Balance
Required compensating balance:
\[
= 20\% \times \$1,000,000 = \$200,000
\]
Funds available to the firm:
\[
= \$1,000,000 - \$200,000 = \$800,000
\]
Interest paid on the total loan:
\[
= \$1,000,000 \times 9\% = \$90,000
\]
Effective interest rate considering the actual funds borrowed:
\[
= \frac{\$90,000}{\$800,000} = 11.25\%
\]
3. 6% Discounted Loan with 20% Compensating Balance
This loan is discounted, meaning interest is deducted upfront:
\[
\text{Discount interest} = 20\% \times \$1,000,000 = \$200,000
\]
Funds received:
\[
= \$1,000,000 - \$200,000 = \$800,000
\]
Interest rate based on the amount actually received:
\[
= \frac{\$200,000}{\$800,000} = 25\%
\]
The effective rate on the discounted loan is approximately 25%, which considerably exceeds the nominal 6% rate, illustrating the high cost of discounted loans with compensating balances.
Effective Interest Rate on Early Payment Discounts
Vendors often offer a discount on early payment, for example 2% if paid within a specified period, typically shorter than the standard credit term. If the discount is not utilized, the effective interest rate is the cost of foregoing the discount relative to the amount paid late.
The formula:
\[
\text{Effective annual interest rate} = \left( \frac{\text{Discount %}}{1 - \text{Discount %}} \right) \times \frac{360}{\text{Difference in days between discount period and full term}}
\]
or more generally:
\[
\text{Effective Rate} = \frac{\text{Discount %}}{\text{Payment amount after discount}} \times \frac{365}{\text{Number of days saved by paying early}}
\]
This reflects the annualized cost of not taking the discount and is crucial in decision-making regarding early payment or cash flow management.
Conclusion
Effective cash flow management, investment evaluation, and understanding of loan costs are fundamental in healthcare finance. The calculations clearly illustrate the importance of timing, transaction costs, compensating balances, and interest rates in financial decision-making. Whether optimizing hospital receivables through lockbox arrangements, assessing investment opportunities, or choosing the most cost-effective financing options, precise calculations and understanding of underlying formulas are essential for informed financial strategies.
References
- Brigham, E. F., & Ehrhardt, M. C. (2017). Financial Management: Theory & Practice (15th ed.). Cengage Learning.
- Ross, S. A., Westerfield, R. W., & Jordan, B. D. (2019). Fundamentals of Corporate Finance (12th ed.). McGraw-Hill Education.
- Ross, S. A., Westerfield, R., Jaffe, J., & Jordan, B. D. (2019). Corporate Finance. McGraw-Hill Education.
- Gitman, L. J., & Zutter, C. J. (2015). Principles of Managerial Finance (14th ed.). Pearson.
- Fabozzi, F. J. (2016). Bond Markets, Analysis and Strategies. Pearson.
- Thomsett, M. C. (2019). The Little Book of Investing Like the Pros. McGraw-Hill.
- Meigs, S. L., & Meigs, R. E. (2014). Financial Accounting: A Business Perspective. Cengage Learning.
- Higgins, R. C. (2018). Analysis for Financial Management. McGraw-Hill Education.
- Kaplan, R. S., & Norton, D. P. (2004). Strategy Maps: Converting Intangible Assets into Tangible Outcomes. Harvard Business Review.
- Bradshaw, M. T. (2014). Business Ratios and Formulas: A Comprehensive Guide. McGraw-Hill Education.