Problem 16: Unsecured Sources Of Short-Term Loans - John Sav

Problem 16 10 Unsecured Sources Of Short Term Loans John Savage Has

Problem 16-10: Unsecured sources of short-term loans. John Savage has obtained a short-term loan from First Carolina Bank. The loan matures in 180 days and is in the amount of $45,000. John needs the money to cover start-up costs in a new business. He hopes to have sufficient banking from other investors by the end of the next 6 months.

First Carolina Bank offers John two financing options for the $45,000 loan: a fixed-rate loan at 2.5% above prime rate, or a variable-rate loan at 1.5% above prime. Currently, the prime rate of interest is 6.5%, and the consensus forecasts of a group of mortgage economists for changes in the prime rate over the next 180 days are as follows: 60 days from today the prime rate will rise by 0.5%; 90 days from today the prime rate will rise another 1%; 180 days from today the prime rate will drop by 0.5%. Using the forecast prime rate changes, answer the following questions:

1. Calculate the total interest cost over 180 days for a fixed-rate loan.
2. Calculate the total interest cost over 180 days for a variable-rate loan.
3. Which is the lower-interest cost loan for the next 180 days?

Paper For Above instruction

John Savage’s decision to borrow short-term funds for his startup necessitates analyzing the cost implications of two different loan structures: a fixed-rate loan and a variable-rate loan, under forecasted changes in the prime interest rate. Evaluating these options requires an understanding of how interest rates evolve over the 180-day period and how these influence total borrowing costs.

Understanding the Loan Options and Forecasted Interest Rates

The current prime rate is 6.5%, serving as the base for calculating both fixed and variable interest rates. The fixed-rate loan is offered at a rate that is 2.5% above prime, resulting in an initial interest rate of 9.0%. Conversely, the variable-rate loan is set at 1.5% above prime, starting at 8.0%. The forecasted changes in the prime rate over the next 180 days significantly influence the total interest payments for both options.

According to the forecast:

• In 60 days, the prime rate will increase by 0.5%, reaching 7.0%.
• In 90 days, the prime rate will increase by an additional 1%, reaching 8.0%.
• In 180 days, the prime rate will decrease by 0.5%, ending at 7.0%.

Calculating the Fixed-Rate Loan

The fixed-rate loan charges 2.5% above the current prime rate of 6.5%, resulting in an initial fixed interest rate of 9.0%. Under fixed-rate conditions, the rate remains constant throughout the 180 days, regardless of changes in the prime rate forecast. Therefore, the total interest paid is based on this fixed rate over the entire period.

Interest calculation for fixed-rate loan:

Interest rate = 9.0% annually.

Loan amount = $45,000

Duration = 180 days = 180/365 ≈ 0.49315 years.

Total interest = Principal x Rate x Time = $45,000 x 9.0% x 0.49315 ≈ $45,000 x 0.09 x 0.49315 ≈ $1,996.58

Calculating the Variable-Rate Loan

The variable-rate loan's interest rate changes according to forecasted changes in the prime rate, with the additional 1.5% premium applied at each period. Since the prime rate is expected to rise and then fall, the total interest must be calculated by segmenting the 180-day period into the intervals dictated by the forecast and applying the relevant rates to each segment.

Prime rate forecast segments:

• Day 0-60: Prime increases from 6.5% to 7.0% (+0.5%)
• Day 61-90: Prime increases from 7.0% to 8.0% (+1.0%)
• Day 91-180: Prime decreases from 8.0% to 7.0% (−1.0%)

Interest rates for the long-term:

• Days 0-60: Prime = 7.0%, Loan rate = 7.0% + 1.5% = 8.5%
• Days 61-90: Prime = 8.0%, Loan rate = 8.0% + 1.5% = 9.5%
• Days 91-180: Prime = 7.0%, Loan rate = 7.0% + 1.5% = 8.5%

Calculating interest for each segment:

• Segment 1 (Day 0-60): 60 days
• Segment 2 (Day 61-90): 30 days
• Segment 3 (Day 91-180): 90 days

Interest for each segment:

Segment 1: $45,000 x 8.5% x (60/365) ≈ $45,000 x 0.085 x 0.164 code ≈ $629.39

Segment 2: $45,000 x 9.5% x (30/365) ≈ $45,000 x 0.095 x 0.082 ≈ $351.45

Segment 3: $45,000 x 8.5% x (90/365) ≈ $45,000 x 0.085 x 0.246 ≈ $941.00

Total variable interest = $629.39 + $351.45 + $941.00 ≈ $1922.84

Comparison and Conclusion

The total interest costs over 180 days are approximately:

• Fixed-rate loan: $1,996.58
• Variable-rate loan: $1,922.84

Given these calculations, the variable-rate loan costs slightly less in interest over the specified period, primarily due to the forecasted decline in the prime rate near the end of the term. Therefore, based on the forecasted interest rate changes, choosing the variable-rate loan would be financially advantageous for John Savage for this 180-day period.

However, it is important to note that these forecasts inherently carry uncertainty, and actual interest costs could vary, which introduces risk in opting for the variable-rate loan. If John prefers certainty and risk mitigation, the fixed-rate loan could be a more suitable choice despite its marginally higher cost.

References

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