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Harper Engine Company needs $687,000 to take a cash discount of 1.50/15, net 70. A banker will loan the money for 55 days at an interest cost of $20,800.

a. What is the effective rate on the bank loan?
(Use a 360-day year. Do not round intermediate calculations. Input your answer as a percent rounded to 2 decimal places.)

b. How much would it cost (in percentage terms) if Harper did not take the cash discount but paid the bill in 70 days instead of 15 days?
(Use a 360-day year. Do not round intermediate calculations. Input your answer as a percent rounded to 2 decimal places.)

c. Should Harper borrow the money to take the discount?
Multiple choice:
1. No
2. Yes

d. If another banker requires a 10 percent compensating balance, how much must Harper borrow to end up with $687,000?
(Round your answer to 2 decimal places.)

e-1. What would be the effective interest rate in part d if the interest charge for 55 days were $12,600?
(Use a 360-day year. Do not round intermediate calculations. Input your answer as a percent rounded to 2 decimal places.)

e-2. Should Harper borrow with the 10 percent compensating balance requirement?
(There are no funds to count against the compensating balance requirement.)
Multiple choice:
1. No
2. Yes

Answer :

Based on the calculations, Harper should not borrow with the 10% compensating balance requirement since the effective interest rate (10.79%) is higher than the effective rate on the bank loan (72.71%).

a. To calculate the effective rate on the bank loan, we need to determine the interest rate per period.

Interest cost = $20,800

Loan period = 55 days

Loan amount = $687,000

Effective rate = (Interest cost / Loan amount) * (360 / Loan period)

Effective rate = ($20,800 / $687,000) * (360 / 55)

Effective rate ≈ 0.1110 * 6.5455

Effective rate ≈ 0.7271

The effective rate on the bank loan is approximately 72.71%.

b. If Harper did not take the cash discount and paid the bill in 70 days instead of 15 days, we need to calculate the cost as a percentage.

Cost of not taking the discount = (Discount % / (100% - Discount %)) * (360 / (Discount period - Net period))

Discount % = 1.50%

Discount period = 15 days

Net period = 70 days

Cost of not taking the discount = (1.50% / (100% - 1.50%)) * (360 / (15 - 70))

Cost of not taking the discount ≈ 1.51%

The cost, in percentage terms, of not taking the cash discount and paying the bill in 70 days instead of 15 days is approximately 1.51%.

c. Based on the calculations, Yes, Harper should borrow the money to take the discount.

since the effective rate on the bank loan (72.71%) is lower than the cost of not taking the discount (1.51%).

d. Harper must borrow approximately $763,333.33 to end up with $687,000 after the 10% compensating balance requirement.

To determine the loan amount required to end up with $687,000 after the 10% compensating balance requirement:

Loan amount = Desired amount / (1 - Compensating balance %)

Desired amount = $687,000

Compensating balance % = 10%

Loan amount = $687,000 / (1 - 0.10)

Loan amount ≈ $763,333.33

e-1. To calculate the effective interest rate in part d with an interest charge of $12,600:

Effective rate = (Interest cost / Loan amount) * (360 / Loan period)

Interest cost = $12,600

Loan period = 55 days

Loan amount = $763,333.33

Effective rate = ($12,600 / $763,333.33) * (360 / 55)

Effective rate ≈ 0.0165 * 6.5455

Effective rate ≈ 0.1079

The effective interest rate in part d, with an interest charge of $12,600, is approximately 10.79%.

e-2. Based on the calculations, Harper should not borrow with the 10% compensating balance requirement .

since the effective interest rate (10.79%) is higher than the effective rate on the bank loan (72.71%).

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