Question

Harper Engine Company needs $634,000 to take a cash discount of 2.50/20, net 120. A banker will loan the money for 100 days at an interest cost of $14,700. 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.) Effective rate of interest b. How much would it cost (in percentage terms) if Harper did not take the cash discount but paid the bill in 120 days instead of 20 days? (Use a 360-day year. Do not round intermediate calculations. Input your answer as a percent rounded to 2 decimal places.) Cost of not taking a cash discount c. Should Harper borrow the money to take the discount? O Yes O No d. If another banker requires a 10 percent compensating balance, how much must Harper borrow to end up with $634,000? (Round your answer to 2 decimal places.) Amount to be borrowed

Answer 1

As per the problem, the bill payable within 20 days assuming a cash discount 2.5% is $634,000 (so, $634,000 is 97.5% of the actual billed amount; this would mean that the actual billed amount has to be $650,256.41).

If Harper doesn't make the payment within the first 20 days, it won't be able to avail of this discount and then would have to repay $650,256.41 (as explained above) within the next 100 days (as total payment time available is 120 days from billing date).

Answer a. If banker is charging $14,700 as interest cost for a 100 days loan of $634,000, then the interest rate for 100 days is $14,700 / $634,000 = 2.3186%

Assuming a 360 day year, the Effective rate on the bank loan is = 2.3186% x 360 / 100 = 8.35%

Answer b. If Harper doesn't avail of the cash discount and pays the bill in 120 days instead of 20 days, then the additional payment it would have to make is $650,256.41 - $634,000 = $16,256.41

Another way of looking at this is that it costs Harper $16,256.41 over the next 100 days for not availing the cash discount. So in percentage terms this amounts to $16,256.41 / $634,000 = 2.5641%

Assuming a 360 day year, the Cost of not availing the cash discount is = 2.5641% x 360 / 100 = 9.23%

Answer c. Yes

Whether or not Harper should borrow the money to take the discount purely depends on the effective rate compared to the cost of not availing the cash discount over the 100 day period.

Since effective rate on the bank loan is lower than the percentage cost of not availing the cash discount, Yes, Harper should borrow the money.

Answer d. If another bank requires a 10% compensating balance, this means that Harper would be required to maintain with this bank, a deposit balance equivalent to 10% of the total borrowed amount. As a result, Harper would have to borrow an amount in such a way that, after deducting 10% from this amount, the remaining 90% would account for Harper's loan requirement. That means, 90% of the borrowed amount should amount to $634,000.

Thus the amount that Harper needs to borrow is $634,000 / 90% = $704,444.44