Brand Advertising is offered a 3/10 net 40 trade discount by its supplier. In the past Brand has been able to get away with paying for supplies on credit in 60 days. Since it doesn’t have money on hand to take advantage of the discount, it tries to negotiate a loan with Portland State Bank. The amount of $400,000 with a 12% compensating balance and a $6,200 interest charge has been negotiated for the month of May. Brand already maintains a $16,250 balance at the bank. Compute the effective rate of interest on the loan, and the cost of not taking the discount. Should Brand take advantage of the cash discount?

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To compute the effective rate of interest on the loan, we need to calculate the effective interest rate. The formula for effective interest rate is:

Effective Interest Rate = (Interest Paid / Loan Amount) * (365 / Number of Days)

Given information:
Loan Amount = $400,000
Interest Charge = $6,200
Compensating Balance = 12%
Balance already maintained = $16,250

First, we need to calculate the adjusted loan amount after considering the compensating balance:

Adjusted Loan Amount = Loan Amount / (1 - Compensating Balance)
Adjusted Loan Amount = $400,000 / (1 - 0.12)
Adjusted Loan Amount = $400,000 / 0.88
Adjusted Loan Amount = $454,545.45

Now, we can calculate the effective interest rate:

Interest Paid = Interest Charge / (Adjusted Loan Amount - Balance already maintained)
Interest Paid = $6,200 / ($454,545.45 - $16,250)
Interest Paid = $6,200 / $438,295.45

Number of Days = 31 (for the month of May)

Effective Interest Rate = ($6,200 / $438,295.45) * (365 / 31)
Effective Interest Rate = 0.014149 * 11.7741935
Effective Interest Rate = 0.1664 or 16.64%

Next, let's calculate the cost of not taking the discount:

Discount Percentage = 3%
Discount Days = 10
Full Payment Days = 40

Value of Discount = Adjusted Loan Amount * Discount Percentage
Value of Discount = $454,545.45 * 0.03
Value of Discount = $13,636.36

Difference in Days = Full Payment Days - Discount Days
Difference in Days = 40 - 10 = 30

Cost of Not Taking the Discount = (Value of Discount / Adjusted Loan Amount) * (365 / Difference in Days)
Cost of Not Taking the Discount = ($13,636.36 / $454,545.45) * (365 / 30)
Cost of Not Taking the Discount = 0.03 * 12.16666667
Cost of Not Taking the Discount = 0.365 or 36.5%

Should Brand take advantage of the cash discount?

The effective rate of interest on the loan is 16.64%, and the cost of not taking the discount is 36.5%. Therefore, it is more beneficial for Brand to take advantage of the cash discount and pay within the discount period.

To calculate the effective rate of interest on the loan and the cost of not taking the discount, we need to follow these steps:

Step 1: Calculate the effective rate of interest on the loan.
The loan amount is $400,000, and a compensating balance of 12% is required. This means that $400,000 * 12% = $48,000 needs to be kept as a compensating balance, leaving only $400,000 - $48,000 = $352,000 available for use.
The interest charge is $6,200.
To find the effective rate of interest, we need to calculate the interest percentage on the effective loan amount, which is $352,000. So, $6,200 / $352,000 = 0.0175 (or 1.75%).
To convert it into an annual rate, we multiply by 12, which gives us 0.0175 * 12 = 0.21 (or 21%).

Therefore, the effective rate of interest on the loan is 21%.

Step 2: Calculate the cost of not taking the discount.
The trade discount is 3/10 net 40. This means that a 3% discount is offered if the payment is made within 10 days; otherwise, the full amount is due within 40 days.
By not taking the discount, Brand would have to pay the full amount of the supplies after 40 days instead of 60 days, which means they are effectively losing 20 days of credit.
To calculate the cost of not taking the discount, we need to find the annualized cost of the discount.
The cost of the discount is 3%, and the number of days saved is 20.
To find the annualized cost, we use the following formula: (Discount % / (1 - Discount %)) * (365 / (Number of Credit Days - Number of Discount Days)).
Plugging in the values, we get: (0.03 / (1 - 0.03)) * (365 / (60 - 20)) = 0.0492 (or 4.92%).

Therefore, the cost of not taking the discount is 4.92%.

Step 3: Determine if Brand should take advantage of the cash discount.
To decide whether Brand should take the cash discount, compare the cost of not taking the discount (4.92%) to the effective rate of interest on the loan (21%).
If the cost of not taking the discount is less than the effective rate of interest on the loan, it is more beneficial to take the discount. Otherwise, it is better to go with the loan.
In this scenario, the cost of not taking the discount (4.92%) is lower than the effective rate of interest on the loan (21%).
Therefore, Brand should take advantage of the cash discount as it is financially advantageous.

In conclusion, the effective rate of interest on the loan is 21% and the cost of not taking the discount is 4.92%. Brand should take advantage of the cash discount.