Add-on-interest Another way of stating interest is with add-on interest, where the total

Add-on-interest Another way of stating interest is with add-on interest, where the total

interest is added to the principal amount of the loan and interest is paid on both the amount borrowed and the interest to be paid on the loan. Used primarily in consumer installment loans, add-on effectively increases the effective cost of the loan.

Consider a loan of $1,000 for five years with 10% add-on interest and the loan is to be paid off in five year-end payments. The funds that are borrowed (available to the borrower) are $1,000 and the “interest”

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is $100 × 5 = $500. The installments are calculated based on a loan principal amount of $1,000 + 500 = $1,500: $1,500/5 = $300 each.

How much is the borrower really paying to borrow $1,000? Let’s restate this loan in more familiar terms:

Present value = $1,000 Number of payments = 5 Amount of each payment = $300

and $1,000 = $300(present value of an annuity for T = 5 and r = ?) The effective annual cost of this loan is r = 15.23%, which is more

than one and one-half times the stated rate of 10%! Compensating Balance

Some financing arrangements require that a balance be maintained in an non-interest-bearing account with the lender. This balance is referred to as a compensating balance because it compensates the lender for mak- ing the loan. Like in the case of a discount loan, this may have the effect of raising the cost of borrowing since you do not have the use of the funds you deposited in this balance for the period of the loan.

The amount of the compensating balance depends on the amount of the loan, ranging from 5% to 20% of the amount of the loan. Once used with nearly all bank loans, the use of compensating balances has declined in the U.S. over the years, replaced with service fees and other direct fees. However, more than two-thirds of U.S. banks still require compensating balances in their lending arrangements.

Let’s see the effective cost of a compensating balance loan. First, suppose you borrow $300,000 for one year from a bank with a single payment loan that requires interest of 10% payable at the end of the year. The cost of this financing is $30,000 or 10%. We don’t have to worry about compounding of interest here since interest is paid at the end of the year.

Now suppose the bank will lend to you on these same terms, with an additional stipulation: you leave 5% of the loan amount (hence, it’s a discount loan) in a non-interest-bearing account for the entire year. What is the cost of the loan now? The cost is more than the 10% since we now are paying 10% of $300,000, but have the use of only 95% of the funds, or $285,000. The effective cost is:

Management of Short-Term Financing

------------------------- Effective cost $30,000 = = 0.1053 or 10.53% per year $285,000

The compensating balance increases the cost of the financing from 10% to 10.53%.

We can generalize the cost of financing with the compensating bal- ance. Let r once again represent the effective cost per period, i represent the stated interest rate per compounding period on the face value of the loan, and b represent the compensating balance as a percentage of the loan face value. Then,

i loan amount r = --------------------------------------- = ------------------------------------------------------- ( ) funds available

costs

( 1 – b ) loan amount ( ) i

(21-4) r = ------------

1 – b Suppose you borrow $500,000 from the bank for three months,

with a nominal annual rate of 12% (compounded every three months), and the bank requires you to maintain a compensating balance for 10% of the loan. Then, the stated quarterly rate is:

i = ----------- =

0.03 or 3% for a three-month period

4 and the compensating balance is b = 10%. The effective cost for a three-

month period is: r = --------------------- 0.03 = 0.0333 or 3.33% per period

– 1 0.10 Since there are four three-month periods in a year, the effective annual

cost of this financing is: EAR = (1 + 0.0333) 4 − 1 = 0.1400 or 14% per year If there were no compensating balance requirement, the effective annual

cost is: EAR = (1 + 0.03) 4 − 1 = 0.1255 or 12.55% per year

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The compensating balance requirement raises the effective annual cost from 12.55% to 14%. We can see the effect of the compensating bal- ance requirement on the effective cost of the loan in Exhibit 21.3, where the cost of the 12% loan is plotted against the compensating balance as

a percentage of the loan face value. The larger the compensating balance percentage, the higher the effective cost of the loan.