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m. What is the firm's current dollar cost of carrying receivables? What would it be
after the proposed change?
Answer: Current situation: the firm's average daily sales currently amount to $1,000,000/365
= $2,739.73. The DSO is 32 days, so accounts receivable amount to 32($2,739.73) =
n. What is the incremental after-tax profit associated with the change in credit
terms? Should the company make the change? (assume a tax rate of 40
percent.)
New Old Difference
Gross sales $1,000,000
Less discounts 0
Net sales $1,000,000
Production costs 750,000
Profit before credit
Costs and taxes $ 250,000
Credit-related costs:
Carrying costs 7,890
Bad debt losses 20,000
Profit before taxes $ 222,110
Taxes (40%) 88,844
Net income $ 133,266
Answer: The income statements and differentials under the two credit policies are shown
below:
New Old Difference
Gross sales $1,100,000 $1,000,000 $100,000
Less discounts 13,068 0 13,068
Thus, if expectations are met, the credit policy change would increase the firm's
However, the new policy is not riskless. If the firm's customers do not react as
predicted, then the firm's profits could actually decrease as a result of the change.
The amount of risk involved in the decision depends on the uncertainty inherent in the
o. Suppose the firm makes the change, but its competitors react by making similar
changes to their own credit terms, with the net result being that gross sales
remain at the current $1,000,000 level. What would the impact be on the firm's
post-tax profitability?
Answer: If sales remain at $1,000,000 after the change is made, then the following situation
would exist:
Gross sales $1,000,000
Less discounts 11,880
Net sales $ 988,120
p. The brothers need $100,000 and are considering a 1-year bank loan with a
quoted annual rate of 8%. The bank is offering the following alternatives: (1)
simple interest, (2) discount interest, (3) discount interest with a 10%
compensating balance, and (4) add-on interest on a 12-month installment loan.
What is the effective annual cost rate for each alternative? For the first three of
these assumptions, what is the effective rate if the loan is for 90 days, but
renewable? How large must the face value of the loan amount actually be in each
of the 4 alternatives to provide $100,000 in usable funds at the time the loan is
originated?
Answer: 1. With a simple interest loan, they gets the full use of the $100,000 for a year, and
If the loan were for 90 days:
Simple interest. The brothers would have had to pay (0.08/4)($100,000) =
In general, the shorter the maturity (within a year), the higher the effective
cost of a simple loan.
2. On a discount interest loan, the bank deducts the interest from the face amount of
the loan in advance; that is, the bank "discounts" the loan. If the loan had a
Effective rate =
000,92$
000,8$
= 0.087 = 8.7%.
Discount interest. If borrow $100,000 face value at a nominal rate of 8
percent, discount interest, for 3 months, then m = 12/3 = 4, and the interest
payment is (0.08/4)($100,000) = $2,000, so
EARdiscount =
1
000,2$000,100$
000,2$
1
4
Discount interest imposes less of a penalty on shorter-term than on
longer-term loans.
The face value (the amount of the loan required to get the desired level
of usable funds) of the loan is calculated as:
RATE NOMINAL1
REQUIRED FUNDS
02.01
000,100$
3. If the loan is a discount loan, and a compensating balance is also required, then
the effective rate is calculated as follows:
Amount borrowed =
1.008.01
000,100$
= $121,951.22.
0 1
| |
100,000.00
If the loan were for 90 days:
Discount interest with compensating balance. Everything is the same as in #2
above, except that we must add the compensating balance term to the
denominator.
EAR =
1
000,10$000,2$000,100$
000,2$
0.1
4
= (1.0227)4 - 1 = 0.0941 = 9.41%
The face value (the amount of the loan required to get the desired level
of usable funds) of the loan is calculated as:
CB-RATE NOMINAL1
REQUIRED FUNDS
10.008.01
000,100$
i = ?
4. In an installment (add-on) loan, the interest is calculated and added on to the
required cash amount, and then this sum is the face amount of loan, and it is
However, the firm would receive only $100,000, and it must begin to repay
the principal after only one month. Thus, it would get the use of $100,000 in the
