Cap 8

Copyright © 2005 by The McGraw-Hill Companies, Inc.S-1

2% 360

98% 40 10

2% 360

98% 30 15

2% 360

98% 45 10

3% 360

97% 90 10

Copyright © 2005 by The McGraw-Hill Companies, Inc. S-2

Problems

8-1. Compute the cost of not taking the following cash discounts.

a. 2/10, net 40. b. 2/15, net 30. c. 2/10, net 45. d. 3/10, net 90.

Solution:

Cost of not = Discount % 3 6 0taking a cash discount

100 % Disc. %

F i n ad lu de a t-eD i s c opnetr i o

a. Cost of =lost discount

= 2.04% x 12.00 = 24.48%

b. Cost of =lost discount

c. Cost of =lost discount

d. Cost of =lost discount

= 2.04 % x 24.00 = 48.96%

= 2.04% x 10.29 = 20.99%

= 3.09% x 4.50 = 13.91%


8-2. Delilah’s Haircuts can borrow from its bank at 13 percent to take a cash discount. The terms of the cash discount are 2/15, net 55. Should the firm borrow the funds?

Solution:Delilah’s Haircuts

First, compute the cost of not taking the cash discount and compare this figure to the cost of the loan.

Cost of not Discount %

360

taking a cash discount

100 %

2%

Disc. %

360

final due date

discount

period

98 % 55 15

2.04 % 9 18 .36 %

The cost of not taking the cash discount is greater than the cost of the loan (18.36% vs. 13%). The firm should borrow the money and take the cash discount.

8-3. Your bank will lend you $4,000 for 45 days at a cost of $50 interest. What is your effective rate of interest?

Solution:Effective

rateInterest

Days

in the year (360)

Principal Days

loan is outstandin g

$50 360

$4,000 45

1.25 % 8 10 %

8-4. Your bank will lend you $3,000 for 50 days at a cost of $45 interest. What is your effective rate of interest?

Solution:


Effective

rateInterest

Days

in the year (360)

Principal Days


$45

$3,000360

50

1.5% 7.2 10 .80 %

8-5. I.M. Boring borrows $5,000 for one year at 13 percent interest. What is the effective rate of interest if the loan is discounted?

Solution:I.M. Boring

Effective rate on a Interest

Days

per year (360)

discounted loan Princ.

Int. Days loan is outstandin g

$650

$5,000 $650

360

360

$650 1

$4,350

14 .94 %


8-6. Ida Kline borrows $8,000 for 90 days and pays $180 interest. What is the effective rate of interest if the loan is discounted?

Solution:Ida Kline

Effective rate on a Interest

Days

per year (360)

discounted loan Princ.

Int. Days loan is outstandin g

$180

$8,000 $180

360

90

$180 4

$7,820

2.30 % 4 9.20 %

8-7. Mo and Chris’ Sporting Goods, Inc., borrows $14,500 for 20 days at 12 percent interest. What is the dollar cost of the loan?

Use the formula:

Dollar cost of loan

Amount borrowed Interest

rateDays loan is outstandin g

Solution:Mo and Chris’ Sporting Goods

Days in the

year 360

Dollar cost of loan =Days loan is outstandin g

Amount Borrowed x Interest rate x Days in the year (360)

$14 ,500

$14 ,500

12 %

12 %

20

3601

18

= $14,500 .67% = $97.15


8-8. Sampson Orange Juice Company normally takes 20 days to pay for its average daily credit purchases of $6,000. Its average daily sales are $7,000, and it collects accounts in 28 days.

a. What is its net credit position? That is, compute its accounts receivable and accounts payable and subtract the latter from the former.

Accounts receivable = Average daily credit sales x Average collection periodAccounts payable = Average daily credit purchases x Average payment period

b. If the firm extends its average payment period from 20 days to 35 days (and all else remains the same), what is the firm's new net credit position? Has it improved its cash flow?

Solution:Sampson Orange Juice Company

a. Net credit position = accounts receivable – accounts payable

Accts rec. = Average Daily Credit Purchases x Average PaymentPeriod = $7,000 x 28 = $196,000

Accounts payable = Average Daily Credit Purchases x AveragePayment Period = $6,000 x 20

= $120,000

Net Credit Position = $196,000 – $120,000 = $76,000

b. Accounts Receivable will remain at $196,000Accounts Payable = $6,000 x 35 = 210,000Net Credit Position ($14,000)

The firm has improved its cash flow position. Instead of extending$76,000 more in credit (funds) than it is receiving, it has reversed the position and is the net recipient of $14,000 in credit.


8-9. Maxim Air Filters, Inc. plans to borrow $300,000 for one year. Northeast National Bank will lend the money at 10 percent interest and require a compensating balance of 20 percent. What is the effective rate of interest?

Solution:Maxim Air Filters, Inc.

Effective rate of interest with 20% compensating balance =

Interest rate 10% 10%12.5%

1 C 1 .2 .8

or

Interest Days

of the Year (360)

Principal

Compensati

ng balance

Days


$30 ,000 1

$30 ,0001 12 .5%

$300 ,000

$60 ,000

$240 ,000


8-10. Digital Access, Inc. needs $400,000 in funds for a project.

a. With a compensating balance requirement of 20%, how much will the firm need to borrow?

b. Given your answer to part a and a stated interest rate of 9 percent on the total amount borrowed, what is the effective rate on the $400,000 actually being used?

Solution:Digital Access, Inc.

a. Amount to

be borrowed

Amount

1

needed

C

$400 ,000 $400 ,000

1 .20 .80

$500 ,000

b. $500,000 total amount borrowed 9% Interest rate$ 45,000 Interest

$45,000

$400 ,000

11 .5%

$24 ,000 360 $24 ,000 360

$200 ,000 $40 ,000 360 $160 ,000

360


8-11. Carey Company is borrowing $200,000 for one year at 12 percent from Second Intrastate Bank. The bank requires a 20 percent compensating balance. What is the effective rate of interest? What would the effective rate be if Carey were required to make 12 equal monthly payments to retire the loan? The principal, as used in Formula 8-6, refers to funds the firm can effectively utilize (Amount borrowed – Compensating balance).

Solution:Carey Company

Effective rate of interest with 20% compensating balance =Interest D

aysin the year 360

Principal

Compensati

ng balance

Days


15 %

Installment loan with compensating balance2 Annual no. payments

Interest

Total no. of payments

1 Principal

2 12 $24,000

12 1 $200 ,000 $40,000

$576 ,000 $576 ,00027.69%

13 $160 ,000 $2,080 ,000


8-12. Capone Child Care Centers, Inc., plans to borrow $250,000 for one year at 10 percent from the Chicago Bank and Trust Company. There is a 20 percent compensating balance requirement. Capone keeps minimum transaction balances of $18,000 in the normal course of business. This idle cash counts toward meeting the compensating balance requirement. What is the effective rate of interest?

Solution:Capone Child Care Centers, Inc.

Effective rate of interest =

Interest Days in the year 360

Principal Compensati ng balance Days loan is outstandin g

$25,000 360 $25,00011.47%

$250,000 $32,000 * 360 $218,000

*Compensating Balance = 20% x 250,000 = $50,000Normal Funds = 18,000Restricted Compensating Balance $32,000


8-13. The treasurer for Neiman Supermarkets is seeking a $30,000 loan for 180 days from Wrigley Bank and Trust. The stated interest rate is 10 percent, and there is a 15 percent compensating balance requirement. The treasurer always keeps a minimum of $2,500 in the firm’s checking accounts. These funds count toward meeting any compensating balance requirements. What is the effective rate of interest on this loan?

Solution:Neiman Supermarkets

Effective rate of interest =

Interest *

Days

in the year 360

Principal

Compensati

ng balance

Days


$1,500 3605.36 % 2

*10 .72 %

$30 ,000

$2,000 * *

180

10% $30,000180

360$1,500

**Compensating Balance = 15% x 30,000 = $4,500Normal Funds = 2,500 Restricted Compensating Balance $2,000


8-14. Tucker Drilling Corp. plans to borrow $200,000. Northern National Bank will lend the money at one half percentage point over the prime rate of 8 ½ percent (9 percent total) and requires a compensating balance of 20 percent. Principal in this case refers to funds that the firm can effectively use in the business.

What is the effective rate of interest? What would the effective rate be if TuckerDrilling were required to make four quarterly payments to retire the loan?

Solution:Tucker Drilling Corp.

Effective rate of interest with 20% compensating balance= $18,000/($200,000 – $40,000) = $18,000/$160,000 = 11.25%

Installment Loan with compensating balance2 4 $18,000

$144 ,000 / $800 ,000

18 .0%

5 $160 ,000


8-15. Your company plans to borrow $5 million for 12 months, and your banker gives you a stated rate of 14 percent interest. You would like to know the effective rate of interest for the following types of loans. (Each of the following parts stands alone.)

a. Simple 14 percent interest with a 10 percent compensating balance. b. Discounted interest.c. An installment loan (12 payments).d. Discounted interest with a 5 percent compensating balance.

Solution:

a. Simple interest with a 10% compensating balance

$700 ,000 1

$700

,00015 .56 %

$5,000 ,000

$500 ,000

$4,500 ,000

b. Discounted interest

$700 ,0001

$700 ,00016.28%

$5,000 ,000

$700 ,000 $4,300 ,000

c. An installment loan with 12 payments

2 12 $700,000 $16,800,00025.85%

13 $5,000,000 $65,000 ,000

d. Discounted interest with a 5% compensating balance

$700,000/($5,000,000 – $700,000 – $250,000) = 17.28%


8-16. If you borrow $12,000 at $900 interest for one year, what is your effective interest cost for the following payment plans?

a. Annual payment.b. Semiannual payments. c. Quarterly payments.d. Monthly payments.

Solution:

a. $900/$12,000 = 7.5%

Use formula 8-6 for b, c, and d.

Rate on installment loan =2 Annual no. of payments Interest

Total no. of payments 1 Principal

b. (2 x 2 x $900)/(3 x $12,000) = $3,600/$36,000 = 10.00%

c. (2 x 4 x $900)/(5 x $12,000) = $7,200/$60,000 = 12.00%

d. (2 x 12 x $900)/(13 x $12,000) = $21,600/$156,000 = 13.85%


8-17. Vroom Motorcycle Company is borrowing $30,000 from First State Bank. The total interest charge is $9,000. The loan will be paid by making equal monthly payments for the next three years. What is the effective rate of interest on this installment loan?

Solution:Vroom Motorcycle Company

Rate on installment loan =

2

Annual

no. of

payments

Interest

Total

no. of payments

1 Principal

2 12

36 1$9,000

$30 ,000

$216 ,000

$1,110 ,000

19 .46 %


8-18. Mr. Paul Promptly is a very cautious businessman. His supplier offers trade credit terms of 3/10, net 70. Mr. Promptly never takes the discount offered, but he pays his suppliers in 60 days rather than the 70 days allowed so he is sure the payments are never late. What is Mr. Promptly’s cost of not taking the cash discount?

Solution:Paul Promptly

Cost of not taking a cash discount

Discount

100 %

%

Disc.% Payment

Discount

360 date

p

erio

d

3% 360

100 % 3% 60 10

3.09 % 7.2 22 .25 %

In this problem, Mr. Promptly has the use of funds for 50 extra days (60-10), instead of 60 extra days (70-10). Mr. Promptly’s suppliers are offering terms of 3/10, net 70. Mr. Promptly is effectively accepting terms of 3/10, net 60.


8-19. The Ogden Timber Company buys from its suppliers on terms of 2/10, net 35.Ogden has not been utilizing the discount offered and has been taking 50 days to pay its bills. The suppliers seem to accept this payment pattern, and Ogden’s credit rating has not been hurt.

Mr. Wood, Ogden Timber Company’s vice president, has suggested that the company begin to take the discount offered. Mr. Wood proposes the company borrow from its bank at a stated rate of 15 percent. The bank requires a 25 percent compensating balance on these loans. Current account balances would not be available to meet any of this compensating balance requirement. Do you agree with Mr. Wood’s proposal?

Solution:The Ogden Timber Company

Cost of not taking a cash D i s c %o u n t

3 6 0

discount 1 0%0 D i %s c F.

i nd audl ea t

D i s c po eu rn

2% 3602.04% 9 18.36%

98% 50 10

We use 50 days instead of 35 days as the final due date because Ogden’s suppliers have effectively made this the due date even though the stated due date is 35 days.

Effective rate of interest with a 25% compensating balance requirement:

= Interest rate/(1 – C)= 15%/(1 – .25)= 15%/(.75) = 20%

The effective cost of the loan, 20%, is more than the cost of passing up


the discount, 18.36%. Ogden Timber Company should continue to pay in 50 days and pass up the discount.

Interest rate 15% 15%

1 C 1 .1 .9


8-20. In problem 19, if the compensating balance requirement were 10 percent instead of 25 percent, would you change your answer? Do the appropriate calculation.

Solution:The Ogden Time Company (Continued)

Effective rate of interest with a 10% compensating balance requirement:

16.67%

The answer now changes. The effective cost of the loan, 16.67%, is less than the cost of passing up the discount. Ogden Timber Company should borrow the funds and take the discount.

8-21. Bosworth Petroleum needs $500,000 to take a cash discount of 2/10, net 70. Abanker will loan the money for 60 days at an interest cost of $8,100.

a. What is the effective rate on the bank loan?b. How much would it cost (in percentage terms) if Bosworth did not take the

cash discount, but paid the bill in 70 days instead of 10 days?c. Should Bosworth borrow the money to take the discount?d. If the banker requires a 20 percent compensating balance, how much must

Bosworth borrow to end up with the $500,000?e. What would be the effective interest rate in part d if the interest charge for

60 days were $13,000? Should Bosworth borrow with the 20 percent compensating balance? (There are no funds to count against the compensating balance requirement.)


Solution:Bosworth Petroleum

a. Effective

rate of interest

$8,100

$500,000

360

60

1.62 % 6 9.72 %

b. Cost of lost discount

2% 360

98% 70 10

2.04% 6 12.24%

c. Yes, because the cost of borrowing is less than the cost of losing the discount.

d. $500,000 $500

,000$500 ,000

$625 ,000

Amount needed1 C 1 .20 .80 to be borrowed

e. Effective interest rate

$13,000

$625,000 - 125,000

360

60

$13,000 6

$500,0002.6% 6 15.6%

No, do not borrow with a compensating balance of 20 percent since the effective rate is greater than the savings from taking the trade discount.

8-21. Continued


8-22. Columbus Shipping Company is negotiating with two banks for a $100,000 loan. Bankcorp of Ohio requires a 20 percent compensating balance, discounts the loan, and wants to be paid back in four quarterly payments. Cleveland Bank requires a 10 percent compensating balance, does not discount the loan, but wants to be paid back in 12 monthly installments. The stated rate for bothbanks is 10 percent. Compensating balances and any discounts will be subtracted from the $100,000 in determining the available funds in part a.

a. Which loan should Columbus accept?b. Recompute the effective cost of interest, assuming Columbus ordinarily

maintains $20,000 at each bank in deposits that will serve as compensating balances.

c. How much did the compensating balances inflate the percentage interest costs? Does your choice of banks change if the assumption in part b is correct?

Solution:Columbus Shipping Company

a. Bankcorp of Ohio

Effective interest rate2 4 $10 ,000

$100 ,000

$20 ,000

$10 ,000 4 1

$80 ,000

/ $350 ,000

22 .86 %

Cleveland Bank

Effective interest rate

2 12 $10 ,000

$100 ,000

$10 ,000

12 1

$240 ,000 / $1,170 ,000

20 .51 %

8-22. Continued


Choose Cleveland Bank since it has the lowest effective cost.

b. The numerators stay the same as in part (a) but the denominator increases to reflect the use of more money because balances are already maintained at both banks.

Bankcorp of Ohio

Effective rate = $80,000/($100,000 – $10,000) x 5 = 17.78%

Cleveland Bank

Effective rate = $240,000/($100,000 x 13) = 18.46%

c. The compensating balance assumption changed interest rates as follows:

Bankcorp ClevelandInterest Cost with Comp/Bal. 22.86% 20.51%

Without Comp/Bal. 17.78% 18.46%Difference in cost 5.08% 2.05%

If compensating balances are maintained at both banks in the normal course of business, then Bankcorp of Ohio’s loan becomes cheaper than Cleveland Bank’s loan.


8-23. Texas Oil Supplies sells to the 12 accounts listed below.

Average Age of theReceivable Balance Account over the Last

Account Outstanding YearA............... $ 50,000 35B............... 80,000 25C............... 120,000 47D............... 10,000 15E............... 250,000 35F............... 60,000 51G............... 40,000 18H............... 180,000 60I................ 15,000 43J................ 25,000 33K............... 200,000 41L............... 60,000 28

J & J Financial Corporation will lend 90 percent against account balances that have averaged 30 days or less; 80 percent for account balances between 30 and40 days; and 70 percent for account balances between 40 and 45 days. Customers that take over 45 days to pay their bills are not considered as adequate accounts for a loan.

The current prime rate is 12 percent, and J & J Financial Corporation charges 3 percent over prime to Texas Oil Supplies as its annual loan rate.

a. Determine the maximum loan for which Texas Oil Supplies could qualify. b. Determine how much one month's interest expense would be on the loan

balance determined in part a.

8-23. Continued


Solution:Texas Oil Supplies

a. 0 - 30 days A m ount B $ 80,000D 10,000G 40,000L 60,000

Total 190,000loan % 90%loan $171,000

31 - 40 days A m ount A $ 50,000E 250,000J 25,000

Total $325,000loan % 80%loan $260,000

41 - 45 days A m ount I $ 15,000K 200,000

Total $215,000loan % 70%loan $150,500

Maximum Loan = $171,000 + $260,000 + $150,500 = $581,500

b. Loan balances $ 581,500Interest, 15% annual (1.25% ) per monthOne month’s interest $7,268.75


8-24. The treasurer for Thornton Pipe and Steel Company wishes to use financial futures to hedge her interest rate exposure. She will sell five Treasury futures contracts at $105,000 per contract. It is July and the contracts must be closed out in December of this year. Long-term interest rates are currently 7.4 percent. If they increase to 8.5 percent, assume the value of the contracts will go down by 10 percent. Also if interest rates do increase by 1.1 percent, assume the firm will have additional interest expense on its business loans and other commitments of $60,800. This expense, of course, will be separate from the futures contracts.

a. What will be the profit or loss on the futures contract if interest rates go to8.5 percent?

b. Explain why a profit or loss took place on the futures contracts.c. After considering the hedging in part a, what is the net cost to the firm of

the increased interest expense of $60,800? What percent of this increased cost did the treasurer effectively hedge away?

d. Indicate whether there would be a profit or loss on the futures contracts if interest rates went down.

Solution:Thornton Pipe and Steel Company

a. Sales price, December Treasury bond contract(Sale takes place in July) 5 x $105,000 = $525,000Purchase price, December Treasury bond contract(10% price decline)

.9 x $105,000 = $ 94,500 New Price of T-Bond5 x $94,000 = $472,500 Value of 5 T-Bond Contracts

Sold 5 T-Bond Contracts in July at $525,000Purchased 5 T-Bond Contracts in December at $472,500Profit on futures contracts $ 52,500

b. A profit took place because the value of the bond went down due to increasing rates. This meant the subsequent price was less than the initial sales price.

8-24. Continued


Net Cost $8,300

Increased interest

cost $60 ,800

c. Increased interest cost $60,800Profit from hedging 52,500Net cost $ 8,300

13 .65 %

The net cost is 13.65%. This means 86.35% of the increased interest cost was hedged away.

d. If interest rates went down, there would be a loss on the futures contracts. The lower interest rates would lead to higher bond prices and a purchase price that exceeded the original sales price.


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