Problems and Questions

1. The following is the balance sheet for Ford Motor Company as of December 31, 1994 (in millions):

Assets Liabilities

Cash $ 19,927 Accounts Payable $ 11,635

Receivables $ 132,904 Debt due within 1 year $ 36,240

Inventory $ 10,128 Other Current Liabilities $ 2,721

Current Assets $ 91,524 Current Liabilities $ 50,596

Fixed Assets $ 45,586 Short Term Debt $ 36,200

Long Term Debt $ 37,490

Equity $ 12,824

Total Assets Total Liabilities $ 137,110

The firm had revenues of $154,951 million in 1994 and cost of goods sold of $ 103,817 million.

a. Estimate the current ratio.

b. Estimate the quick ratio.

c. Estimate the accounts receivable and inventory turnover ratios.

d. Estimate the required financing period.

2. You are analyzing the balance sheet for Bed, Bath and Beyond, a retail firm that sells home furnishings, from February 26, 1995 (in millions):

Assets Liabilities

Cash $ 6.5 Accounts Payable $ 27.5

Receivables $ 0.0 Other Current Liabilities $ 18.6

Inventory $ 108.4

Current Assets $ 118.0 Current Liabilities $ 46.1

Fixed Assets $ 53.8 Long Term Debt $ 16.8

Equity $ 108.9

Total Assets $ 171.8 Total Liabilities $ 171.8

The firm had revenues of $440.3 million in 1994 and cost of goods sold of $249.2 million.

a. Estimate the current ratio.

b. Estimate the quick ratio.

c. Estimate the accounts receivable and inventory turnover ratios.

d. Estimate the required financing period.

3. Assume, in the previous problem, that Bed, Bath and Beyond was able to halve its inventory requirement by adopting better inventory policies. Estimate the following ñ

a. the investment in working capital, after the change.

b. the savings in cash flow that would accrue from this change

How would you estimate the increase in firm value that would arise from the better inventory policy, if revenues at the firm are expected to grow 6% a year forever, and the firm had a cost of capital of 11%?

4. You have been asked to estimate the optimal working capital, as a percent of revenues, for an auto-parts manufacturing firm that currently maintains a net working capital of 10% of revenues. The firm currently has revenues of $10 million and after-tax operating income of $10 million, and it expects the latter to grow 5% a year in perpetuity. The current cost of capital is 11%. The following table provides estimates of growth and costs of capital at different levels of working capital, ranging from 0% to 90%:
70%
5.55%
11.80%
80%
WC as % of Revenue
Expected Growth
Cost of Capital
0%
4.75%
10.90%
10%
5.00%
11.00%
20%
5.20%
11.11%
30%
5.35%
11.23%
40%
5.45%
11.36%
50%
5.50%
11.50%
60%
5.54%
11.65%

a. Estimate the value of the firm at the current working capital ratio.

b. Estimate the optimal working capital policy for this firm.

c. What would the optimal working capital proportion for this firm be if the cost of capital were unaffected by the changes in working capital?

5. You are advising a small retailing firm which is considering a significant change in inventory policy. The firm currently has net working capital of $ 20 million on revenues of $ 100 million; it had net after-tax operating income of $ 5 million. The firm is considering reducing its inventory by 40%, but revenues might be affected adversely by the change. If the expected growth rate in the firmís revenues and operating income is 5% and the cost of capital is 12%, how much would the revenues have to drop for this change in inventory to negatively affect value?

6. The following table summarizes working capital and revenue for the following firms in the chemical industry, as well as information on betas, expected growth, and size.
Firm
Net Working
Expected
Market
Capital
Revenues
Beta
Growth
Value
Arco Chemical $ 579 $ 3,423
0.80
13.00%
$ 4,517
Dow Chemical $ 2,075 $ 20,015
1.25
16.00%
$ 19,398
DuPont $ 3,543 $ 39,333
1.00
17.50%
$ 44,946
Georgia Gulf $ 127 $ 955
1.70
26.50%
$ 1,386
Lyondell Petro $ 264 $ 3,857
1.10
23.50%
$ 2,080
Monsanto $ 2,948 $ 8,272
1.10
11.50%
$ 9,296
Olin Corp. $ 749 $ 2,658
1.00
22.00%
$ 1,205
Sterling Chemical $ 21 $ 701
0.95
43.00%
$ 724
Union Carbide $ 329 $ 4,865
1.30
16.00%
$ 4,653

a. Estimate the average and standard deviation in working capital ratios across these firms.

b. What proportion of the differences in net working capital investments across firms can you explain using the information you have been provided in the table.

c. How would you use this information to estimate the optimal working capital as a percent of revenues for an individual firm?

7. You have been provided with the current assets and current liabilities of a retailing firm each quarter for the last 5 years, together with the revenues in each quarter: 1992 ñ 4 $ 880 $ 460 $ 9,000 1993 ñ 1 $ 550 $ 260 $ 5,400
PeriodCurrent Assets Current Liabilities Revenues
1990 ñ 1 $ 300 $ 150 $ 3,000
1990 ñ 2 $ 325 $ 160 $ 3,220
1990 ñ 3 $ 350 $ 180 $ 3,450
1990 ñ 4 $ 650 $ 300 $ 6,300
1991 ñ 1 $ 370 $ 170 $ 3,550
1991 ñ 2 $ 400 $ 200 $ 4,100
1991 ñ 3 $ 420 $ 220 $ 4,350
1991 ñ 4 $ 755 $ 380 $ 7,750
1992 ñ 1 $ 450 $ 220 $ 4,500
1992 ñ 2 $ 480 $ 240 $ 4,750
1992 ñ 3 $ 515 $ 265 $ 5,200

a. Based on this information, estimate the permanent, seasonal, and transitory components of current assets.

b. How would you propose financing these current assets? Why?

8. You have been asked to estimate the effect of float on a small manufacturing company. Each day the company receives about $5 million in checks from customers and takes 4 days to clear these checks. It pays out $4 million in checks and the recipients generally take 5 days to clear these checks. If the firm faces an interest rate of 10%,

a. Estimate the processing float for the company.

b. Estimate the disbursement float for the company.

c. Estimate the net float for the firm.

d. How much would the net float change if the firm can reduce the number of days it takes to clear checks to 3 days?

e. What would the effect on value of this change be?

9. You have been asked to estimate the optimal cash balance for a firm, that

a. Estimate the optimal using the Baumol model.

b. How would your answer change if the firm were able to earn 3% on cash (i.e., it uses an interest bearing checking account)?

10. Assume that interest rates increase significantly from current levels. What effect would you expect this change to have on optimal cash balances? Why?

11. Miller Electronics has used the Baumol Model to estimate its optimal cash balance to be $ 100 million. Its opportunity cost is 10%, and there is a cost of $ 125 every time marketable securities have to be converted into cash. Estimate the weekly cash usage rate.

12. A firm that has a standard deviation in daily cash flows of $12,000 pays $75 every time it buys or sells securities, and faces a daily interest rate of .0125% is trying to estimate the upper and lower limits for its cash balance.

a. Estimate the spread using the Miller-Orr Model.

b. What will the average cash balance be?

c. How would your answers change if there were a minimum cash balance of $50,000.

13. How would the spread and average cash balance you computed in the previous problem change if the standard deviation doubled? Provide an intuitive rationale for your findings.

14. You are analyzing the inventory policy of HighTech Retail, a retailer of stereo systems. You collect the following information:

a. Estimate the optimal order quantity for this firm.

b. When would you reorder units for this firm? What is your safety inventory?

c. Estimate the average inventory the firm will maintain.

15. A electronics retail firm, that has traditionally required customers to pay cash for items is considering introducing credit sales. The firm currently has revenues of $300,000 and after-tax operating income of $100,000. Without the credit sales, the growth in earnings and cash flows is expected to be 5%, while the cost of capital is 12%. With the introduction of credit sales, there is expected to be a increase in revenues by $ 5 million from $30 million to $35 million. The cost of goods sold will remain at 50% of revenues, and the firm faces a tax rate of 40%. The cost of capital will remain unchanged.

a. Estimate the cash flows associated with introduction of credit sales.

b. Estimate the net present value of the credit sales decision.

16. You are considering offering your customers a 2% discount if they pay cash on their purchases within 10 days; if they do not pay cash, the balance will be due within 50 days. The trade credit deal is 2/10 net 50.

a. Estimate the implied interest rate (annualized) being charged credit customers.

b. Estimate the actual interest rate earned if customers take 100 days to make payment instead of 50 days.

17. A firm, that has an average monthly working capital requirement of $10 million is evaluating two options for financing this requirement:

1. It can borrow $ 12 million long term to cover not only the average requirement but also any seasonal and random requirements that may arise. The interest rate on the borrowing is 9%.

2. It can borrow $ 8 million long term to cover the permanent component of working capital and use a $ 4 million line of credit to cover any seasonal or random changes, which are expected (based on past history) to occur in 4 out of the 12 months of the year. The line of credit will be at 1.5% above the prime rate (which is currently 6.5%), but it requires that the firm maintain a compensating balance of 20%.

a. Estimate the interest cost associated with the first option.

b. Estimate the interest cost associated with the second option.