8/7/2019 Solution to WC Mgmt Questions

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WCM1. Cost of trade credit

Nominal percentage cost = = 37.24%.

2. Interest rate on borrowed funds = 0.09 + 0.015 = 10.5%.

Cost of unused portion: $4,000,000 0.005 = $ 20,000

Cost of used portion: $6,000,000 0.105 = 630,000

Total cost of loan agreement $650,000

3.

Construct simplified comparative balance sheets and income

statements for the restricted and relaxed policies (In

thousands of dollars):

15% of Sales

25% of Sales

Balance sheet: Restricted

Relaxed

Current assets $ 60.0

$100.0

Fixed assets 100.0

100.0

Total assets $160.0

$200.0

Debt $ 80.0

$100.0

Equity 80.0

100.0

Total liabilities and equity $160.0

$200.0

Income statement:

EBIT $ 36.0

$ 36.0

Interest (10%) (8.0)

(10.0)

EBT $ 28.0

$ 26.0

Taxes (40%) (11.2)

(10.4)

Net income $ 16.8

$ 15.6

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ROE = NI/Equity $16.8/$80 = 0.21

$15.6/$100 = 0.156.

Difference in ROEs = 0.21 - 0.156 = 0.054 = 5.4%.

4. Inventory conversion period (ICP) = .

Annual sales = 12 $2 million = $24 million.

Inventory = 0.5 $2 million = $1 million.

ICP = = 15.2 days.

5.

Old With

Change

ICP = = = 91.25 = = 73.000

+ +

DSO = = 73.00 = 63.875

DP = 35 days -35.00 DP

-35.000

CCC = 129.25 days New

CCC = 101.875 days

Change in CCC = 101.875 129.25 = -27.375 days -27 days.

Net change is 27 days (CCC is 27 days shorter).

6. Calculate each of the three main components of the cash

conversion cycle:

Inventory Conversion period (ICP):

ICP = = = 73 days.

Days sales outstanding (DSO):

DSO = = = 96 days.

Payables deferral period (PDP):

PDP = = = 25 days.

Cash conversion cycle (CCC):CCC = ICP + DSO PDP = 73 + 96 25 = 144 days.

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7. Calculate the net reduction in A/R:

Current A/R = $2,500,000. New A/R with 20% reduction:

$2,500,000 - 0.20($2,500,000) = $2,000,000.

Net reduction in A/R = $500,000.

Calculate the interest savings and net savings:

Interest savings = $500,000(0.11) = $55,000.

Net savings = Interest savings - Annual lockbox cost

= $55,000 - $15,000 = $40,000.

8. Calculate A/P with and without taking discounts:

A/PNo discount = $11,760 30 days = $352,800.

A/PDiscount = $11,760 10 days = $117,600.

Calculate financing amount in notes payable and interest cost. The

firm will need to borrow the difference in notes payable.

$352,800 - $117,600 = $235,200.

The additional interest cost is $235,200 0.10 = $23,520.

Calculate total purchases and discounts lost:

Total purchases = 365 days 12,000 gross purchases = $4,380,000.

Discounts lost = $4,380,000 0.02 = $87,600.

Construct comparative financial statements:

I. Partial balance sheet:

Take Discounts Dont

Take Discounts

(Borrow N/P) (Use Max. Trade Cdt)Difference

Accounts payable $117,600 $352,800

-$235,200

Notes payable (10%) 235,200 -

+235,200

Total current liab. $352,800 $352,800

$ 0

II. Partial income statement:

EBIT* $140,000 $140,000

$ 0Less: Interest 23,520 0

+23,520

Discounts lost 0 87,600

-87,600

EBT $116,480 $ 52,400

+$ 64,080

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Less: Taxes (at 40%) 46,592 20,960

+25,632

Net income $ 69,888 $ 31,440

+$ 38,448

*Any EBIT can be used, since the difference in EBIT from

the two policies is zero.

9. Step 1: Calculate net fixed assets, which will be the same

under either policy.

FA turnover =

4.0 =

NFA = $900,000.

Step 2: Determine total assets under each policy, given the

total assets turnover ratio for each one.

Restricted: Total assets turnover =

2.5 =

TA = $1,440,000.

Relaxed: 2.2 =

TA = $1,636,364.

Step 3: Develop balance sheets for each policy to determine

the debt level.

Restricted

Relaxed

Current assets $ 540,000

$ 736,364

Fixed assets 900,000900,000

Total assets $1,440,000

$1,636,364

Debt $ 720,000

$ 818,182

Equity 720,000

818,182

Total liabilities & equity $1,440,000

$1,636,364

Step 4: Determine interest under each policy:

Restricted: $720,000 0.10 = $72,000.

Relaxed: $818,182 0.10 = $81,818.

Step 5: Calculate the difference in interest expense (the

savings) between the 2 policies:

$81,818 - $72,000 = $9,818.

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Step 1: From the previous problem we can now set up an

income statement for each policy.

Restricted Relaxed

EBIT $150,000

$150,000

Interest (10%) 72,00081,818

EBT $ 78,000 $

68,182

Taxes 31,200

27,273

Net income $ 46,800 $

40,909

Step 2: Calculate ROE using common equity as calculated in

the prior problem for each policy.

Restricted: ROE = Relaxed: ROE == 6.5%. = 5.0%.

Step 3: Calculate the difference in ROEs.

ROE = 6.5% - 5.0% = 1.5%.

11.

From the prior two problems, we know that the ROE for the

relaxed policy is 5%. Now, we need to calculate the new

ROE under the restricted policy.

Step 1: Calculate the new sales and EBIT levels.New sales = $3,600,000 0.85 = $3,060,000.

New EBIT = $150,000 0.90 = $135,000.

Step 2: Calculate the new level of assets under the

restricted policy.

S/TA = 2.5

$3,060,000/2.5 = $1,224,000.

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Step 3: Develop the firms balance sheet under the

restricted policy.

Total assets $1,224,000

Debt $ 612,000

Equity 612,000

Total liabilities & equity $1,224,000

Step 4: Develop the firms income statement under the

restricted policy.

EBIT $135,000

Interest (10%) 61,200

EBT $ 73,800

Taxes (40%) 29,520

Net income $ 44,280

Step 5: Calculate the firms ROE under the restricted

policy.

ROE = NI/E = $44,280/$612,000

ROE = 7.24%.

Step 6: Calculate the difference in ROEs between the 2

policies.

ROE = 7.24% - 5% = 2.24