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Chapter 6

Credit Policy and Collections

Contents

Evaluating Changes in Credit Policy: The CFTimelineMonitoring CollectionsCollection ProceduresEvaluating the Credit DepartmentInternational Credit ManagementFOCUSED CASE: KIMBALLINTERNATIONAL, INC.Appendix 6A: Sophisticated ReceivablesMonitoring

Techniques

Page 100

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Chapter 6 - Page 101

Answers to Questions:

Answers to Questions: 1. When evaluating credit terms changes one must consider

the effect on dollar profits (and related cash flows), sales effect,receivables effect, and the return on investment effect.Surveyed managers expressed an ability to incorporate creditpolicy risk (default probability, delinquency probability, creditlimits, opportunity cost of funds, and overall cost of capital)when making decisions about credit terms. The incremental

profit approach involves determining the incrementalreceivables investment, the change in per unit as well as totalprofits, and the change in bad debt expense. In contrast, theNPV approach has been formulated so that, with the properdata, one can determine the credit policy alternative with the

largest net present value. By following the capital budgetingapproach to policy evaluation, the manager is assured of selecting the wealth-maximizing alternative.

2. Assumptions: (1) all sales are credit sales; (2) the bad debt

loss rate used for the proposed credit terms is the forecastedaverage of loss rates for new and existing customers and thereis no difference in the loss rate for buyers taking the cashdiscount versus those paying at the end of the credit period; (3)other than the change in receivables investment, the new policydoes not necessitate additional investment outlays for

inventories or fixed assets, nor does it change the variable costratio (VCR); (4) the analyst is able to forecast each of therelevant variables' future values. While the NPV formulation canbe adapted to incorporate violations of Assumptions 1-3,violation of the fourth assumption creates difficulties.Probabilistic sales reactions would be difficult to specify for sucha dramatic change from industry standards, especially if none of the competitors follow suit.

3. DSO and receivables turnover are sensitive to recent sales

patterns and are reliable measures of a changing collection

experience only if the credit sales patterns for current andpreceding periods are identical. Second, the measures give quitedifferent readings depending on whether the measures arefigured from monthly, quarterly, or annual data. The agingschedule is likewise plagued with a sensitivity to the salespattern, even if collection rates are stable.

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4. According to Equation 6-11 (or 6-9, which can be solved for A/R), a companys balance sheet investment in receivables is equal to daily credit sales multiplied byDSO. Any increase in DSO increases the necessary investment in receivables,and any reduction in DSO (say through better collections) frees up receivables onthe balance sheet.

5. Uncollected balance percentages accurately depict a

company's collection experience, even when sales arechanging. They are not sensitive to the period over which theyare being calculated because uncollected balance percentagesare always linked back to the month in which the unpaid creditsales originated.

6. Surveyed managers prefer the aging schedule, with DSOalmost as popular, and accounts receivable turnover (whichequals 365/DSO) utilized by some managers. Perhaps a better

measure, such as weighted DSO or uncollected balancepercentages, will show up on the list in future surveys. 7. Uncollected balances for each month are divided by the credit

sales in the month in which the receivables originated. To drawconclusions regarding trends in the collection pattern, thebalances are then compared to the comparable month-earlier(or where sales are very seasonal, year-earlier) percentages.

This avoids the biases present with DSO and the aging schedule,as noted in the answer to 6-4 (above).

8. The payment index represents an overall index and checksaggregate collection experience. Mathematically, it is the sumof each month's uncollected balance percentage. If this numberincreases, we would conclude that a greater percentage of previous months' credit sales remains uncollected. While highernumbers indicate deteriorating and/or poor collection ability, theabsolute number carries no meaning.

9. Customers that are delinquent in payments may be

experiencing temporary problems or have simply overlooked ormisplaced the invoice. The credit manager can then indicate his

understanding of the situation and make sure an understandingis gained about when the payment will be forthcoming. If necessary, the seller could renegotiate the terms, stressing thatthe revised terms must be met. The credit manager should notalienate the customer and be understanding of any mailingproblems or other circumstances.

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10. The initial contact with the customer is made within ten daysof delinquency. A statement of account is sent to the customer,and a copy of the unpaid invoices may also be sent. A reminderletter may be followed up by phone or even personal contact,with referral to a collection agency and/or legal action as a last

resort. 11. Companies are more aggressive in their collection effort when

their level of accounts receivable grow relatively large.Companies behave as if they understand the good will tradeoff when selecting their collection methods. Companies usetechniques such as garnishment (creditors have amounts owedtaken out of the delinquent payor's wages), which are veryeffective in collecting amounts owed.

12. The main differences faced by US credit managers when

selling on credit abroad include complications caused byexchange rate changes, arbitrariness of customer paymentbehavior, and the legal and economic environment. Forexample, inflation and devaluation in a foreign country reducethe dollar value of receivables denominated in that countryscurrency. Credit histories and bank references may also bedifficult to obtain. Managing the entire cash flow timeline andautomating the credit process aid the credit manager in creatingshareholder value from foreign credit sales.

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1. When evaluating credit terms changes one must consider the effect on dollar profits (and related cash flows), sales effect, receivables effect, and the return oninvestment effect. Surveyed managers expressed an ability to incorporate credit

policy risk (default probability, delinquency probability, credit limits, opportunitycost of funds, and overall cost of capital) when making decisions about creditterms. The incremental profit approach involves determining the incrementalreceivables investment, the change in per unit as well as total profits, and thechange in bad debt expense. In contrast, the NPV approach has been formulatedso that, with the proper data, one can determine the credit policy alternative withthe largest net present value. By following the capital budgeting approach to

policy evaluation, the manager is assured of selecting the wealth-maximizingalternative.

2. Assumptions: (1) all sales are credit sales; (2) the bad debt loss rate used for the proposed credit terms is the forecasted average of loss rates for new and existingcustomers and there is no difference in the loss rate for buyers taking the cashdiscount versus those paying at the end of the credit period; (3) other than thechange in receivables investment, the new policy does not necessitate additionalinvestment outlays for inventories or fixed assets, nor does it change the variablecost ratio (VCR); (4) the analyst is able to forecast each of the relevant variables'future values. While the NPV formulation can be adapted to incorporateviolations of Assumptions 1-3, violation of the fourth assumption createsdifficulties. Probabilistic sales reactions would be difficult to specify for such adramatic change from industry standards, especially if none of the competitorsfollow suit.

3. DSO and receivables turnover are sensitive to recent sales patterns and arereliable measures of a changing collection experience only if the credit sales

patterns for current and preceding periods are identical. Second, the measuresgive quite different readings depending on whether the measures are figured frommonthly, quarterly, or annual data. The aging schedule is likewise plagued with asensitivity to the sales pattern, even if collection rates are stable.

4. According to Equation 6-11 (or 6-9, which can be solved for A/R), a companys balance sheet investment in receivables is equal to daily credit sales multiplied byDSO. Any increase in DSO increases the necessary investment in receivables,and any reduction in DSO (say through better collections) frees up receivables onthe balance sheet.

5. Uncollected balance percentages accurately depict a company's collectionexperience, even when sales are changing. They are not sensitive to the periodover which they are being calculated because uncollected balance percentages arealways linked back to the month in which the unpaid credit sales originated.

6. Surveyed managers prefer the aging schedule, with DSO almost as popular, andaccounts receivable turnover (which equals 365/DSO) utilized by some managers.Perhaps a better measure, such as weighted DSO or uncollected balance

percentages, will show up on the list in future surveys.

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7. Uncollected balances for each month are divided by the credit sales in the monthin which the receivables originated. To draw conclusions regarding trends in thecollection pattern, the balances are then compared to the comparablemonth-earlier (or where sales are very seasonal, year-earlier) percentages. Thisavoids the biases present with DSO and the aging schedule, as noted in theanswer to 6-4 (above).

8. The payment index represents an overall index and checks aggregate collectionexperience. Mathematically, it is the sum of each month's uncollected balance

percentage. If this number increases, we would conclude that a greater percentage of previous months' credit sales remains uncollected. While higher numbers indicate deteriorating and/or poor collection ability, the absolute number carries no meaning.

9. Customers that are delinquent in payments may be experiencing temporary problems or have simply overlooked or misplaced the invoice. The creditmanager can then indicate his understanding of the situation and make sure anunderstanding is gained about when the payment will be forthcoming. If necessary, the seller could renegotiate the terms, stressing that the revised termsmust be met. The credit manager should not alienate the customer and beunderstanding of any mailing problems or other circumstances.

10. The initial contact with the customer is made within ten days of delinquency. Astatement of account is sent to the customer, and a copy of the unpaid invoicesmay also be sent. A reminder letter may be followed up by phone or even

personal contact, with referral to a collection agency and/or legal action as a lastresort.

11. Companies are more aggressive in their collection effort when their level of accounts receivable grow relatively large. Companies behave as if theyunderstand the good will tradeoff when selecting their collection methods.Companies use techniques such as garnishment (creditors have amounts owedtaken out of the delinquent payor's wages), which are very effective in collectingamounts owed.

12. The main differences faced by US credit managers when selling on credit abroadcomplications casused by exchange rate changes, arbitrariness of customer

payment behavior, and the legal and economic environment. For example,inflation and devaluation in a foreign country reduce the dollar value of receivables denominated in that countrys currency. Credit histories and bank references may also be difficult to obtain. Managing the entire cash flowtimeline and automating the credit process aid the credit manager in creatingshareholder value from foreign credit sales.

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TEACHING NOTES:1). Consider adding thoughts on discounting in general being a

poor mechanism to move cash flows forward.2). Incentives backwards.3). Thoughts on estimation of credit administration and

collection costs. Most examples here are too high to bereal. Distinguishing between accounting and marginal costs.

Solutions to Problems: Chapter 6

1. Norton Wrench - credit standards tightening.Current ProposedTerms (E) Terms (N)

Sales per 365-day year $275,000 $255,000Sales per day, S $753.42 $698.63Sales growth rate, g -7.27%Up-front Variable Cost Ratio (VCR) 70.00% 70.00%Collection expenses (EXP) at DSO 1.25% 1.45%Bad debt expense ratio, b , at DSO 7.00% 7.00%Discount percent, d 0 0Discount period, days 0 0Proportion taking discount, p 0 0

Non-discount period, days 56 56k = company's annual nominal cost of capital 15%i = daily cost of capital 15% / 365 = 4.1096%

Note: an annual nominal cost of 15% compounded daily implies an annualeffective cost of { [ (1 + .15/365)^365 ] - 1 } * 100 = 16.18% per year.

a.) Cashflow timeline under current termsDay 0 Day 56---|-------------------------------------------------------------------|------------------

>

Variable Costs = VCR * sales / day $753.42 cash collected / day= (0.70) * ($753.42) ($9.42) EXP / day = 1.25% *$753.42($527.40) = PV cash out flow / day ($52.74) bad debt loss/day = 7% *

$753.42$691.27 total cash in flow / day

|$691.27 * 1 / [ 1 + (0.15/365)(56) ] using simple interest |

$675.72 = PV of cash in flow / day | NPV = $675.72 - $527.40 = $148.32 per day from current terms

In terms of the Ze formula Current Terms1st term PV from discount period $0.00 no discount period2nd term PV from credit period $684.92 = $753.42 -

$52.74

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discounted from Day 56

3rd term PV variable costs ($527.40) = 70%*$753.42 at Day0

4th term PV credit expenses ($9.21) = 1.25% * $753.42discounted from Day 56

Ze =$148.32 = NPV per day of current termsNote: The 2nd term subtracts bad debts from cash collections.

b.) Cashflow timeline under proposed termsDay 0 Day 56---|---------------------------------------------------------------------|----------------

->

Variable Costs = VCR * sales / day $698.63 cash collected / day

= (0.70) * ($698.63) ($10.13) EXP / day = 1.45% *$698.63

($489.04) ($48.90) bad debt loss/day = 7% *$698.63

= PV of cash out flow / day $639.60 total cash in flow /day

|$639.60 * 1 / [ 1 + (0.15/365)(56) ] using simple interest |$625.21 |= PV of cash in flow per day

NPV = $625.21 - $489.04 = $136.17 per day from proposed terms

In terms of the Zn formula Proposed Terms1st term PV from discount period $0.00 no discount period2nd term PV from credit period $635.11 = $698.63 - $48.90

discounted from Day 563rd term PV variable costs ($489.04)=70% VCR*$698.63 at day

04th term PV credit expenses ($9.90)= 1.45% EXP

*$698.63

discounted from Day 56Zn = $136.17 = NPV / day of proposed terms

Therefore, Z = Zn - Ze = $136.167 - $148.32 = ($12.15)Note: The 2nd term subtracts bad debts from cash collections.

c.) Overall Value Effect ( NPV) NPV = Z / I = - ($12.15 / 15%) * 365 = ($29,571.27)This is the overall value effect assuming the daily NPV lasts indefinitely.

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d.) Non-financial considerationsHow customers react to the change will be important. While the estimate is thatthe firm will lose about $30,000, the loss might be much greater, especially if competitors don't change.

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2. EvansGilbert Knitwear - credit period lengthening.

Current ProposedTerms (E) Terms (N)

Sales per 365-day year $100,000,000 $105,000,000Sales per day, S $273,972.60 $287,671.23Sales growth rate, g 5%Up-front Variable Cost ratio (VCR) 65.00% 65.00%Collection expenses (EXP) at DSO 2.00% 2.50%Bad debt expense ratio, b , at DSO 24.500%34.500%Discount percent, d 0.00% 0.00%Discount period, days 0 0Proportion taking discount, p 0.00% 0.00%

Non-discount period, days 42 52k = company's annual nominal cost of capital 12%i = daily cost of capital = 12% / 365 0.0003288

Cashflow timeline under current termsDay 0 Day 42---|--------------------------------------------------------------------------|------------>Variable Costs = VCR * sales / day $273,972.60 cash collected / day= (0.65) * ($100 million) / 365 ($5,479.45) EXP/day = 2.5%

*$273,972.60($178,082.19) ($ 6,849.3210,958.90 ) bad debt loss /

day= PV of cash out flow per day = 2.54 % *

$273,972.60 $261,643.8457,534.25 totalcash in flow / day

|$261,643.8457,534.25 * 1 / [ 1 + (0.15/365 * 42) ] simple interest |$258,080.214,026.59 |= PV of cash in flow /day

NPV = $254,026.59258,080.21 - $178,082.19 = $7 9,998.025,944.4 per dayfrom current terms

In terms of the Ze formula Current Terms1st term PV from discount period $0.00 no discount period2nd term PV from credit period $259,431.41= $273,972.60 -

$6,849.3210,958.90discounted from Day 42

3rd term PV variable costs ($178,082.19) = 65% * $273,972.60 at Day0

4th term PV credit expenses ($5,404.82) = 2% *$273,972.60

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discounted from Day 42Ze = $79,998.025,944.40 = NPV per day of current

termsNote : the 2nd term subtracts bad debt costs from collections.

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Cashflow timeline under proposed termsDay 0 Day 52---|-------------------------------------------------------------------------|----------

->

Variable Costs = VCR * sales / day $287,671.23 cash collected / day= 65% * $105 million = $105 million / 365 days($186,986.30) ($7,191.78) EXP / day = 2.5% *

$287,671.23= PV of cash out flow / day ($ 7,191.7811,506.85 ) bad debt loss /

day= 2.54 % *

$287,671.23$268,972.60 total cash in flow / day

|$273,287.6768,972.60 * 1 / [ 1 + (0.12 / 365 * 52) ] simple interest |$2684,694.10451.57 |= PV of cash in flow / day

NPV = $268,694.10 264,451.65 - $186,986.30 = $ 77,465.381,707.80

In terms of the Zn formula Proposed Terms1st term PV from discount period $0.00 no discount period2nd term PV from credit period $271,522.46 = $287,671.23 -

$7,191.7811,506.85 bad debt discounted from Day

52

3rd term PV variable costs ($186,986.30)= 65% VCR *$287,671.23

at Day 04th term PV credit expenses ($7,070.89) = 2.5% EXP *

$287,671.23discounted from Day 52 Zn =

$81,707.8077,465.27 = NPV / day of proposed termsNote: the 2nd term subtracts bad debt costs from cash collections

a.) Calculation of Z, the one day change in valueTherefore, Z = Zn - Ze = $ 81,707.877,465.27 - $79,998.02 75,944.40 =$1,520.871,709.78

b.) Calculation of the overall value effect NPV = Z / i = ( $ 1,709.78 1,520.86 / 0.12 ) * 365 =

$4,625,964.455,200,580.83

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This is the overall value effect assuming the daily NPV lasts indefinitely.

c.) The credit period decisionYes, we would recommend lengthening the credit period since Z is positivewhich means that shareholder wealth would increase, assuming our forecastswere correct.

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d.) Effect of revised "new terms" bad debt loss rate.Cashflow timeline under proposed terms with 3.58% bad debt loss rate.Day 0 Day 52---|--------------------------------------------------------------------------|-------------->Variable Costs = VCR * sales / day $287,671.23 cash collected / day= 65% * $105 million = $105 mil / 365 days($186,986.30) ($7,191.78) EXP / day = 2.5% *

$287,671.23($23,013.7010,068.49 ) bad

debt loss / day= 3.58 % *

$287,671.23= PV of cash out flow / day $ 257,465.75270,410.96 total

cash in flow / day|

$270,410.96 257,465.75 * 1 / [ 1 + (0.12 / 365 * 52) ] simple interest |$26553 ,865138 .7513 |= PV of cash in flow / day

NPV = $265,865.75253,138.13 - $186,986.30 = $ 78,879.4566,151.8 per dayfrom proposed terms

Z = Zn - Ze = $ 78,879.4566,151.83 - $75,944.40 =($9,7 3592 .0557 ) per day

No, the recommendation does not change. One would stillno longer adviselengthening terms, as this would indecrease forecasted shareholder

wealth.

3. J. James Book PublishersA. Walton -- cash discount consideration.


Sales per 365-day year $250,000,000 $250,000,000Sales per day, S $684,931.51 $684,931.51Sales growth rate, g 0%Up-front Variable Cost Ratio (VCR) 60.00% 60.00%Collection expenses (EXP) at DSO 52.00%41.00%Bad debt expense ratio, b , at DSO 3.00% 3.00%Discount percent, d 0.00% 3.00%Discount period, days 0 10Proportion taking discount, p 0.00% 40.00%

Non-discount period, days 40 40k = company's annual nominal cost of capital 10%i = daily cost of capital = 10% / 365 0.0002740

0.0002740

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Cashflow timeline under current termsDay 0 Day 40---|-------------------------------------------------------------------------|--------------

->Variable Costs = VCR * sales / day $684,931.51 cash collected / day= (0.60) * ($250 million) / 365 ($ 34,246.5813,698.63 ) EXP / day = 52.0% *

$684,931.51($410,958.90) ($20,547.95) bad debt loss / day= PV of cash out flow / day = 3.0% * $684,931.51

$630,136.9850,684.93 totalcash in flow / day

|$630,136.98 650,684.93 * 1 / [ 1 + (0.10/365 * 40) ] simple interest |$623,306.2343,631.44 |= PV of cash in flow per day

NPV = $623,306.23 643,631.44 - $410,958.90 = $ 232,672.53212,347.33 per day from current terms

In terms of the Ze formula Current Terms1st term PV from discount period $0.00 no discount period2nd term PV from credit period $657,181.57 = $684,931.51 -

20,547.95discounted from Day 40

3rd term PV variable costs ($410,958.90) = 60% * $250 million /365

at Day 0

4th terms PV credit expenses ($ 34,246.5813,550.14 ) = 52%*$684,931.51discounted from Day 40

Ze =$212,347.33 232,672.53 = NPV per day of current terms

Note: The 2nd term subtracts bad debt costs from cash collections.

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Cashflow timeline under proposed termsDay 0 Day 10 Day 40---|------------------------------------------|--------------------------------------|------

->VCR * sales / day $273,972.60 = 0.4 * $250 mil/365 collections w/o discount= 0.60 * $250 M / 365 $265,753.42 = $273,972.60 * 0.97 (after discount of 3%)($410,958.90) $0.00 = credit collection expenses at Day 10= PV of cash out flow ($7,972.60)= 0.03 * $265,753.42 bad debt losses

per day (based on after -discount cash collections)$257,780.82 = total cash in flow/day from discount period

| |$257,780.82 at Day 10 | $410,958.90=cash / day=60%*250mil/365* 1 / [1+ (.10 / 365 * 10)] | ($27,397.266,849.32 )=EXP/day=( 41%)

($410,958.90)$257,076.50 | + $273,972.60)= PV of cash in flow / day (based on before -discount cash flow

at Day 10 plus cash flow at Day 40)

($12,328.77) = bad debt loss / day

= 0.03 * $410,958.90$371,232.8791,780.82 = total cashin flow/day from non-discount period

|$371,232.87 391,780.82 * 1 / {[ 1 + (0.10/365 * 40) ]}

|$367,208.6787,533.88

|

= PV of cash in flow / day

NPV = $257,076.50 + $367,208.67 387,533.9 - $410,958.90 =$213,326.2733,651.47

per day from proposedterms

In terms of the Zn formula Proposed Terms1st term PV of discount period $257,076.50 = $265,753.42 -

$7,972.60discounted from Day 10

2nd term PV from credit period $394,308.94 = $410,958.90-12,328.77discounted from Day 40

3rd term PV variable costs ($410,958.90)= 60% * $250 million /365

at Day 04th terms PV credit expenses ($27,100.276,775.07 ) = 41% *

$410,958.90

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+ $273,972.60)discounted from Day 40

Zn = $213,326.2733,651.47 = NPV per day of currentterms


a.) Calculating the one-day change in valueTherefore, the one-day change in value related to the proposed terms isZ = Zn - Ze = $ 213,326.27 233,651.47 - $212,347.33 232,672.53 = $978.94

per day

b.) Calculating the change in daily net present value NPV = Z / I = $978.94 / 0.10 * 365 = $3,573,137.41This is the overall (very positive) value effect assuming the daily NPV lastsindefinitely.

c.) RecommendationYes, A. Walton J. James should initiate the cash discount since it will increaseshareholder wealth assuming the forecasts are correct.

d.) The optimal cash discount percent.Using the Hill-Riener optimal cash discount formula, the optimal cash discountis: d* = [ (1 - (1 + i)^(DPn - CPn) ] / 2 = 0.4092% from Equation 6-8 in thetext.

Since this is less than 1/2 of 1%, on an integer basis it rounds to zero percent.Thus, no cash discount would be implemented if this model is used. Caution thestudents that the solution has some amount of inaccuracy because of the varying(decreasing) EXP which violates the assumptions of the Hill-Riener formula.

4. The Hill and Reiner one-period model produces the following estimates:

D* = [1 (1 + i )(DP N CP N ) ] / 2

DP CP I Opt. Disc.4. a). 5 75 0.000411 1.4176%b). 10 30 0.000329 0.3279%

c). 10 45 0.000493 0.8554%d). 10 30 0.000603 0.5989%

Teaching Note: In general, these are not very meaningful results. Students should bedirected to footnotes 14, 15, and 16 in the text for a fuller understanding of the process andan explanation for the unrealistically low estimations that this formula produces.

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5. Flying High Gliders - credit lengthening using compound interest. (Thissame credit period lengthening problem using simple interest appears on pp. 179-180 of the text.)


Sales per 365-day year $30 million $35 millionSales per day, S $82,192 $95,890Sales growth rate, g 16.67%Up-front Variable Cost Ratio (VCR) 70.00% 70.00%Collection expenses (EXP) at DSO 2.00% 2.50%Bad debt expense ratio, b , at DSO 5.00% 6.00%Discount percent, d 0.00% 0.00%Discount period, days 0 0Proportion taking discount, p 0.00% 0.00%

Non-discount period, days 45 68k = company's effective annual cost of capital 14%i = daily compounded cost of capital = (1+k)^(1/365)1 0.035905%

Note: If k had been a nominal (APR) rate, then we would have found the dailyrate by using the formula 0.14 / 365 = 0.038356% / day which would have

produced an annual effective rate (EAR) of [(1.00038356)^365)-1]*100 =15.02%.

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a.) Cashflow timeline under current termsDay 0 Day 68---|--------------------------------------------------------------------------|-----------

->Variable Costs = VCR * sales / day $82,191.78 cash collected / day= 0.70 * $82,191.78 ($1,643.84) EXP / day = 2%

*$82,191.78($57,534.25) ($4,109.59) bad debts = 5% *

$82,191.78= PV cash out flow / day $76,438.36 total cash in flow /

day|

$76,438.36 * 1 / [ 1.00035905^45 ] using simple interest |$75,213.48 |= PV of cash in flow per day

NPV = $75,213.48 - $67,123.3 =$17,679.23 per day from current terms

In terms of the Ze formula Current Terms1st term PV from discount period $0.00 no discount period2nd term PV from credit period $76,830.97 = $82,191.78 -


3rd term PV variable costs ($57,534.2)= 70% * $82,191.78 at Day0

4th term PV credit expenses ($1,617.49) = 2% * $82,191.78discounted from Day 45

Ze = $17,679.23 = NPV per day of current termsNote: The 2nd term subtracts bad debt costs from cash collections.

Cashflow timeline under proposed termsDay 0 Day 68---|-----------------------------------------------------------------------------|----------

->Variable Costs = VCR * sales / day $95,890.41 cash collected / day= (0.70) * ($95,890.41) ($2,397.26)EXP / day = 2.5% *

$95,890.41 ($67,123.29) ($5,753.42)bad debt loss/ day

= PV cash out flow / day = 6% * $95,890.41$87,739.73 total cash in flow / day

|$87,739.73 * 1 / [ 1.00035905^68 ] compound interest |$85,623.86 |= PV of cash inflow / day

NPV = $85,623.86 - $67,123.29 = $18,500.58 per day from current terms

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In terms of the Zn formula Proposed Terms1st term PV from discount period $0.00 no discount period2nd term PV from credit period $87,963.31= $95,890.41 -


3rd term PV variable costs ($67,123.29)= 70% * $95,890.41 at Day0

4th term PV credit expenses -$2,339.45= 2.5% *$95,890.41

discounted from Day 68Zn = $18,500.58 = NPV per day of current termsZ = Zn-Ze = $821.34


b.) Effect on one-day value change from compound vs. simple interest

The one-day value change from lengthening the credit period is higher than the$778.93 using simple interest.

c.) Change in NPV NPV = Z /i = $821.34 / 0.035905% = $2,287,575.32The overall value effect is higher than the $2,030,579 found using simple interest.Again, this assumes the effect lasts indefinitely.

d.) Reason for differences in answersUsing the simple interest calculations will understate the value impact of thedecision. Compounding is the more appropriate procedure. It takes a larger

simple interest rate, compared with a compound rate, to arrive at the same FV.

65. Marvelous Siegel Apparel Mills - cash discount decision with daily compound interest versus simple interest .


Sales per 365-day year $20,000,000 $20,600,000Sales per day, S $54,794.52 $56,438.36Sales growth rate, g 3%Up-front Variable Cost Ratio (VCR) 60.00% 60.00%Collection expense (EXP) at DSO 4.00% 4.00%Bad debt expense, b, at DSO 3.00% 2.50%Discount percent, d 0.00% 2.00%Discount period, days 0 10Proportion taking discount, p 0.00% 40.00%

Non-discount period, days 35 35k = company's effective annual cost of capital 12.00%i, daily compound cost of capital = [(1+k)^(1/365) - 1] * 100 0.03105%

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Cashflow timeline under current termsDay 0 Day 35---|------------------------------------------------------------------------------------|---

->Variable Costs = VCR * sales / day $54,794.52 cash collected / day= (0.60) * ($54,794.52) ($2,191.78) EXP / day = 4% *

$54,794.52($32,876.71) ($1,643.84) bad debt loss / day= PV of cash out flow per day = 3% * $54,794.52

$50,958.90 total cash in flow / day|

$50,958.90 * 1 / [ 1.0003105^35 ] using compound interest |$50,408.12 |= PV of cash in flow per day

NPV = $50,408.19 - $32,876.71 = $17,531.41 per day from current terms

In terms of the Ze formula Current Terms1st term PV from discount period $0.00 no discount period2nd term PV from credit period $52,576.22= $54,794.52 -


3rd term PV variable costs ($32,876.71)= 60% *$54,794.52

at Day 04th term PV credit expenses ($2,168.09)= 4% *

$54,794.52

discounted from Day 35Ze = $17,531.41 = NPV per day of current terms

Note: the 2nd term subtracts bad debt costs from cash collections.

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Cashflow timeline under proposed termsDay 0 Day 10 Day 35

---|-----------------------------|------------------------------------------|----->

VCR * sales / day $22,575.34 0.4*$20.6 mil/365 collections w/o discount= 0.60 * $20.6 M / 365 $22,123.84 0.4*$20.6 mil / 365 * 0.98 after discount($33,863.01) $0.00 credit collection expenses (EXP)/day at Day

10= PV of cash out flow ($553.10) 0.025 *$22,123.84 = bad debt losses based

per day at Day 0 on an after -discount basis$21,570.74 total cash in flow at Day |

10 from discount period || |

| $33,863.01 0.6 * 20.6 mil /365cash/day

| at Day 35$21,570.74 at day 10 | ($2,257.53) EXP / day = 4% *

$22,575.34* {1 / [ 1 + (0.12/365 * 35)]} | plus 4% * $33,863.01 (basedusing simple interest | on before-discount cash flow$21,503.87 | at Day 10 plus non-discount= PV of cash in flow / day from cash flow at Day 35Day 10 of discount period ($846.58) bad debt loss / day

2.5% * $33,863.01$30,758.90 total cash in flow/day at

Day

35 from non-discount period|

$30,758.90 * 1 / [ 1 + (0.12/365 * 35) ] simple interest |$30,426.45 |= PV of cash in flow / day from day 35

NPV = $30,426.49 + $21,503.88 - $33,863.01 = $18,067.31 per day from proposed terms

In terms of the Zn formula Proposed Terms1st term PV of discount period $21,503.87 = $21,570.74

discountedfrom Day 10

2nd term PV from credit period $32,659.59 = $33,863.01 - $846.58discounted from Day 35

3rd term PV variable costs ($33,863.01)= 70% * $20.6 mil at Day0

4th term PV credit expenses ($2,233.13)= (4%)($33,863.01 +$22,575.34)

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discounted from Day 35Zn = $18,067.31 = NPV per day of current terms

Z = Zn - Ze = $535.89Note: The 2nd term subtracts bad debt costs from cash collections

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a.) Effect on one-day value change from compound vs. simple interestThe one-day value change from lengthening the credit period (using compoundinterest) is now $539.89, lower than the $543.55 found using simple interest. Thecash discount offered more than offsets the lower bad debt costs.

b.) Change in NPV NPV = Z / I = $535.86 / 0.00031053776 = $1,725,699.97The overall value effect is higher than the $1,653,163 found using simple interest.Again,this assumes the effect lasts indefinitely.

c.) Reason for differences in answersThe interesting result is that while the PV of one day's sales is less using the dailycompounding assumption, the value impact for the perpetual horizon is actuallymore. This results from the impact of a lower daily rate over the horizon whichincreases the NPV.

76. Besley, Inc. - aging schedule and DSO for previous 180 days.

UncollectedAmount as

Credit Uncollected Percent of Month Late Sales Amount June 30 A/R January over 90 days $75,000 $5,000 11.90% = $5 K / $42 K February over 90 days $50,000 $5,000 11.90% = $5 K / $42 K March 61-90 days $100,000 $6,000 14.29% =

$6 K / $42 K April 31-60 days $40,000 $6,000 14.29% =

$6 K / $42 K May 0-30 days $45,000 $8,000 19.05% =$8 K / $42 K

June (current) $50,000 $12,000 28.57%=$12 K / $42 K Total credit sales $360,000June 30 A/R Balance: $42,000 100.00%

Age Current 0-30 31-60 61-90 Over 90Month June May April March Feb & Prior Total

A/R $12000 $8,000 $6,000 $6,000 $10,000 $42,000

Percentof Total 28.57% 19.05% 14.29% 14.29% 23.81% 100.00%

Avg. daily sales / 6-month period = sum of sales / 180 days = $360,000 / 180=$2,000 per day

DSO for the six-month period = $42,000 / ($2,000 / day) = 21 daysA/R turnover for the 6-month period = 180 days / 21 days = 8.57 times

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87. Uncollected balance percentages for the Besley, Inc. situation in problem 76.UncollectedBalance

Credit Uncollected Percent (of Month Late Sales Amount credit sales)January > 90 days $75,000 $5,000 6.67% = $5 K / $75 K February > 90 days $50,000 $5,000 10.00% = $5 K / $ 50 K March 61-90 days $100,000 $6,000 6.00% = $6 K / $ 100 K April 31-60 days $40,000 $6,000 15.00% = $6 K / $40 K May 0-30 days $45,000 $8,000 17.78% = $8 K / $45 K June current $50,000 $12,000 24.00% =$12 K / $50 K Total Credit Sales $360,000June 30, AR balance $42,000

Payment Index =79.44%=sum of uncollected balance percents

98 . Recalculation of DSO, A/R Turnover, Aging Schedule, Uncollected Balance

Percentages for Besley, Inc. situation one year later.

The Aging Schedule UncollectedAmount as

Credit Uncollected Percent of Month Late Sales Amount June 30 A/R January over 90 days $100,000 $10,000 11.90% =10K / 84 K February over 90 days $90,000 $10,000 11.90% =10K / 84K March 61-90 days $80,000 $12,000 14.29%

=12K / 84K April 31-60 days $200,000 $12,000 14.29%

=12K / 84K May 0-30 days $100,000 $16,000 19.05%

=16K / 84K June current $150,000 $24,000 28.57%

=24K / 84K Total credit sales $720,000June 30 A/R Balance: $84,000 100.00%

Aging Schedule:Age Current 0-30 31-60 61-90 Over 90Month June May April March Feb & Prior TotalA/R $24,000 $16,000 $12,000 $12,000 $20,000 $84,000Percentof Total 28.57% 19.05% 14.29% 14.29% 23.81% 100.00%

a.) Calculating DSOAvg. daily sales / 6-month period = sum of sales / 180 days = $360,000 / 180

= $4,000 per day

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DSO for the six-month period = $84,000 / $4,000 = 21 days

b.) Calculating accounts receivable (A/R) turnoverA/R turnover for the 6-month period = 180 days / 21 days = 8.57 times

c.) The aging schedule (see above)

d.) Uncollected Balance PercentagesUncollected

BalanceCredit Uncollected Percent (of

Month Late Sales Amount credit sales)January over 90 days $100,000 $10,000 10.00% =$10 K / $100 K February over 90 days $90,000 $10,000 11.11% =$10 K / $90 K March 61-90 days $80,000 $12,000 15.00%

=$12 K / $80 K April 31-60 days $200,000 $12,000 6.00%

=$12 K / $200 K May 0-30 days $100,000 $16,000 16.00%

=$16 K / $100 K June current $150,000 $24,000 16.00%

=$24 K / $150Accounts Receivable Balance = $80,000Payment Index =74.11%=sum of uncollected balance percents

e.) Why the difference in conclusions? Notice that the aging schedule and DSO (and A/R turnover) give the same result

as for the prior year. However, the uncollected balance percentages indicate thata change has occurred. The payment index has dropped. We discover that whenyou look at the uncollected balances in relation to the sales generating the balancethat a larger percent of the sales are collected for the more recent time period.

f.) On-time payments?"Most" are paying on time. The rate of payment is increasing according to theuncollected balance percentage method (74.11% vs. 79.44% a year ago).

g.) How to improve the collection effort.The credit personnel should be very proactive at following up on those customerstaking longer than 30 days to pay. They should determine if the problem is withthe merchandise received, if the customer is unhappy with the product, or if thecustomer is having financial difficulties.

h.) Reduction in A/R turnover from all customers paying on due date.If all customers paid on the due date, i.e., 30 days from the purchase date, thenthe accounts receivable turnover should be 360 / 30 = 12 and the payment indexwould be zero.

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