Chapter 6 Credit Policy and Collections

Contents Evaluating Changes in Credit Policy: The CF Timeline Monitoring Collections Collection Procedures Evaluating the Credit Department International Credit Management FOCUSED CASE: KIMBALL INTERNATIONAL, INC. Appendix 6A: Sophisticated Receivables Monitoring Techniques

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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 credit policy risk (default probability, delinquency probability, credit limits, opportunity cost of funds, and overall cost of capital) when making decisions about credit terms. The incremental profit approach involves determining the incremental receivables investment, the change in per unit as well as total profits, and the change in bad debt expense. In contrast, the NPV approach has been formulated so that, with the proper data, one can determine the credit policy alternative with the largest net present value. By following the capital budgeting approach to policy evaluation, the manager is assured of selecting the wealth-maximizing alternative. 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 existing customers and there is no difference in the loss rate for buyers taking the cash discount versus those paying at the end of the credit period; (3) other than the change in receivables investment, the new policy does not necessitate additional investment outlays for inventories or fixed assets, nor does it change the variable cost ratio (VCR); (4) the analyst is able to forecast each of the relevant variables' future values. While the NPV formulation can be adapted to incorporate violations of Assumptions 1-3, violation of the fourth assumption creates difficulties. Probabilistic sales reactions would be difficult to specify for such a dramatic change from industry standards, especially if none of the competitors follow suit. 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 and preceding periods are identical. Second, the measures give quite different readings depending on whether the measures are figured from monthly, quarterly, or annual data. The aging schedule is likewise plagued with a sensitivity to the sales pattern, even if collection rates are stable.

2.

3.

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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 by DSO. Any increase in DSO increases the necessary investment in receivables, and any reduction in DSO (say through better collections) frees up receivables on the balance sheet. Uncollected balance percentages accurately depict a company's collection experience, even when sales are changing. They are not sensitive to the period over which they are being calculated because uncollected balance percentages are always linked back to the month in which the unpaid credit sales originated. Surveyed managers prefer the aging schedule, with DSO almost as popular, and accounts 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. Uncollected balances for each month are divided by the credit sales in the month in which the receivables originated. To draw conclusions regarding trends in the collection pattern, the balances 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). The payment index represents an overall index and checks aggregate collection experience. 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. Customers that are delinquent in payments may be experiencing temporary problems or have simply overlooked or misplaced the invoice. The credit manager can then indicate his understanding of the situation and make sure an understanding is gained about when the payment will be forthcoming. If necessary, the seller could renegotiate the terms, stressing that the revised terms must be met. The credit manager should not alienate the customer and be understanding of any mailing problems or other circumstances.

5.

6.

7.

8.

9.

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10.

The initial contact with the customer is made within ten days of delinquency. A statement of account is sent to the customer, and a copy of the unpaid invoices may 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 last resort. 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 use techniques such as garnishment (creditors have amounts owed taken out of the delinquent payor's wages), which are very effective in collecting amounts owed. The main differences faced by US credit managers when selling on credit abroad include complications caused 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 flow timeline and automating the credit process aid the credit manager in creating shareholder value from foreign credit sales.

11.

12.

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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 on investment effect. Surveyed managers expressed an ability to incorporate credit policy risk (default probability, delinquency probability, credit limits, opportunity cost of funds, and overall cost of capital) when making decisions about credit terms. The incremental profit approach involves determining the incremental receivables investment, the change in per unit as well as total profits, and the change in bad debt expense. In contrast, the NPV approach has been formulated so that, with the proper data, one can determine the credit policy alternative with the largest net present value. By following the capital budgeting approach to policy evaluation, the manager is assured of selecting the wealth-maximizing alternative. 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 existing customers and there is no difference in the loss rate for buyers taking the cash discount versus those paying at the end of the credit period; (3) other than the change in receivables investment, the new policy does not necessitate additional investment outlays for inventories or fixed assets, nor does it change the variable cost ratio (VCR); (4) the analyst is able to forecast each of the relevant variables' future values. While the NPV formulation can be adapted to incorporate violations of Assumptions 1-3, violation of the fourth assumption creates difficulties. Probabilistic sales reactions would be difficult to specify for such a dramatic change from industry standards, especially if none of the competitors follow suit. 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 and preceding periods are identical. Second, the measures give quite different readings depending on whether the measures are figured from monthly, quarterly, or annual data. The aging schedule is likewise plagued with a sensitivity to the sales pattern, even if collection rates are stable. 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 by DSO. Any increase in DSO increases the necessary investment in receivables, and any reduction in DSO (say through better collections) frees up receivables on the balance sheet. Uncollected balance percentages accurately depict a company's collection experience, even when sales are changing. They are not sensitive to the period over which they are being calculated because uncollected balance percentages are always linked back to the month in which the unpaid credit sales originated. Surveyed managers prefer the aging schedule, with DSO almost as popular, and accounts 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.

2.

3.

4.

5.

6.

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7.

Uncollected balances for each month are divided by the credit sales in the month in which the receivables originated. To draw conclusions regarding trends in the collection pattern, the balances 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). The payment index represents an overall index and checks aggregate collection experience. 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. Customers that are delinquent in payments may be experiencing temporary problems or have simply overlooked or misplaced the invoice. The credit manager can then indicate his understanding of the situation and make sure an understanding is gained about when the payment will be forthcoming. If necessary, the seller could renegotiate the terms, stressing that the revised terms must be met. The credit manager should not alienate the customer and be understanding of any mailing problems or other circumstances. The initial contact with the customer is made within ten days of delinquency. A statement of account is sent to the customer, and a copy of the unpaid invoices may 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 last resort. 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 use techniques such as garnishment (creditors have amounts owed taken out of the delinquent payor's wages), which are very effective in collecting amounts owed. The main differences faced by US credit managers when selling on credit abroad complications 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 flow timeline and automating the credit process aid the credit manager in creating shareholder value from foreign credit sales.

8.

9.

10.

11.

12.

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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 be real. Distinguishing between accounting and marginal costs.

Solutions to Problems: Chapter 6

1. Norton Wrench - credit standards tightening. Current Terms (E) Sales per 365-day year $275,000 Sales per day, S $753.42 Sales growth rate, g -7.27% Up-front Variable Cost Ratio (VCR) 70.00% Collection expenses (EXP) at DSO 1.25% Bad debt expense ratio, b , at DSO 7.00% Discount percent, d 0 Discount period, days 0 Proportion taking discount, p 0 Non-discount period, days 56 k = company's annual nominal cost of capital 15% i = daily cost of capital 15% / 365 = Proposed Terms (N) $255,000 $698.63 70.00% 1.45% 7.00% 0 0 0 56 4.1096%

Note: an annual nominal cost of 15% compounded daily implies an annual effective cost of { [ (1 + .15/365)^365 ] - 1 } * 100 = 16.18% per year. a.) Cashflow timeline under current terms Day 0 Day 56 ---|-------------------------------------------------------------------|-----------------> $753.42 cash collected / day ($9.42) EXP / day = 1.25% *$753.42 ($52.74) bad debt loss/day = 7% *

Variable Costs = VCR * sales / day = (0.70) * ($753.42) ($527.40) = PV cash outflow / day $753.42

$691.27 total cash inflow / day | $691.27 * 1 / [ 1 + (0.15/365)(56) ] using simple interest | $675.72 = PV of cash inflow / day | NPV = $675.72 - $527.40 = $148.32 per day from current terms In terms of the Ze formula 1st term PV from discount period 2nd term PV from credit period $52.74 Current Terms $0.00 no discount period $684.92 = $753.42 -

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discounted from Day 56 3rd term 0 4th term ($9.21) = 1.25% * $753.42 discounted from Day 56 Ze =$148.32 = NPV per day of current terms Note: The 2nd term subtracts bad debts from cash collections. b.) Cashflow timeline under proposed terms Day 0 Day 56 ---|---------------------------------------------------------------------|----------------> Variable Costs = VCR * sales / day = (0.70) * ($698.63) $698.63 ($489.04) $698.63 = PV of cash outflow / day day $698.63 cash collected / day ($10.13) EXP / day = 1.45% * ($48.90) bad debt loss/day = 7% * $639.60 total cash inflow / | $639.60 * 1 / [ 1 + (0.15/365)(56) ] using simple interest | $625.21 | = PV of cash inflow per day NPV = $625.21 - $489.04 = $136.17 per day from proposed terms Proposed Terms $0.00 no discount period $635.11 = $698.63 - $48.90 discounted from Day 56 ($489.04)=70% VCR*$698.63 at day ($9.90)= 1.45% EXP PV credit expenses PV variable costs ($527.40) = 70%*$753.42 at Day

In terms of the Zn formula 1st term PV from discount period 2nd term PV from credit period 3rd term 0 4th term *$698.63 PV credit expenses PV variable costs

discounted from Day 56 Zn = $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 considerations How customers react to the change will be important. While the estimate is that the 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 Terms (E) $100,000,000 $273,972.60 5% 65.00% 2.50% 0.00% 0 0.00% 52 12% 0.0003288 Proposed Terms (N) $105,000,000 $287,671.23

Sales per 365-day year Sales per day, S Sales growth rate, g Up-front Variable Cost ratio (VCR) 65.00% Collection expenses (EXP) at DSO 2.00% Bad debt expense ratio, b , at DSO 24.500% 34.500% Discount percent, d 0.00% Discount period, days 0 Proportion taking discount, p 0.00% Non-discount period, days 42 k = company's annual nominal cost of capital i = daily cost of capital = 12% / 365

Cashflow timeline under current terms Day 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 outflow per day = 2.54% * $273,972.60 $261,643.8457,534.25 total cash inflow / day | $261,643.8457,534.25 * 1 / [ 1 + (0.15/365 * 42) ] simple interest | $258,080.214,026.59 | = PV of cash inflow /day NPV = $254,026.59258,080.21 - $178,082.19 = $79,998.025,944.4 per day from current terms In terms of the Ze formula 1st term PV from discount period 2nd term PV from credit period $6,849.3210,958.90 3rd term 0 4th term $273,972.60 PV credit expenses ($5,404.82) = 2% * PV variable costs Current Terms $0.00 no discount period $259,431.41= $273,972.60 discounted from Day 42 ($178,082.19) = 65% * $273,972.60 at Day

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discounted from Day 42 Ze = $79,998.025,944.40 = NPV per day of current terms Note: the 2nd term subtracts bad debt costs from collections.

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Cashflow timeline under proposed terms Day 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 outflow / day ($7,191.7811,506.85) bad debt loss / day = 2.54% * $287,671.23 $268,972.60 total cash inflow / day | $273,287.6768,972.60 * 1 / [ 1 + (0.12 / 365 * 52) ] simple interest | $2684,694.10451.57 | = PV of cash inflow / day NPV = $268,694.10 264,451.65 - $186,986.30 = In terms of the Zn formula 1st term PV from discount period 2nd term PV from credit period $7,191.7811,506.85 52 3rd term $287,671.23 4th term $287,671.23 PV variable costs ($186,986.30)= 65% VCR * at Day 0 ($7,070.89) = 2.5% EXP * discounted from Day 52 Zn = $81,707.8077,465.27= NPV / day of proposed terms Note: the 2nd term subtracts bad debt costs from cash collections a.) Calculation of Z, the one day change in value Therefore, Z = Zn - Ze = $81,707.877,465.27 - $79,998.02 75,944.40 = $1,520.871,709.78 $77,465.381,707.80

Proposed Terms $0.00 no discount period $271,522.46 = $287,671.23 bad debt discounted from Day

PV credit expenses

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 decision Yes, we would recommend lengthening the credit period since Z is positive which means that shareholder wealth would increase, assuming our forecasts were 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 outflow / day $257,465.75270,410.96 total cash inflow / day | $270,410.96 257,465.75 * 1 / [ 1 + (0.12 / 365 * 52) ] simple interest | $26553,865138.7513 | = PV of cash inflow / day NPV = $265,865.75253,138.13 - $186,986.30 = $78,879.4566,151.8 per day from proposed terms Z = Zn - Ze = $78,879.4566,151.83 - $75,944.40 = ($9,73592.0557) per day No, the recommendation does not change. One would stillno longer advise lengthening terms, as this would indecrease forecasted shareholder wealth. 3. J. James Book PublishersA. Walton -- cash discount consideration. Current Terms (E) $250,000,000 $684,931.51 Proposed Terms (N) $250,000,000 $684,931.51 0% 60.00%

Sales per 365-day year Sales per day, S Sales growth rate, g Up-front Variable Cost Ratio (VCR) 60.00% Collection expenses (EXP) at DSO 52.00% 41.00% Bad debt expense ratio, b , at DSO 3.00% Discount percent, d 0.00% Discount period, days 0 Proportion taking discount, p 0.00% Non-discount period, days 40 k = company's annual nominal cost of capital i = daily cost of capital = 10% / 365 0.0002740

3.00% 3.00% 10 40.00% 40 10% 0.0002740

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Cashflow timeline under current terms Day 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 outflow / day = 3.0% * $684,931.51 $630,136.9850,684.93 total cash inflow / day | $630,136.98 650,684.93 * 1 / [ 1 + (0.10/365 * 40) ] simple interest | $623,306.2343,631.44 | = PV of cash inflow 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 1st term PV from discount period 2nd term PV from credit period 20,547.95 3rd term 365 4th terms *$684,931.51 PV credit expenses at Day 0 ($34,246.5813,550.14) = 52% discounted 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. PV variable costs Current Terms $0.00 no discount period $657,181.57 = $684,931.51 discounted from Day 40 ($410,958.90) = 60% * $250 million /

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Cashflow timeline under proposed terms Day 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 outflow ($7,972.60)= 0.03 * $265,753.42 bad debt losses per day (based on after-discount cash collections) $257,780.82 = total cash inflow/day from discount period

$257,780.82 at Day 10 * 1 / [1+ (.10 / 365 * 10)]

($410,958.90)

| | | $410,958.90=cash / day=60%*250mil/365 | ($27,397.266,849.32)=EXP/day=(41%) | + $273,972.60) (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

$257,076.50 = PV of cash inflow / day

$371,232.8791,780.82 = total cash inflow/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 inflow / day NPV = $257,076.50 + $367,208.67 387,533.9 - $410,958.90 = $213,326.2733,651.47 per day from proposed terms In terms of the Zn formula 1st term PV of discount period $7,972.60 2nd term -12,328.77 3rd term 365 at Day 0 4th terms
$410,958.90

Proposed Terms $257,076.50 = $265,753.42 discounted from Day 10 $394,308.94 = $410,958.90 discounted from Day 40 ($410,958.90)= 60% * $250 million /

PV from credit period

PV variable costs

PV credit expenses

($27,100.276,775.07) = 41% *

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+ $273,972.60)

Zn terms

discounted from Day 40 = $213,326.2733,651.47 = NPV per day of current

Note: The 2nd term subtracts bad debt costs from cash collections. a.) per day b.) Calculating the one-day change in value Therefore, the one-day change in value related to the proposed terms is Z = Zn - Ze = $213,326.27 233,651.47 - $212,347.33 232,672.53 = $978.94 Calculating the change in daily net present value NPV = Z / I = $978.94 / 0.10 * 365 = $3,573,137.41 This is the overall (very positive) value effect assuming the daily NPV lasts indefinitely. Recommendation Yes, A. Walton J. James should initiate the cash discount since it will increase shareholder wealth assuming the forecasts are correct. The optimal cash discount percent. Using the Hill-Riener optimal cash discount formula, the optimal cash discount is: d* = [ (1 - (1 + i)^(DPn - CPn) ] / 2 = 0.4092% from Equation 6-8 in the text. 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 the students 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)(DPN CPN) ]/ 2 DP 4. a). b). c). d). 5 10 10 10 30 45 30 CP 75 I Opt. Disc. 0.000411 1.4176% 0.000329 0.3279% 0.000493 0.8554% 0.000603 0.5989%

c.)

d.)

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

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5.

Flying High Gliders - credit lengthening using compound interest. (This same credit period lengthening problem using simple interest appears on pp. 179180 of the text.) Current Proposed Terms (E) Terms (N) Sales per 365-day year $30 million $35 million Sales per day, S $82,192 $95,890 Sales 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 0 Proportion taking discount, p 0.00% 0.00% Non-discount period, days 45 68 k = 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 daily rate 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 terms Day 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 outflow / day $76,438.36 total cash inflow / day | $76,438.36 * 1 / [ 1.00035905^45 ] using simple interest | $75,213.48 | = PV of cash inflow per day NPV = $75,213.48 - $67,123.3 In terms of the Ze formula 1st term PV from discount period 2nd term PV from credit period $4,109.59 3rd term 0 4th term ($1,617.49) = 2% * $82,191.78 discounted from Day 45 Ze = $17,679.23 = NPV per day of current terms Note: The 2nd term subtracts bad debt costs from cash collections. Cashflow timeline under proposed terms Day 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 outflow / day = 6% * $95,890.41 $87,739.73 total cash inflow / 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 PV credit expenses PV variable costs =$17,679.23 per day from current terms Current Terms $0.00 no discount period $76,830.97 = $82,191.78 discounted from Day 45 ($57,534.2)= 70% * $82,191.78 at Day

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In terms of the Zn formula 1st term PV from discount period 2nd term PV from credit period $5,753.42 3rd term 0 4th term $95,890.41 PV credit expenses PV variable costs

Proposed Terms $0.00 no discount period $87,963.31= $95,890.41 discounted from Day 68 ($67,123.29)= 70% * $95,890.41 at Day -$2,339.45= 2.5% *

discounted from Day 68 Zn = $18,500.58 = NPV per day of current terms Z = Zn-Ze = $821.34 Note: The 2nd term subtracts bad debt costs from cash collections. 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. Change in NPV NPV = Z /i = $821.34 / 0.035905% = $2,287,575.32 The overall value effect is higher than the $2,030,579 found using simple interest. Again, this assumes the effect lasts indefinitely. Reason for differences in answers Using the simple interest calculations will understate the value impact of the decision. Compounding is the more appropriate procedure. It takes a larger simple interest rate, compared with a compound rate, to arrive at the same FV. Marvelous Siegel Apparel Mills - cash discount decision with daily compound interest versus simple interest. Current Proposed Terms (E) Terms (N) Sales per 365-day year $20,000,000 $20,600,000 Sales per day, S $54,794.52 $56,438.36 Sales 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 10 Proportion taking discount, p 0.00% 40.00% Non-discount period, days 35 35 k = company's effective annual cost of capital 12.00% i, daily compound cost of capital = [(1+k)^(1/365) - 1] * 100 0.03105%

c.)

d.)

65.

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Cashflow timeline under current terms Day 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 outflow per day = 3% * $54,794.52 $50,958.90 total cash inflow / day | $50,958.90 * 1 / [ 1.0003105^35 ] using compound interest | $50,408.12 | = PV of cash inflow per day NPV = $50,408.19 - $32,876.71 = $17,531.41 per day from current terms In terms of the Ze formula 1st term PV from discount period 2nd term PV from credit period $1,643.84 3rd term $54,794.52 4th term $54,794.52 PV variable costs Current Terms $0.00 no discount period $52,576.22= $54,794.52 discounted from Day 35 ($32,876.71)= 60% * at Day 0 ($2,168.09)= 4% * discounted from Day 35 Ze = $17,531.41 = NPV per day of current terms Note: the 2nd term subtracts bad debt costs from cash collections.

PV credit expenses

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Cashflow timeline under proposed terms Day 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 outflow ($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 inflow at Day | 10 from discount period | | | | $33,863.01 0.6 * 20.6 mil /365 cash/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 (based using simple interest | on before-discount cash flow $21,503.87 | at Day 10 plus non-discount = PV of cash inflow / day from cash flow at Day 35 Day 10 of discount period ($846.58) bad debt loss / day 2.5% * $33,863.01 $30,758.90 total cash inflow/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 inflow / 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 1st term PV of discount period discounted 2nd term 3rd term 0 4th term $22,575.34) PV credit expenses ($2,233.13)= (4%)($33,863.01 + PV from credit period PV variable costs Proposed Terms $21,503.87 = $21,570.74 from Day 10 $32,659.59 = $33,863.01 - $846.58 discounted from Day 35 ($33,863.01)= 70% * $20.6 mil at Day

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discounted from Day 35 Zn = $18,067.31 = NPV per day of current terms Z = Zn - Ze = $535.89 Note: 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 interest The one-day value change from lengthening the credit period (using compound interest) is now $539.89, lower than the $543.55 found using simple interest. The cash discount offered more than offsets the lower bad debt costs. Change in NPV NPV = Z / I = $535.86 / 0.00031053776 = $1,725,699.97 The overall value effect is higher than the $1,653,163 found using simple interest. Again,this assumes the effect lasts indefinitely. Reason for differences in answers The interesting result is that while the PV of one day's sales is less using the daily compounding assumption, the value impact for the perpetual horizon is actually more. This results from the impact of a lower daily rate over the horizon which increases the NPV. Besley, Inc. - aging schedule and DSO for previous 180 days. Uncollected Amount as Credit Uncollected Percent of Sales Amount June 30 A/R $75,000 $5,000 11.90% = $5 K / $42 K $50,000 $5,000 11.90% = $5 K / $42 K $100,000 $6,000 14.29% = $40,000 $45,000 $50,000 $360,000 $42,000 31-60 April $6,000 14.29% 61-90 March $6,000 14.29% 100.00% Over 90 Feb & Prior $10,000 23.81% Total $42,000 100.00% $6,000 $8,000 $12,000 14.29% = 19.05% = 28.57%

b.)

c.)

76.

Month Late January over 90 days February over 90 days March 61-90 days $6 K / $42 K April 31-60 days $6 K / $42 K May 0-30 days $8 K / $42 K June (current) =$12 K / $42 K Total credit sales June 30 A/R Balance: Age Current Month June A/R $12000 Percent of Total 28.57%

0-30 May $8,000 19.05%

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 days A/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. Uncollected Balance 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 $360,000 June 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 Month Late January over 90 days February over 90 days March 61-90 days =12K / 84K April 31-60 days $200,000 =12K / 84K May 0-30 days $100,000 =16K / 84K June current $150,000 =24K / 84K Total credit sales $720,000 June 30 A/R Balance: Credit Sales $100,000 $90,000 $80,000 Uncollected Amount as Uncollected Percent of Amount June 30 A/R $10,000 11.90% =10K / 84 K $10,000 11.90% =10K / 84K $12,000 14.29% $12,000 $16,000 $24,000 $84,000 61-90 March $12,000 14.29% 100.00% Over 90 Feb & Prior $20,000 23.81% 14.29% 19.05% 28.57%

Aging Schedule: Age Current 0-30 31-60 Month June May April A/R $24,000 $16,000 $12,000 Percent of Total 28.57% 19.05% 14.29% a.)

Total $84,000 100.00%

Calculating DSO Avg. 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.) c.) d.) Calculating accounts receivable (A/R) turnover A/R turnover for the 6-month period = 180 days / 21 days = 8.57 times The aging schedule (see above) Uncollected Balance Percentages Uncollected Balance Uncollected Percent (of Amount credit sales) $10,000 10.00% =$10 K / $100 K $10,000 11.11% =$10 K / $90 K $12,000 15.00% 6.00% 16.00% 16.00%

Credit Month Late Sales January over 90 days $100,000 February over 90 days $90,000 March 61-90 days $80,000 =$12 K / $80 K April 31-60 days $200,000 $12,000 =$12 K / $200 K May 0-30 days $100,000 $16,000 =$16 K / $100 K June current $150,000 $24,000 =$24 K / $150 Accounts Receivable Balance = $80,000 Payment 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 that a change has occurred. The payment index has dropped. We discover that when you look at the uncollected balances in relation to the sales generating the balance that a larger percent of the sales are collected for the more recent time period. On-time payments? "Most" are paying on time. The rate of payment is increasing according to the uncollected balance percentage method (74.11% vs. 79.44% a year ago). How to improve the collection effort. The credit personnel should be very proactive at following up on those customers taking longer than 30 days to pay. They should determine if the problem is with the merchandise received, if the customer is unhappy with the product, or if the customer is having financial difficulties. 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, then the accounts receivable turnover should be 360 / 30 = 12 and the payment index would be zero.

f.)

g.)

h.)

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