Chapter 16.pdf

# B 5 1000 2000 we can multiply b times nr to determine

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B 5 [1000 2000] We can multiply B times NR to determine how much of the \$3000 will be collected and how much will be lost. For example BNR 5 5 [1000 2000] 3 0.89 0.74 0.11 0.26 4 [2370 630] Thus, we see that \$2370 of the accounts receivable balances will be collected and \$630 will be written off as a bad debt expense. Based on this analysis, the accounting department would set up an allowance for doubtful accounts of \$630. The matrix multiplication of BNR is simply a convenient way of computing the eventual collections and bad debts of the accounts receivable. Recall that the NR matrix showed a 0.89 probability of collecting dollars in the 0–30-day category and a 0.74 probability of collecting dollars in the 31–90-day category. Thus, as was shown by the BNR calculation, we expect to collect a total of (1000)0.89 1 (2000)0.74 5 890 1 1480 5 \$2370. Suppose that on the basis of the previous analysis Heidman’s would like to investigate the possibility of reducing the amount of bad debts. Recall that the analysis indicated that a 0.11 probability or 11% of the amount in the 0–30-day age category and 26% of the amount in the 31–90-day age category will prove to be uncollectible. Let us assume that Heidman’s is considering instituting a new credit policy involving a discount for prompt payment. Management believes that the policy under consideration will increase the probability of a transition from the 0–30-day age category to the paid category and decrease the prob- ability of a transition from the 0–30-day to the 31–90-day age category. Let us assume that 23610_ch16_ptg01_Web.indd 14 01/10/14 6:20 PM

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16-15 a careful study of the effects of this new policy leads management to conclude that the following transition matrix would be applicable: P 5 3 1.0 0.0 u 0.0 0.0 0.0 1.0 u 0.0 0.0 — — — — — — 0.6 0.0 u 0.3 0.1 0.4 0.2 u 0.3 0.1 4 We see that the probability of a dollar in the 0–30-day age category making a transition to the paid category in the next period has increased to 0.6 and that the probability of a dollar in the 0–30-day age category making a transition to the 31–90-day category has decreased to 0.1. To determine the effect of these changes on bad debt expense, we must calculate N , NR , and BNR. We begin by using equation (16.5) to calculate the fundamental matrix N : N 5 s I 2 Q d 2 1 5 5 3 1.0 0.0 0.0 1.0 4 2 3 0.3 0.3 0.1 0.1 4 6 2 1 5 3 0.7 2 0.3 2 0.1 0.9 4 2 1 5 3 1.5 0.5 0.17 1.17 4 By multiplying N times R , we obtain the new probabilities that the dollars in each age cat- egory will end up in the two absorbing states: NR 5 5 3 1.5 0.5 0.17 1.17 43 0.6 0.4 0.0 0.2 4 3 0.97 0.77 0.03 0.23 4 We see that with the new credit policy we would expect only 3% of the funds in the 0–30-day age category and 23% of the funds in the 31–90-day age category to prove to be uncollectible. If, as before, we assume a current balance of \$1000 in the 0–30-day age cate- gory and \$2000 in the 31–90-day age category, we can calculate the total amount of accounts receivable that will end up in the two absorbing states by multiplying B times NR. We obtain BNR 5 5 [1000 2000] 3 0.97 0.77 0.03 0.23 4 [2510 490] Thus, the new credit policy shows a bad debt expense of \$490. Under the previous credit policy, we found the bad debt expense to be \$630. Thus, a savings of \$630 – \$490
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• Spring '18
• Markov process, Markov chain, Andrey Markov, Markov decision process

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