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Average Collection Days in period

On page 88 Schweser Notes Book 4 there is table Figure 3. Weighed Average Collection Period - March, could someone explain how Average Collection Days are calculated there? (for interval <31 days;31-61;61-90;>90) 

I know there is formula for Days of Sales outstanding = 365/avg.rec, but how to apply it here for intervals?

Figure 1:Receivable Aging (thousands of dollars)

Days Outstanding
March
April
May

<31
200
212
195

31-60
150
165
140

61-90
100
90
92

>90
50
70
66

Figure2:Receivbales Aging (% of totals)
 

Days Outstanding
March
April
May

<31
40%
39%
40%

31-60
30%
31%
28%

61-90
20%
17%
19%

>90
10%
13%
13%

Figure3.Weighed Avarage Collection Period-March

Days Outstanding
Average Collection Days
% weight
Days*Weight

<31
22
40%
8.8

31-60
33
30%
13.2

61-90
74
20%
14.8

>90
135
10%
13.5

Weighted Average Collection Period
50.3

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I would also be very interested in an answer to this question. I started to draft an answer myself, but I am not very happy with it and it could very well be very wrong (see below and take it with a grain of salt)

Unsatisfying answer draft … use at your own risk:

Is there additional information provided? To me it seems that you cannot calculate e.g. that you will collect receivables in the “<31” category on average on day 22, unless you are given the sales volume for the month and the average age of receivables in the different categories to start with. Also be careful with your formula for days of sales outstanding (DSO). DSO = 365 * average receivables / annual sales, which also requires a sales figure.

If you assume that the receivables outstanding are equally distributed (in time) in the “<31” category, then the current average age is 15 days. Using the 22 days average collection period for the company given in table 3 that implies monthly sales of roughly 869.

The assumption of equal distribution in time breaks down for the “31-60” category. If this was the case, then the average collection period in this category should be above 45 days.

So to conclude, I do not think you can calculate the weighted average collection period if you are just given the data in figure 1.

< 31 days:

(1) Sum up receivables that are still due (but aged less than 31 days).

(2) Sum up the total credit sales for the receivables within this age group (which are not given in your post).

DSO for “<31 days” = (1) / (2) x 365

Apply the same concept for the rest of the intervals.