Receivable management question

sales are 15m on 30 days credit

SOFP shows Receivables at 2.466m, Co. is thinking of giving 1% discount for early settlement within 30 days and increasing credit days to 45 days. 50% will take the discount, 30% will pay after 45d and 20% will not change current payment behavior.
OD is at 6%

what is the cost benefit?

this is what i did:

New Receivables = 45 x 15000/365 = 1.849m
reduction in recvables is 2.466-1.849=617
saving is 6% 617 = 37

since 50% will take up the 1% discount, this means:
Cost of discount=15000/2 x 1% = 75

therefore, cost (75) > benefit (37)
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what the kit did:

now, the answer in the kit came to the same conclusion but they
1. calculated the revised average credit days and they calculated the actual credit days and came up with a figure of 47 as reduced cost of OD, thus arriving at the same conclusion

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my question is that had i done the working my way, wd that have been acceptable?

thanks