This is (360 / 60) × (2 / [100 ? 2]) = 6 × .0204 = .1224. This is incorrect for two reasons. One, the first part of the formula is incorrect. It should be (360 / [60 ? 10]), the Total Period ? Period for Discount. And two, it does not take into consideration the 6% return available in a money market account.
This is {(360 / 60) × (2 / [100 ? 2])} ? .06. The first part of the formula is incorrect. It should be (360 / [60 ? 10]), the Total Period ? Period for Discount.
This question is a little bit more involved than the standard cash discount question because we need to take into account the fact that they can invest money at 6% if they have it. If they pay within the discount period, they will save $2. However, if they do not pay within the period, they will have an additional $98 available for 50 days that they would not have had if they had paid. That money will be able to earn 6%. Over the 50 days, that $98 will earn $.817. This means that they would have an incremental $1.183 for the 50 days covered by this receivable ($2 ? $.817). Dividing this by the $98 that they have available from not paying early, we get a cost of 1.2%. However, this is for a period of only 50 days so it needs to be multiplied by 7.2 (calculated as 360 ÷ 50) in order to get an annual rate. The annual rate is 8.7%. An alternative way of reaching the same answer is to calculate the cost of not taking the discount and then subtract from that the annual rate that could be received by investing the money in a money market account, as follows: (360/[Total Period ? Period for Discount]) × (Discount % / [100 ? Discount %]) (360 / [60 ? 10]) × (2 / [100 ? 2]) = 7.2 × .0204 = .1469 .1469 ? .06 = .0869 0r 8.7%
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