Discount Stacking on a Bulk Order
A procurement officer buys 240 units at a list price of 18.50 per unit. The supplier offers a trade discount of 12 percent on list, then a further 8 percent on the reduced amount for orders above 200 units. Separately, a cash discount of 3 percent applies if the invoice is settled within 10 days; the officer intends to pay on day 9. A rival supplier quotes a flat 21 percent off the same list price with no further discounts. The officer must decide which supplier is cheaper and by how much, and must also report the effective single discount rate of the stacked offer for the budget file.
1. Compute the net amount payable to each supplier.
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List total = 240 × 18.50 = 4,440.00.
Stacked supplier: after 12 percent: 4,440 × 0.88 = 3,907.20. After 8 percent: 3,907.20 × 0.92 = 3,594.624. After 3 percent cash discount: 3,594.624 × 0.97 = 3,486.785 (about 3,486.79).
Rival: 4,440 × 0.79 = 3,507.60.
The stacked supplier is cheaper by 3,507.60 − 3,486.79 ≈ 20.81.
2. What single effective discount rate does the stacked offer represent, and why is it not 23 percent?
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Combined multiplier = 0.88 × 0.92 × 0.97 = 0.785312.
Effective discount = 1 − 0.785312 = 0.214688, i.e. about 21.47 percent.
It is not 23 percent because the 8 percent and 3 percent are taken on successively smaller bases, not on the original list total. Adding the rates (12+8+3=23) overstates the discount; the true compounding gives roughly 21.5 percent.
3. The officer could instead take the rival's flat 21 percent but lose the 3 percent cash discount by paying on day 30. Does the ranking change?
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The rival's terms are unchanged at 3,507.60 (no cash discount offered).
Stacked supplier without the 3 percent cash discount: 3,907.20 × 0.92 = 3,594.62.
Now the rival at 3,507.60 is cheaper by 3,594.62 − 3,507.60 = 87.02.
So the ranking flips: paying late destroys the advantage. The stacked offer only wins when the cash discount is captured.