United Fruits now offers volume discounts by the 10-kilogram (10-kilo) pack to small, as well as large, supermarket chains for organically grown in-season fruit shipped directly from the orchard. Over the last 8 years, the food market chain CoopForAll has purchased the number of 10-kilo packs shown below when United Fruits has California free-stone peaches in season. Through a special arrangement, the price per 10-kilo pack has remained constant at $15.00 per pack. United Fruits will now charge CoopForAll according to the volume discount schedule shown. The no-discount price this year is $19.95 per 10-kilo pack. Based on the progressive discounts of 10% more for increased-size orders, if CoopForAll buys the same amount as last year, the total cost with discounts will be: 2000 packs ×
$19.95[1 ? (3 × 0.10)] = 2000 × 13.97 = $27,940. This is less than $30,000, the cost for 2000 packs at the flat rate of $15.00 per pack. Calculate the equivalent worth now of the annual costs for the 8 years of prior purchases at the flat rate of (a) $15.00 per pack, and (b) the cost had they been purchased using the discount schedule. Let i= 8% per year. (Hint: This is a future worth value now at the end of year 1.)
What will be an ideal response?
First determine the discount cost schedule. Develop the annual cost series for the flat rate of
$15.00 and the corresponding series using the discounted rates. The future worth values
using a spreadsheet are:
(a) F flat = $136,307
(b) F disc = $132,549
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