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

Question

× $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.)

Answer 1

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) Fflat = $136,307

(b) Fdisc = $132,549