Question

4. Two alternatives are being considered by a food processor for the warehousing and distribution of its

canned products in a sales region. These canned products come in standard cartons of 24 cans per carton.

The two alternatives are:

Alternative A – Distribute the product themselves. The administrative costs are estimated at $43,000

per year, and other general operating expenses are calculated at $.0009 per carton. A warehouse will

have to be purchased, which costs $300,000.

Alternative B – Sign an agreement with an independent distribution company, which is asking a

payment of $0.10 per carton distributed.

Assume a study period of 10 years and that the warehouse can be sold at the end of this period for $200,000.

Find the minimum number of cartons per year that will make Alternative A preferable to Alternative

B.

Assume MARR is 8%

Answer 1

Since study period is the same for both options, we can do a Present Worth (PW) analysis.

If minimum number of cartons is Q per year, then

PW of Alternative A = PW of Alternative B

- $300,000 + $[43,000 + (0.0009 x Q)] x P/A(8%, 10) + $200,000 x P/F(8%, 10) = $0.1 x Q x P/A(8%, 10)

- $300,000 + $(43,000 + 0.0009Q) x 6.7101** + $200,000 x 0.4632** = $0.1Q x 6.7101**

- 300,000 + 92,640 = 6.7101 x [0.1Q - (43,000 + 0.0009Q)]

- 207,360 = 6.7101 x (0.1Q - 43,000 - 0.0009Q)

0.0991Q - 43,000 = - 30,902.67

0.0991Q = 12,097.33

Q = 122,072