[TheGuyCPA]

Why do they multiply it by 1/2 for the time?

American Coat Company estimates that 60,000 special zippers will be used in the manufacture of men’s jackets during the next year. Reese Zipper Company has quoted a price of $.60 per zipper. American would prefer to purchase 5,000 units per month, but Reese is unable to guarantee this delivery schedule. In order to ensure availability of these zippers, American is considering the purchase of all 60,000 units at the beginning of the year. Assuming American can invest cash at eight percent, the company’s opportunity cost of purchasing the 60,000 units at the beginning of the year is?

a.

$1,440

b.

$2,640

c.

$1,320

d.

$1,500

Explanation

Choice “c” is correct.

Cost to purchase 60,000 zippers:

60,000 × .60 = $36,000

The opportunity cost is the forgone interest on the $33,000 cash payment (the first $3,000 would have had to be paid in either case).

The $33,000 cash payment made evenly throughout the period is the same as making the total payment in the middle of the period. The solution is:

Principal

xRate

xTime

xInterest

33,000

×

.08

×

1/2

=

$1,320

FAR - 80
REG - 78
AUD - 88
BEC - 84

State of Illinois Licensed CPA as of September 2015

[Anonymous]

I could be wrong, but I think the underlying concept here is similar to ROA in B3. ROA=Net Income/”Average” asset. By using the “average” instead of the end of the year asset number, it would reflect better what asset you actually had throughout the year. For example, if the beginning asset is $1, and the ending asset is $33k, and you accumulate asset evenly throughout the year. if you just use either the $1 or the $33k as your asset number, it would distort the ROI. Instead, the average asset ($16.5k) is a better number to use.

Likewise, in this problem they are making purchases every month, so the 33k investment is spread out over 12 months:

1/1: $0 invested

1/31: $2750 invested

2/31: $5500 invested cumulatively

…

6/31:$16,500 invested cumulatively

….

12/31: $33,000 invested cumulatively

Instead of making you compute the interest compounded monthly, the easier approach that's similar to ROI is adding the beginning invested amount ($0) and the ending invested amount ($33k), divided it by 2, to get the “average” amount of investment invested during the year.

[Author]

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