[Anonymous]

MCQ gives the situation to buy 60,000 zippers up front or 5,000 monthly @ .60 per zipper. Assuming American can invest cash at eight percent, what is the company’s opportunity cost of purchasing the 60,000 units at the beginning of the year?

The answer steps are given below. What I don’t get is why do you calculate an average balance not invested by dividing the total by 2? Can someone further clarify and explain this part. I understand the calculation all the way getting to the $33,000 amount. I went on to do $33,000 x 8% which came out to be wrong.

Can someone help to explain the answer solution to this?

Solution:

Cost to purchase 60,000 zippers is 60,000 zippers × $.60 per zipper = $36,000

The opportunity cost is the forgone interest on the $33,000 cash payment. (Computed 36,000 − 3,000, the first $3,000 would have had to be paid at the beginning of the month in either case.)

The invested cash is the average balance available for investment. Some $33,000 is available at the beginning of the year and is reduced by $3,000 per month for the remainder of the year until no cash is available in the final month. The average balance not invested is estimated at $33,000/2.

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> WHY???

Principal x Rate x Time x Interest

($33,000 / 2) × .08 × 12 / 12 = $ 1,320

[acamp]

Think of it this way, since you would have to continue buying zippers each month, the amount that could be invested drops by $3,000 each month–so this needs to be factored in. So in month 3, you no longer have the full $33,000 to invest, now you're down to $27K because you've been buying more zippers.

Amount you can invest

Month 1: 33,000

Month 2: 30,000

Month 3: 27,000

.

.

.

Month 12: 0

Average balance is: ($33,000 + 0)/2

Manual proof: You get to invest $33,000 at 8% for one month, $33,000*8%*(1/12), the next month you have $30,000 to invest also for one month, $30,000*8%*(1/12)…

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[Anonymous]

Thanks for the clarification!

[Author]

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