[Anonymous]

Hi,

I don’t understand why we have to divided by 2 (time). The question didn’t mention much about timing. Anyone can help? Thank you very much!

American Coat company estimates that 60,000 special zipper will be used in the manufacture of men’s jackets during the next year. Reese Zipper company has quoted a price of $0.6 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. 1320

b. 1440

c. 1500

d. 2640

Choice “a” is correct.

Cost to purchase 60,000 zippers:

60,000 x 0.6 = 36,000

The opportunity cost is the forgone interest on the 33,000 cash payment (the first 3000 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:

Principle Rate Time Interest

33,000 x 0.08 x 1/2 = 1320

[fdt]

It's because the principle balance on which you would earn the interest would be decreasing incrementally with each monthly purchase. Since the monthly purchases are made in equal installments over the year, the interest earned would be the average principle balance during the year ($33,000 / 2 = $16,500) times the 8% annual interest rate. This comes to the $1320. The below schedule should help to illustrate it:

_	Principle	Interest Rate	Interest

Month	Balance		(8% / 12)	Earned



Jan	33,000		0.006666667	$220

Feb	30,000		0.006666667	200

Mar	27,000		0.006666667	180

Apr	24,000		0.006666667	160

May	21,000		0.006666667	140

Jun	18,000		0.006666667	120

Jul	15,000		0.006666667	100

Aug	12,000		0.006666667	80

Sep	9,000		0.006666667	60

Oct	6,000		0.006666667	40

Nov	3,000		0.006666667	20

Dec	0		0.006666667	0

TOTAL:					1,320

[Anonymous]

Hi fdt,

Thanks for the explanation. What kind of situation that we don't need to divided by 2? I would like to make a comparison. Thank you!

[Author]

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