25. Cindy\'s Toys has an average cash balance of $18,000 (-C/2) opportunity cost

Question

25. Cindy's Toys has an average cash balance of $18,000 (-C/2) opportunity cost of carrying cash is 5%. Cindy replenishes with $36,000 (-C ) on the first of each month and the order cost is $25 (So, total cash needs for the year = C x 12 432000) (i) What are the total carrying (opportunity) costs under the current system? (ii) What are the total replenishment costs under the current system (C)? (ii) By looking at the results from parts (i) and (ii) above, state, in one, very short sentence, whether the firm is replenishing cash balances optimally. If not, find the firms optimal cash replenishment amount(C*) (iv) What are the costs savings (i.e. the difference between the total (carrying and replenishing) costs using the current system and total costs using C*? (v)When the firm replenishes cash optimally, how many times a year would it replenish? How frequently would it replenish (every 20 days, or 30 days, etc.)?

Explanation / Answer

Part ( a)

Total carrying cost under the present system =

Average cash balance * opportunity cost * no. of operating cycle

= 18000 * 0.05 * 12/0.5

=$21600

Part ( c)

Total Replanishment cost= Replanishment cost per month * 12

= 36000 * 12

=$432000

Part ( c )

By the analysis of part a and b, the company should not be replanished the cost under the present system. Because the cost of cash replanishment is more than the carrying cost.

The optimum cash replanishment is (2FT/r)

=(2*25*432000/0.05)

=$20785

Part ( d )

Total cost under present system = Total fixed cost+Total carrying cost

= 25*(12*2)+21600

=$22200

Total cost under optimum level = (432000/20785*25)+(20785*0.05*432000/20785)

=520+21600

=22120

Total savings = 22200-22120

=$80

Part ( e )

No. Of times cash replanishment = 432000/20785

=20.78 times

No. Of days = 360/20.78

= 18 days

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