Question

Novelty Toys, Inc. sells a variety of new and innovative children’s toys. Management learned that the preholiday season is the best time to introduce a new toy, because many families use this time to look for new ideas for December holiday gifts. When Novelty discovers a new toy with good market potential, it choses an October market entry date.

In order to get toys in its stores by October, Novelty places one-time orders with its manufactures in July of each year. Demand for children’s toys can be highly volatile. If a new toy catches on, a sense of shortage in the marketplace often increases the demand to high levels and large profits can be realized. However, new toys can also flop, leaving Novelty stuck with high levels of inventory that must be sold at reduced prices. The most important question the company faces is deciding how many units of a new toy should be purchased to meet anticipated sales demand. If too few are purchased, sales will be lost; if too many are purchased, profits will be reduced because of low prices realized in clearance sales.   

For the coming season, Novelty plans to introduce a new product called Weather Teddy. This variation of a talking teddy bear is made by a company in Taiwan. When a child presses Teddy’s hand, the bear begins to talk. A built-in barometer selects one of five responses that predict weather conditions. The responses range from “It looks to be a very nice day! Have fun” to “I think it may rain today. Don’t forget your umbrella”. Tests with the product show that, even though it is not a perfect weather predictor, its predictions are surprisingly good. Several of Novelty’s managers claimed Teddy gave predictions of the weather as good as local television weather forecasters.

As with other products, Novelty faces the decision of how many Weather Teddy units to order for the coming holiday season. Members of the management team suggested order quantities of 15,000, 18,000, 24,000 or 28,000 units. The wide range of order quantities suggested indicates considerable disagreement concerning the market potential. The product management team asked you for an analysis of the stock-out probabilities for various order quantities, an estimate of the profit potential, and to help make an order quantity recommendation. Novelty expects to sell Weather Teddy for $24 based on a cost of $16 per unit. If inventory remains after the holiday season, Specialty will sell all surplus inventories for $5 per unit. Novelty’s sales forecaster predicted the demand for Weather Teddy with an expected value of 20,000 units and a standard deviation of 5,100 units.

Compute the projected profit for the four order quantities suggested by the management team under three scenarios: worst case in which sales = 10,000 units, most likely case in which sales = 20,000 units, and best case in which sales = 30,000 units

For example, assuming the order quantity of 15,000 and the worst case scenario, the projected profit is 10,000($24) + 5,000($5) – 15,000($16) = $25,000. On the other hand, assuming the order quantity of 18,000 and the best case scenario, the projected profit is 18,000($24) – 18,000($16) = $144,000. You are expected to show all 4(3) = 12 projected profits.

Answer 1

Solution:

We are supposed to find 12 projected profits: denoting worst case scenario by WCS, most likely case scenario by MLCS and Best case scenario by BCS, for the ease of writing. So, the 12 cases to be considered here are order quantity of:

15,000 units under WCS,15,000 units under MLCS, 15,000 units under BCS, 18,000 units under WCS, 18,000 units under MLCS, 18,000 units under BCS, 24,000 units under WCS, 24,000 units under MLCS, 24,000 units under BCS, 28,000 units under WCS, 28,000 units under BLCS, and 28,000 units under BCS.

Also, Profits = Total revenue - total cost

Now, given the per unit market price, P = $24, per unit cost, C = $16, and per unit price for surplus inventories, Ps = $5, we can say that:

It's important to note that total revenue can be measured in one of the two ways for any case:

a) If order (or supply for that matter) exceeds the demand, total revenue function becomes:

TR = P*D + Ps*Surplus; where D is the demand case scenario and surplus (inventory) is measured as excess of order quantity over the demand case scenario, i.e, Surplus = Q - D

b) If the supply or order falls short of demand (i.e, Q < D), surplus inventory will equal 0 as entire order has been sold and the revenue will be earned on the number of units sold i.e, Q and not what is demanded (as Novelty couldn't meet the demand)

So, TR = P*Q in this case (as surplus = 0)

Similarly, cost will be incurred only on the number of units ordered thus, total cost, TC = C*Q, where again Q is order quantity and C is the per unit cost of teddy (as already defined)

Then, we can find the projected profits (PP), under all cases, as follows (also refer to the example mentioned in the question to see how it works).

1. 15,000 units under WCS, that is Q = 15,000 and D = 10,000

Here, Q > D, so, Surplus = 15000 - 10000 = 5000

So, TR = 24*10000 + 5*5000 = 240,000 + 25,000 = $265,000

And TC = 16*15000 = $240,000

Thus, PP = TR - TC = 265,000 - 240,000 = $25,000

This way, we can solve for remaining 11 cases as follows

2. 15,000 units under MLCS, that is Q = 15,000 and D = 20,000:

Here, Q < D, so, Surplus = 0

So, TR = 24*15000 = 360,000

And TC = 16*15000 = $240,000

Thus, PP = 360,000 - 240,000 = $120,000

3. 15,000 units under BCS, that is, Q = 15,000 and D = 30,000:

Here again, Q < D, so, Surplus = 0

So, TR = 24*15000 = 360,000

And TC = 16*15000 = $240,000

Thus, PP = 360,000 - 240,000 = $120,000 (same as above case)

4. 18,000 units under WCS, that is, Q = 18,000 and D = 10,000:

Here, Q > D, so Surplus = 18000 - 10000 = 8000

So, TR = 24*10000 + 5*(8000) = 240,000 + 40,000

And TC = 16*18000 = $288,000

Thus, PP = 240,000 + 40,000 - 288,000 = -$8,000

5. 18,000 units under MLCS, that is, Q = 18,000 and D = 20,000:

Here, Surplus = 0

So, TR = 24*18000 = 432,000

And TC = 16*18000 = $288,000

Thus, PP = 432,000 - 288,000 = $144,000

6. 18,000 units under BCS, that is, Q = 18,000 and D = 30,000:

Here, Surplus = 0

So, TR = 24*18000 = 432,000

And TC = 16*18000 = $288,000

Thus, PP = 432,000 - 288,000 = $144,000

7. 24,000 units under WCS, that is Q = 24000 and D = 10000:

Here, Surplus = 24000 - 10000 = 14000

So, TR = 24*10000 + 5*(14000) = 240,000 + 70,000

And TC = 16*24000 = $384,000

Thus, PP = 240,000 + 70,000 - 384,000 = -$74,000

8. 24,000 units under MLCS, that is, Q = 24,000 and D = 20,000:

Here, Surplus = 24000 - 20000 = 4000

So, TR = 24*20000 + 5*(4000) = 480,000 + 20,000

And TC = 16*24000 = $384,000

Thus, PP = 480,000 + 20,000 - 384,000 = $116,000

9. 24,000 units under BCS, that is Q = 24000 and D = 30000:

Here, Surplus = 0

So, TR = 24*24000 = $576,000

And TC = 16*24000 = $384,000

Thus, PP = 576,000 - 384,000 = $192,000

10. 28,000 units under WCS, that is Q = 28000 and D = 10000:

Here, Surplus = 28000 - 10000 = 18000

So, TR = 24*10000 + 5*(18000) = 240,000 + 90,000

And TC = 16*28000 = $448,000

Thus, PP = 240,000 + 90,000 - 448,000 = -$118,000

11. 28,000 units under MLCS, that is, Q = 28,000 and D = 20,000:

Here, Surplus = 28000 - 20000 = 8000

So, TR = 24*20000 + 5*(8000) = 480,000 + 40,000

And TC = 16*28000 = $448,000

Thus, PP = 480,000 + 40,000 - 448,000 = $72,000

12. 28,000 units under BCS, that is Q = 28000 and D = 30000:

Here, Surplus = 0

So, TR = 24*28000 = $672,000

And TC = 16*28000 = $448,000

Thus, PP = 672,000 - 448,000 = $224,000

Hope you find the answer helpful. Thank you!