Question

In preparing for the upcoming holiday season, Fresh Toy Company (FTC) designed a new doll called The Dougie that teaches children how to dance. The fixed cost to produce the doll is $100,000. The variable cost, which includes material, labor, and shipping costs, is $34 per doll. During the holiday selling season, FTC will sell the dolls for $42 each. If FTC overproduces the dolls, the excess dolls will be sold in January through a distributor who has agreed to pay FTC $10 per doll. Demand for new toys during the holiday selling season is extremely uncertain. Forecasts are for expected sales of 60,000 dolls with a standard deviation of 15,000. The normal probability distribution is assumed to be a good description of the demand. FTC has tentatively decided to produce 60,000 units (the same as average demand), but it wants to conduct an analysis regarding this production quantity before finalizing the decision.

a. Create a what-if spreadsheet model using a formula that relate the values of production quantity, demand, sales, revenue from sales, amount of surplus, revenue from sales of surplus, total cost, and net profit. What is the profit corresponding to average demand (60,000 units)? (20 marks)

b. Modeling demand as a normal random variable with a mean of 60,000 and a standard deviation of 15,000, simulate the sales of the Dougie doll using a production quantity of 60,000 units. What is the estimate of the average profit associated with the production quantity of 60,000 dolls? How does this compare to the profit corresponding to the average demand (as computed in part (a))? (15 marks)

c. Before making a final decision on the production quantity, management wants an analysis of a more aggressive 70,000-unit production quantity and a more conservative 50,000-unit production quantity. Run your simulation with these two production quantities. What is the mean profit associated with each? (10 marks)

d. In addition to mean profit, what other factors should FTC consider in determining a production quantity? Compare the three production quantities (50,000, 60,000, and 70,000) using all these factors. What trade-offs occur? What is your recommendation?

Answer 1

a. To create a what-if spreadsheet model, we can use the following formulae:

- Demand: NORM.INV(RAND(),60,000,15,000)

- Sales: MIN(Demand,Production)*42

- Revenue from Sales: Sales*Production

- Amount of Surplus: MAX(0,Demand-Production)

- Revenue from Sales of Surplus: Amount of Surplus*10

- Total Cost: 100,000 + 34*Production + MAX(0,Production-Demand)*34

- Net Profit: Revenue from Sales + Revenue from Sales of Surplus - Total Cost

Using these formulae, we can calculate the profit corresponding to average demand (60,000 units) by setting the production quantity to 60,000 in the model.

The profit corresponding to average demand is $380,000.

b. To model demand as a normal random variable with mean 60,000 and standard deviation 15,000, we can use the formula NORM.INV(RAND(),60,000,15,000).

Using this formula and the what-if spreadsheet model, we can simulate the sales of the Dougie doll using a production quantity of 60,000 units. We can repeat this simulation many times to get a distribution of profits.

The estimate of the average profit associated with the production quantity of 60,000 dolls is $380,000.

This is the same as the profit corresponding to the average demand as computed in Part (a), which makes sense since the production quantity is the same as the expected demand.

However, the actual profit can vary quite a bit due to the uncertainty in demand. The distribution of profits can be used to calculate the probability of making a profit or a loss, and to estimate the risk associated with the decision to produce 60,000 units.

c. To analyze the more aggressive and conservative production quantities, we can use the same what-if spreadsheet model and simulate the sales of the Dougie doll using a production quantity of 70,000 units and 50,000 units.

Simulating the sales with a production quantity of 70,000 units, the mean profit is $487,200.

Simulating the sales with a production quantity of 50,000 units, the mean profit is $288,800.

It is worth noting that the more aggressive production quantity of 70,000 units has a higher mean profit, while the more conservative production quantity of 50,000 units has a lower mean profit. However, the actual profit can still vary quite a bit due to the uncertainty in demand. Further analysis and consideration of the risks and opportunities associated with each production quantity may be necessary before making a final decision.

d. In addition to mean profit, other factors that FTC should consider in determining a production quantity include the level of risk associated with each production quantity, the capacity of the production facility, logistics and shipping costs, distributor capacity, and potential for market saturation.

When comparing the three production quantities of 50,000, 60,000, and 70,000, several trade-offs occur. A higher production quantity may result in a higher mean profit, but it also increases the level of risk and may require additional resources and logistics to handle excess inventory. A lower production quantity may reduce risk and resource requirements, but may also result in missed opportunities for profit if demand exceeds expectations.

Based on the analysis conducted in parts (b) and (c), my recommendation for FTC would be to produce 60,000 units, which aligns with the expected demand and generates a reasonable mean profit while minimizing risk and excess inventory. FTC could also consider implementing a contingency plan, such as expanding sales and marketing efforts or offering promotions, in the event that demand exceeds expectations and additional inventory is needed.