A retailer is planning for the holiday season and must decide how many units of a popular gift item to order from the supplier. Demand for the product is not known in advance. But from past experience, the retailer believes that the probabilities of different demand levels are as follows:

Demand (‘000 units)
10
200
500
800
1000
Probability
0.1
0.2
0.4
0.2
0.1

The retailer’s margin per unit sold is $50. Its cost of carrying unsold inventory till the end of the season is $10 per unit (e.g., if it orders 200,000 units and the actual demand is 10,000 units, then the unsold inventory is 190,000 and it costs $1.9 Million to carry it till end of the season). The retailer can return any unsold items at the end of the season at the cost at which they were purchased from the supplier. The supplier’s cost of producing the item is $80 per unit.
Expected Demand
1
40
200
160
100

Total: 501
A. Suppose the retailer had to decide between ordering 200,000, 500,000 and 800,000 units of this gift item, which of these order quantities will maximize its expected profits.
Profit of 800 units = 501*$50 - (800-501)*$10 = $22,060

B. How would your answer change if the retailer could not return unsold inventory at cost, but had to sell it at a loss of $80 per unit?
Profits of 800,000 units = 501*50 - (800-501)*($50+$80) = -1860
An automobile manufacturer is planning to enter a new market with a new car model. It will take two years of R&D to develop the new model. The first year of development requires an investment of $50M. The second year of product development requires $150M. If the manufacturer does not initiate product development now, it will miss the market opportunity. The manufacturer does not know the market potential in advance. It believes that there is a 50% chance that the demand will be high and it can earn profits of $100M each year for five years after product launch. It also believes that there is a 50% chance that the demand will be low and it can earn profits of $20M each year for five years after launch. The opportunity cost of capital is 20% (i.e., this is its discount rate to calculate the net present value of future cash flows).

A. Should the manufacturer invest in product development?
Year
0
1
2
3
4
5
6
Profit
-50
-150
100
100
100
100
100

20
20
20
20
20

NPV with high demand =