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- A major manufacturer of batteries, Static Inc., is preparing to invest in capacity for its next generation of technology. The price at which it will sell the batteries will be $60 per unit. Before production can begin, Static must install capacity. The investment required to install capacity is equal to $30 for each unit of annual capacity. There is no fixed cost. For example, an investment of $120 Million (M) would be required to install capacity that would allow up to 4M units of production per year. Assume that, after the capacity is installed in year 0, Static can observe the demand that occurs in each year before deciding how much to produce for that year. The production cost (for labor and materials) will be $30 per unit produced. The amount of capacity cannot be changed after year 0, and after two years, any capacity that they install will cease to have any value.

For all Net Present Value (NPV) calculations, assume that the annual cost of capital is 10%. Assume that the investment occurs at time = 0, and that all cash flows from production and sales in year t = 1 and t = 2 occur at the end of the year.

Questions:

1) The demand for batteries is expected to be 4M units in each of the two years that they will be sold. One approach to the analysis of capacity would be to treat the expected demand forecast of 4M units per year as completely deterministic, i.e. no uncertainty. Calculate the NPV of an investment in 4M units of capacity in which you assume that there will be exactly 4M units of demand in each year.

2) In order to do a more sophisticated analysis of the capacity investment, we need to know a bit more about the uncertainty of the demand forecast. Static’s demand planning group has characterized the uncertainty in terms of five distinct quantities of annual demand and the relative likelihoods of each as shown below:

Scenario

Very Weak

Weak

Moderate

Strong

Very Strong

Demand Quantity

2 Million

3 Million

4 Million

5 Million

6 Million

Probability

0.15

0.2

0.3

0.2

0.15

They believe that it is appropriate to assume that the above quantities and probabilities apply to each of the two years for which they will sell the batteries, and that the demands in year 2 are independent of the demands in year 1.

a) Suppose that Static were to install capacity to produce 4 Million units per year.

What would be the expected volume of unit sales in each year?

b) What would be the Net Present Value (NPV) associated with an investment in 4M units of capacity?

c) What is the amount of capacity in which they should invest in order to maximize the NPV of this project? (Hint: Given that the only possible demand realizations are integer multiples of 1M units, we need only consider capacity sizes of 2M, 3M, 4M,

5M, and 6M units. )

- A company can choose between two types of plant:

· Plant A: The plant contains a dual unit. The capacity is enough to serve the whole market. The initial capital cost is $50,000, and the operating cost for each unit is $11,000 per year.

· Plant B: The plant only contains a single unit. Hence the capacity of one plant B is only enough to serve half of the market. The initial capital cost for one plant B is $30,000, and currently the operating cost is $10,000 per year for the unit.

The operating cost for plant B is uncertain in the near future. Staring from next year, the cost for each unit could be $5,000 or $15,000 per year, with equal likelihood. The revenue obtained from serving the whole market is $60,000 per year. Assume that the revenue and operating cost occur at the end of each year. The annual interest rate is 5%. Consider a fouryear planning horizon.

Compare the following three strategies:

Strategy 1: start building one Plant A now

Strategy 2: start building two Plant B now (to serve the whole market)

Strategy 3: start building one Plant B now (to serve only half of the market). In the next year, build another Plant B if the operating cost goes down, and build a Plant A if the operating cost goes up.