Question

A company determined to expand its existing capacity for the next three years. Assume the demand for the next three years are 15, 30, and 60, respectively and the existing capacity is 8. The cost of capacity expansion is 100 + x² where x is the amount of the capacity expanded (Note that if expansion is zero, then the cost is zero, NOT 100!).

Find the optimal capacity expansion plan for the next three years using discount rate of one.

Answer 1

In the given question, let us analyse various expansion plans:

1. Expand all the capacity in 1st year itself at cost of 100+(60-8)*2 = 204 at end of year 1

2. Expand yearwise for 3 times: at 1st year at cost of 100+(15-8)*2 = 114

   at 2nd year at cost of 100+(30-15)*2 = 130

at 3rd year at cost of 100+(60-30)*2 = 160

So, Total Cost of Expansion comes to 404.

3. Expand yearwise for 2 times: at 1st year at cost of 100+(15-8)*2 = 114

   at 2nd year(incl expansion for 3rd year) at cost of 100+(60-15)*2 = 190

So, Total Cost of Expansion comes to 304.

Since in the question it is said to discount at rate of one, considering the projected outflows, it is suggested to expand the capacity one time at 1st year in order to save the fixed costs of Expansion on Multiple Times.

Happy Learning and All the Best.