Aacorp has experienced an increase in demand for its product and has decided that it will expand its factory, since capacity is currently too low to meet demand. It is not sure whether demand will continue to increase in the future or not. It is considering two options. A small expansion will be sufficient to meet its current demand and also its future demand if demand levels off. Its second option is a large expansion, which will be more than sufficient for current demand and will also handle future demand even if continues to increase. They have estimated that the probability that demand will continue to increase is 40%.
A small expansion will cost $2 million while a large expansion will cost $4 million. If they make a small expansion and demand continues to increase, they will have to make a second expansion in 18 months and the net present value of that second expansion is $3 million.
The net present value of the future revenue resulting from the expansion will be $5 million under two conditions: 1) demand levels off, or 2) demand continues to increase, but Aacorp chooses a small expansion and does not make a second expansion in 18 months. The net present value of the future revenue will be $9 million if demand continues to increase and Aacorp either chooses a large expansion or makes a second expansion in 18 months after choosing a small expansion.
(a) Construct a decision tree and solve it.
(b) Should Aacorp make a small expansion or a large expansion?
(c) What is the resulting expected net present value of its future profits?

Question

Quizplus · Accepted Answer

The Answer of Aacorp has experienced an increase in demand for its product and has decided that it will expand its factory, since capacity is currently too low to meet demand. It is not sure whether demand will continue to increase in the future or not. It is considering two options. A small expansion will be sufficient to meet its current demand and also its future demand if demand levels off. Its second option is a large expansion, which will be more than sufficient for current demand and will also handle future demand even if continues to increase. They have estimated that the probability that demand will continue to increase is 40%.
A small expansion will cost $2 million while a large expansion will cost $4 million. If they make a small expansion and demand continues to increase, they will have to make a second expansion in 18 months and the net present value of that second expansion is $3 million.
The net present value of the future revenue resulting from the expansion will be $5 million under two conditions: 1) demand levels off, or 2) demand continues to increase, but Aacorp chooses a small expansion and does not make a second expansion in 18 months. The net present value of the future revenue will be $9 million if demand continues to increase and Aacorp either chooses a large expansion or makes a second expansion in 18 months after choosing a small expansion.
(a) Construct a decision tree and solve it.
(b) Should Aacorp make a small expansion or a large expansion?
(c) What is the resulting expected net present value of its future profits?

Aacorp Has Experienced an Increase in Demand for Its Product