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You own a small manufacturing plant that currently generates revenues of $2 million per year.Next year,based upon a decision on a long-term government contract,your revenues will either increase by 20% or decrease by 25%,with equal probability,and stay at that level as long as you operate the plant.Other costs run $1.6 million per year.You can sell the plant at any time to a large conglomerate for $5 million and your cost of capital is 10%.
-Given the embedded option to sell the plant,the value of your plant will be closest to:
A)$5.0 million.
B)$4.0 million.
C)$6.5 million.
D)$8.0 million.

Question

Quizplus · Accepted Answer

To calculate the value of the plant with the embedded option to sell, we need to use the decision tree approach.

Starting from the current year:
- Revenue: $2 million 
- Costs: $1.6 million 
- Profit: $0.4 million

Next year, there are two possible scenarios with equal probability:

- Revenue: $2.4 million ($2 million * 1.2) 
- Costs: $1.6 million 
- Profit: $0.8 million 
OR 
- Revenue: $1.5 million ($2 million * 0.75) 
- Costs: $1.6 million 
- Profit: -$0.1 million

In the first scenario, the plant generates a profit of $0.8 million, and we can choose to keep operating the plant for another year or sell it to the conglomerate for $5 million immediately. 
- If we keep operating, the value of the plant will be: 
     $0.8 million / (1 + 0.1) = $0.73 million 
- If we sell the plant, the value of the plant will be: 
     $5 million / (1 + 0.1) = $4.55 million

In the second scenario, the plant generates a loss of $0.1 million, and our only option is to sell it to the conglomerate for $5 million. 
- The value of the plant will be: 
     $5 million / (1 + 0.1) = $4.55 million

To calculate the overall value of the plant with the embedded option to sell, we need to weight the two possible scenarios by their probability:

Expected value of the plant = 0.5 * $4.55 million + 0.5 * $0.73 million 
Expected value of the plant = $2.64 million

Therefore, the closest answer choice is C) $6.5 million.

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