$1.$ #expand option, option value

A company is considering investing in a project.

If the market condition is good, the project payoff is $39,000,$ with probability $0\mathrm{.}3.$

If the market condition is normal, the project payoff is $8,000,$ with probability $0\mathrm{.}2.$

If the market condition is bad, the project payoff is $3,000($the probability is $1$ minus the sum of above two probabilities$)$

The initial investment is $16,000.$ The firm needs to borrow money from a VC to finance this investment.

After extensive research, the firm finds that if the market condition is good, the company could investment addition money $4,000$ to expand operations, which would result in twice the original payoff.

The VC provides the firm an option to borrow the additional investment if needed. How much is this expansion option worth?

$2.$ #convert option, option value$\_$exam

Let's consider a company that is evaluating an investment in a real estate development project. The initial investment required is $$7$ million to acquire the land and start construction. However, there is uncertainty regarding the future demand for commercial space in the area and that will affect the project value.

High demand for commercial space: $0\mathrm{.}5$ probability. The project value will be $$22$ million.

Low demand for commercial space: $(1-0\mathrm{.}5)$ probability. The project value will be $$3$ million.

The company has the option to convert the property into condominiums if the demand for commercial space is low. If the demand is high, they will continue with the rental income from the commercial spaces.

The company estimates that if they convert the property into condominiums, it will require an additional investment of $$6$ million. They expect the condominium conversion to generate sales revenue of $$14$ million.

The real option value is million?

#convert option, option value$\_$exam

Let's consider a company that is evaluating an investment in a real estate development project. The initial investment required is $$7$ million to acquire the land and start construction. However, there is uncertainty regarding the future demand for commercial space in the area and that will affect the project value.

High demand for commercial space: $0\mathrm{.}5$ probability. The project value will be $$22$ million.

Low demand for commercial space: $(1-0\mathrm{.}5)$ probability. The project value will be $$3$ million.

The company has the option to convert the property into condominiums if the demand for commercial space is low. If the demand is high, they will continue with the rental income from the commercial spaces.

The company estimates that if they convert the property into condominiums, it will require an additional investment of $$6$ million. They expect the condominium conversion to generate sales revenue of $$14$ million.

The real option value is million?