Using the Bi-nomial model for an asset with the following information, what is the risk neutral probability of up movement and down movement?
 The size of up-move = 1.4
The size of down-move = 0.7
Risk free rate = 4%

 If you have purchased a call option on a stock with X of $30 for a premium of $4, later on the share’s price has increased to $40 and the premium increased to $5, what is the breakeven point?

On a one-year binomial model the of value of an asset in the up case is 1.2 and 0.85 in the down case. The current value of the asset is 1 and the annual interest rate is 6 percent. What is the risk neutral probability of an up move?

 In a one-year binomial model the value of the up movement is 1.3 and the value of the downside movement is 0.75 and the current value of the asset is 1 and the interest rate is 5 percent. What is the risk neutral probability of an up move?

The Black Scholes model of option pricing uses which of the following inputs

How does an increase in interest rates affect the value of a timing option and an expansion option?

(hint both are like calls)

If the volatility increased, what would be the effect on the value of Timing Option and Expansion Option:

In real options valuation using Black Scholes Model BSM, the result will be:

Which of the following would be the most accurate way of characterizing growth options and options to delay investments

A micro chip manufacturer currently manufactures under exclusive patent on technology that slows it to produce chips that process faster while using less energy.
The company is considering building a new plant to expand production of the chips but is concerned that its chip may not be competitive by the time the construction is completed. It is considering licensing the production immediately to a competitor to expand production immediately but will lose some of its potential profits.
Which of the following describes the type(s) of real option that ownership of the patent creates for the company?

Difficult Q: An automobile dealer has obtained the exclusive right to sell Teslas in Egypt if they invest EGP 100 million in building a showroom and servicing facility exclusively for Teslas which will be priced in USD. They are unsure if the local demand will generate enough profits to justify this investment. Tesla has given the dealer two years to complete construction of the showroom and servicing facility but the dealer estimated that construction should only take one year at the most. An analysis of the venture indicates the value of the investment including the option to delay construction for one year, is equal to the NPV projected for the dealership if construction begins immediately.

Which of the following might be valid reasons for deciding to delay construction despite the two alternatives having equal expected value.

 i) Concerns that Tesla's recent quality control problems might damage future demand.
ii) Expectations of lower risk free interest rates that would impact the value of the option to delay.
 iii) concerns about other electric vehicle manufacturers opening new dealerships.
iv) Projections of a strengthening of EGP versus the USD

Difficult Q: Bisco Misr is evaluating a plan to construct a new biscuit factory in stages over the next two years. Including the value of the expansion options, the staged construction of the biscuit factory has a positive  NPV. Recently Bisco Misr's marketing department has indicated that they are able to make estimates of biscuit sales with greater confidence. This has reduced the volatility of their sales projections. have also forecast that biscuit prices will increase more than expected. How will the value of the expansion options be affected?

If your company is making future investment stages, and the volatility of the sales projections has decreased (strong confidence in forecast) and the prices have been forecasted to increase, which will increase overall sales.
How will the value of the expansion options be affected?

ABC Company management is reviewing the value of a future investment opportunity (Growth option) based on current projections. The forecasted operating net revenues have an NPV that is less than the cost of building the manufacturing capacity.

Which of the following actions might the management take to enhance the value of the real option inherent in the future investment opportunity:

i.    Enter into long term contracts with suppliers to obtain better prices on input cost
ii.    Engage in technology research and development to bring down projected manufacturing costs of the product
iii.   Conduct a marketing campaign to increase the projected sales revenue of the product
iv.   Alter the company’s capital structure reduce the firm’s WACC to increase the NPV of projected cash flow

Difficult Q: An investor has an agreement with a national hamburger chain operator giving him the exclusive regional rights to open a franchise. The agreement gives the investor the right to open the restaurant immediately or in 1 year. If the investor fails to open the franchises either right away or in 1 year, the agreement expires. The investor has the following information regarding revenues, costs and interest rates:
Cost of investment (today or in 1 year): $3.6 million
First year free cash flow: $350,000
Annual growth rate of free cash flow: 3%
Risk-free rate: 6%
Opportunity cost of capital: 14%
Volatility: 36%
What is the value of making the investment in 1 year EXCLUDING  the option to delay?