help me solve decision tree real option problem

Real Options in a Technology Firm

Your firm has completed an analysis of its e-commerce business. Based on the findings of your evaluation team, a proposal has been developed to partner with an Internet startup as a basis for creating value for the firm (i.e., the potential of the complementary assets held by the firm to increase your firm's cash flows). The details of the proposal follow:

Proposal Description: An equity investment of $12 million (a 15% interest in the startup's equity) in the startup would give you full access to the complementary assets of the startup and would allow you to have significant influence over the development of these assets.

Expected Benefits (equivalent to after tax cash flows):

The partnership will leverage the firm's tightly held assets allowing it to expand its presence and reduce costs. An added benefit would be that the value of the equity in the startup could appreciate.

The risks/uncertainties are:

• The degree to which the complementary assets can increase your revenues and decrease your costs may vary within a wide range.
• The startup may not have a good business model, in which case your firm would lose all its equity investment by the end of year 2.

There are four possible scenarios:

1. Scenario one (good news, good news)

a. Your firm purchases the 15% equity interest for $12 million at time 0 (now)

b. The startup proves to be viable after 1 year, but there are no benefits yet (probability = .4)

c. By the end of year 2 the startup helps your firm, through the partnership, to leverage your assets and reduce operating costs by $3 million annually forever (a perpetuity beginning at the end of year 2). In addition, your equity in the firm is now worth $25 million. (Probability = .2)

The probability of this scenario is: .4 X .2 = .08

2. Scenario two (good news, bad news)

a & b are the same as scenario 1

c. By the end of year 2 the startup helps your firm, through the partnership, to leverage your assets and reduce annual operating costs by $2 million annually forever (a perpetuity beginning at the end of year 2). In addition, your equity in the firm is now worth $14 million. (Probability = .8)

The probability of this scenario is: .4 X .8 = .32

3. Scenario three (bad news, good news)

a. Your firm purchases the 15% equity interest for $12 million at time 0 (now)

b. At the end of year 1, the startup is having problems generating sufficient demand to attain profitability and will require another $6 million in cash from your firm (probability = .6)

c. By the end of year 2 the startup helps your firm, through the partnership, to leverage your assets and reduce annual operating costs by $2 million annually forever (a perpetuity beginning at the end of year 2). In addition, your equity in the firm is now worth $8 million. (Probability = .2)

The probability of this scenario is: .6 X .2 = .12

4. Scenario four (bad news, bad news)

a & b are the same as scenario 3

c. By the end of year 2 the startup the startup goes out of business, there is no annual gain to your firm (Probability = .8)

The probability of this scenario is: .6 X .8 = .48

Your firm's normal cost of capital is 12%. For investments of this nature, your CFO recommends using a rate of 25% to discount cash flows. Why?

Part I: Using the risk-adjusted cost of capital (25%), what is the expected net present value of accepting the proposal? All cash flows are after tax.

Based solely on the NPV should the company accept or reject the project?

The completed decision tree format at http://polaris.umuc.edu/~jhoward/655online/real-opt-prob-sol-decision-tree.doc may be helpful in laying out the cash flows.

Part II: Now suppose, instead of a direct equity investment, the startup, for a $2 million infusion of cash today, they grant you the option after year two, to purchase a 15% equity interest in the firm for $16 million. Under this arrangement the expected benefits of the partnership in terms of higher revenues and reduced costs would be the same as the basic proposal if your firm purchases the 15% interest. In scenarios where the firm will require more cash to stay afloat, the founders will provide the funding. Benefits to your firm will be zero if the $16 million investment is foregone. All cash flows are after tax. List all, if any, assumptions you make in analyzing the proposal.

Evaluate this proposal quantitatively and qualitatively.