Your firm is considering an immediate investment ...



Problems: Fourth Group

Finance-Moeller

1. Your company is considering investing $100 million today in R&D for a new, more efficient production method. One year later, this technology has a 75% chance of being worth 20% higher or a 25% chance of being worth 20% lower than the original investment. In a year, the company has a choice to invest an additional $100 million to implement the new production method. The second year cash inflows will again (same probability as the first year flows) be either 20% higher or lower than the previous inflow. Assume the r which reflects the riskiness of these cash flows is 10%.

a. Draw a decision tree with the relevant cash flows and information at each node.

b. Using a discounted cash flow analysis, what is the value of just the investing in R&D phase?

c. Using a discounted cash flow analysis and assuming you must make the second investment, what is the NPV of this project?

d. Now assume your company has the option to abandon the project at time 1 and not implement the new production method. Now what is the NPV using a discounted cash flow analysis.

e. Using the values above, what is the value of the option to abandon?

f. Using a binomial option pricing method, calculate the value of the option to abandon. Compare and contrast this value with the value from part (e).

2. You have been offered the right to buy a new sorting technology for $10 million in the next four years for your air cargo company. If you developed this technology today, you estimate that the PV of the after tax cash inflows from this development would be $9 million (i.e., NPV=9-10). However, there is some uncertainty about the cash inflows from this project. You estimate that the cash inflows may go up by 20% or down by 15% each year and the risk free rate is 5%.

a. Assume it is a European option, what is the most you are willing to pay for the right?

b. Assume it is an American option, what is the most you are willing to pay for the right?

3. Using the Black Scholes option pricing model find the value of the put and call for the following European non-dividend paying options. The underlying asset price is 50, the exercise price is 40, standard deviation is 20%, risk free rate is 3% and the time to maturity is 5 years (base case).

a. Relative to the base case, i.e., change only one variable relative to the base case for each cell, fill in the following table.

| |Call |Put | | | |

|Base | | | | | |

|S=70 | | |S=30 | | |

|X=60 | | |X=20 | | |

|Std Dev=40% | | |Std Dev=5% | | |

|Rf=5% | | |Rf=0.01% | | |

|t=10 | | |t=0.01 | | |

b. Compute the delta of the base case call and put. Interpret those numbers.

4. Your firm is considering an immediate investment opportunity that will require a $100 million outlay and the present value of the expected after-tax cash inflows is $90 million. The estimated standard deviation of the cash inflows is 65% per year and the risk free rate is 5%. In addition, depending upon the profitability of this project over the next three years, the project can either be abandoned for a liquidation value of $65 million or after tax cash inflows increased by 40% at a cost of $45 million. What is the NPV of this investment opportunity considering all its options? Is this estimate accurate, high or low? Explain.

5. At your company retreat you end up lingering over dinner with the V.P. of sales and the V.P. of manufacturing. Both are lamenting over the imminent rejection of their proposed investment in a joint venture in India. The estimated NPV is negative but both are convinced the project should be done for strategic reasons. You begin asking questions and realize that the valuation has not considered these strategic issues. The V.P. of sales believes that if the joint venture is completed, the firm will have the opportunity to open a sales office in India next year and drastically increase sales. The V.P. of manufacturing adds that if the sales office is a success, your firm will have the opportunity to buy the remainder of the business in three years from the J.V. partner.

Market and cash flow information: The risk free rate is 5%, the appropriate discount rate for the investment is 10%, assume that for each investment the last reported year’s cash flows continue forever with a growth rate of 2% and the standard deviation of the cash flows from the investment is 50%. NOTE: The FCF number excludes capital expenditures.

| |0 |1 |2 |3 |4 |5 |

|J.V. | | | | | | |

|FCF(excluding Capex) | |15 |15 |30 | | |

|Capex |300 |5 |5 |5 | | |

|Sales Office | | | | | | |

|FCF(excluding Capex) | | |7 | | | |

|Capex | |70 |1 | | | |

|Buyout | | | | | | |

|FCF(excluding Capex) | | | | |10 |30 |

|Capex | | | |120 |130 |3 |

a) You begin to explain to them the concept of real options and they seem willing to listen. Draw and label a decision tree which characterizes the Indian investment opportunity.

b) What is the value of the joint venture without the strategic issues?

c) What is the value of the joint venture with the strategic issues?

d) You have an elevator ride to convince the CEO that the strategic issues should not have a value of zero. Be concise.

6. Draw and label decision tree’s which characterizes the following situations. Describe the option(s), i.e. put(s), call(s)?

a. You are renovating your plant and you need to make a final decision whether to add another production line.

b. Your company produces personal computers. Because the speed of technology changes is unpredictable, you manage your inventory and production process so you can stop production quickly.

c. Instead of buying additional warehouse space you have leased so you can easily decrease your amount of storage.

d. You have purchased a production process which is very flexible. It allows you to leave the plant open for successive years, shut down then reopen a year later or abandon the process all together.

7. You work for a commodity chemical company. The project will cost $60 million immediately for permits and preparation, which will take a year. At the end of that year, the firm could invest $400 million to complete the design phase. Once the design phase is over, the firm has a two-year window during which it can invest the $800 million needed to build the plant. The present value of the cash inflows for the plant is $1 billion and these flows will increase by 20% and decrease by 16.67%. The risk free rate is 8%. Assume the underlying asset has a lognormal distribution.

(This problem is from Copeland and Tufano, HBR 2004.)

8. The board of directors is listening to a presentation by the head financial analyst for launching a new product. The analyst performs an NPV analysis on the first possible investment and finds that the NPV is negative so she recommends that the project be rejected. In justifying her discount rate, the analyst discusses the uncertainty of the future expansion of this product so though the company’s WACC is 10%, this project is riskier than your core business. The head analyst on this project thinks the appropriate discount rate should be 13% (risk free rate is 5%).

The analyst valued the following cash flows at 13%. The new product requires an initial investment of $200 million and after tax cash inflows are expected to be $20 forever. You believe these cash flows will have a normal distribution.

However, the president of the division believes that the analyst is wrong on two counts and has the lunch break to put together a quick analysis showing the project is worth while. The president has texted you to meet him in the conference room because he needs your assistance.

Once in the conference room, he shows you the analyst’s presentation and begins to explain where he disagrees with the analyst. First, he believes that the discount rate is too high. At a minimum the project should be valued at the company’s WACC because the uncertainty the analyst mentions is based on the expansion opportunities, not on the riskiness of the valued cash flows. The president even argues that the rate should be lower (say 8%) because of its strategic importance.

Second, he believes that the analyst’s cash flows are wrong and she should have included the expansion cash flows. If all goes well, he believes that after three years, he can invest $400 million and get $50 million forever. Finally, after that three year investment, the division can invest another $800 million and yield after tax cash inflows of $110 forever. The president believes that the standard deviation of those flows is approximately 30%.

First Invest |0 |1 |2 |3 |4 |5 |6 |7 |8 |9 | |FCF |-200 |20 |20 |forever | | | | | | |Second Invest | | | | | | | | | |FCF | | | |-400 |50 |50 |forever | | | |Third Invest | | | | | | | | | | |FCF | | | | | | |-800 |110 |110 |forever | |

What are you are you going to recommend the president do? What is the appropriate r? If you include all the investment opportunities in a DCF analysis what is the NPV? Is there a better way to value this project?

9. If you assume the cash flows of the underlying asset is normally distributed, does it change your valuation? If so, calculate the new value.

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