## Info

The machine is currently priced at \$1,000,000. The cost of the machine will decline by \$100,000 per year until it reaches \$500,000, where it will remain. If your required return is 12 percent, should you purchase the machine? If so, when should you purchase it?

Abandonment Value We are examining a new project. We expect to sell 6,000 units per year at \$65 net cash flow apiece for the next 10 years. In other words, the annual operating cash flow is projected to be \$65 X 6,000 = \$390,000. The relevant discount rate is 16 percent, and the initial investment required is \$1,750,000.

a. What is the base-case NPV?

b. After the first year, the project can be dismantled and sold for \$1,250,000. If expected sales are revised based on the first year's performance, when would it make sense to abandon the investment? In other words, at what level of expected sales would it make sense to abandon the project?

c. Explain how the \$1,250,000 abandonment value can be viewed as the opportunity cost of keeping the project in one year.

Abandonment In the previous problem, suppose you think it is likely that expected sales will be revised upwards to 8,000 units if the first year is a success and revised downwards to 4,000 units if the first year is not a success.

a. If success and failure are equally likely, what is the NPV of the project? Consider the possibility of abandonment in answering.

b. What is the value of the option to abandon?

Abandonment and Expansion In the previous problem, suppose the scale of the project can be doubled in one year in the sense that twice as many units can be produced and sold. Naturally, expansion would only be desirable if the project is a success. This implies that if the project is a success, projected sales after expansion will be 16,000. Again assuming that success and failure are equally likely, what is the NPV of the project? Note that abandonment is still an option if the project is a failure. What is the value of the option to expand? Intuition and Option Value Suppose a share of stock sells for \$60. The risk-free rate is 5 percent, and the stock price in one year will be either \$70 or \$80.

a. What is the value of a call option with a \$70 exercise price?

b. What's wrong here? What would you do?

Intuition and Convertibles Which of the following two sets of relationships, at time of issuance of convertible bonds, is more typical? Why?

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