Capital Budgeting Decisions under Uncertainty: Case Study

A professor in the Computer Science department at Dar Al Uloom University has

just patented a new search engine technology and would like to sell it to you, an

interested venture capitalist. The patent has a $17-$year life. The technology will take

a year to implement $($there are no cash flows in the first year$)$ and has an upfront cost

of $$100$ million. You believe this technology will be able to capture $1\%$ of the

Internet search market, and currently this market generates profits of $$1$ billion per

year. Over the next five years, the risk$-$neutral probability that profits will grow at

$10\%$ per year is $20\%$ and the risk$-$neutral probability that profits will grow at $5\%$ per

year is $80\%.$ This growth rate will become clear one year from now $($after the first

year of growth$).$ After five years, profits are expected to decline $2\%$ annually. No

profits are expected after the patent runs out. Assume that all risk$-$free interest rates

are constant $($regardless of the term$)$ at $10\%$ per year.

a$.$ Calculate the NPV of undertaking the investment today.

b$.$ Calculate the NPV of waiting a year to make the investment decision using

Scenario Analysis and Decision Trees.

c$.$ What is your optimal investment strategy?