A company specializing in computer games is evaluating an investment project to create a new game. The project requires collaboration of two teams: (1) creative artists and (2) programmers.

Creative artists

The artists team will start working immediately and will require 8 equal consecutive monthly investments of $2 million each. The investments occur at the end of the month, with the first investment made at the end of month 1 and the last investment made at the end of month 8.

Programmers

The programmers team will start working in month 5 and will require 5 monthly investments. The first investment, in the amount of $4 million, will occur at the end of month 5. The remaining 4 investments will be made at the end of each of the following 4 months, and their amounts will decrease by 10% per month.

The game

The game, which is expected to have infinite life, will be released in month 9 and will generate its first cash flow at the end of month 9. The after-tax cash flow per one game copy is $20, and the initial monthly sales will be 100,000 copies in month 9. After month 9, the after-tax cash flow per copy will remain the same, but the number of copies sold will decline at a constant monthly rate g, as users start switching to newer games. All cash flows from game sales accrue at the end of the month.

The task

If the Profitability Index for this project is 1.1, what is the monthly rate of decline in sales (g)? The annual discount rate is quoted as an APR of 12%.

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