A firm is considering investing in a digital camera factory. The factory can be built instantly at a cost I, and can produce one camera forever, with no operating costs. The investment is assumed to be irreversible. Currently the price of the camera is $400 but it will change. With a given probability q the price will rise to $500, and with probability (1-q) will fall to $300. After that the price will remain at that level, higher or lower, forever. We assume that the risk over the future price of camera is unrelated to the rest of the economy, so cash flows can be discounted using the riskfree rate of interest. Take the interest rate to be 10%. Set I= $4000, and q = 0.5. Required:
a. Given those above values, should the firm invest now, or would it be better to wait a year and see how the price of cameras changes? How much is it worth to have the flexibility to make the investment decision next year, rather than having to invest either now or never?
b. If we think of this in another way, how high an investment cost I would the firm be willing to accept to have a fexible investment opportunity rather than an inflexible "now or never" one.
c. If the probability of change in price changes to q = 0.80, and the high price is now $425, and the low price is still $300, should the firm invest now, or would it be a better option to wait a year? Interpret your results.
d. Now suppose that the uncertainty over price increases. Assume that next period there is a probability q-0.5 of the price of cameras going up to $600, and the same probability of going down to $200, then would it be better to invest now or to wait? Interpret your results.
e. Based on the original conditions given in the question except that the investment I decreases to $2000, should the firm invest now or is it better to wait a year?