10,11,12,13, and 14 Introduction to Risk A firm is considering investing in a di
ID: 1155300 • Letter: 1
Question
10,11,12,13, and 14
Introduction to Risk A firm is considering investing in a digital camera factory. The factory can be built instantly at a cos, 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 risk-free rate of interest. Take the interest rate to be 10%, Set-$4000, and q = 0.5. 10. 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? 11. 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 12. 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. 13. 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. 14. 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?Explanation / Answer
Ans for 10
Expected Profit=q(500)+(1-q)(300)=400 as q=0.5
Initial Investment=I=$4000
We have that Expected Profit forever with rate=10%
NPW=I-Discounted Future Profit=4000-400/(0.1)=0
As Expected Price of Camera is $400 to Current Market Price of Camera there is no such added advantage if it waits for next year because there is chance for both Price would go up or go down
Hence it should wait to see whether Expected Price would go above $400 in future ( Next Year)
Ans b)
For given Price of Camera Investment should be less than $4000 to choose flexible option of investing
Ans c)
q=0.8
Expected Price=q(425)+(1-q)300=125q+300=125(0.8)+300=400
Even in this case NPW =0 which says that firm should wait for Expected Price to chnage
Ans d)
q=0.5
Ph=$600 and Pl=$200
E(P)=400. It should wait for change in Expected Price that is higher than Market Price $400
Ans e)
I=$2000
q=0.5
Ph=500 and Pl=300
r=10%
Discountd Future CashFlow=E(P)/r=400/0.1=$4000
NPV=-Investment+Discounted Future Cash Flow=$4000-$2000=$2000>0
Hence It should invest now.
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