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Probability Distribution Assignment

PART 2

8.The probability distribution of possible net present values for project X has an expected value of $20,000 and a standard deviation of $10,000. Assuming a normal distribution:

  • Calculate the probability that the net present value will be zero or less,
    • Calculate the probability that the NPV will be greater than $30,000,
    • Calculate the probability that the NPV will be less than $5,000

9. Macy announced they will pay a dividend of $2 on its common stock next year.  Thereafter, you expect dividends to grow at a rate of 6 percent a year in perpetuity. 

  • If you require a return of 12 percent on your investment, how much should you be prepared to pay for the stock?

10. Lord & Taylor bond has a 10 percent coupon rate and a $1,000 face value.  Interest is paid semiannually, and the bond has 20 years to maturity. 

  • If investors require a 12 percent yield, what is the bond’s value?

  1. General Electric bond carries a coupon rate of 8 percent, has 9 years until maturity, and sells at a yield to maturity of 9 percent.
    1. At what price does the bond sell?
  1. New York Concrete Cement Co  just paid its annual dividend of $2 per share, and it is widely expected that the dividend will increase by 5 percent per year indefinitely. What price should the stock sell at?  The discount rate is 15 percent.
  2. Black Bear catering is proposing to market a world renown kitchen appliance. The product will be test-marketed for 2 years in New York at an initial cost of $500,000. This test launch is not expected to produce any profits but should reveal consumer preferences. There is a 60 percent chance that demand will be satisfactory. In this case, Black Bear will spend $5 million to launch the scotch nationwide and will receive an expected annual profit of $700,000 in perpetuity. If demand is not satisfactory, diet scotch will be withdrawn. Black Bear requires a 12 percent return on its investments.
    • What is the expected NPV of the diet scotch?
  3. Two machines, A and B, which perform the same functions, have the following costs and lives.

TypePV costs Llife
Machine A $ 60005
Machine B $8000 7

            Which machine would you choose? Justify your decision. The two machines are mutually exclusive and the cost of capital is 15%.          

15.The following table shows the one-year return distribution of Startup, Inc.

Probability40%20%20%10%10%
Return-100%-75%-50%-25%1000%
  • Calculate the expected return.
    • Calculate the standard deviation of the return.

16. Using the data in the following table:

 MicrosoftDellAlaska AirSouthwestFordG MGMills
Volatility (Standard Deviation)37%50%38%31%42%41%18%
        
Correlation with       
Microsoft1.62.25.23.26.23.10
Dell.621.19.21.31.28.07
Alaska Air.25.191.30.16.13.11
Southwest.23.21.301.25.22.20
Ford.26.31.16.251.62.07
GM.23.28.13.22.621.02
GMills.10.07.11.20.07.021
  • What is the volatility (standard deviation) of an equally weighted portfolio of the seven stocks?
    • What is the covariance between the stocks of Alaska Air and Southwest?

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