# 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?

- 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.
- At what price does the bond sell?

- 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.
- 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 If demand is not satisfactory, diet scotch will be withdrawn.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?

- Two machines, A and B, which perform the same functions, have the following costs and lives.

Type | PV costs | Llife |

Machine A | $ 6000 | 5 |

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.

Probability | 40% | 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:

Microsoft | Dell | Alaska Air | Southwest | Ford | G M | GMills | |

Volatility (Standard Deviation) | 37% | 50% | 38% | 31% | 42% | 41% | 18% |

Correlation with | |||||||

Microsoft | 1 | .62 | .25 | .23 | .26 | .23 | .10 |

Dell | .62 | 1 | .19 | .21 | .31 | .28 | .07 |

Alaska Air | .25 | .19 | 1 | .30 | .16 | .13 | .11 |

Southwest | .23 | .21 | .30 | 1 | .25 | .22 | .20 |

Ford | .26 | .31 | .16 | .25 | 1 | .62 | .07 |

GM | .23 | .28 | .13 | .22 | .62 | 1 | .02 |

GMills | .10 | .07 | .11 | .20 | .07 | .02 | 1 |

- 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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