1. Sixty-five years old Ashley Taylor has received $300,000 as a lump sum pension settlement. She has invested the money in an account that pays 6% interest per annum, compounded monthly. Ashley plans to withdraw $2,000 per month from this account. The first withdrawal will be after one month. How long will it be before this money is exhausted? If Ashley epects to live another 17 years, with a standard deviation of 7 years, what is the probability that the money will be used up during her life?
2. Mountaintop Corporation expects to pay a dividend of $3.00 next year, $3.25 after two years, $3.50 after three years, and $3.75 after the fourth and subsequent years. The required rate of return for the stockholders is 16%. Find the price of the stock now, and just after payment of the first $3.00 dividend.
3. Arthur Company is planning to acquire a machine for $90,000 which has an uncertain life. The machine may break down after 4 years (probability 10%), 5 years (probability 20%), or 6 years (probability 70%). The machine will be depreciated on a straight line basis for 5 years with no resale value. The income tax rate of Arthur is 30%, and its after-tax cost of capital 8%. Find the annual earnings generated by this machine so that its NPV is $10,000.
4. Frankfurt Corp has zero coupon bonds maturing after 10 years. The overall value of the firm is 4 times the face value of the bonds. The company has sigma of .55 and the riskless rate is 6%. You own $10,000 (face value) of these bonds. Find the present value of your investment.
5. Austin Company stock sells at $40 a share. It has Beta = 1.12 and sigma = .5. The risk-free rate is 40%, and thee expected return on the market is 11%. You have formed a portfolio with these two items in it:
1) 500 shares of Austin stock
2) A zero-coupon risk-free bond with face value $25,000, maturing after 1 year.
Calculate the following:
A) Initial value of the portfolio
B) Expected value of the portfolio after one year
C0 The Sigma of the portfolio