DO NOT USE EXCEL1. Sixty-five years old Ashley Taylor has received $300,000 as a lump sum pension...

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DO NOT USE EXCEL1. 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 stock2) A zero-coupon risk-free bond with face value $25,000, maturing after 1 year.Calculate the following:A) Initial value of the portfolioB) Expected value of the portfolio after one yearC0 The Sigma of the portfolio

David · Accepted Answer

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 expects 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? 
          Solution:- 
         
          Amount received as lump sum pension = $300,000 
      Interest rate on investment = 6% p.a Compounded monthly 
     monthly withdrawal = $2,000 
        
          Computation of time period it will take to exhaust the total investment:- 
   
          Let the time period = t 
        
          Using the following method we can find the time period in which the total money will exhaust 
 
          At correct time period the investment balance would be Zero:- 
    
          Let t = 20 years 
         
          Balance in the investment at the end of 20 years:- 
      
          Balance = current amount in the investment account - Future value of $2,000 withdrawn per month @6% 
Balance = 300000 -  2,000*PVAF 6%/12, 20*12 -  
      Balance = 300000- (2000*139.581) 
       Balance = $20,838 
         
          Let t = 23 years 
         
          Balance in the investment at the end of 23 years:- 
      
          Balance = current amount in the investment account - Future value of $2,000 withdrawn per month @6% 
Balance = 300000 -  2,000*PVAF 6%/12, 23*12 -  
      Balance = 300000- (2000*149.511) 
       Balance = $978 
         
          Thus it will take approximately 23 years and few months for the investment to exhaust in case Ashley 
Taylor withdrew $2,000 per month from her account and the account offers 6% rate of interest per 
annum compounded monthly.
          Computation of 
probability:-
          Z = The Number of standard deviations away from the mean point of interest lines. 
  
          Z = (X-µ)/σ 
         Z = (23 - 8.17)/7 
         Z = 2.1186 Standard 
deviation
          Note: Look at the Z value tables available in you textbook or internet, 
    
          The positive sign of standard deviation signifies that the point of interest will lie on the right hand side of the mean. 
          At 2.12 the area between the mean and the point of interest is 0.0170 or 1.7% 
   
          50% + 1.70% = 51.

DO NOT USE EXCEL 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...

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