# Basic concepts in Finance

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Q5-7

DR. FRANKENSTEIN IS CONSIDERING BUILDING A PORTFOLIO CONTAINING TWO ASSETS, S AND G.

ASSET S WILL REPRESENT 70% OF THE DOLLAR VALUE OF THE PORTFOLIO, AND ASSET G WILL REPRESENT THE REMAINING 30%. THE EXPECTED RETURNS OVER THE NEXT 5 YEARS 2001-2005, FOR EACH OF THESE ASSETS IS SHOWN BELOW:

EXPECTED RETURN

YEAR ASSET S ASSET G Expect. Port. Return Expect. Value of Port. Std. Deviation.

2001 15% 15%

2002 16% 14%

2003 17% 13%

2004 19% 11%

2005 21% 9%

5. CALCULATE THE EXPECTED PORTFOLIO RETURN, k p, FOR EACH OF THE 5 YEARS.

6. CALCULATE THE EXPECTED VALUE OF PORTFOLIO RETURNS, k p, OVER THE 5-YEAR PERIOD.

7.CALCULATE THE STANDARD DEVIATION OF EXPECTED PORTFOLIO RETURNS, s k p, OVER THE 5-YEAR PERIOD.

Q8-10

James Snooka is building a portfolio containing two assets, S and P. Asset S will represent 70 Percent of the dollar value of the portfolio, and asset P will account for the other 30 percent. The expected returns over the next 8 years, 2002 - 2009, for each of these assets, are shown in the following table:

Expected Return

Year Asset S Asset P Exp. Port. Ret. Expect. Value Std. Dev.

2002 15% 20%

2003 15 17

2004 17 15

2005 18 14

2006 18 14

2007 19 14

2008 20 12

2009 20 10

8. Calculate expected portfolio return kp, for each of the 8 years.

9. Calculate the expected value of portfolio returns kp over the 8 year period.

10. Calculate the standard deviation of expected portfolio returns, skp, over the 8 year period.

Q11-20

10. - 15. Calculate the present value of the annuity assuming that it is an ordinary annuity.

16-20. Calculate the present value of the annuity assuming that it is an annuity due.

Case Amount of Annuity Interest Rate Period / Years

A $14,000 9% 3

B $17,500 13% 15

C $975 18% 7

D $1,127,000 4% 9

E $10,000 7% 3

21- 25. Calculate the future value of the annuity assuming that it is an ordinary annuity.

26-30. Calculate the future value of the annuity assuming that it is an annuity due.

Case Amount of Annuity Interest Rate Period / Years

A $42,000 4% 7

B $77,500 11% 13

C $975,000 17% 11

D $27,000 20% 16

E $1,000 7% 4

Albertus Magnus College wishes to set Prof. Sulkis up for life with a jumbo bonus upon his retirement. By contract Mike will retire at the end of 22 years. Upon retirement, he is entitled to receive a bonus payment of $750,000. If he dies prior to retirement, the bonus will pass to his three heirs; Bud, Weis and Er.

During the 22-year "accumulation period" Albertus wishes to fund the annuity by making equal annual end-of-year deposits into an account earning 11% interest.

A) How large must Albertus's equal annual end-of-year deposits into the account be over the 22-year accumulation period to fully fund Prof. Sulkis's retirement bonus?

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#### Solution Summary

Solutions to given problems provide methodology to find the mean and standard deviation of return, present value of annuities and future values of annuities.