Question

Please show all your work if you use the Calculator. If done in Excel, please send me the spreadsheet / workbook.

1. What is the market value of the following bond?

Coupon 8%

Maturity date 2038

Interest paid semiannually

Par Value $1000

Market interest rate 10%

1. What is the market value of the following bond?

Coupon 9%

Maturity date 2028

Interest paid semiannually

Par Value $1000

Market interest rate 8%

1. What is the yield to maturity of the following bond?

Coupon 9%

Maturity date   2027

Interest paid semiannually

Par Value $1000

Market price $955.00

1. What is the current yield of bond in Question 3?

1. The risk free rate is 7%, the return in the market is 10%, and the beta is 1.30. What return must you receive to be satisfied that you are being fairly compensated for the risk of the firm?

1. What should a zero coupon bond maturing for $1000 in 9 years with a 7% market rate sell for?

Page Two

1. Preferred stock has a dividend of $12 per year. The required return is 6%. What should be the price per share?

1. Hurricane Corporation expects to grow its dividend by 5% per year. The current dividend is $2 per share. The required return is 8%.

1. What is the estimated value of a share of common stock?
2. If price is $40 and dividends were $1.50 per share but expected to grow at 4% per year, what would be the required rate of return?   

1. Compute the expected return for the following investment

State of nature            Probability                  Return

                              Boom                    25%                             20%

                              Average                60%                             8%

                              Recession             15%                             0%

1. The following are the expected returns on a portfolio of investments.    What is the expected rate of return on the portfolio?

Investment        # of shares         Price per share        Expected return

A.                    2000                            $20                              10%

B.                    3000                            $10                              15%

                        C.                    1000                            $15                              8%

1. You take out a $200,000 mortgage for 20 years at 6%.
   What is your monthly payment?

What is the principle and interest on the first payment?

What is the principle and interest on the twelfth payment?

How much interest will you pay over the 20 years?

1. You bought a house 8 years ago with a $250,000 mortgage. It was a 15 year loan with monthly payments which will pay off the loan when you make the last payment. The interest rate was 6%. What are your monthly payment and your current loan balance? How much interest will you pay in the upcoming year?  
   
   
   
   
   
   

Page Three

1. You want to retire has a millionaire. How much do you need to put away each month if:
   1. You use common stocks and have an average return of 10%?
   2. You use corporate bonds and have an average return of 6%?
   3. You use government bonds and have an average return of 4%?
   4. You put your money in a CD at 2.5% interest rate?
      (Please use your own age. If you are over 45, please solve for saving a $100,000.)
      
2. You are offered a contract with a signing bonus. If they offered you either $215,000 in cash or $2,000 a month for 15 years, guaranteed, which do you take (based strictly on the math)? Your safe rate of return is 7.5%.
   
3. You are 30 years old today and planning to retire at age 62. You want to plan your finances for living 35 years past age 62 and die dead broke. You determine you will need $3000 per month from age 62 for the 35 years.
   
   Your plan is to go live in the tropics, on the beach, and live on coconuts and fishing. Also, you need to conclude your retirement savings at age 55 because all your spare money then will be going to your children’s education.  
   
   The question is how much money you will need to save each month between now and 55 so that you can quit contributing.   The expected return on your investments over the whole period is 10% per year. Please ignore inflation.
   

Answer 1

Compute the semi-annual interest, using the equation as shown below:

Semi-annual = Face value*Rate of interest/ 2

                     = $1,000*8%/ 2

                     = $40

Hence, the semi-annual interest rate is $40.

Compute the semi-annual market rate, using the equation as shown below:

Semi-annual market rate = Annual rate/ 2

                                        = 10%/ 2

                                        = 5%

Hence, the semi-annual rate is 5%.

The maturity date is 2038 and the issue date is 2020, thus the time period in maturity is 18 years.

Compute the present value annuity factor (PVIFA), using the equation as shown below:

PVIFA = {1 – (1 + Rate)-Number of periods}/ Rate

                   = {1 – (1 + 0.05)-36}/ 5%

             = 16.5468517047

Hence, the present value annuity factor is 16.5468517047.

Compute the price of the bond, using the equation as shown below:

Bond price = (Semi-annual interest*PVIFA) + {Maturity value/ (1 + Rate)Time}

                   = ($40*16.5468517047) + {$1,000/ (1 + 0.05)36}

                   = $661.874068188 + ($1,000/ 5.79181613558)

                   = $661.874068188 + $172.657414633

                   = $834.531482821

Hence, the price of the bond is $834.531482821.