**2. (Calculating rates of return) **The S&P stock index represents a portfolio comprised of 500 large publicly traded companies. On December 24, 2007, the index had a value of 1,410 and on December 24, 2008, the index was approximately 926. If the average dividend paid on the stocks in the index is approximately 3.0 percent of the value of the index at the beginning of the year, what is the rate of return earned on the S&P index? What is your assessment of the relative riskiness of investing in a single stock such as Google compared to investing in the S&P index

a. The rate of return earned on the S&P 500 is what percent? (Round to two decimal places.)

34.85 is wrong

b. What is your assessment of the relative riskiness of investing in a single stock, such as Google, compared to investing in the S&P index? (Select the best choice below.)

In general, investing in a single stock has the same relative riskiness as investing in the S&P index.

There is not enough information given to answer this question.

In general, investing in the S&P index is riskier than investing in a single stock.

In general, investing in a single stock is riskier than investing in the S&P index.

____________________________________________________________________________________

4. Blaxo Balloons manufactures and distributes birthday balloons. At the beginning of the year Blaxo’s common stock was selling for $17.66 but by year end it was only $15.41.

The firm paid a total cash dividend of $2.71 during the year.

The rate of return you would have earned is 2.60%

What is the perecent rate of return you would have earned if the firm paid no cash dividend? (Round to two decimal places.)

-12.70% is wrong

____________________________________________________________________________________

- Syntex, Inc. is considering an investment in one of two common stocks. Given the information that follows, which investment is better, based on the risk (as measured by the standard deviation) and return?

Common Stock A | | Common Stock B | |

Probability | Return | Probability | Return |

0.2 | 13% | 0.25 | -6% |

0.6 | 17% | 0.25 | 8% |

0.2 | 21% | 0.25 | 15% |

0.25 | 23% |

- Given the information in the table, the expected rate of return for stock A is ____%

(Round to two decimal places.)

b. The standard deviation of stock A is _____% (Round to two decimal places.)

c. Given the information in the table, the expected rate of return for stock A is _____ %

(Round to two decimal places.)

- Given the information in the table, the expected rate of return for stock B is ____%

(Round to two decimal places.)

- The standard deviation of stock B is _____% (Round to two decimal places.)

- Given the information in the table, the expected rate of return for stock B is _____ % (Round to two decimal places.)

8. Marsh Inc. had the following end-of-year stock prices over the last five years and paid no cash dividends:

Time | Marsh |

1 | $8 |

2 | $13 |

3 | $17 |

4 | $5 |

5 | $8 |

The annual rate of return at the end of year 2 is 62.50

The annual rate of return at the end of year 3 is 30.77%

The annual rate of return at the end of year 4 is -70.59%

The annual rate of return at the end of year 5 is 60.00%

- What is the percentage for the arithmetic average rate of return of Marsh’s stock over this period? (Round to two decimal places.) –

-2.32% is wrong.

- What is the geometric average rate of return earned by investing in Marsh’s stock over this period?
- Considering the beginning and ending stock prices for the five-year period are the same, which type of average rate of return (the arithmetic or geometric) better describes the average annual rate of return earned over the period?

9. ** **The common stock of the Brangus Cattle Company had the following end-of-year stock prices over the last five years and paid no cash dividends:

Time | Brangus Cattle Company |

1 | $15 |

2 | $11 |

3 | $13 |

4 | $21 |

5 | $29 |

The annual rate of return at the end of year 2 is -26.67%

The annual rate of return at the end of year 3 is 18.18%

The annual rate of return at the end of year 4 is 61.54%

The annual rate of return at the end of year 5 is 38.10%

**b. **The arithmetic average rate of return earned by investing in Brangus Cattle Company’s stock over this period is What percent? (Round to two decimal places.)

18.23% is wrong

10.

Time | Value of Harris Stock | Annual Rate of Return | Value of Pinwheel Stock | Annual Rate of Return |

1 | $8 | $19 | ||

2 | $9 | 12.50% | $34 | 78.95% |

3 | $13 | 44.44% | $31 | -8.82% |

4 | $16 | 23.08% | $25 | -19.35% |

**a.**

**b. **The arithmetic average rate of return earned by investing in Harris stock over this period is 26.67%

The arithmetic average rate of return earned by investing in Pinwheel stock over this period is 16.93%

The geometric average rate of return earned by investing in Harris stock over this period is _____%

(Round to two decimal places.)

27.95% is wrong

**c. **Compute a three-year rate of return spanning the entire period (i.e., using the ending price for period 1 and ending price for period 4).

**d. **Since the rate of return calculated in part **c** is a three-year rate of return, convert it to an annual rate of return by using the following equation:

1+

**e. **How is the annual rate of return calculated in part **d** related to the geometric rate of return? When you are evaluating the performance of an investment that has been held for several years, what type of average rate of return (arithmetic or geometric) should you use? Why?

11. Imagine that Homer Simpson actually invested the $100,000 he earned providing Mr. Burns entertainment 10 years ago at 9 percent annual interest and that he starts investing an additional

$1,600 a year today and at the beginning of each year for 10 years at the same 9 percent annual rate. How much money will Homer have 10 years from today?

(Round to the nearest cent.)

$764918.49 is wrong

12. Calvin Johnson has a $5,500 debt balance on his Visa card that charges 17.7 percent APR compounded monthly. In 2009, Calvin’s minimum monthly payment is 3 percent of his debt balance, which is $165. How many months (round up) will it take Calvin Johnson to pay off his credit card if he pays the current minimum payment of $165 at the end of each month? In 2010, as the result of a federal mandate, the minimum monthly payment on credit cards rose to 4 percent.

A. If Calvin made monthly payments of $165 at the end of each month, how long would it take to pay off his credit card? (Round up to the nearest unit.) 66 and 87 is wrong

b. If Calvin made monthly payments of $220 at the end of each month, how long would it take to pay off his credit card? (Round up to the nearest unit.)

13. Selma and Patty Bouvier are twins and both work at the Springfield DMV. Selma and Patty Bouvier decide to save for retirement, which is 35 years away. They’ll both receive an annual return of 9 percent on their investment over the next 35 years. Selma invests $2,100 per year at the end of each year only for the first 10 years of the 35-year period—for a total of $21,000 saved. Patty doesn’t start saving for 10 years and then saves $2,100 per year at the end of each year for the remaining 25 years—for a total of $52,500 saved.

**a.** How much will Selma have when she retires? (Round to the nearest cent.)

$153,371.54 is wrong

b. How much will Patty have when she retires? (Round to the nearest cent.)

16. What is the present value of a perpetual stream of cash flows that pays $90,000 at the end of year one and then grows at a rate of 5% per year indefinitely? The rate of interest used to discount the cash flows is 12%.

The present value of the growing perpetuity is _____ (Round to the nearest cent.)

$750,000.00. is wrong

____________________________________________________________________________________

17. **(Present value of annuities and complex cash flows)**

You are given three investment alternatives to analyze. The cash flows from these three investments are as follows:

Year | A | B | C |

1 | 14000 | 0 | 14000 |

2 | 14000 | 0 | 0 |

3 | 14000 | 0 | 0 |

4 | 14000 | 0 | 0 |

5 | 14000 | 14000 | 0 |

6 | 14000 | 70000 | |

7 | 14000 | 0 | |

8 | 14000 | 0 | |

9 | 14000 | 0 | |

10 | 14000 | 14000 |

Assuming an annual discount rate of 18 percent, find the present value of each investment.

**a.** What is the present value of investment A at an annual discount rate of

18 percent? $______ (Round to the nearest cent.)

**b.** What is the present value of investment B at an annual discount rate of 22 percent? **______ **(Round to the nearest cent.)

18. ** **How much do you have to deposit today so that beginning 11 years from now you can withdraw $9,000 a year for the next 8 years (periods 11 through 18) plus an *additional *amount of $18,000 in the last year (period 18)? Assume an interest rate of 11 percent.

What amount of money needs to be deposited today? ______ (Round to the nearest cent.)

$34410.43 is incorrect

______________________________________________________________________________________________________

19. You would like to have $59,000 in 14 years. To accumulate this amount, you plan to deposit an equal sum in the bank each year that will earn 7 percent interest compounded annually. Your first payment will be made at the end of the year.

**a. **How much must you deposit annually to accumulate this amount?

$34290.78 is incorrect

**b. **If you decide to make a large lump-sum deposit today instead of the annual deposits, how large should this lump-sum deposit be? (Assume you can earn 7 percent on this deposit.)

**c. **At the end of five years, you will receive $20,000 and deposit this in the bank toward your goal of

$59,000 at the end of year 14. In addition to the lump-sum deposit, how much must you deposit in equal annual amounts, beginning in year 1 to reach your goal? (Again, assume you can earn 7 percent on your deposits.)

20. Don Draper has signed a contract that will pay him $60,000 at the end of each year for the next 5 years, plus an additional $110,000 at the end of year 5. If 11 percent is the appropriate discount rate, what is the present value of this contract?

What is the present value of the contract? ____ (Round to the nearest cent.)

$297676.35 is incorrect

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