# 1. Suppose someone offered you your choice of two equally

1. Suppose someone offered you your choice of two equally risky annuities, each paying \$5,000 per year for 5 years. One is an annuity due, while the other is a regular (or deferred) annuity. If you are a rational wealth-maximizing investor which annuity would you choose?

A) The annuity due.

B) The deferred annuity.

C) Either one, because as the problem is set up, they have the same present value.
D) Without information about the appropriate interest rate, we cannot find the values of the two annuities, hence we cannot tell which is better.

E) The annuity due; however, if the payments on both were doubled to \$10,000, the deferred annuity would be preferred.

2. Financial Calculator Section

The following question(s) may require the use of a financial calculator.

Your client just turned 75 years old and plans on retiring in 10 years on her 85th birthday. She is saving money today for her retirement and is establishing a retirement account with your office. She would like to withdraw money from her retirement account on her birthday each year until she dies. She would ideally like to withdraw \$50,000 on her 85th birthday, and increase her withdrawals 10 percent a year through her 89th birthday (i.e., she would like to withdraw \$73,205 on her 89th birthday). She plans to die on her 90th birthday, at which time she would like to leave \$200,000 to her descendants. Your client currently has \$100,000. You estimate that the money in the retirement account will earn 8 percent a year over the next 15 years. Your client plans to contribute an equal amount of money each year until her retirement. Her first contribution will come in one year; her tenth and final contribution will come in ten years (on her 85th birthday). How much should she contribute each year in order to meet her objectives?

A) \$12,401.59

B) \$12,998.63

C) \$13,243.18

D) \$13,759.44

E) \$14,021.53

3.

Which of the following payments (receipts) would probably not be considered an annuity due? Based on your knowledge and using logic, think about the timing of the payments.

A) Rent payments associated with a five-year lease

B) Payments for a magazine subscription for a two-year period where the payments are made annually

C) Interest payments associated with a corporate bond that was issued today

D) Annual payments associated with lottery winnings that are paid out as an annuity

4. The effective annual rate is less than the simple rate when we have monthly compounding.

A) True

B) False

5. Assume that you will receive \$2,000 a year in Years 1 through 5, \$3,000 a year in Years 6 through 8, and \$4,000 in Year 9, with all cash flows to be received at the end of the year. If you require a 14 percent rate of return, what is the present value of these cash flows?

A) \$9,851

B) \$13,250

C) \$11,714

D) \$15,129

E) \$17,353

6. The greater the number of compounding periods within a year, the greater the future value of a lump sum invested initially, and the greater the present value of a given lump sum to be received at maturity.

A) True

B) False

7. Financial Calculator Section

The following question(s) may require the use of a financial calculator.

Assume that you just had a child, and you are now planning for her college education. You would like to make 43 equal payments over the next 21 years (the first payment to be made immediately, all other payments to be made at 6-month intervals, with the final payment to be made at her 21st birthday) so that you will be able to cover her expected expenses while in school. You expect to pay expenses on her 18th, 19th, 20th, and 21st birthdays. Assume that the current (time period 0) annual cost of college is \$6,000, that you expect annual inflation to be 8 percent for the next 5 years, and then 5 percent thereafter. If you expect to be able to earn a return of 4 percent every 6 months on your investments (a simple rate of 8 percent with semiannual compounding), what will be the amount of each of the 43 payments?

A) \$705.86

B) \$731.93

C) \$692.15

D) \$650.46

E) \$785.72

8. Which of the following statements is correct?

A) Other things held constant, an increase in the number of discounting periods per year increases the present value of a given annual annuity.

B) Other things held constant, an increase in the number of discounting periods per year increases the present value of a lump sum to be received in the future.

C) The payment made each period under an amortized loan is constant, and it consists of some interest and some principal. The later we are is the loan's life, the smaller the interest portion of the payment.

D) There is an inverse relationship between the present value interest factor of an annuity and the future value interest factor of an annuity, (i.e., one is the reciprocal of the other).
E) Each of the above statements is true.

9. You have the opportunity to buy a perpetuity which pays \$1,000 annually. Your required rate of return on this investment is 15 percent. You should be essentially indifferent to buying or not buying the investment if it were offered at a price of

A) \$5,000.00

B) \$6,000.00

C) \$6,666.67

D) \$7,500.00

E) \$8,728.50

10.

In its first year of operations, 1999, the Gourmet Cheese Shoppe had earnings per share (EPS) of \$0.26. Four years later, in 2003, EPS was up to \$0.38, and 7 years after that, in 2010, EPS was up to \$0.535. It appears that the first 4 years represented a supernormal growth situation and since then a more normal growth rate has been sustained. What are the rates of growth for the earlier period and for the later period?

A) 6%; 5%

B) 6%; 3%

C) 10%; 8%

D) 10%; 5%

E) 12%; 7%

A) 6%; 5%

B) 6%; 3%

C) 10%; 8%

D) 10%; 5%

E) 12%; 7%

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