Deck 3: Time Value of Money: The Universal Tool

Question 1

Comment on the following statement: "One of the most valuable concepts in financial planning is the internal rate of return."

Answer 1

A frequently asked question relates to the internal rate of return on an investment. Assume that Judy Kelly wishes to purchase 10-year, zero-coupon bonds for $250 each. Upon maturity, each bond will pay her $1,000, or a total of $10,000. She wants to know how much money this investment is making for her, or, to put in technical jargon, what is the internal rate of return (IRR) on this investment, assuming that the tax consequences and commissions are ignored.
The calculation of the IRR on this investment, which can be made by using the calculator, shows that Judy Kelly would receive an annual return of 14.35 percent. Judy can compare this rate with alternative investments which she should consider before making an investment in these zero-coupon bonds.

Question 2

Most people are concerned about the erosion of the value of the dollar due to inflation. Explain the role of inflation in financial calculations.

Answer 2

Frequently, it is important to take into consideration the effect of inflation in making decisions about future income needs. Assume that Bob Smith wishes to receive $36,000 a year ($3,000 a month) in today's dollars at the beginning of each year for the next five years. Bob assumes that the rate of inflation over this period will be 5 percent a year and that he will be able to generate an after-tax return of 8 percent on his investments. How much money should he invest now to meet his objective? The financial planner can determine that Bob needs to invest $170,273.94 today in order to meet his objective. This calculation is presented in Table 3.8.

Question 3

Explain the time value of money (TVM) concept. Why is TVM an important tool in the financial planner's tool kit?

Answer 3

The TVM concept refers to the fact that a dollar in hand today is worth more than a dollar to be received next year, because if you had it now, you could invest it, earn interest, and end up next year with more than one dollar. The process of determining the future value is called compounding. By contrast, the value, or present value as it is called, of an amount today is less than the amount expected to be received in the future.
The financial planner needs to use the TVM tool in all areas of financial planning, including savings, investment, retirement, and risk management planning. In each of these areas, it is necessary to calculate either the future value or the present value of money as the basis for developing appropriate strategies.

Question 4

Hank Clobukar just attended a seminar where the speaker startled the audience by demonstrating that one dollar doubled each day for only 37 days will exceed $1 billion. Hank has approached you for investment planning, hoping that you will produce spectacular results. Are you interested in accepting the challenge?

Question 5

Explain the annuity due concept. Is it always preferable?

Question 6

Question 3. Assume that for his retirement an investor invests $2,000 per year for 35 years. If the investor can earn ten percent return, what will be the ending value?

A) $542,049
B) $19,288
C) $77,000
D) $596,254
E) None of the above

Question 7

It is asserted that the power of the time value of money concept is demonstrated nowhere more clearly than when the future value concept is used. Explain this statement by means of a numerical example.

Question 8

Jay Brown, a relatively new financial planner, who is a friend of yours, is unable to determine the internal rate of return of an investment which is expected to generate an uneven cash flow for the next 10 years. Can you help him?

Question 9

Contrast the present value of a fixed sum concept with the present value of an annuity concept. Explain the circumstances which would call for the use of these two tools.

Question 10

You have noticed that the present value of an investment is significantly influenced by the discount rate you use. However, you are not sure what discount rate to use. Can someone help?

Question 11

Is there a way to "fool" the HB-12C calculator so it would directly calculate the internal rate of return on an investment generating uneven cash payments?

Question 12

Use the following to answer questions #4 and #8.
Bob Lower wants to retire in 10 years. At that time he wants to have a lump sum accumulated that would allow him to withdraw $35,000 a year for the next 20 years. Assume that Bob earns an after-tax return of eight percent. Ignore the inflation in these calculations.
Question 4. How much does Bob need to invest today in order to fulfill his needs?

A) $171,903
B) $151,169
C) $51,212
D) $55,308
E) None of the above

Question 13

Question 2. What would an initial investment of $3,000 grow to if it is compounded annually at 10% for 5 years?

A) $4,832
B) $4,500
C) $6,286
D) $1,863
E) None of the above

Question 14

JoAnne Morris is deadly set against buying life insurance because she is convinced that most people are "tricked" into buying insurance. How can you explain the theoretical foundations of life insurance as an effective planning tool?

Question 15

Contrast the future value of a fixed sum concept with the future value of an annuity concept. Give examples of situations where they are used by the financial planner.

Question 16

How do you calculate the present value of perpetuity? Give an example of a situation where this concept would be relevant.

Question 17

Which formulas) listed below represents) the time value of money equation?

A) FV=(PV1 + r?)
B) FV=(PV1 + r)?
C) PV=(FV/1 + r?)
D) PV=(FV/1 + r)?
E) Both B and D

Question 18

John Stern, a business executive, is planning to retire in two years when he will turn 65. You are surprised to hear that he would like to have a monthly income of $9,000, three times his current monthly budget. Upon further questioning, you discover that the $9,000 amount is to take care of future inflation. How do you explain to John that he should start with a realistic budget?

Question 19

Question 5. If an investor can earn nine percent on his money, how many years will it take to double the principal?

A) 9
B) 6
C) 7
D) 12
E) None of the above answers are correct

Question 20

Contrast nominal interest rate with effective interest rate. Which one should be used in making financial decisions?

Question 21

Question 12. Assume that an investor owns TKB preferred stock, which pays an annual dividend of $4.50. What is the present value of the stock if the investor's discount rate is six percent?

A) $0.27
B) $75
C) $27
D) $62.50
E) None of the above

Question 22

Question 6. Suppose an investor invests $2,000 in a Certificate of Deposit which earns eight percent compounded quarterly. What is the value of the CD in five years?

A) $2,208
B) $2,939
C) $2,800
D) $2,972
E) None of the above

Question 23

Use the following information for questions #7 and #10.
Question 7. Mary needs $145,000 in 15 years to buy her son a new Ferrari. Assume that she can earn an 8% after-tax return on her investment. You may ignore inflation in these calculations. How much ignore cents) will Mary need to invest today?

A) $5,340
B) $459,965
C) $45,710
D) $47,401
E) None of the above. No one should own a Ferrari.

Question 24

Question 11. Suppose an investor invests $2,000 at the beginning of each year. What will be the value of the investment at the end of ten years if he earns ten percent?

A) $31,875
B) $35,062
C) $13, 518
D) $12,289
E) $20,000

Question 25

Question 10. How much will Mary need to invest each year for the next 15 years if investments are made at the end of each year?

A) $5,340
B) $22,280
C) $45,710
D) $9,667
E) None of the above. No one should own a Ferrari.

Question 26

Which of the following definitions of "Present Value of an Uneven Payment Series" is true?

A) We are calculating the future value of a series of uneven payments by averaging out the uneven payments.
B) We calculate the present value of a series of uneven payments by averaging out the uneven payments.
C) We calculate the present value by using the following equation after taking an average of all payments,
$\begin{array} { c } N \\\text { PVA=PMT } \left. \sum _ { n = 1 } [ 1 / 1 + \mathrm { r } ) ^ { \mathrm { n } } \right]\end{array}$
D) There is no simple equation. We must calculate the present value for each payment separately and then sum up the individual PVs.
E) There is no way to determine this amount accurately.

Question 27

Question 9. If you calculate "Future Value of an Annuity":

A) You know the total value of this fund at the end of the annuity period
B) You know the present value of a series of future payments
C) You can determine how long a sum of money would last if you withdrew a fixed sum on a regular basis
D) You know the total value of the fund at the end of the specified period even if you don't know the interest rate
E) You can determine the outcome even when the payments vary from year to year

Question 28

Question 8. How much does Bob need to invest for each of the next ten years to fulfill his needs?

A) $171, 903
B) $55,308
C) $23,721
D) $51,212
E) None of the above

Question 29

Question 14. Assume that an investor expects to receive the following dividends: year 1: $8, years 2-7: $10, and years 11-12: $12. If the investor's discount rate is 5 percent, what is the present value of this dividend stream?

A) $91.06
B) $74
C) $62.77
D) $69.66
E) Cannot be determined

Question 30

Question 13. Present Value of a Perpetuity implies that

A) The payments will last until the life expectancy of the recipient
B) You have to determine the present value of the payments that will last indefinitely
C) We are dealing exclusively with a preferred stock which makes dividend payments indefinitely
D) We are indulging in a fantasy because no one makes payments forever
E) One can obtain the correct answer by using the following simple formula: PV=PMT 1 + r)

Question 31

Question 18. Mr. Hall wants to receive $45,000 at the end of each year in today's dollars for the next 15 years. He is concerned about inflation and wants you to determine the lump sum he would need if the annual rate of inflation averages four percent and he could earn nine percent on his investment.

A) $407,085
B) $495,967
C) $473,216
D) $462,689
E) None of the above

Question 32

Question 17. Which of the following statements are true?

A) Banks typically pay interest on an annual basis
B) Banks typically pay interest on a daily basis
C) Bond holders are usually paid on a semi-annual basis
D) Stockholders are usually paid dividends on a quarterly basis
E) C and D

Question 33

Question 16. What is the effective interest rate on a bank savings account which pays six percent, compounded semi-annually?

A) 6.03%
B) 6.09%
C) 6%
D) 6.14%
E) None of the above