Chat with AIExam 3: Time Value of Money: The Universal Tool
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?
(38) 
VerifiedThe challenge is to educate Hank about the magic of compounding. Money compounded at a daily rate of 100 percent indeed produces spectacular results, but a reasonable rate of return on equity investment over the long term is about 11-12 per cent. At that rate, money will double approximately every six years or so.
Present Value of a Perpetuity implies that
(41) VerifiedB
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.
(42) VerifiedFixed Sum
A dollar in hand today could be worth more than a dollar to be received next year. If an investor had it now, he or she could invest it, earn interest, and end up next year with more than one dollar. For instance, if $100 is invested at 5 percent for one year, the amount will grow to $105. Put differently, the present value of $105 expected to be received next year, discounted for one year at 5 percent, is $100. In general, the present value of a sum due n periods in the future is the amount which, if it were on hand today, would grow to equal the future sum. The present value of a fixed sum can be calculated by using the PV equation, or it could be calculated by using a financial calculator.
2. Present Value: Annuity
Perhaps the most important tool in the financial planner's kit is the present value of an annuity (PVA) concept. This is a valuable concept, since identification of an undervalued stock, evaluation of an income-producing limited partnership, or a lump sum versus a pension for life retirement settlement can be solved by using the PVA concept.
The PVA is calculated by using equation 3.5, or it could be calculated by using a financial calculator as demonstrated in Table 3.6.
Here are two examples to demonstrate when the present value of a fixed sum and the present value of an annuity are used. An investor expects to receive $10,000 from a limited partnership seven years from today. Using a discount rate of 10 percent, the present value of this fixed sum equals $5,131.58 (see Table 3.3). Next, we present an interesting problem which requires the use of the PVA concept. A client has just won a lottery. He is offered the following alternatives: (a) a four-year annuity with payments of $1,000 at the end of each year; or (b) a lump sum payment of $3,170 rounded off today. Which one should he choose if the market interest rate is 10 percent? At first blush, either the four-year payment or the lump sum may appear more attractive. However, if the money is expected to earn 10 percent a year, both alternatives are of equal value. The calculation of a present value of an annuity is presented in equation 3.7.
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?
(43) Which of the following definitions of "Present Value of an Uneven Payment Series" is true?
(39) 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.
(40) 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?
(45) Use the following information for questions
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?
(32) Use the following to answer questions
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.
- 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?
(41) Use the following information for questions
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 does Bob need to invest for each of the next ten years to fulfill his needs?
(38) Use the following to answer questions
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.
- If an investor can earn nine percent on his money, how many years will it take to double the principal?
(29) 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?
(33) 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.
(40) Use the following information for questions
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.
- If you calculate "Future Value of an Annuity":
(43) Use the following information for questions
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 will Mary need to invest each year for the next 15 years if investments are made at the end of each year?
(29) Which formulas) listed below represents) the time value of money equation?
(43) Explain the time value of money (TVM) concept. Why is TVM an important tool in the financial planner's tool kit?
(28) Most people are concerned about the erosion of the value of the dollar due to inflation. Explain the role of inflation in financial calculations.
(36) 
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