TBApp II.docx

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23. The time value of money and present value are important business concepts. Required:

Briefly explain these concepts to someone with a limited business background.

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Appendix II Compound Interest and the Concept of Present Value Answer

Key

1. The main idea behind the time value of money is that:

cash flows received in the distant future are less valuable than cash flows received in the near-term future.

B. cash received in year 3, say, $80,000, has the same value as $40,000 received in year 3 plus $40,000 received in year 4.

C. cash flows received in different years are treated as equal in value.

D. cash payments made in the future have the same value as payments made today. E. timing considerations of cash flows have little value in decision making.

AACSB: Reflective Thinking AICPA BB: Critical Thinking AICPA FN: Measuremen

Blooms: Understan Difficulty: 2 Medium Learning Objective: II-01 Explain the importance of the time value of money in capital-budgeting decisions.

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2. The procedure used to compute the future value of a series of cash flows is known as:

compounding. B. the annuity method. C. discounting.

D. the future-cost approach. E. indexing.

Blooms: Understan Difficulty: 2 Medium Learning Objective: II-02 Compute the future value and present value of cash flows occurring over several time periods.

3. Norton Company has a 12% compound annual interest rate. If the firm invests $60,000 today, how much will have accumulated by the end of eight years?

A. $117,600. $148,560. C. $298,080. D. $738,000.

E. None of the other answers are correct.

Blooms: Appl Difficulty: 3 Har Learning Objective: II-02 Compute the future value and present value of cash flows occurring over several time periods.

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4. Lawson Company invests $60,000 today and has $148,560 by the end of eight years. What is the firm's compound annual interest rate?

A. 10.00%. 12.00%. C. 18.45%. D. 40.39%.

5. The procedure used to compute the present value of a series of cash flows is known as:

A. compounding. B. the annuity method.

discounting.

D. the present-cost approach. E. indexing.

AACSB: Analytic AICPA BB: Critical Thinking AICPA FN: Measuremen

Blooms: Understan Difficulty: 2 Medium Learning Objective: II-02 Compute the future value and present value of cash flows occu rring over several time periods.

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6. All other things being equal, which of the following would be the most attractive to an investor?

A. A cash inflow of $10,000 in five years.

B. A cash inflow of $2,000 each year for the next five years. C. A cash inflow of $5,000 in year 1 and $5,000 in year 5.

A cash inflow of $10,000 today.

E. All of these would be equally attractive to an investor.

7. All other things being equal, which of the following would be most attractive to an investor?

A cash outflow of $60,000 in six years.

B. A cash outflow of $10,000 each year for the next six years. C. A cash outflow of $30,000 in year 1 and $30,000 in year 6. D. A cash outflow of $60,000 today.

E. All of these would be equally attractive to an investor.

Blooms: Understan Difficulty: 2 Medium Learning Objective: II-02 Compute the future value and present value of cash flows occurring over s everal time periods.

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8. A series of equal cash flows is called a (n):

A. ongoing cash flow. B. payback.

C. accrual.

D. cash accumulation. annuity.

9. The sum of the discount factors applicable to individual cash flows in a series of equal cash flows is called the:

A. single-sum, present-value factor. B. total discount factor.

annuity discount factor. D. compound discount factor. E. internal rate discount factor.

Blooms: Remembe Difficulty: 1 Eas Learning Objective: II-02 Compute the future value and present value of cash flows occurring over several time periods.

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10. Consider the following items of information: I. The target recovery period.

II. The discount rate.

III. The timing (i.e., year) of a cash flow.

Which of the above items would be needed to calculate the present value of a cash flow?

A. I only. B. II only. C. I and II.

II and III. E. I, II, and III.

11. You desire to invest $3,000 at the end of each year for the next five years to accumulate the funds needed for a down payment on a home. Which table factor(s) should be used to most efficiently determine the amount accumulated by the end of the five-year period?

A. Future value of $1.

Future value of a $1 annuity. C. Present value of $1.

D. Present value of a $1 annuity.

E. Both Future value of $1 and Future value of a $1 annuity.

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AICPA BB: Critical Thinking AICPA FN: Measuremen

12. Uncle Roscoe, a wealthy relative, has given you a choice of receiving $10,000 today or $3,000 at the end of each year for the next four years. Which table factor(s) should be used to most efficiently determine the "value" of the $3,000 cash-flow stream?

B. Future value of a $1 annuity. C. Present value of $1.

Present value of a $1 annuity.

E. Both Present value of $1 and Present value of a $1 annuity.

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13. You are a sports agent who is representing Jack Lofton, a star football player, in contract negotiations with the New York Landmarks. The Landmarks have offered Lofton a four-year contract, with annual raises and performance bonuses that will result in a growing cash-flow stream for Lofton each year. Which table factor(s) should you use to most efficiently determine the "value" of the contract?

B. Future value of a $1 annuity. Present value of $1.

D. Present value of a $1 annuity.

E. Both Present value of $1 and Present value of a $1 annuity.

14. How much money must be invested today in order to have $25,000 at the end of four years if the rate of return is 12% compounded annually?

$15,900. B. $17,100. C. $19,900. D. $22,300.

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Difficulty: 3 Har Learning Objective: II-02 Compute the future value and present value of cash flows occurring over several time periods.

15. You estimate that it will take five years to complete your college education. Your parents want to invest enough money today at an interest rate of 8% compounded annually to allow you to withdraw $10,000 at the end of each year for the next five years, with nothing left at the end. The amount of money to invest today is:

A. $14,690. B. $34,050.

$39,930. D. $50,000.

16. You received a $5,000 loan at the end of each of your four years of college. Aunt Rose agreed to pay off your loans at the end of your fourth year of school. How much will she have to pay? Assume a 4% interest rate compounded annually on student loans.

A. $20,000. $21,235. C. $39,930. D. $50,000.

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AICPA BB: Critical Thinking AICPA FN: Measuremen

Blooms: Appl Difficulty: 3 Har Learning Objective: II-02 Compute the future value and present value of cash flows occu rring over several time periods.

17. You received a $5,000 loan at the end of each of your four years of college. Your grandparents agreed to pay off your loans at the end of your fourth year of school. Assume a 4% annual compound interest rate on student loans. How much will they have to deposit when you start school so that they will have enough money to pay off your loans after four years? Their interest rate is 6% compounded annually.

A. $20,000. B. $21,235. $16,818. D. $15,000.

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18. You want to buy a new car in five years. You want to have saved $25,000 by then. You can invest $4,000 at the end of each of the next five years at an interest rate of 6% compounded annually. Will you have enough money at the end of the fifth year?

No. You are short $2,452.

B. Yes. You have $1,532 more than you need. C. No. You are short $1,532.

D. Yes. You have $2,452 more than you need. E. None of the other answers are correct.

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19. Green Company owes White Company money for the purchase of equipment. White has given Green the following payment options:

I. Immediate payment in full of $38,000.

II. Annual payments of $15,000 made at the end of each of the next three years. III. A single payment of $48,000 made at the end of three years.

Green uses a 10% annual compound interest rate and will choose the option with the lowest present value. Which option should Green choose, and what is the present value of that option?

A. Option I, $34,542. B. Option I, $38,000. C. Option II, $37,305. D. Option III, $34,164. Option III, $36,048. AACSB: Analytic AICPA BB: Critical Thinking AICPA FN: Measuremen

Blooms: Appl Difficulty: 3 Har Learning Objective: II-02 Compute the future value and present value of cash flows occu rring over several time periods.

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20. Nelson Company owes money to Nash Company for the purchase of equipment. Nash Company has given Nelson the following payment options:

I. Immediate payment in full of $38,000.

II. Annual payments of $15,000 made at the end of each of the next three years. III. A single payment of $48,000 made at the end of three years.

Assume that both Nelson and Nash use a 10% interest rate compounded annually. What option would prefer, and what is the present value of that option?

A. Option I, $34,542. Option I, $38,000. C. Option II, $37,305. D. Option III, $34,164. E. Option III, $36,048. AACSB: Analytic AICPA BB: Critical Thinking AICPA FN: Measuremen

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21. Future value and present value are two key business tools. Required:

Ignoring income taxes, answer the following independent questions:

A. Your best friend won the state lottery and has offered to give you $15,000 at the end of eight years (after he has made his first million). You figure that if you had the money now, you could invest it at a rate of 10% compound annually. What is the value today of your friend's future gift? B. Suppose that you invest $11,000 today in an account that bears interest at the rate of 6% compounded annually. What will your investment grow to at the end of seven years?

C. Suppose that your best friend won the state lottery and promised to give you $9,000 per year for five years. The first payment will be made at the end of 20x1. Using a 12% annual compound discount rate, what is the value of these payments at the beginning of 20x1?

D. Suppose that you invest $2,000 at the end of each year for nine years in an investment that provides a return of 8% compounded annually. What will be the value of your investment at the end of nine years?

A. Present value: $15,000 × 0.467 = $7,0₀₅ B. Future value: $11,000 × 1.504 = $16,544 C. Present value: $9,000 × 3.605 = $32,445 D. Future value: $2,000 × 12.488 = $24,976

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22. Your Uncle Otto has struck it rich by investing in racehorses and desires to share some of his newfound wealth with you. Assume that you must choose from among the following three options:

Receive a lump sum of $400,000 in 20 years.

Receive $20,000 at the end of each year for the next 10 years. Receive $90,000 now.

Required:

A. Why is it inappropriate to compare $400,000 (no. 1) vs. $200,000 (no. 2) vs. $90,000 (no. 3) and conclude that no. 1 is the best option? Explain.

B. What should you do to determine which option is the best? What does this process do? C. If Uncle Otto agreed to revise option no. 1 so that you could receive $200,000 in 10 years and the remaining $200,000 in another 10 years, would you likely p refer the revision or the option as originally stated? Why?

D. What is an annuity? Do any of the options involve an annuity?

A. The cash flows do not occur at the same points in time, and such an analysis disregards the time value of money. Dollars received in earlier years are worth more than dollars received in the future.

B. The cash flows should be discounted, and the option with the highest present value should be selected. Such a process integrates the time value of money into the decision process.

C. The revision should be preferred. Both options involve the same total dollars; however, because significant inflows occur sooner with the revision, this option would have a higher present value.

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AACSB: Analytic AICPA BB: Critical Thinking AICPA FN: Research Blooms: Understan Difficulty: 2 Medium Learning Objective: II-01 Explain the importance of the time value of money in capital-budgeting decisions. Learning Objective: II-02 Compute the future value and present value of cash flows occurring over several time periods.

Briefly explain these concepts to someone with a limited business background.

The time value of money recognizes that a dollar received today is worth more than a dollar received in the future. Such monies can be invested to earn additional returns for the individual and/or firm. Present value, an approach that is based on time values, weights dollars in earlier years of an investment more heavily than dollars of later years. The result is present value, namely, the amount that a company (or individual) should be willing to pay today to secure a future cash flow at a given rate of return.

AACSB: Analytic AICPA BB: Critical Thinking AICPA FN: Research Blooms: Understan Difficulty: 2 Medium Learning Objective: II-01 Explain the importance of the time value of money in capital-budgeting decisions.

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Differentiate between the concepts discounting and compounding.

Discounting refers to the mathematical process whereby we calculate the present value of a future amount. Compounding refers to the mathematical process whereby we calculate the future value of a present amount.

Both terms recognize that a dollar received today is worth more than a dollar received in the future. The end result of the calculations will depend on the length of time of the investment and the interest rate used.

AACSB: Analytic AICPA BB: Critical Thinking AICPA FN: Research Blooms: Understan Difficulty: 2 Medium Learning Objective: II-01 Explain the importance of the time value of money in capital-budgeting decisions.