APPENDIX A

tIME vALUE OF MONEY

CHAPTER LEARNING OBJECTIVES

1. Compute interest and future values. Simple interest is computed on the principal only, while compound interest is computed on the principal and any interest earned that has not been withdrawn.

To solve for future value of a single amount, prepare a time diagram of the problem. Identify the principal amount, the number of compounding periods, and the interest rate. Using the future value of 1 table, multiply the principal amount by the future value factor specified at the intersection of the number of periods and the interest rate.

To solve for future value of an annuity, prepare a time diagram of the problem. Identify the amount of the periodic payments (receipts), the number of payments (receipts), and the interest rate. Using the future value of an annuity of 1 table, multiply the amount of the payments by the future value factor specified at the intersection of the number of periods and the interest rate.

2. Compute present values. The following three variables are fundamental to solving present value problems: (1) the future amount, (2) the number of periods, and (3) the interest rate (the discount rate).

To solve for present value of a single amount, prepare a time diagram of the problem. Identify the future amount, the number of discounting periods, and the discount (interest) rate. Using the present value of a single amount table, multiply the future amount by the present value factor specified at the intersection of the number of periods and the discount rate.

To solve for present value of an annuity, prepare a time diagram of the problem. Identify the amount of future periodic receipts or payment (annuities), the number of payments (receipts), and the discount (interest) rate. Using the present value of an annuity of 1 table, multiply the amount of the annuity by the present value factor specified at the intersection of the number of periods and the interest rate.

To compute the present value of notes and bonds, determine the present value of the principal amount and the present value of the interest payments. Multiply the principal amount (a single future amount) by the present value factor (from the present value of 1 table) intersecting at the number of periods (number of interest payments) and the discount rate. To determine the present value of the series of interest payments, multiply the amount of the interest payment by the present value factor (from the present value of an annuity of 1 table) intersecting at the number of periods (number of interest payments) and the discount rate. Add the present value of the principal amount to the present value of the interest payments to arrive at the present value of the note or bond.

3. Compute the present value in capital budgeting situations. Compute the present values of all cash inflows and all cash outflows related to the capital budgeting proposal (an investment-type decision). If the net present value is positive, accept the proposal (make the investment). If the net present value is negative, reject the proposal (do not make the investment).

4. Use a financial calculator to solve time value of money problems. Financial calculators can be used to solve the same and additional problems as those solved with time value of money tables. Enter into the financial calculator the amounts for all of the known elements of a time value of money problem (periods, interest rate, payments, future or present value), and the calculator solves for the unknown element. Particularly useful situations involve interest rates and compounding periods not presented in the tables.

TRUE-FALSE STATEMENTS

1. Interest is the difference between the amount borrowed and the principal.

2. Compound interest is computed on the principal and any interest earned that has not been paid or received.

3. The future value of a single amount is the value at a future date of a given amount invested now, assuming compound interest.

4. When the periodic payments are not equal in each period, the future value can be computed by using a future value of an annuity table.

5. The process of determining the present value is referred to as discounting the future amount.

6. A higher discount rate produces a higher present value.

7. In computing the present value of an annuity, it is not necessary to know the number of discount periods.

8. The present value of a long-term note or bond is a function of two variables.

9. The present value of an annuity is the value now of a series of future receipts or payments, discounted assuming compound interest.

10. The decision to make long-term capital investments is best evaluated without considering the time value of money.

11. In a capital budgeting decision, a positive net present value means the decision to invest should be accepted.

12. With a financial calculator, one can solve for any interest rate or for any number of periods in a time value of money problem.

MULTIPLE CHOICE QUESTIONS

Note: Students will need future value and present value tables for some questions.

13. Compound interest is the return on principal

a. only.

b. for one or more periods.

c. plus interest for two or more periods.

d. for one period.

14. The factor 1.08160 is taken from the 4% column and 2 periods row in a certain table. From what table is this factor taken?

a. Future value of 1

b. Future value of an annuity of 1

c. Present value of 1

d. Present value of an annuity of 1

15. If $40,000 is deposited in a savings account paying interest of 4% compounded annually, what amount will be in the account at the end of 5 years?

a. $32,878

b. $48,000

c. $48,620

d. $48,666

Ex. 45

Jose Reynolds deposited $10,000 in an account paying interest of 4% compounded annually. What amount will be in the account at the end of 4 years?

Ex. 46

Wingate Company borrowed $90,000 on January 2, 2022. This amount plus accrued interest of 6% compounded annually will be repaid at the end of 3 years. What amount will Wingate repay at the end of the third year?

Ex. 47

Pleasant Company has decided to begin accumulating a fund for plant expansion. The company deposited $80,000 in a fund on January 2, 2020. Pleasant will also deposit $40,000 annually at the end of each year, starting in 2020. The fund pays interest at 4% compounded annually. What is the balance of the fund at the end of 2024 (after the 2024 deposit)?

Ex. 48

Mandy How plans to buy an automobile and can deposit $3,000 toward the purchase today. If the annual interest rate is 8%, how much can Mandy expect to have as a down payment in 3 years?

Ex. 49

Rob Honda plans to buy a home and can deposit $15,000 for the purchase today. If the annual interest rate is 8%, how much can Rob expect to have for a down payment in 5 years?

Ex. 50

Bill and Ellen Sweatt plan to invest $2,500 a year in an educational IRA for their granddaughter, Sloane Martin. They will make these deposits on January 2 of each year. Bill and Ellen feel they can safely earn 8%. How much will be in this account on December 31 of the year 18?

Ex. 51

Bill Cigarettes acquired a bad habit of smoking in high school. Bill spends approximately $70 a month or $840 a year on cigarettes. He is not concerned with health issues, but he is keenly aware of financial issues. Show Bill how much he would have at retirement in 20 years if he invested $840 a year at 8% instead of smoking.

Ex. 52

Robin Clark’s internet service provider has offered an upgrade at an additional cost of $10 a month ($120 a year). Robin thinks it would be “cool” to have this benefit and after all $10 a month is not so much. Show Robin how much she will have in 20 years if she invests this $120 a year at 9% instead of accepting the upgrade.

Ex. 53

Lamb Company deposited $15,000 annually for 6 years in an account paying 5% interest compounded annually. What is the balance of the account at the end of the 6th year?

Ex. 54

Martin Company issued $900,000, 10-year bonds and agreed to make annual sinking fund deposits of $72,000. The deposits are made at the end of each year to a fund paying 5% interest compounded annually. What amount will be in the sinking fund at the end of the 10 years?

Ex. 55

What is future value of $6,000 invested at the end of every year for 20 years at an interest rate of 9%?

Ex. 56

Flower Company is considering an investment which will return a lump sum of $2,500,000 six years from now. What amount should Flower Company pay for this investment to earn an 11% return?

Ex. 57

Chang Company earns 12% on an investment that will return $400,000 eleven years from now. What is the amount Chang Company should invest now to earn this rate of return?

Ex. 58

If Kelly Cranford invests $11,970 now, she will receive $40,000 at the end of 14 years. What annual rate of return will Kelly earn on her investment?

Ex. 59

Luis Rodriguez wants to buy a car in 3 years. He will need $3,000 for a down payment. The annual interest rate is 9%. How much money must Rodriguez invest today for the purchase?

Ex. 60

Amy Brown plans to buy a surround sound stereo system for $1,100 after 3 years. If the interest rate is 6%, how much money should Brown set aside today for the purchase?

Ex. 61

(a) What is the present value of $90,000 due 7 years from now discounted at 9%?

(b) What is the present value of $150,000 due 5 years from now discounted at 12%?

Ex. 62

Kim Black plans to buy a truck for $24,000 after 3 years. If the interest rate is 6%, how much money should Black set aside today for the purchase?

Ex. 63

The North Carolina DMV leases a building for 20 years. The lease requires 20 annual payments of $12,000 each, with the first payment due immediately. The interest rate in the lease is 10%. What is the present value of the cost of leasing the building?

Ex. 64

Frye Company is considering investing in an annuity contract that will return $50,000 annually at the end of each year for 20 years. What amount will Frye Company pay for this investment if the company earns an 8% return?

Ex. 65

Sarah Denny purchased an investment for $40,260.48. From this investment, she will receive $6,000 annually for the next 10 years starting one year from now. What rate of interest will Denny be earning on her investment?

Ex. 66

On January 1, 2022, Neel Das purchases a car for $25,000 and makes a 10% down payment. He obtains financing at12% interest with semiannual payments over 5 years beginning July 1, 2022.

Instructions

Compute the payment Das will make at the end of every 6 months.

Ex. 67

Brandi Frostmore is retiring this year and is considering investing her retirement savings in an annuity contract that will return $66,000 annually at the end of each year for 20 years. What amount will Frostmore pay for this investment if it earns an 8% return?

Ex. 68

Cecilia Jeffries purchased an investment for $49,090.75. From this investment, she will receive $5,000 annually for the next 20 years starting one year from now. What rate of interest will Cecilia be earning on her investment?

Ex. 69

Lucky Lou has just won the lottery and will receive an annual payment of $100,000 every year for the next 20 years. If the annual interest rate is 8%, what is the present value of the winnings?

Ex. 70

CVS leases a building for 20 years. The lease requires 20 annual payments of $10,000 each, with the first payment due immediately. The interest rate in the lease is 10%. What is the present value of the cost of leasing the building?

Ex. 71

Warleggan Company owns a garage and is contemplating purchasing a tire retreading machine. Warleggan projects a net cash flow from the retreading machine of $10,000 annually for 7 years. It estimates a salvage value of $8,000 at the end of the asset’s useful life. Warleggan hopes to earn a return of 10% on such investments. Should Warleggan purchase the retreading machine if it costs $50,000?

Ex. 72

Keren Daniel has signed a mortgage note to pay the Truro National Bank and Trust Co. $9,000 every 6 months for 20 years. At the date the mortgage is signed, the purchase price of the home was $230,000 and Keren made a down payment of $20,000. The first payment will be made 6 months after the date the mortgage is signed. Using a financial calculator, compute the annual rate of interest paid by Daniels and earned by the bank on the mortgage.