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# Time Value of Money- Apendix-G

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Learning Objectives
After studying this chapter, you should be able to:
[1] Indicate the benefits of budgeting.
[2] Distinguish between simple and compound interest.
[2] Identify the variables fundamental to solving present value problems.
[3] Solve for present value of a single amount.
[4] Solve for present value of an annuity.
[5] Compute the present value of notes and bonds.

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### Time Value of Money- Apendix-G

1. 1. Prepared by Coby Harmon University of California, Santa Barbara Westmont College G- 1
2. 2. Appendix G Time Value of Money Learning Objectives After studying this chapter, you should be able to: [1] Indicate the benefits of budgeting. [2] Distinguish between simple and compound interest. [2] Identify the variables fundamental to solving present value problems. [3] Solve for present value of a single amount. [4] Solve for present value of an annuity. [5] Compute the present value of notes and bonds. G- 2
3. 3. Nature of Interest Interest  Payment for the use of money.  Excess cash received or repaid over the amount borrowed (principal). Elements involved in financing transaction: 1. Principal (p) – Original amount borrowed or invested. 2. Interest Rate (i) – An annual percentage. 3. Time (n) - The number of years or portion of a year that the principal is borrowed or invested. G- 3 LO 1 Distinguish between simple and compound interest.
4. 4. Nature of Interest Simple Interest  Interest computed on the principal amount only. Illustration: Assume you borrow \$5,000 for 2 years at a simple interest of 6% annually. Calculate the annual interest cost. Illustration G-1 Interest = p x i x n FULL YEAR = \$5,000 x .06 x 2 = \$600 G- 4 Advance slide in presentation mode to reveal answer. LO 1 Distinguish between simple and compound interest.
5. 5. Nature of Interest Compound Interest  Computes interest on ► ►  G- 5 the principal and any interest earned that has not been paid or withdrawn. Most business situations use compound interest. LO 1 Distinguish between simple and compound interest.
6. 6. Compound Interest Illustration: Assume that you deposit \$1,000 in Bank Two, where it will earn simple interest of 9% per year, and you deposit another \$1,000 in Citizens Bank, where it will earn compound interest of 9% per year compounded annually. Also assume that in both cases you will not withdraw any interest until three years from the date of deposit. Illustration G-2 Simple versus compound interest Year 1 \$1,000.00 x 9% \$ 1,090.00 Year 2 \$1,090.00 x 9% \$ 98.10 \$ 1,188.10 Year 3 \$1,188.10 x 9% G- 6 \$ 90.00 \$106.93 \$ 1,295.03 LO 1
7. 7. Present Value Concepts Present value is the value now of a given amount to be paid or received in the future, assuming compound interest. Present value variables: 1. Dollar amount to be received (future amount), 2. Length of time until amount is received (number of periods), and 3. Interest rate (the discount rate). G- 7 The process of determining The process of determining the present value is referred the present value is referred to as discounting the to as discounting the future amount. future amount. LO 2 Identify the variables fundamental to solving present value problems.
8. 8. Present Value of a Single Amount Illustration G-3 Formula for present value Present Value = Future Value ÷ (1 + i )n p = principal (or present value) i = interest rate for one period n = number of periods G- 8 LO 3 Solve for present value of a single amount.
9. 9. Present Value of a Single Amount Illustration: If you want a 10% rate of return, you would compute the present value of \$1,000 for one year as follows: Illustration G-4 G- 9 LO 3 Solve for present value of a single amount.
10. 10. Present Value of a Single Amount Illustration G-4 Illustration: If you want a 10% rate of return, you can also compute the present value of \$1,000 for one year by using a present value table. What table do we use? G- 10 LO 3 Solve for present value of a single amount.
11. 11. Present Value of a Single Amount TABLE 1 Present Value of 1 What factor do we use? \$1,000 Future Value G- 11 x .90909 Factor = \$909.09 Present Value LO 3 Solve for present value of a single amount.
12. 12. Present Value of a Single Amount Illustration G-5 Illustration: If you receive the single amount of \$1,000 in two years, discounted at 10% [PV = \$1,000 ÷ 1.102], the present value of your \$1,000 is \$826.45. What table do we use? G- 12 LO 3 Solve for present value of a single amount.
13. 13. Present Value of a Single Amount TABLE 1 Present Value of 1 What factor do we use? \$1,000 Future Value G- 13 x .82645 Factor = \$826.45 Present Value LO 3 Solve for present value of a single amount.
14. 14. Present Value of a Single Amount TABLE 1 Present Value of 1 Illustration: Suppose you have a winning lottery ticket and the state gives you the option of taking \$10,000 three years from now or taking the present value of \$10,000 now. The state uses an 8% rate in discounting. How much will you receive if you accept your winnings now? \$10,000 Future Value G- 14 x .79383 Factor = \$7,938.30 Present Value LO 3 Solve for present value of a single amount.
15. 15. Present Value of a Single Amount TABLE 1 Present Value of 1 Illustration: Determine the amount you must deposit now in a bond investment, paying 9% interest, in order to accumulate \$5,000 for a down payment 4 years from now on a new Toyota Prius. \$5,000 Future Value G- 15 x .70843 Factor = \$3,542.15 Present Value LO 3 Solve for present value of a single amount.
16. 16. Present Value of an Annuity The present value of an annuity is the value now of a series of future receipts or payments, discounted assuming compound interest. Present Value \$100,000 0 G- 16 100,000 100,000 100,000 100,000 100,000 1 2 3 4 19 20 ..... LO 4 Solve for present value of an annuity.
17. 17. Present Value of an Annuity Illustration G-8 Illustration: Assume that you will receive \$1,000 cash annually for three years at a time when the discount rate is 10%. What table do we use? G- 17 LO 4 Solve for present value of an annuity.
18. 18. Present Value of an Annuity TABLE 1 Present Value of an Annuity of 1 What factor do we use? \$1,000 Future Value G- 18 x 2.48685 Factor = \$2,484.85 Present Value LO 4 Solve for present value of an annuity.
19. 19. Present Value of an Annuity TABLE 1 Present Value of an Annuity of 1 Illustration: Kildare Company has just signed a capitalizable lease contract for equipment that requires rental payments of \$6,000 each, to be paid at the end of each of the next 5 years. The appropriate discount rate is 12%. What is the amount used to capitalize the leased equipment? \$6,000 G- 19 x 3.60478 = \$21,628.68 LO 4 Solve for present value of an annuity.
20. 20. Time Periods and Discounting Illustration: When the time frame is less than one year, you need to convert the annual interest rate to the applicable time frame. Assume that the investor received \$500 semiannually for three years instead of \$1,000 annually when the discount rate was 10%. TABLE 1 Present Value of an Annuity of 1 \$500 G- 20 x 5.07569 = \$2,537.85 LO 4
21. 21. Present Value of a Long-term Note or Bond Two Cash Flows:  Periodic interest payments (annuity).  Principal paid at maturity (single-sum). 100,000 \$5,000 0 G- 21 5,000 5,000 5,000 1 2 3 4 ..... 5,000 5,000 9 10 LO 5 Compute the present value of notes and bonds.
22. 22. Present Value of a Long-term Note or Bond Illustration: Assume a bond issue of 10%, five-year bonds with a face value of \$100,000 with interest payable semiannually on January 1 and July 1. Calculate the present value of the principal and interest payments. 100,000 \$5,000 0 5,000 5,000 5,000 1 2 3 4 ..... 5,000 5,000 9 10 Year 1 G- 22 LO 5 Compute the present value of notes and bonds.
23. 23. Present Value of a Long-term Note or Bond TABLE 1 Present Value of 1 \$100,000 Principal G- 23 x .61391 Factor PV of Principal = \$61,391 Present Value LO 5 Compute the present value of notes and bonds.
24. 24. Present Value of a Long-term Note or Bond TABLE 1 Present Value of an Annuity of 1 \$5,000 Principal G- 24 x 7.72173 Factor = PV of Interest \$38,609 Present Value LO 5 Compute the present value of notes and bonds.
25. 25. Present Value of a Long-term Note or Bond Illustration: Assume a bond issue of 10%, five-year bonds with a face value of \$100,000 with interest payable semiannually on January 1 and July 1. Present value of Principal \$ 61,391 Present value of Interest Bond current market value Date Account Title Cash Bonds Payable G- 25 38,609 \$100,000 Debit Credit 100,000 100,000 LO 5
26. 26. Present Value of a Long-term Note or Bond Illustration: Now assume that the investor’s required rate of return is 12%, not 10%. The future amounts are again \$100,000 and \$5,000, respectively, but now a discount rate of 6% (12% ÷ 2) must be used. Calculate the present value of the principal and interest payments. Illustration G-14 G- 26 LO 5 Compute the present value of notes and bonds.
27. 27. Present Value of a Long-term Note or Bond Illustration: Now assume that the investor’s required rate of return is 8%. The future amounts are again \$100,000 and \$5,000, respectively, but now a discount rate of 4% (8% ÷ 2) must be used. Calculate the present value of the principal and interest payments. Illustration G-15 G- 27 LO 5 Compute the present value of notes and bonds.
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