The Time Value of Money

1. The Time Value of Money Slide M2.1

2. Module 2 Learning Objectives • Distinguish between simple and compound interest. • Compute the future value of a single amount. • Compute the future value of an annuity. • Compute the present value of a single amount. • Compute the present value of an annuity. Slide M2.2

3. Time is money. Ben Franklin • Time value of money concept: the economic value of a cash receipt or payment is a function of both the amount and timing of that receipt or payment. • Simple premise: A dollar in your pocket today is worth more than a dollar you will receive in one year. • Why study the time value of money concept? Because it influences the accounting treatment of several financial statement items. Slide M2.3

4. Key Terms • Interest • Simple Interest • Compound Interest • Annuity • Future value • Present value Slide M2.4

5. Four Basic Time Value of Money Scenarios • Computing the future value of a single amount • Computing the future value of an annuity • Computing the present value of a single amount • Computing the present value of an annuity Slide M2.5

6. Each time value of money scenario can be solved either of two ways: • Directly with the appropriate mathematical equation. • Or, by using a simplified version of that equation and the assistance of “time value” tables. Slide M2.6

7. Each time value of money factor has two parameters . . . . . . an assumed interest (or discount) rate and a given number of time periods. a. Table 1: Future Value Factors (FVFs) for a Single Amount b. Table 2: Future Value of Annuity Factors (FVAFs) c. Table 3: Present Value Factors (PVFs) for a Single Amount d. Table 4: Present Value of Annuity Factors (PVAFs) Slide M2.7

8. Future Value of a Single Amount Representative scenario: $50,000 invested for five years in a 5% CD. Basic structure of this scenario: Present Future Value Value $50,000 ? 5 years @ 5% Slide M2.8

9. Solution: 1. FV = PV x FVF 2. Where: FVF = the appropriate future value factor from Table 1 3. For 5 years and 5%, the appropriate FVF is 1.27628 4. FV = $50,000 x 1.27628 = $63,814 Slide M2.9

10. Future Value of an Annuity Representative scenario: Series of $50,000 investments at the end of each of the following five years in a mutual fund yielding 12%. Basic structure of this scenario: $50K $50K $50K $50K $50K Year 1 Year 2 Year 3 Year 4 Year 5 What is the future value of this annuity? That is, its value on December 31, Year 5? Slide M2.10

11. Solution: 1. FVA = A x FVAF 2. Where: FVAF = the appropriate future value of an annuity factor from Table 2 3. For 5 years and 12%, the appropriate FVAF is 6.35285 4. FVA = $50,000 x 6.35285 = $317,642 Slide M2.11

12. Present Value of a Single Amount Representative scenario: $100,000 to be paid in three years with an appropriate discount rate of 6% Basic structure of this scenario: Present Value Future Value ? $100,000 3 years @ 6% Slide M2.12

13. Solution: 1. PV = FV x PVF 2. Where: PVF = the appropriate present value factor from Table 3 3. For 3 years and 6%, the appropriate PVF is .83962 4. PV = $100,000 x .83962 = $83,962 Slide M2.13

14. Present Value of an Annuity Representative scenario: Series of $400,000 receipts, one at the end of each of the following three years. Appropriate discount rate is 10%. Basic structure of this scenario: $400K $400K $400K Year 1 Year 2 Year 3 What is the present value of this annuity on Day One of Year 1? Slide M2.14

15. Solution: 1. PVA = A x PVAF 2. Where: PVAF = the appropriate present value of an annuity factor from Table 4 3. For 3 years and 10%, the appropriate PVAF is 2.48685 4. FVA = $400,000 x 2.48685 = $994,740 Slide M2.15