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- 1. PowerPoint Authors: Susan Coomer Galbreath, Ph.D., CPA Charles W. Caldwell, D.B.A., CMA Jon A. Booker, Ph.D., CPA, CIA Cynthia J. Rooney, Ph.D., CPA Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education. The Concept of Present Value Appendix 13A
- 2. 13A-2 Learning Objective 7 (Appendix 13A) Understand present value concepts and the use of present value tables.
- 3. 13A-3 The Mathematics of Interest A dollar received today is worth more than a dollar received a year from now because you can put it in the bank today and have more than a dollar a year from now.
- 4. 13A-4 The Mathematics of Interest – An Example Assume a bank pays 8% interest on a $100 deposit made today. How much will the $100 be worth in one year? FFnn = P(1 + r)= P(1 + r)nn F = the balance at the end of the period n. P = the amount invested now. r = the rate of interest per period. n = the number of periods.
- 5. 13A-5 The Mathematics of Interest – An Example FFnn = P(1 + r)= P(1 + r)nn FF11 = $100(1 + .08)= $100(1 + .08)11 FF11 = $108.00= $108.00 Assume a bank pays 8% interest on a $100 deposit made today. How much will the $100 be worth in one year?
- 6. 13A-6 Compound Interest – An Example FFnn = P(1 + r)= P(1 + r)nn What if the $108 was left in the bank for a second year? How much would the original $100 be worth at the end of the second year? F = the balance at the end of the period n. P = the amount invested now. r = the rate of interest per period. n = the number of periods.
- 7. 13A-7 Compound Interest – An Example FF22 = $100(1 + .08)= $100(1 + .08)22 FF22 = $116.64= $116.64 The interest that is paid in the second year on the interest earned in the first year is known as compound interest.
- 8. 13A-8 Computation of Present Value Present Value Future Value An investment can be viewed in two ways—its future value or its present value. Let’s look at a situation where the future value is known and the present value is the unknown.
- 9. 13A-9 Present Value – An Example If a bond will pay $100 in two years, what is the present value of the $100 if an investor can earn a return of 12% on investments? (1 + r)(1 + r)nnP =P = FFnn F = the balance at the end of the period n. P = the amount invested now. r = the rate of interest per period. n = the number of periods.
- 10. 13A-10 Present Value – An Example (1 + .12)(1 + .12)22P =P = $100$100 P =P = $79.72$79.72 This process is called discounting. We have discounted the $100 to its present value of $79.72. The interest rate used to find the present value is called the discount rate.
- 11. 13A-11 Present Value – An Example Let’s verify that if we put $79.72 in the bank today at 12% interest that it would grow to $100 at the end of two years. Year 1 Year 2 Beginning balance 79.72$ 89.29$ Interest @ 12% 9.57 10.71 Ending balance 89.29$ 100.00$ If $79.72 is put in the bank today and earnsIf $79.72 is put in the bank today and earns 12%, it will be worth $100 in two years.12%, it will be worth $100 in two years. If $79.72 is put in the bank today and earnsIf $79.72 is put in the bank today and earns 12%, it will be worth $100 in two years.12%, it will be worth $100 in two years.
- 12. 13A-12 Rate Periods 10% 12% 14% 1 0.909 0.893 0.877 2 0.826 0.797 0.769 3 0.751 0.712 0.675 4 0.683 0.636 0.592 5 0.621 0.567 0.519 Present Value – An Example $100 × 0.797 = $79.72 present value Present value factor of $1 for 2 periods at 12%.Present value factor of $1 for 2 periods at 12%.Present value factor of $1 for 2 periods at 12%.Present value factor of $1 for 2 periods at 12%.
- 13. 13A-13 Quick Check How much would you have to put in the bank today to have $100 at the end of five years if the interest rate is 10%? a. $62.10 b. $56.70 c. $90.90 d. $51.90 How much would you have to put in the bank today to have $100 at the end of five years if the interest rate is 10%? a. $62.10 b. $56.70 c. $90.90 d. $51.90
- 14. 13A-14 How much would you have to put in the bank today to have $100 at the end of five years if the interest rate is 10%? a. $62.10 b. $56.70 c. $90.90 d. $51.90 How much would you have to put in the bank today to have $100 at the end of five years if the interest rate is 10%? a. $62.10 b. $56.70 c. $90.90 d. $51.90 Quick Check $100$100 ×× 0.621 = $62.100.621 = $62.10$100$100 ×× 0.621 = $62.100.621 = $62.10
- 15. 13A-15 Present Value of a Series of Cash Flows 11 22 33 44 55 66 $100$100 $100$100 $100$100 $100$100 $100$100 $100$100 An investment that involves a series of identical cash flows at the end of each year is called an annuity.
- 16. 13A-16 Present Value of a Series of Cash Flows – An Example Lacey Inc. purchased a tract of land on which a $60,000 payment will be due each year for the next five years. What is the present value of this stream of cash payments when the discount rate is 12%?
- 17. 13A-17 Present Value of a Series of Cash Flows – An Example We could solve the problem like this . . . Periods 10% 12% 14% 1 0.909 0.893 0.877 2 1.736 1.690 1.647 3 2.487 2.402 2.322 4 3.170 3.037 2.914 5 3.791 3.605 3.433 Present Value of an Annuity of $1 $60,000 × 3.605 = $216,300
- 18. 13A-18 Quick Check If the interest rate is 14%, how much would you have to put in the bank today so as to be able to withdraw $100 at the end of each of the next five years? a. $34.33 b. $500.00 c. $343.30 d. $360.50 If the interest rate is 14%, how much would you have to put in the bank today so as to be able to withdraw $100 at the end of each of the next five years? a. $34.33 b. $500.00 c. $343.30 d. $360.50
- 19. 13A-19 If the interest rate is 14%, how much would you have to put in the bank today so as to be able to withdraw $100 at the end of each of the next five years? a. $34.33 b. $500.00 c. $343.30 d. $360.50 If the interest rate is 14%, how much would you have to put in the bank today so as to be able to withdraw $100 at the end of each of the next five years? a. $34.33 b. $500.00 c. $343.30 d. $360.50 Quick Check $100$100 ×× 3.433 = $343.303.433 = $343.30$100$100 ×× 3.433 = $343.303.433 = $343.30
- 20. 13A-20 End of Appendix 13A

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