1. Perhitungan Nilai Waktu Uang Pertemuan 12

2. © The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Time Value of Money Business investments extend over long periods of time, so we must recognize the time value of money. Investments that promise returns earlier in time are preferable to those that promise returns later in time.

3. © The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Time Value of Money A dollar today is worth more than a dollar a year from now since a dollar received today can be invested, yielding more than a dollar a year from now.

4. © The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin If $100 is invested today at 8% interest, how much will you have in two years? At the end of one year: $100 + 0.08  $100 = (1.08)  $100 = $108 At the end of two years: $116.64 (1.08)  $108 = $116.64 or (1.08) 2 × $100 = $116.64 Interest and the Time Value of Money

5. © The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Interest and the Time Value of Money If P dollars are invested today at the annual interest rate r, then in n years you would have F n dollars computed as follows: F n = P(1 + r) n

6. © The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin The present value of any sum to be received in the future can be computed by turning the interest formula around and solving for P: (1 + r) n P = F n 1 Interest and the Time Value of Money

7. © The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Time Value of Money Excerpt from Present Value of $1 Table in the Appendix to Chapter 14

8. © The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin 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? Interest and the Time Value of Money (1 +.12) 2 P = 100 1 P = $100 (0.797) P = $79.70

9. © The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin What does this mean? If $79.70 is put in the bank today, it will be worth $100 in two years. In that sense, $79.70 today is equivalent to $100 in two years. What does this mean? If $79.70 is put in the bank today, it will be worth $100 in two years. In that sense, $79.70 today is equivalent to $100 in two years. Interest and the Time Value of Money Present Value = $79.70 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?

10. © The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Let’s verify that if we put $79.70 in the bank today at 12% interest that it would grow to $100 at the end of two years. Let’s verify that if we put $79.70 in the bank today at 12% interest that it would grow to $100 at the end of two years. Interest and the Time Value of Money We can also determine the present value using present value tables.

11. © The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Time Value of Money Excerpt from Present Value of $1 Table in the Appendix to Chapter 14

12. © The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Time Value of Money $100 × 0.797 = $79.70 present value Present value factor of $1 for 2 periods at 12%. Atau dapat dihitung dengan mempergunakan kalkulator. Caranya: Tekan angka 1 dan tekan bagi 1,12, terus tekan sama dengan, yang akan menghasilkan 0.893 untuk tahun pertama. Lalu tekan sama dengan lagi untuk menghasikan 0.797, dan seterusnya.

13. © The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Time Value of Money 123456$100$100$100$100$100$100 annuity An investment that involves a series of identical cash flows at the end of each year is called an annuity.

14. © The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin 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

15. © The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin 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  0.621 = $62.10

16. © The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Time Value of Money 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. © The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Time Value of Money We could solve the problem like this... Look in Appendix C of this Chapter for the Present Value of an Annuity of $1 Table

18. © The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Time Value of Money We could solve the problem like this... $60,000 × 3.605 = $216,300

19. © The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin 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

20. © The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin 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  3.433 = $343.30

21. © The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Quick Check If the interest rate is 14%, what is the present value of $100 to be received at the end of the 3rd, 4th, and 5th years? a. $866.90 b. $178.60 c. $ 86.90 d. $300.00 If the interest rate is 14%, what is the present value of $100 to be received at the end of the 3rd, 4th, and 5th years? a. $866.90 b. $178.60 c. $ 86.90 d. $300.00

22. © The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin If the interest rate is 14%, what is the present value of $100 to be received at the end of the 3rd, 4th, and 5th years? a. $866.90 b. $178.60 c. $ 86.90 d. $300.00 If the interest rate is 14%, what is the present value of $100 to be received at the end of the 3rd, 4th, and 5th years? a. $866.90 b. $178.60 c. $ 86.90 d. $300.00 Quick Check $100  (3.433-1.647)= $100  1.786 = $178.60 or $100  (0.675+0.592+0.519)= $100  1.786 = $178.60

23. © The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Typical Cash Outflows Repairs and maintenance Incrementaloperatingcosts InitialinvestmentWorkingcapital

24. © The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Typical Cash InflowsReduction of costs Salvagevalue Incrementalrevenues Release of workingcapital

25. © The McGraw-Hill Companies, Inc., 2003 McGraw-Hill/Irwin Akhir Pertemuan 12: Terima kasih