Pertemuan 12 Perhitungan Nilai Waktu Uang Time Value

Pertemuan 12 Perhitungan Nilai Waktu Uang

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. Mc. Graw-Hill/Irwin © The Mc. Graw-Hill Companies, Inc. , 2003

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. Mc. Graw-Hill/Irwin © The Mc. Graw-Hill Companies, Inc. , 2003

Interest and the Time Value of Money 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: (1. 08) $108 = $116. 64 or (1. 08)2 × $100 = $116. 64 Mc. Graw-Hill/Irwin © The Mc. Graw-Hill Companies, Inc. , 2003

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 Fn dollars computed as follows: Fn = P(1 + Mc. Graw-Hill/Irwin n r) © The Mc. Graw-Hill Companies, Inc. , 2003

Interest and the Time Value of Money 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: P = Fn Mc. Graw-Hill/Irwin 1 n (1 + r) © The Mc. Graw-Hill Companies, Inc. , 2003

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

Interest and the Time Value of Money 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 P = 100 (1 +. 12)2 P = $100 (0. 797) P = $79. 70 Mc. Graw-Hill/Irwin © The Mc. Graw-Hill Companies, Inc. , 2003

Interest and the Time Value of Money 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? Present Value = $79. 70 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. Mc. Graw-Hill/Irwin © The Mc. Graw-Hill Companies, Inc. , 2003

Interest and the Time Value of Money 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. We can also determine the present value using present value tables. Mc. Graw-Hill/Irwin © The Mc. Graw-Hill Companies, Inc. , 2003

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

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. © The Mc. Graw-Hill Companies, Inc. , 2003 Mc. Graw-Hill/Irwin

Time Value of Money An investment that involves a series of identical cash flows at the end of each year is called an annuity $100 1 Mc. Graw-Hill/Irwin $100 2 $100 3 $100 4 $100 5 6 © The Mc. Graw-Hill Companies, Inc. , 2003

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 Mc. Graw-Hill/Irwin © The Mc. Graw-Hill Companies, Inc. , 2003

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 $100 0. 621 = $62. 10 b. $56. 70 c. $90. 90 d. $51. 90 Mc. Graw-Hill/Irwin © The Mc. Graw-Hill Companies, Inc. , 2003

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%? Mc. Graw-Hill/Irwin © The Mc. Graw-Hill Companies, Inc. , 2003

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 Mc. Graw-Hill/Irwin © The Mc. Graw-Hill Companies, Inc. , 2003

Time Value of Money We could solve the problem like this. . . $60, 000 × 3. 605 = $216, 300 Mc. Graw-Hill/Irwin © The Mc. Graw-Hill Companies, Inc. , 2003

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 Mc. Graw-Hill/Irwin © The Mc. Graw-Hill Companies, Inc. , 2003

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 $100 3. 433 = $343. 30 d. $360. 50 Mc. Graw-Hill/Irwin © The Mc. Graw-Hill Companies, Inc. , 2003

Quick Check If the interest rate is 14%, what is the present value of $100 to be received at the end of the 3 rd, 4 th, and 5 th years? a. $866. 90 b. $178. 60 c. $ 86. 90 d. $300. 00 Mc. Graw-Hill/Irwin © The Mc. Graw-Hill Companies, Inc. , 2003

Quick Check If the interest rate is 14%, what is the present value of $100 to be received at the end of the 3 rd, 4 th, and 5 th years? a. $866. 90 b. $178. 60 c. $ 86. 90 d. $300. 00 $100 (3. 433 -1. 647)= $100 1. 786 = $178. 60 or $100 (0. 675+0. 592+0. 519)= $100 1. 786 = $178. 60 Mc. Graw-Hill/Irwin © The Mc. Graw-Hill Companies, Inc. , 2003

Typical Cash Outflows Repairs and maintenance Working capital Initial investment Incremental operating costs Mc. Graw-Hill/Irwin © The Mc. Graw-Hill Companies, Inc. , 2003

Typical Cash Inflows Salvage value Release of working capital Reduction of costs Incremental revenues Mc. Graw-Hill/Irwin © The Mc. Graw-Hill Companies, Inc. , 2003

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