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The Time Value of Money Chapter 5. LEARNING OBJECTIVES 1. Explain the mechanics of compounding when invested. 2. Present value and future value. 3. Ordinary.

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Presentation on theme: "The Time Value of Money Chapter 5. LEARNING OBJECTIVES 1. Explain the mechanics of compounding when invested. 2. Present value and future value. 3. Ordinary."— Presentation transcript:

1 The Time Value of Money Chapter 5

2 LEARNING OBJECTIVES 1. Explain the mechanics of compounding when invested. 2. Present value and future value. 3. Ordinary annuity and its future value. 4. An ordinary annuity and an annuity due. 5. Non-annual future or present value of a sum. 6. Determine the present value of a perpetuity.

3 Power of time of value of money History of Interest Rates $1000 ( 1 +.08) 400 = ?

4 Power of time value of money Money Angles: by Andrew Tobias. 1.Chessboard with the King 2.Manhattan

5 Terms Compound Interest Future value and Present Value Annuities Annuities Due Amortized Loans Compound Interest with Non-annual Periods Present Value of an Uneven Stream· Perpetuities

6 COMPOUND INTEREST FV1=PV (1+i) (5-1) Where FV1=the future value of the investment at the end of one year i=the annual interest (or discount) rate PV=the present value, or original amount invested at the beginning of the first year

7 Future value 1.Simple compounding 2.Complex compounding

8

9 Future value

10 FV1=PV (1+i) =$100(1+0.06) =$100(1.06) =$106

11 Compound twice a year

12 Compound four times a year

13 Compound 12 times a year

14 Compound 360 times a year

15 Continuous compounding

16 Illustration of Compound Interest Calculations Year Beginning Value Interest Earned Ending Value 1 $100.00 $6.00 $106.00 2 106.00 6.36 112.36 3 112.36 6.74 119.10 4 119.10 7.15 126.25 5 126.25 7.57 133.82 6 133.82 8.03 141.85 7 141.85 8.51 150.36 8 150.36 9.02 159.38 9 159.38 9.57 168.95 10 168.95 10.13 179.08

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18

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20 Future value and future value interest factor

21 FVn=PV(FVIFi,n)

22 Table 5-2 FVIFi,n or the Compound Sum of $1 N 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 1 1.010 1.020 1.030 1.040 1.050 1.060 1.070 1.080 1.090 1.100 2 1.020 1.040 1.061 1.082 1.102 1.124 1.145 1.166 1.188 1.210 3 1.030 1.061 1.093 1.125 1.158 1.191 1.225 1.260 1.295 1.331 4 1.041 1.082 1.126 1.170 1.216 1.262 1.311 1.360 1.412 1.464 5 1.051 1.104 1.159 1.217 1.276 1.338 1.403 1.469 1.539 1.611 6 1.062 1.126 1.194 1.265 1.340 1.419 1.501 1.587 1.677 1.772 7 1.072 1.149 1.230 1.316 1.407 1.504 1.606 1.714 1.828 1.949 8 1.083 1.172 1.267 1.369 1.477 1.594 1.718 1.815 1.993 2.144 9 1.094 1.195 1.305 1.423 1.551 1.689 1.838 1.999 2.172 2.358 10 1.105 1.219 1.344 1.480 1.629 1.791 1.967 2.159 2.367 2.594 11 1.116 1.243 1.384 1.539 1.710 1.898 2.105 2.332 2.580 2.853 12 1.127 1.268 1.426 1.601 1.796 2.012 2.252 2.518 2.813 3.138 13 1.138 1.294 1.469 1.665 1.886 2.133 2.410 2.720 3.066 3.452 14 1.149 1.319 1.513 1.732 1.980 2.261 2.579 2.937 3.342 3.797 15 1.161 1.346 1.558 1.801 2.079 2.397 2.759 3.172 3.642 4.177

23 PV=$300, Vn=$774; i=9 % N=

24 PV=$100; FVn=$179.10; n=10 years. I= ?

25 PRESENT VALUE

26 FV10=$500, n=10, i=6 % PV = ?

27 (PVIF i, n) present-value interest factor for I and n (PVIF i, n), (PVIF i, n) = 1/(1+i)

28 Present value FV 10 =$1,500 N= 10 years discount rate= 8 % PV=$1500(0.463) =$694.50

29 Table 5-3 PVIFi,n or the Present Value of $1 N 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 1 0.990 0.980 0.971 0.962 0.952 0.943 0.935 0.926 0.917 0.909 2 0.980 0.961 0.943 0.925 0.907 0.890 0.873 0.857 0.842 0.826 3 0.971 0.942 0.915 0.889 0.864 0.840 0.816 0.794 0.772 0.751 4 0.961 0.924 0.888 0.855 0.823 0.792 0.763 0.735 0.708 0.683 5 0.951 0.906 0.863 0.822 0.784 0.747 0.713 0.681 0.650 0.621 6 0.942 0.888 0.837 0.790 0.746 0.705 0.666 0.630 0.596 0.564 7 0.933 0.871 0.813 0.760 0.711 0.655 0.623 0.583 0.547 0.513 8 0.914 0.837 0.766 0.703 0.645 0.592 0.544 0.500 0.460 0.424 9 0.905 0.820 0.744 0.676 0.614 0.558 0.508 0.463 0.422 0.386

30 ANNUITIES Annuity: equal annual cash flows. Ordinary annuity: at the end of each period. Annuity due: at the beginning of each eriod.

31 Table 5-4 Illustration of a Five-Year $500 Annuity Compounded at 6 percent YEAR 0 1 2 3 4 5 DOLLAR DEPOSITS AT END OF YEAR 500 500 500 500 500 $500.00 530.00 562.00 595.50 631.00 Future value of the annuity $2,818.50

32

33 FVIFA k, n = [(1/k) ( (1+ k) n – 1)] Ordinary annuity

34 Present value of an Annuity

35 Table 5-6 Illustration of a Five-Year $500 Annuity Discounted to the Present at 6 percent YEAR 0 1 2 3 4 5 Dollars received at the 500 500 500 500 500 the end of year $471.50 445.00 420.00 396.00 373.50 PV annuity $2,106.00

36 PVIFA K, n = (1/k) [( 1 – 1/(1+k) n ]

37 Table 5-7 PVIFi,n or the Present Value of an Annuity of $1 N 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 1 0.990 0.980 0.971 0.962 0.952 0.943 0.935 0.926 0.917 0.909 2 1.970 1.942 1.913 1.886 1.859 1.833 1.808 1.783 1.759 1.736 3 2.941 2.884 2.829 2.775 2.723 2.673 2.642 2.577 2.531 2.487 4 3.902 3.808 3.717 3.630 3.546 3.465 3.387 3.312 3.240 3.170 5 4.853 4.713 4.580 4.452 4.329 4.212 4.100 3.003 3.890 3.791 6 5.795 5.601 5.417 5.242 5.076 4.917 4.767 4.623 4.486 4.355 7 6.728 6.472 6.230 6.002 5.786 5.582 5.389 5.206 5.033 4.868 8 7.652 7.326 7.020 6.733 6.463 6.210 5.971 5.747 5.535 5.335 9 8.566 8.162 7.786 7.435 7.108 6.802 6.515 6.247 5.995 5.759 10 9.471 8.983 8.530 8.111 7.722 7.360 7.024 6.710 6.418 6.145

38 PV= $1,000(7.722) = $7,722 n=10 years, I=5 percent, and current PMT=$1,000

39 PMT Annuity: $5,000, n =5 years, i=8 percent, PMT:? $5,000 = PMT (3.993) $1,252.19=PMT

40 AMORTIZED LOANS

41 Loan Amortization Schedule Involving a $6,000 Loan at 15 Percent to Be Repaid in Four Years Year Annuity Interest Portion Repayment of Outstanding Of The Annuity1 The Principal Loan Balance Portion Of The After The An- Annuity2 nuity Payment 1 $2,101.58 $900.00 $1,201.58 $4,798.42 2 2,101.58 719.76 1,381.82 3,416.60 3 2,101.58 512.49 1,589.09 1,827.51 4 2,101.58 274.07 1,827.51

42 ANNUITIES DUE FVn ( annuity due )=PMT(FVIFA I,n )(1+I) (5-10) FV 5 =$500(FVIFA5%,5)(1+0.06) =$500(5.637)(1.06) =$2,987.61 from $2,106 to $2,232.36, PV=$500(PVIFA6%,5)(1+0.06) =$500(4.212)(1.06) =$2,232.36

43 End year Loan payment (1) Beginning principal (2) paymentsEnd of year principal( 5) [(2) (4) ] Interest(3) [0. 1 × (2) ] Princip al(4) [(1 ) (3)] 1 $ 1892.74 $ 6000.00 $ 600.00 $ 1292. 74 $ 4707.26 2 $ 1892.7 4 $ 4707.26 $ 470.73 $ 1422.0 1 $ 3285.25 3 $ 1892.74 $ 3285.25 $ 328.53 $ 1564.2 1 $ 1721.04 4 $ 1892.74 $ 1721.04 $ 172.10 $ 1720.6 4

44 The Value of $100 Compounded at Various Intervals FOR 1 YEAR AT i PERCENT I = 2% 5% 10% 15% Compounded annually $102.00 $105.00 $110.00 $115.00 Compounded semiannually 102.01 105.06 110.25 115.56 Compounded quarterly 102.02 105.09 110.38 115.87 Compounded monthly 102.02 105.12 110.47 116.08 Compounded weekly (52) 102.02 105.12 110.51 116.16 Compounded daily (365) 102.02 105.13 110.52 116.18

45 PRESENT VALUE OF AN UNEVEN STREAM YEAR CASH FLOW YEAR CASH FLOW 1 $500 6 500 2 200 7 500 3 -400 8 500 4 500 9 500 5 500 10 500

46 1.Present value of $500 received at the end of one year = $500(0.943) = $471.50 2. Present value of $200 received at the end of tree years = $200(0.890) = 178.00 3. Present value of a $400 outflow at the end of three years = -400(0.840) = -336.00 4. (a) Value at the end of year 3 and a $500 annuity, years 4 through 10 = $500 (5.582) = $2,791.00 (b) Present value of $2,791.00 received at the end of year 3 = 2,791(0.840) = 2,344.44 5. Total present value = $2,657.94

47 Quiz 1 Warm up Quiz. Terms: : n = 5, m = 4, I =12 percent, and PV =$100 solve for fv

48 Quiz 2 What is the present value of an investment involving $200 received at the end of years 1 through 4, a $300 cash outflow at the end of year 5 to 8, and $500 received at the end of years 9 through 10, given a 5 percent discount rate?

49 Quiz 3 1A 25 year-old graduate has his $50,000 salary a year. How much will he get when he reaches to 60 (35 years later)year-old with a value rate of 8%(annual compounding). 2The graduate will have his $80,000 salary at age of 30. How much will he get when he reaches to his age of 60(30 years later) with the value rate of 8%(semi-annual compounding).

50 Quiz 4 3.The graduate will have his $100,000 salary at age of 40. How much will he get when he reaches to his age of 60(20 years later) with the value rate of 12%(quarterly-annual compounding). 4.Compute the future value from 25-30/30- 40/40-60 year old with the same rate and the compounding rate.

51 PERPETUITIES $500 perpetuity discounted back to the present at 8 percent? PV = $500/0.08 = $6,250

52 Power of time of value of money History of Interest Rates $1000 ( 1 +.08) 400 = ?

53 Power of time value of money Money Angles: by Andrew Tobias. Chessboard with the King Manhattan


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