2. Time Decision

3. Time decisions u The principle to be discussed in this chapter involves expenditures that must be made several years before returns are obtained.

4. Value of $1,00 Compounded Annually at Specified Interest Rates for Periods Up to 20 years. No.of years Rate of interest 789101214 1$1,0700$1,0800$1,0900$1,1000$1,1200$1,1400 21,14491,16641,18811,21001,25441,2996 31,22501,25971,29501,33101,40491,4815 41,31081,36051,41161,46411,57351,6890 51,40261,46931,53861,61051,76231,9254 61,50071,58691,67711,77161,97382,1950 71,60581,71381,82801,94882,21072,5023 81,71821,85091,99252,14372,47602,8526 91,83851,99902,17182,35812,77313,2520 101,96722,15892,36732,59393,10593,7072 152,75903,17223,64244,17835,47367,1380 203,86974,66105,60436,73009,646313,7435

5. Present Value of $1,00 To Be Received in the year Specified No.of years Rate of interest 789101214 1$0,9346$0,9259$0,9174$0,9091$0,8929$0,8772 20,87340,85780,84170,82640,79720,7695 30,81630,79380,77220,75130,71180,6750 40,76290,73500,70840,68300,63550,5921 50,71300,68060,64990,62090,56740,5194 60,66630,63020,59630,56450,50660,4556 70,62270,58350,54700,51310,45240,3996 80,58200,54030,50190,46650,40390,3506 90,54390,50020,46040,42410,36060,3076 100,50830,46320,42240,38550,32200,2697 150,36240,31520,27450,23930,18270,1401 200,25840,21450,17840,14860,10370,0728

6. u INTEREST- a payment made for the use of money over a period of time. u INTEREST RATE - The price of using the money over a period of time

7. COMPOUNDING - calculating the future value u FUTURE VALUE FACTOR - The value by which a present value must be multiplied to calculate its future value u COMPOUNDING - Calculation of the future value of a present sum accounting for the rate of interest FVF=(1+i) n FV=PV*(1+i) n

8. AN EXAMPLE FOR CALCULATING COMPOUNDED VALUE u What is the future value of 4,000$ after 8 months, where the compound interest rate is 2% per month pv=4,000 i=0.02 n=8 fv=? u F.V.F=(1+0.02) 8 =1.1717 FV=4,000*1.1717=4,686.6

9. 8 DISCOUNTING – calculating the present value u Present Value Factor - The value by which a future value must be multiplied to calculate its present value u Discounting - Calculation of the present value of the future sum 1 (1+i) n PVF=

10. 9 An Example for Calculating Present Value (Discounting ) What is the present value of $2000 due in 10 years at 5% ? fv=2000 i=0.05 n=10 pv=? pvf=1/ (1+0.05) 10 =0.6139 pv=2000*0.6139 =1227.83

11. 10 Present Value Annuity Factor R Denotes the present value of a series of equal sums of $1 each, appearing during n periods of time at i interest rate R a - the annual sum R n - number of periods of time the sum appears R i - interest rate (1+i) n -1 pvaf= i*(1+i) n

12. PVAF - EXAMPLE u We need to buy a new machine We are offered to pay 3200$ in cash or 500 a year, for 10 years. u Which way should we prefer, if the interest rate is 8%? i=8% n=10 a=500 pv=? (1+0.08) 10 -1 0.08* (1+0.08) 10 pv=500* 6.7101 =3355 =6.7101pvaf=

13. 12 Future Value Annuity Factor R Denotes the future value of a series of sums of $1 each, appearing during n periods of time at i interest rate. (1+i) n -1 FVAF= i

14. 13 FVAF - EXAMPLE u We want to save money to buy a new asset in 8 years. The asset’s price is 3,000$ interest rate is 5%. Is 300$ a year enough ? FVAF (5%,8) = 9.5491 300*9.5491=2864.73 u Conclusion - 300$ a year would not be enough.

15. 14 u is used to distribute a single amount invested today over a uniform series of end year payments which have a present value equal to the amount invested today. i*(1+i) n (1+i) n - 1 where a=end year payment i=interest rate n=number of years CAPITAL RECOVERY FACTOR CRF=

16. 15 Capital Recovery Payments - Example u A loan of 90,000$ was taken for 20 years at an interest rate of 5% a year, what are the annual payment required to recover the loan. u pv=90,000 n=20 i=5% a=? CRF(5%,20)=0.0802 90,000*0.0802=7,218