Slide 1 ___________________________________ 8.4 T ime value of - PDF document

Slide 1 ___________________________________ 8.4 T ime value of money ___________________________________ Money has time value o Most people ar e willing to ac cept o less today than they would if ___________________________________ o they wer e paid the same amount in the futur e ___________________________________ ___________________________________ ___________________________________ 2005 K D Ha the wa y-Dia l ___________________________________ Slide 2 ___________________________________ Calculating Present value fac tor s – Pr esent value of a lump sum ___________________________________ 1. F inanc ial c alc ulator 2. PV tables (see appendix in ___________________________________ online Wiley text) 3. PV factor equations – per sonal ___________________________________ favor ite PV factor Where “i” equals 1 ___________________________________ for lump = interest rate and “N” sum ( 1 + i ) N equals periods ___________________________________ ___________________________________ Slide 3 ___________________________________ Pr esent Value and F utur e Value o Pr esent value of $1 ___________________________________ o T he value today of $1 to be r eceived or paid at some futur e date, given a spec ified inter est r ate ___________________________________ ___________________________________ Present Value Future Value $90.91 $100 ___________________________________ One year @ 10% ___________________________________ ___________________________________

Slide 4 ___________________________________ Pr esent Value and F utur e Value ___________________________________ F utur e value……….…….……$10,000 PV fac tor of $1 ___________________________________ wher e n=4 wher e i=10%.....................X 0.6830 ___________________________________ PV of payment $ 6,830 ___________________________________ ___________________________________ ___________________________________ Slide 5 ___________________________________ Pr esent Value and F utur e Value Pr esent Value in Savings…….$ 6.830 ___________________________________ F V fac tor of a $1 wher e n=4 ___________________________________ wher e i=10%......................x1.4641 F utur e Value………………......$10,000 ___________________________________ ___________________________________ ___________________________________ ___________________________________ Slide 6 ___________________________________ Calculating pr esent value of a lump sum ___________________________________ Computing PV of a single Sum 1. $15,000 due in 5 year s at 8% c ompounded annually ___________________________________ 2. $25,000 due in 8 ½ year s at 10% c ompounded semi- annually ___________________________________ 3. $9,500 due in 4 year s at 12% c ompounded quar ter ly ___________________________________ 4. $20,000 due in 20 year s at 8% c ompounded semi-annually ___________________________________ ___________________________________

Slide 7 ___________________________________ Calculating futur e value of a lump sum ___________________________________ Computing the F V of a single sum 1. $10,209 invested to ear n inter est 8% c ompounded annually for 5 year s ___________________________________ 2. $10,907 invested to ear n inter est 10% c ompounded semi-annually 8 ½ year s ___________________________________ 3. $5,920 invested to ear n inter est 12% c ompounded quar ter ly for 4 year s 4. $4,166 invested to ear n inter est 8% ___________________________________ c ompounded semi-annually for 20 yr s ___________________________________ ___________________________________ Slide 8 ___________________________________ Calc ulating Pr esent value fac tor s – Pr esent value of an annuity ___________________________________ PV factor for an annuity or a str eam of equal c ash flows ___________________________________ This part of the expression is ___________________________________ essentially the present value factor of a lump sum Where “i” equals 1 - 1 ___________________________________ interest rate and “N” PV factor for an = ( 1 + i ) N equals periods annuity i ___________________________________ ___________________________________ Slide 9 ___________________________________ Pr esent Value of an Annuity Amount of the annual ___________________________________ payment.....................................$10,000 PV fac tor of an annuity ___________________________________ wher e n= 10 payments wher e i = 12% ___________________________________ X5.6502 Pr esent Value $56,502 ___________________________________ ___________________________________ ___________________________________

Slide 10 ___________________________________ Calc ulating pr esent value of an annuity What is the pr esent value ___________________________________ (r ounded to the near est dollar ) of an annuity of $8,000 per year for ___________________________________ five year s if the inter est r ate is: 1. 8% compounded annually 2. 10% c ompounded annually ___________________________________ ___________________________________ ___________________________________ ___________________________________ Slide 11 ___________________________________ Calc ulating pr esent value of an annuity Answer : ___________________________________ 1. 8% compounded annually 2. 10% c ompounded annually ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________