Time Value of Money. Types of Interest. Compounding and Discounting Single Sums. Page 1. Ch. 6  The Time Value of Money. The Time Value of Money


 Gerald White
 2 years ago
 Views:
Transcription
1 Ch. 6  The Tme Value of Money Tme Value of Money The Interest Rate Smple Interest Compound Interest Amortzng a Loan FIN21 Ahmed Y, Dasht TIME VALUE OF MONEY OR DISCOUNTED CASH FLOW ANALYSIS Very Important concept  Almost everythng from ths pont on n fnance based upon understandng ths concept. You must get ths materal down cold. You can do problems usng formulas, calculators, and spreadsheets. We wll prmarly use fnancal calculators. Please have your fnancal calculators wth you n class. The Concept of TVM s One of Fnance s BIG contrbutons: t provdes: A vald way for valung dfferent patterns of cash flows on a common bass. A way of cuttng through exaggerated clams. The easest way to envson ths s usng Tme Lnes: Types of Interest usmple Interest Interest pad (earned) on only the orgnal amount, or prncpal borrowed (lent). The Tme Value of Money Compoundng and Dscountng Sngle Sums Compound Interest Interest pad (earned) on prevous nterest earned, as well as on the prncpal borrowed (lent). Page 1
2 Why TIME Why s TIME such an mportant element n your decson? TIME allows you the opportunty to postpone consumpton and earn INTEREST. We know that recevng $1 today s worth more than $1 n the future. Ths s due to opportunty costs. The opportunty cost of recevng $1 n the future s the nterest we could have earned f we had receved the $1 sooner. Today Future If we can measure ths opportunty cost, we can: If we can measure ths opportunty cost, we can: Translate $1 today nto ts equvalent n the future (compoundng). If we can measure ths opportunty cost, we can: Translate $1 today nto ts equvalent n the future (compoundng). Today Future? If we can measure ths opportunty cost, we can: Translate $1 today nto ts equvalent n the future (compoundng). Today Future? Translate $1 n the future nto ts equvalent today (dscountng). Page 2
3 If we can measure ths opportunty cost, we can: Translate $1 today nto ts equvalent n the future (compoundng). Today Translate $1 n the future nto ts equvalent today (dscountng). Today? Future? Future Look carefully at the tmelne: The tmelne allows you to vsualze the actual stuaton. nclude all elements (n,,fv,pv,+$,$) understand the dynamcs. make accurate calculatons, every tme. speed up the process of problem solvng. Why use Tmelnes? useful for accurate TVM calculatons. essental for captal budgetng. Future Value essental for understandng TVM. essental for ncremental cash flows. essental for succeedng n Fnance. Future Value  sngle sums If you depost $100 n an account earnng 6%, how much would you have n the account after 1 year? Future Value  sngle sums If you depost $100 n an account earnng 6%, how much would you have n the account after 1 year? PV = FV = 0 1 Page 3
4 Future Value  sngle sums If you depost $100 n an account earnng 6%, how much would you have n the account after 1 year? PV = 100 FV = 0 1 P/Y = 1 I = 6 N = 1 PV = 100 FV = $106 Future Value  sngle sums If you depost $100 n an account earnng 6%, how much would you have n the account after 1 year? PV = 100 FV = P/Y = 1 I = 6 N = 1 PV = 100 FV = $106 Future Value  sngle sums If you depost $100 n an account earnng 6%, how much would you have n the account after 1 year? Future Value  sngle sums If you depost $100 n an account earnng 6%, how much would you have n the account after 5 years? PV = 100 FV = FV = PV (FVIF, n ) FV = 100 (FVIF.06, 1 ) (use FVIF table, or) FV = PV (1 + ) n FV = 100 (1.06) 1 = $106 Future Value  sngle sums If you depost $100 n an account earnng 6%, how much would you have n the account after 5 years? PV = FV = 0 5 Future Value  sngle sums If you depost $100 n an account earnng 6%, how much would you have n the account after 5 years? PV = 100 FV = 0 5 P/Y = 1 I = 6 N = 5 PV = 100 FV = $ Page 4
5 Future Value  sngle sums If you depost $100 n an account earnng 6%, how much would you have n the account after 5 years? PV = 100 FV = P/Y = 1 I = 6 N = 5 PV = 100 FV = $ Future Value  sngle sums If you depost $100 n an account earnng 6%, how much would you have n the account after 5 years? PV = 100 FV = FV = PV (FVIF, n ) FV = 100 (FVIF.06, 5 ) (use FVIF table, or) FV = PV (1 + ) n FV = 100 (1.06) 5 = $ Future Value  sngle sums If you depost $100 n an account earnng 6% wth quarterly compoundng, how much would you have n the account after 5 years? Future Value  sngle sums If you depost $100 n an account earnng 6% wth quarterly compoundng, how much would you have n the account after 5 years? PV = FV = 0? Future Value  sngle sums If you depost $100 n an account earnng 6% wth quarterly compoundng, how much would you have n the account after 5 years? PV = 100 FV = 0 20 P/Y = 4 I = 6 N = 20 PV = 100 FV = $ Future Value  sngle sums If you depost $100 n an account earnng 6% wth quarterly compoundng, how much would you have n the account after 5 years? PV = 100 FV = P/Y = 4 I = 6 N = 20 PV = 100 FV = $ Page 5
6 Future Value  sngle sums If you depost $100 n an account earnng 6% wth quarterly compoundng, how much would you have n the account after 5 years? PV = 100 FV = Future Value  sngle sums If you depost $100 n an account earnng 6% wth monthly compoundng, how much would you have n the account after 5 years? 0 20 FV = PV (FVIF, n ) FV = 100 (FVIF.015, 20 ) (can t use FVIF table) FV = PV (1 + /m) m x n FV = 100 (1.015) 20 = $ Future Value  sngle sums If you depost $100 n an account earnng 6% wth monthly compoundng, how much would you have n the account after 5 years? PV = FV = 0? Future Value  sngle sums If you depost $100 n an account earnng 6% wth monthly compoundng, how much would you have n the account after 5 years? PV = 100 FV = 0 60 P/Y = 12 I = 6 N = 60 PV = 100 FV = $ Future Value  sngle sums If you depost $100 n an account earnng 6% wth monthly compoundng, how much would you have n the account after 5 years? PV = 100 FV = P/Y = 12 I = 6 N = 60 PV = 100 FV = $ Future Value  sngle sums If you depost $100 n an account earnng 6% wth monthly compoundng, how much would you have n the account after 5 years? PV = 100 FV = FV = PV (FVIF, n ) FV = 100 (FVIF.005, 60 ) (can t use FVIF table) FV = PV (1 + /m) m x n FV = 100 (1.005) 60 = $ Page 6
7 $300 Compound Interest The Future Value of a Sngle Amount Graphcal Presentaton Dfferent Interest Rates $250 $200 $ k = 8% $150 $100 $50 $ Amount k = 4% k = 0% Year 38 Future Value  contnuous compoundng What s the FV of $1,000 earnng 8% wth contnuous compoundng, after 100 years? Future Value  contnuous compoundng What s the FV of $1,000 earnng 8% wth contnuous compoundng, after 100 years? PV = FV = 0? Future Value  contnuous compoundng What s the FV of $1,000 earnng 8% wth contnuous compoundng, after 100 years? PV = FV = FV = PV (e n ) FV = 1000 (e.08x100 ) = 1000 (e 8 ) FV = $2,980, Future Value  contnuous compoundng What s the FV of $1,000 earnng 8% wth contnuous compoundng, after 100 years? PV = FV = $2.98m FV = PV (e n ) FV = 1000 (e.08x100 ) = 1000 (e 8 ) FV = $2,980, Page 7
8 Compoundng Perods Frequency wth whch nterest s credted for calculatng future nterest, usually annually, semannually, quarterly, or monthly. The shorter the perod, the more nterest s earned on nterest Annually 12% $100 $112 Semannually 6% 6% $100 $106 $ Quarterly 3% 3% 3% 3% $100 $103 $ $ $ The Effectve Annual Rate (EAR) The rate of annually compounded nterest equvalent to the nomnal rate compounded more frequently Table 52 Compoundng Fnal balance Annual $ Semannual $ Quarterly $ Monthly $ Year End Balances at Varous Compoundng Perods $100 Intal Depost and k nom = 12% In general: EAR = 1 + k m m nom 1 Quote the annual (nomnal) rate (k nom ) statng the compoundng perod mmedately afterward "12% compounded quarterly" Present Value Present Value  sngle sums If you receve $100 one year from now, what s the PV of that $100 f your opportunty cost s 6%? Present Value  sngle sums If you receve $100 one year from now, what s the PV of that $100 f your opportunty cost s 6%? PV = FV = 0? Present Value  sngle sums If you receve $100 one year from now, what s the PV of that $100 f your opportunty cost s 6%? PV = FV = P/Y = 1 I = 6 N = 1 FV = 100 PV = Page 8
9 Present Value  sngle sums If you receve $100 one year from now, what s the PV of that $100 f your opportunty cost s 6%? PV = FV = P/Y = 1 I = 6 N = 1 FV = 100 PV = Present Value  sngle sums If you receve $100 one year from now, what s the PV of that $100 f your opportunty cost s 6%? PV = FV = PV = FV (PVIF, n ) PV = 100 (PVIF.06, 1 ) (use PVIF table, or) PV = FV / (1 + ) n PV = 100 / (1.06) 1 = $94.34 Present Value  sngle sums If you receve $100 fve years from now, what s the PV of that $100 f your opportunty cost s 6%? Present Value  sngle sums If you receve $100 fve years from now, what s the PV of that $100 f your opportunty cost s 6%? PV = FV = 0? Present Value  sngle sums If you receve $100 fve years from now, what s the PV of that $100 f your opportunty cost s 6%? PV = FV = P/Y = 1 I = 6 N = 5 FV = 100 PV = Present Value  sngle sums If you receve $100 fve years from now, what s the PV of that $100 f your opportunty cost s 6%? PV = FV = P/Y = 1 I = 6 N = 5 FV = 100 PV = Page 9
10 Present Value  sngle sums If you receve $100 fve years from now, what s the PV of that $100 f your opportunty cost s 6%? Present Value  sngle sums What s the PV of $1,000 to be receved 15 years from now f your opportunty cost s 7%? PV = FV = PV = FV (PVIF, n ) PV = 100 (PVIF.06, 5 ) (use PVIF table, or) PV = FV / (1 + ) n PV = 100 / (1.06) 5 = $74.73 Present Value  sngle sums What s the PV of $1,000 to be receved 15 years from now f your opportunty cost s 7%? PV = FV = 0 15 Present Value  sngle sums What s the PV of $1,000 to be receved 15 years from now f your opportunty cost s 7%? PV = FV = P/Y = 1 I = 7 N = 15 FV = 1,000 PV = Present Value  sngle sums What s the PV of $1,000 to be receved 15 years from now f your opportunty cost s 7%? PV = FV = P/Y = 1 I = 7 N = 15 FV = 1,000 PV = Present Value  sngle sums What s the PV of $1,000 to be receved 15 years from now f your opportunty cost s 7%? PV = FV = PV = FV (PVIF, n ) PV = 100 (PVIF.07, 15 ) (use PVIF table, or) PV = FV / (1 + ) n PV = 100 / (1.07) 15 = $ Page 10
11 Present Value  sngle sums If you sold land for $11,933 that you bought 5 years ago for $5,000, what s your annual rate of return? Present Value  sngle sums If you sold land for $11,933 that you bought 5 years ago for $5,000, what s your annual rate of return? PV = FV = 0 5 Present Value  sngle sums If you sold land for $11,933 that you bought 5 years ago for $5,000, what s your annual rate of return? PV = FV = 11, P/Y = 1 N = 5 PV = 5,000 FV = 11,933 I = 19% Present Value  sngle sums If you sold land for $11,933 that you bought 5 years ago for $5,000, what s your annual rate of return? PV = FV (PVIF, n ) 5,000 = 11,933 (PVIF?, 5 ) PV = FV / (1 + ) n 5,000 = 11,933 / (1+ ) = ((1/ (1+) 5 ) = (1+) 5 (2.3866) 1/5 = (1+) =.19 Present Value  sngle sums Suppose you placed $100 n an account that pays 9.6% nterest, compounded monthly. How long wll t take for your account to grow to $500? PV = FV = 0 Present Value  sngle sums Suppose you placed $100 n an account that pays 9.6% nterest, compounded monthly. How long wll t take for your account to grow to $500? PV = 100 FV = 500 0? P/Y = 12 FV = 500 I = 9.6 PV = 100 N = 202 months Page 11
12 Present Value  sngle sums Suppose you placed $100 n an account that pays 9.6% nterest, compounded monthly. How long wll t take for your account to grow to $500? PV = FV / (1 + ) n 100 = 500 / (1+.008) N 5 = (1.008) N ln 5 = ln (1.008) N ln 5 = N ln (1.008) = N N = 202 months Hnt for sngle sum problems: In every sngle sum future value and present value problem, there are 4 varables: FV, PV,, and n When dong problems, you wll be gven 3 of these varables and asked to solve for the 4th varable. Keepng ths n mnd makes tme value problems much easer! Present Value  An Example Suppose you have the opportunty to buy a pece of land for $10,000 today, and sell t n eght years for $20,000. Is ths a good deal f you can put your money n a rskequvalent that s expected to earn 10 percent a year compounded annually? Present Value  An Example The present value of the $20,000 you expect to receve at the end of eght years s: PV = $20,000 [ 1/(1.10) 8 ] = $ I=10% Facts Tmelne n= 8 Ths s a bad deal snce the present value of return n eght years s less than the cost of the land. The Tme Value of Money Compoundng and Dscountng Cash Flow Streams Annutes Annuty: a sequence of equal cash flows, occurrng at the end of each perod. 4 Page 12
13 Annutes Annuty: a sequence of equal cash flows, occurrng at the end of each perod. 4 Examples of Annutes: If you buy a bond, you wll receve equal semannual coupon nterest payments over the lfe of the bond. If you borrow money to buy a house or a car, you wll pay a stream of equal payments. Examples of Annutes: If you buy a bond, you wll receve equal semannual coupon nterest payments over the lfe of the bond. If you borrow money to buy a house or a car, you wll pay a stream of equal payments. Future Value  annuty If you nvest $1,000 each year at 8%, how much would you have after 3 years? Future Value  annuty If you nvest $1,000 each year at 8%, how much would you have after 3 years? Future Value  annuty If you nvest $1,000 each year at 8%, how much would you have after 3 years? P/Y = 1 I = 8 N = 3 PMT = 1,000 FV = $3, Page 13
14 Future Value  annuty If you nvest $1,000 each year at 8%, how much would you have after 3 years? Future Value  annuty If you nvest $1,000 each year at 8%, how much would you have after 3 years? P/Y = 1 I = 8 N = 3 PMT = 1,000 FV = $3, Future Value  annuty If you nvest $1,000 each year at 8%, how much would you have after 3 years? Future Value  annuty If you nvest $1,000 each year at 8%, how much would you have after 3 years? FV = PMT (FVIFA, n ) Future Value  annuty If you nvest $1,000 each year at 8%, how much would you have after 3 years? FV = PMT (FVIFA, n ) FV = 1,000 (FVIFA.08, 3 ) (use FVIFA table, or) Future Value  annuty If you nvest $1,000 each year at 8%, how much would you have after 3 years? FV = PMT (FVIFA, n ) FV = 1,000 (FVIFA.08, 3 ) (use FVIFA table, or) FV = PMT (1 + ) n 1 Page 14
15 Future Value  annuty If you nvest $1,000 each year at 8%, how much would you have after 3 years? Present Value  annuty What s the PV of $1,000 at the end of each of the next 3 years, f the opportunty cost s 8%? FV = PMT (FVIFA, n ) FV = 1,000 (FVIFA.08, 3 ) (use FVIFA table, or) FV = PMT (1 + ) n 1 FV = 1,000 (1.08) 31 = $ Present Value  annuty What s the PV of $1,000 at the end of each of the next 3 years, f the opportunty cost s 8%? Present Value  annuty What s the PV of $1,000 at the end of each of the next 3 years, f the opportunty cost s 8%? P/Y = 1 I = 8 N = 3 PMT = 1,000 PV = $2, Present Value  annuty What s the PV of $1,000 at the end of each of the next 3 years, f the opportunty cost s 8%? Present Value  annuty What s the PV of $1,000 at the end of each of the next 3 years, f the opportunty cost s 8%? P/Y = 1 I = 8 N = 3 PMT = 1,000 PV = $2, Page 15
16 Present Value  annuty What s the PV of $1,000 at the end of each of the next 3 years, f the opportunty cost s 8%? Present Value  annuty What s the PV of $1,000 at the end of each of the next 3 years, f the opportunty cost s 8%? PV = PMT (PVIFA, n ) Present Value  annuty What s the PV of $1,000 at the end of each of the next 3 years, f the opportunty cost s 8%? PV = PMT (PVIFA, n ) PV = 1,000 (PVIFA.08, 3 ) (use PVIFA table, or) Present Value  annuty What s the PV of $1,000 at the end of each of the next 3 years, f the opportunty cost s 8%? PV = PMT (PVIFA, n ) PV = 1,000 (PVIFA.08, 3 ) (use PVIFA table, or) 1 PV = PMT 1  (1 + ) n Present Value  annuty What s the PV of $1,000 at the end of each of the next 3 years, f the opportunty cost s 8%? The Tme Value of Money PV = PMT (PVIFA, n ) PV = 1,000 (PVIFA.08, 3 ) (use PVIFA table, or) 1 PV = PMT 1  (1 + ) n 1 PV = (1.08 ) 3 = $2, Other Cash Flow Patterns Page 16
17 Perpetutes Suppose you wll receve a fxed payment every perod (month, year, etc.) forever. Ths s an example of a perpetuty. You can thnk of a perpetuty as an annuty that goes on forever. Present Value of a Perpetuty When we fnd the PV of an annuty, we thnk of the followng relatonshp: Present Value of a Perpetuty Mathematcally, When we fnd the PV of an annuty, we thnk of the followng relatonshp: PV = PMT (PVIFA, n ) Mathematcally, (PVIFA, n ) = Mathematcally, (PVIFA, n ) = 11 (1 + ) n Page 17
18 Mathematcally, (PVIFA, n ) = 11 (1 + ) n When n gets very large, We sad that a perpetuty s an annuty where n = nfnty. What happens to ths formula when n gets very, very large? When n gets very large, When n gets very large, 11 (1 + ) n 11 (1 + ) n ths becomes zero. When n gets very large, 11 (1 + ) n ths becomes zero. Present Value of a Perpetuty So, the PV of a perpetuty s very smple to fnd: So we re left wth PVIFA = 1 Page 18
19 Present Value of a Perpetuty So, the PV of a perpetuty s very smple to fnd: What should you be wllng to pay n order to receve $10,000 annually forever, f you requre 8% per year on the nvestment? PV = PMT What should you be wllng to pay n order to receve $10,000 annually forever, f you requre 8% per year on the nvestment? PV = PMT = $10, What should you be wllng to pay n order to receve $10,000 annually forever, f you requre 8% per year on the nvestment? PV = PMT = $10, = $125,000 Begn Mode vs. End Mode Ordnary Annuty vs. Annuty Due $1000 $1000 $ Page 19
20 Begn Mode vs. End Mode year year year Begn Mode vs. End Mode year year year PV n END Mode Begn Mode vs. End Mode year year year Begn Mode vs. End Mode year year year PV n END Mode FV n END Mode Begn Mode vs. End Mode year year year Begn Mode vs. End Mode year year year PV n BEGIN Mode PV n BEGIN Mode FV n BEGIN Mode Page 20
21 Earler, we examned ths ordnary annuty: Earler, we examned ths ordnary annuty: Earler, we examned ths ordnary annuty: Usng an nterest rate of 8%, we fnd that: Earler, we examned ths ordnary annuty: Usng an nterest rate of 8%, we fnd that: The Future Value (at 3) s $3, Earler, we examned ths ordnary annuty: Usng an nterest rate of 8%, we fnd that: The Future Value (at 3) s $3, The Present Value (at 0) s $2, What about ths annuty? Same 3year tme lne, Same 3 $1000 cash flows, but The cash flows occur at the begnnng of each year, rather than at the end of each year. Ths s an annuty due. Page 21
22 Future Value  annuty due If you nvest $1,000 at the begnnng of each of the next 3 years at 8%, how much would you have at the end of year 3? Future Value  annuty due If you nvest $1,000 at the begnnng of each of the next 3 years at 8%, how much would you have at the end of year 3? Mode = BEGIN P/Y = 1 I = 8 N = 3 PMT = 1,000 FV = $3, Future Value  annuty due If you nvest $1,000 at the begnnng of each of the next 3 years at 8%, how much would you have at the end of year 3? Future Value  annuty due If you nvest $1,000 at the begnnng of each of the next 3 years at 8%, how much would you have at the end of year 3? Smply compound the FV of the ordnary annuty one more perod: Mode = BEGIN P/Y = 1 I = 8 N = 3 PMT = 1,000 FV = $3, Future Value  annuty due If you nvest $1,000 at the begnnng of each of the next 3 years at 8%, how much would you have at the end of year 3? Smply compound the FV of the ordnary annuty one more perod: FV = PMT (FVIFA, n ) (1 + ) Future Value  annuty due If you nvest $1,000 at the begnnng of each of the next 3 years at 8%, how much would you have at the end of year 3? Smply compound the FV of the ordnary annuty one more perod: FV = PMT (FVIFA, n ) (1 + ) FV = 1,000 (FVIFA.08, 3 ) (1.08) (use FVIFA table, or) Page 22
23 Future Value  annuty due If you nvest $1,000 at the begnnng of each of the next 3 years at 8%, how much would you have at the end of year 3? Smply compound the FV of the ordnary annuty one more perod: FV = PMT (FVIFA, n ) (1 + ) FV = 1,000 (FVIFA.08, 3 ) (1.08) (use FVIFA table, or) FV = PMT (1 + ) n 1 (1 + ) Future Value  annuty due If you nvest $1,000 at the begnnng of each of the next 3 years at 8%, how much would you have at the end of year 3? Smply compound the FV of the ordnary annuty one more perod: FV = PMT (FVIFA, n ) (1 + ) FV = 1,000 (FVIFA.08, 3 ) (1.08) (use FVIFA table, or) FV = PMT (1 + ) n 1 (1 + ) FV = 1,000 (1.08) 31 = $3, (1.08).08 Present Value  annuty due What s the PV of $1,000 at the begnnng of each of the next 3 years, f your opportunty cost s 8%? Present Value  annuty due What s the PV of $1,000 at the begnnng of each of the next 3 years, f your opportunty cost s 8%? Mode = BEGIN P/Y = 1 I = 8 N = 3 PMT = 1,000 PV = $2, Present Value  annuty due What s the PV of $1,000 at the begnnng of each of the next 3 years, f your opportunty cost s 8%? Present Value  annuty due Mode = BEGIN P/Y = 1 I = 8 N = 3 PMT = 1,000 PV = $2, Page 23
24 Present Value  annuty due Smply compound the FV of the ordnary annuty one more perod: Present Value  annuty due Smply compound the FV of the ordnary annuty one more perod: PV = PMT (PVIFA, n ) (1 + ) Present Value  annuty due Smply compound the FV of the ordnary annuty one more perod: PV = PMT (PVIFA, n ) (1 + ) PV = 1,000 (PVIFA.08, 3 ) (1.08) (use PVIFA table, or) Present Value  annuty due Smply compound the FV of the ordnary annuty one more perod: PV = PMT (PVIFA, n ) (1 + ) PV = 1,000 (PVIFA.08, 3 ) (1.08) (use PVIFA table, or) 1 PV = PMT 1  (1 + ) n (1 + ) Present Value  annuty due Smply compound the FV of the ordnary annuty one more perod: PV = PMT (PVIFA, n ) (1 + ) PV = 1,000 (PVIFA.08, 3 ) (1.08) (use PVIFA table, or) 1 PV = PMT 1  (1 + ) n (1 + ) 1 PV = (1.08 ) 3 (1.08) = $2, Uneven Cash Flows 10,000 2,000 4,000 6,000 7,000 4 Is ths an annuty? How do we fnd the PV of a cash flow stream when all of the cash flows are dfferent? (Use a 10% dscount rate). Page 24
25 Uneven Cash Flows 10,000 2,000 4,000 6,000 7,000 4 Uneven Cash Flows 10,000 2,000 4,000 6,000 7,000 4 Sorry! There s no qucke for ths one. We have to dscount each cash flow back separately. Sorry! There s no qucke for ths one. We have to dscount each cash flow back separately. Uneven Cash Flows 10,000 2,000 4,000 6,000 7,000 4 Uneven Cash Flows 10,000 2,000 4,000 6,000 7,000 4 Sorry! There s no qucke for ths one. We have to dscount each cash flow back separately. Sorry! There s no qucke for ths one. We have to dscount each cash flow back separately. Uneven Cash Flows 10,000 2,000 4,000 6,000 7,000 4 Sorry! There s no qucke for ths one. We have to dscount each cash flow back separately. 10,000 2,000 4,000 6,000 7,000 4 perod CF PV (CF) 010,00010, ,000 1, ,000 3, ,000 4, ,000 4, PV of Cash Flow Stream: $ 4, Page 25
26 Annual Percentage Yeld (APY) Annual Percentage Yeld (APY) Whch s the better loan: 8% compounded annually, or 7.85% compounded quarterly? We can t compare these nomnal (quoted) nterest rates, because they don t nclude the same number of compoundng perods per year! We need to calculate the APY. Annual Percentage Yeld (APY) quoted rate m APY = ( 1 + ) m  1 Annual Percentage Yeld (APY) quoted rate m APY = ( 1 + ) m  1 Fnd the APY for the quarterly loan: Annual Percentage Yeld (APY) quoted rate m APY = ( 1 + ) m  1 Fnd the APY for the quarterly loan:.0785 APY = ( 1 + ) Annual Percentage Yeld (APY) quoted rate m APY = ( 1 + ) m  1 Fnd the APY for the quarterly loan:.0785 APY = ( 1 + ) APY =.0808, or 8.08% Page 26
27 Annual Percentage Yeld (APY) quoted rate m APY = ( 1 + ) m  1 Fnd the APY for the quarterly loan: Practce Problems.0785 APY = ( 1 + ) APY =.0808, or 8.08% The quarterly loan s more expensve than the 8% loan wth annual compoundng! Example Cash flows from an nvestment are expected to be $40,000 per year at the end of years 4, 5, 6, 7, and 8. If you requre a 20% rate of return, what s the PV of these cash flows? Example Cash flows from an nvestment are expected to be $40,000 per year at the end of years 4, 5, 6, 7, and 8. If you requre a 20% rate of return, what s the PV of these cash flows? $ $ Ths type of cash flow sequence s often called a deferred annuty. $ How to solve: 1) Dscount each cash flow back to tme 0 separately. Page 27
28 $ $ How to solve: 1) Dscount each cash flow back to tme 0 separately. How to solve: 1) Dscount each cash flow back to tme 0 separately. $ $ How to solve: 1) Dscount each cash flow back to tme 0 separately. How to solve: 1) Dscount each cash flow back to tme 0 separately. $ $ How to solve: 1) Dscount each cash flow back to tme 0 separately. How to solve: 1) Dscount each cash flow back to tme 0 separately. Or, Page 28
29 $ $ ) Fnd the PV of the annuty: PV: End mode; P/YR = 1; I = 20; PMT = 40,000; N = 5 PV = $119,624 2) Fnd the PV of the annuty: PV3: End mode; P/YR = 1; I = 20; PMT = 40,000; N = 5 PV3= $119,624 $ $ , ,624 Then dscount ths sngle sum back to tme 0. PV: End mode; P/YR = 1; I = 20; N = 3; FV = 119,624; Solve: PV = $69,226 $ $ , ,624 69, ,624 The PV of the cash flow stream s $69,226. Page 29
30 Retrement Example After graduaton, you plan to nvest $400 per month n the stock market. If you earn 12% per year on your stocks, how much wll you have accumulated when you retre n 30 years? Retrement Example After graduaton, you plan to nvest $400 per month n the stock market. If you earn 12% per year on your stocks, how much wll you have accumulated when you retre n 30 years? Usng your calculator, P/YR = 12 N = 360 PMT = 400 I%YR = 12 FV = $1,397, Retrement Example If you nvest $400 at the end of each month for the next 30 years at 12%, how much would you have at the end of year 30? Retrement Example If you nvest $400 at the end of each month for the next 30 years at 12%, how much would you have at the end of year 30? Page 30
31 Retrement Example If you nvest $400 at the end of each month for the next 30 years at 12%, how much would you have at the end of year 30? Retrement Example If you nvest $400 at the end of each month for the next 30 years at 12%, how much would you have at the end of year 30? FV = PMT (FVIFA, n ) FV = PMT (FVIFA, n ) FV = 400 (FVIFA.01, 360 ) (can t use FVIFA table) Retrement Example If you nvest $400 at the end of each month for the next 30 years at 12%, how much would you have at the end of year 30? Retrement Example If you nvest $400 at the end of each month for the next 30 years at 12%, how much would you have at the end of year 30? FV = PMT (FVIFA, n ) FV = 400 (FVIFA.01, 360 ) FV = PMT (1 + ) n 1 (can t use FVIFA table) FV = PMT (FVIFA, n ) FV = 400 (FVIFA.01, 360 ) (can t use FVIFA table) FV = PMT (1 + ) n 1 FV = 400 (1.01) = $1,397, House Payment Example If you borrow $100,000 at 7% fxed nterest for 30 years n order to buy a house, what wll be your monthly house payment? House Payment Example If you borrow $100,000 at 7% fxed nterest for 30 years n order to buy a house, what wll be your monthly house payment? Page 31
32 ???? ???? Usng your calculator, P/YR = 12 N = 360 I%YR = 7 PV = $100,000 PMT = $ House Payment Example House Payment Example PV = PMT (PVIFA, n ) House Payment Example House Payment Example PV = PMT (PVIFA, n ) 100,000 = PMT (PVIFA.07, 360 ) (can t use PVIFA table) PV = PMT (PVIFA, n ) 100,000 = PMT (PVIFA.07, 360 ) (can t use PVIFA table) 1 PV = PMT 1  (1 + ) n Page 32
33 House Payment Example PV = PMT (PVIFA, n ) 100,000 = PMT (PVIFA.07, 360 ) (can t use PVIFA table) 1 PV = PMT 1  (1 + ) n 1 100,000 = PMT 1  ( ) 360 PMT=$ Team Assgnment Upon retrement, your goal s to spend 5 years travelng around the world. To travel n style wll requre $250,000 per year at the begnnng of each year. If you plan to retre n 30 years, what are the equal monthly payments necessary to acheve ths goal? The funds n your retrement account wll compound at 10% annually How much do we need to have by the end of year 30 to fnance the trp? PV30 = PMT (PVIFA.10, 5) (1.10) = = 250,000 (3.7908) (1.10) = = $1,042, Usng your calculator, Mode = BEGIN PMT = $250,000 N = 5 I%YR = 10 P/YR = 1 PV = $1,042, ,042,466 Now, assumng 10% annual compoundng, what monthly payments wll be requred for you to have $1,042,466 at the end of year 30? ,042,466 Usng your calculator, Mode = END N = 360 I%YR = 10 P/YR = 12 FV = $1,042,466 PMT = $ Page 33
34 Formulas PV FV So, you would have to place $ n your retrement account, whch earns 10% annually, at the end of each of the next 360 months to fnance the 5year world tour. Sngle Payment Annuty ( ) 1 (1 + ) n n n ( 1+ ) ( 1 + ) n 1 Effectve Annual Rates (EAR) vs. Quoted Rate Quoted Rate EAR = m Q : You are offered 12 percent compounded monthly, what s m the EAR? EAR A: Effectve Annual Rates (EAR) = 1 + = 1 + = = = % Quoted (.12) m 121 rate  1 m  1 APR vs. EAR A: An APR of 18 percent wth monthly payments s really.18/12 =.015 or 1.5 percent per month..18 EAR = = = = % Page 34
Section 2.3 Present Value of an Annuity; Amortization
Secton 2.3 Present Value of an Annuty; Amortzaton Prncpal Intal Value PV s the present value or present sum of the payments. PMT s the perodc payments. Gven r = 6% semannually, n order to wthdraw $1,000.00
More information10.2 Future Value and Present Value of an Ordinary Simple Annuity
348 Chapter 10 Annutes 10.2 Future Value and Present Value of an Ordnary Smple Annuty In compound nterest, 'n' s the number of compoundng perods durng the term. In an ordnary smple annuty, payments are
More informationUsing Series to Analyze Financial Situations: Present Value
2.8 Usng Seres to Analyze Fnancal Stuatons: Present Value In the prevous secton, you learned how to calculate the amount, or future value, of an ordnary smple annuty. The amount s the sum of the accumulated
More informationLecture 3: Annuity. Study annuities whose payments form a geometric progression or a arithmetic progression.
Lecture 3: Annuty Goals: Learn contnuous annuty and perpetuty. Study annutes whose payments form a geometrc progresson or a arthmetc progresson. Dscuss yeld rates. Introduce Amortzaton Suggested Textbook
More informationLecture 3: Force of Interest, Real Interest Rate, Annuity
Lecture 3: Force of Interest, Real Interest Rate, Annuty Goals: Study contnuous compoundng and force of nterest Dscuss real nterest rate Learn annutymmedate, and ts present value Study annutydue, and
More informationSimple Interest Loans (Section 5.1) :
Chapter 5 Fnance The frst part of ths revew wll explan the dfferent nterest and nvestment equatons you learned n secton 5.1 through 5.4 of your textbook and go through several examples. The second part
More informationSection 5.4 Annuities, Present Value, and Amortization
Secton 5.4 Annutes, Present Value, and Amortzaton Present Value In Secton 5.2, we saw that the present value of A dollars at nterest rate per perod for n perods s the amount that must be deposted today
More informationSection 2.2 Future Value of an Annuity
Secton 2.2 Future Value of an Annuty Annuty s any sequence of equal perodc payments. Depost s equal payment each nterval There are two basc types of annutes. An annuty due requres that the frst payment
More information7.5. Present Value of an Annuity. Investigate
7.5 Present Value of an Annuty Owen and Anna are approachng retrement and are puttng ther fnances n order. They have worked hard and nvested ther earnngs so that they now have a large amount of money on
More informationSection 5.3 Annuities, Future Value, and Sinking Funds
Secton 5.3 Annutes, Future Value, and Snkng Funds Ordnary Annutes A sequence of equal payments made at equal perods of tme s called an annuty. The tme between payments s the payment perod, and the tme
More informationSolution: Let i = 10% and d = 5%. By definition, the respective forces of interest on funds A and B are. i 1 + it. S A (t) = d (1 dt) 2 1. = d 1 dt.
Chapter 9 Revew problems 9.1 Interest rate measurement Example 9.1. Fund A accumulates at a smple nterest rate of 10%. Fund B accumulates at a smple dscount rate of 5%. Fnd the pont n tme at whch the forces
More informationCompound Interest: Further Topics and Applications. Chapter 9
92 Compound Interest: Further Topcs and Applcatons Chapter 9 93 Learnng Objectves After letng ths chapter, you wll be able to:? Calculate the nterest rate and term n ound nterest applcatons? Gven a nomnal
More information10. (# 45, May 2001). At time t = 0, 1 is deposited into each of Fund X and Fund Y. Fund X accumulates at a force of interest
1 Exam FM questons 1. (# 12, May 2001). Bruce and Robbe each open up new bank accounts at tme 0. Bruce deposts 100 nto hs bank account, and Robbe deposts 50 nto hs. Each account earns an annual e ectve
More information9 Arithmetic and Geometric Sequence
AAU  Busness Mathematcs I Lecture #5, Aprl 4, 010 9 Arthmetc and Geometrc Sequence Fnte sequence: 1, 5, 9, 13, 17 Fnte seres: 1 + 5 + 9 + 13 +17 Infnte sequence: 1,, 4, 8, 16,... Infnte seres: 1 + + 4
More information1. Math 210 Finite Mathematics
1. ath 210 Fnte athematcs Chapter 5.2 and 5.3 Annutes ortgages Amortzaton Professor Rchard Blecksmth Dept. of athematcal Scences Northern Illnos Unversty ath 210 Webste: http://math.nu.edu/courses/math210
More information0.02t if 0 t 3 δ t = 0.045 if 3 < t
1 Exam FM questons 1. (# 12, May 2001). Bruce and Robbe each open up new bank accounts at tme 0. Bruce deposts 100 nto hs bank account, and Robbe deposts 50 nto hs. Each account earns an annual effectve
More informationThursday, December 10, 2009 Noon  1:50 pm Faraday 143
1. ath 210 Fnte athematcs Chapter 5.2 and 4.3 Annutes ortgages Amortzaton Professor Rchard Blecksmth Dept. of athematcal Scences Northern Illnos Unversty ath 210 Webste: http://math.nu.edu/courses/math210
More informationFinite Math Chapter 10: Study Guide and Solution to Problems
Fnte Math Chapter 10: Study Gude and Soluton to Problems Basc Formulas and Concepts 10.1 Interest Basc Concepts Interest A fee a bank pays you for money you depost nto a savngs account. Prncpal P The amount
More informationLevel Annuities with Payments Less Frequent than Each Interest Period
Level Annutes wth Payments Less Frequent than Each Interest Perod 1 Annutymmedate 2 Annutydue Level Annutes wth Payments Less Frequent than Each Interest Perod 1 Annutymmedate 2 Annutydue Symoblc approach
More informationFINANCIAL MATHEMATICS. A Practical Guide for Actuaries. and other Business Professionals
FINANCIAL MATHEMATICS A Practcal Gude for Actuares and other Busness Professonals Second Edton CHRIS RUCKMAN, FSA, MAAA JOE FRANCIS, FSA, MAAA, CFA Study Notes Prepared by Kevn Shand, FSA, FCIA Assstant
More information8.4. Annuities: Future Value. INVESTIGATE the Math. 504 8.4 Annuities: Future Value
8. Annutes: Future Value YOU WILL NEED graphng calculator spreadsheet software GOAL Determne the future value of an annuty earnng compound nterest. INVESTIGATE the Math Chrstne decdes to nvest $000 at
More informationTime Value of Money Module
Tme Value of Money Module O BJECTIVES After readng ths Module, you wll be able to: Understand smple nterest and compound nterest. 2 Compute and use the future value of a sngle sum. 3 Compute and use the
More informationA Master Time Value of Money Formula. Floyd Vest
A Master Tme Value of Money Formula Floyd Vest For Fnancal Functons on a calculator or computer, Master Tme Value of Money (TVM) Formulas are usually used for the Compound Interest Formula and for Annutes.
More informationA) 3.1 B) 3.3 C) 3.5 D) 3.7 E) 3.9 Solution.
ACTS 408 Instructor: Natala A. Humphreys SOLUTION TO HOMEWOR 4 Secton 7: Annutes whose payments follow a geometrc progresson. Secton 8: Annutes whose payments follow an arthmetc progresson. Problem Suppose
More informationChapter 6. Discounted Cash Flow Valuation. Key Concepts and Skills. Multiple Cash Flows Future Value Example 6.1. Answer 6.1
Chapter 6 Key Concepts and Skills Be able to compute: the future value of multiple cash flows the present value of multiple cash flows the future and present value of annuities Discounted Cash Flow Valuation
More informationDISCOUNTED CASH FLOW VALUATION and MULTIPLE CASH FLOWS
Chapter 5 DISCOUNTED CASH FLOW VALUATION and MULTIPLE CASH FLOWS The basic PV and FV techniques can be extended to handle any number of cash flows. PV with multiple cash flows: Suppose you need $500 one
More informationChapter 4. The Time Value of Money
Chapter 4 The Time Value of Money 42 Topics Covered Future Values and Compound Interest Present Values Multiple Cash Flows Perpetuities and Annuities Inflation and Time Value Effective Annual Interest
More informationEXAMPLE PROBLEMS SOLVED USING THE SHARP EL733A CALCULATOR
EXAMPLE PROBLEMS SOLVED USING THE SHARP EL733A CALCULATOR 8S CHAPTER 8 EXAMPLES EXAMPLE 8.4A THE INVESTMENT NEEDED TO REACH A PARTICULAR FUTURE VALUE What amount must you nvest now at 4% compoune monthly
More information3. Present value of Annuity Problems
Mathematcs of Fnance The formulae 1. A = P(1 +.n) smple nterest 2. A = P(1 + ) n compound nterest formula 3. A = P(1.n) deprecaton straght lne 4. A = P(1 ) n compound decrease dmshng balance 5. P = 
More informationFinancial Mathemetics
Fnancal Mathemetcs 15 Mathematcs Grade 12 Teacher Gude Fnancal Maths Seres Overvew In ths seres we am to show how Mathematcs can be used to support personal fnancal decsons. In ths seres we jon Tebogo,
More informationFINANCIAL MATHEMATICS
3 LESSON FINANCIAL MATHEMATICS Annutes What s an annuty? The term annuty s used n fnancal mathematcs to refer to any termnatng sequence of regular fxed payments over a specfed perod of tme. Loans are usually
More informationIn our example i = r/12 =.0825/12 At the end of the first month after your payment is received your amount in the account, the balance, is
Payout annutes: Start wth P dollars, e.g., P = 100, 000. Over a 30 year perod you receve equal payments of A dollars at the end of each month. The amount of money left n the account, the balance, earns
More informationCHAPTER 2. Time Value of Money 21
CHAPTER 2 Time Value of Money 21 Time Value of Money (TVM) Time Lines Future value & Present value Rates of return Annuities & Perpetuities Uneven cash Flow Streams Amortization 22 Time lines 0 1 2 3
More informationAn Overview of Financial Mathematics
An Overvew of Fnancal Mathematcs Wllam Benedct McCartney July 2012 Abstract Ths document s meant to be a quck ntroducton to nterest theory. It s wrtten specfcally for actuaral students preparng to take
More informationThe Time Value of Money
The Time Value of Money Time Value Terminology 0 1 2 3 4 PV FV Future value (FV) is the amount an investment is worth after one or more periods. Present value (PV) is the current value of one or more future
More informationMathematics of Finance
5 Mathematcs of Fnance 5.1 Smple and Compound Interest 5.2 Future Value of an Annuty 5.3 Present Value of an Annuty;Amortzaton Chapter 5 Revew Extended Applcaton:Tme, Money, and Polynomals Buyng a car
More informationIntrayear Cash Flow Patterns: A Simple Solution for an Unnecessary Appraisal Error
Intrayear Cash Flow Patterns: A Smple Soluton for an Unnecessary Apprasal Error By C. Donald Wggns (Professor of Accountng and Fnance, the Unversty of North Florda), B. Perry Woodsde (Assocate Professor
More informationIn our example i = r/12 =.0825/12 At the end of the first month after your payment is received your amount owed is. P (1 + i) A
Amortzed loans: Suppose you borrow P dollars, e.g., P = 100, 000 for a house wth a 30 year mortgage wth an nterest rate of 8.25% (compounded monthly). In ths type of loan you make equal payments of A dollars
More informationMathematics of Finance
Mathematcs of Fnance 5 C H A P T E R CHAPTER OUTLINE 5.1 Smple Interest and Dscount 5.2 Compound Interest 5.3 Annutes, Future Value, and Snkng Funds 5.4 Annutes, Present Value, and Amortzaton CASE STUDY
More informationTexas Instruments 30X IIS Calculator
Texas Instruments 30X IIS Calculator Keystrokes for the TI30X IIS are shown for a few topcs n whch keystrokes are unque. Start by readng the Quk Start secton. Then, before begnnng a specfc unt of the
More informationFuture Value. Basic TVM Concepts. Chapter 2 Time Value of Money. $500 cash flow. On a time line for 3 years: $100. FV 15%, 10 yr.
Chapter Time Value of Money Future Value Present Value Annuities Effective Annual Rate Uneven Cash Flows Growing Annuities Loan Amortization Summary and Conclusions Basic TVM Concepts Interest rate: abbreviated
More informationDiscounted Cash Flow Valuation
BUAD 100x Foundations of Finance Discounted Cash Flow Valuation September 28, 2009 Review Introduction to corporate finance What is corporate finance? What is a corporation? What decision do managers make?
More informationANALYSIS OF FINANCIAL FLOWS
ANALYSIS OF FINANCIAL FLOWS AND INVESTMENTS II 4 Annutes Only rarely wll one encounter an nvestment or loan where the underlyng fnancal arrangement s as smple as the lump sum, sngle cash flow problems
More informationIDENTIFICATION AND CORRECTION OF A COMMON ERROR IN GENERAL ANNUITY CALCULATIONS
IDENTIFICATION AND CORRECTION OF A COMMON ERROR IN GENERAL ANNUITY CALCULATIONS Chrs Deeley* Last revsed: September 22, 200 * Chrs Deeley s a Senor Lecturer n the School of Accountng, Charles Sturt Unversty,
More informationChapter 4. Time Value of Money. Copyright 2009 Pearson Prentice Hall. All rights reserved.
Chapter 4 Time Value of Money Learning Goals 1. Discuss the role of time value in finance, the use of computational aids, and the basic patterns of cash flow. 2. Understand the concept of future value
More informationChapter 4. Time Value of Money. Learning Goals. Learning Goals (cont.)
Chapter 4 Time Value of Money Learning Goals 1. Discuss the role of time value in finance, the use of computational aids, and the basic patterns of cash flow. 2. Understand the concept of future value
More informationAn Alternative Way to Measure Private Equity Performance
An Alternatve Way to Measure Prvate Equty Performance Peter Todd Parlux Investment Technology LLC Summary Internal Rate of Return (IRR) s probably the most common way to measure the performance of prvate
More informationDiscounted Cash Flow Valuation
Discounted Cash Flow Valuation Chapter 5 Key Concepts and Skills Be able to compute the future value of multiple cash flows Be able to compute the present value of multiple cash flows Be able to compute
More informationTexas Instruments 30Xa Calculator
Teas Instruments 30Xa Calculator Keystrokes for the TI30Xa are shown for a few topcs n whch keystrokes are unque. Start by readng the Quk Start secton. Then, before begnnng a specfc unt of the tet, check
More informationMultiple discount and forward curves
Multple dscount and forward curves TopQuants presentaton 21 ovember 2012 Ton Broekhuzen, Head Market Rsk and Basel coordnator, IBC Ths presentaton reflects personal vews and not necessarly the vews of
More informationChapter 5 Time Value of Money 2: Analyzing Annuity Cash Flows
1. Future Value of Multiple Cash Flows 2. Future Value of an Annuity 3. Present Value of an Annuity 4. Perpetuities 5. Other Compounding Periods 6. Effective Annual Rates (EAR) 7. Amortized Loans Chapter
More informationMathematics of Finance
CHAPTER 5 Mathematcs of Fnance 5.1 Smple and Compound Interest 5.2 Future Value of an Annuty 5.3 Present Value of an Annuty; Amortzaton Revew Exercses Extended Applcaton: Tme, Money, and Polynomals Buyng
More informationTT03 Financial Calculator Tutorial And Key Time Value of Money Formulas November 6, 2007
TT03 Financial Calculator Tutorial And Key Time Value of Money Formulas November 6, 2007 The purpose of this tutorial is to help students who use the HP 17BII+, and HP10bll+ calculators understand how
More informationTime Value of Money Problems
Time Value of Money Problems 1. What will a deposit of $4,500 at 10% compounded semiannually be worth if left in the bank for six years? a. $8,020.22 b. $7,959.55 c. $8,081.55 d. $8,181.55 2. What will
More informationChapter 7 SOLUTIONS TO ENDOFCHAPTER PROBLEMS
Chapter 7 SOLUTIONS TO ENDOFCHAPTER PROBLEMS 71 0 1 2 3 4 5 10% PV 10,000 FV 5? FV 5 $10,000(1.10) 5 $10,000(FVIF 10%, 5 ) $10,000(1.6105) $16,105. Alternatively, with a financial calculator enter the
More informationChapter 3. Understanding The Time Value of Money. PrenticeHall, Inc. 1
Chapter 3 Understanding The Time Value of Money PrenticeHall, Inc. 1 Time Value of Money A dollar received today is worth more than a dollar received in the future. The sooner your money can earn interest,
More informationDiscounted Cash Flow Valuation
6 Formulas Discounted Cash Flow Valuation McGrawHill/Irwin Copyright 2008 by The McGrawHill Companies, Inc. All rights reserved. Chapter Outline Future and Present Values of Multiple Cash Flows Valuing
More informationCHAPTER 2. Time Value of Money 61
CHAPTER 2 Tme Value of Moey 6 Tme Value of Moey (TVM) Tme Les Future value & Preset value Rates of retur Autes & Perpetutes Ueve cash Flow Streams Amortzato 62 Tme les 0 2 3 % CF 0 CF CF 2 CF 3 Show
More informationPRESENT VALUE ANALYSIS. Time value of money equal dollar amounts have different values at different points in time.
PRESENT VALUE ANALYSIS Time value of money equal dollar amounts have different values at different points in time. Present value analysis tool to convert CFs at different points in time to comparable values
More informationWeek 4. Chonga Zangpo, DFB
Week 4 Time Value of Money Chonga Zangpo, DFB What is time value of money? It is based on the belief that people have a positive time preference for consumption. It reflects the notion that people prefer
More informationOn some special nonlevel annuities and yield rates for annuities
On some specal nonlevel annutes and yeld rates for annutes 1 Annutes wth payments n geometrc progresson 2 Annutes wth payments n Arthmetc Progresson 1 Annutes wth payments n geometrc progresson 2 Annutes
More informationChapter 4 Time Value of Money ANSWERS TO ENDOFCHAPTER QUESTIONS
Chapter 4 Time Value of Money ANSWERS TO ENDOFCHAPTER QUESTIONS 41 a. PV (present value) is the value today of a future payment, or stream of payments, discounted at the appropriate rate of interest.
More informationTIME VALUE OF MONEY. In following we will introduce one of the most important and powerful concepts you will learn in your study of finance;
In following we will introduce one of the most important and powerful concepts you will learn in your study of finance; the time value of money. It is generally acknowledged that money has a time value.
More information1. If you wish to accumulate $140,000 in 13 years, how much must you deposit today in an account that pays an annual interest rate of 14%?
Chapter 2  Sample Problems 1. If you wish to accumulate $140,000 in 13 years, how much must you deposit today in an account that pays an annual interest rate of 14%? 2. What will $247,000 grow to be in
More informationFinding the Payment $20,000 = C[1 1 / 1.0066667 48 ] /.0066667 C = $488.26
Quick Quiz: Part 2 You know the payment amount for a loan and you want to know how much was borrowed. Do you compute a present value or a future value? You want to receive $5,000 per month in retirement.
More informationInterest Rate Forwards and Swaps
Interest Rate Forwards and Swaps Forward rate agreement (FRA) mxn FRA = agreement that fxes desgnated nterest rate coverng a perod of (nm) months, startng n m months: Example: Depostor wants to fx rate
More informationTime Value of Money. If you deposit $100 in an account that pays 6% annual interest, what amount will you expect to have in
Time Value of Money Future value Present value Rates of return 1 If you deposit $100 in an account that pays 6% annual interest, what amount will you expect to have in the account at the end of the year.
More informationChapter 2 Applying Time Value Concepts
Chapter 2 Applying Time Value Concepts Chapter Overview Albert Einstein, the renowned physicist whose theories of relativity formed the theoretical base for the utilization of atomic energy, called the
More information5. Time value of money
1 Simple interest 2 5. Time value of money With simple interest, the amount earned each period is always the same: i = rp o We will review some tools for discounting cash flows. where i = interest earned
More informationChapter 6 Contents. Principles Used in Chapter 6 Principle 1: Money Has a Time Value.
Chapter 6 The Time Value of Money: Annuities and Other Topics Chapter 6 Contents Learning Objectives 1. Distinguish between an ordinary annuity and an annuity due, and calculate present and future values
More informationPresent Value and Annuities. Chapter 3 Cont d
Present Value and Annuities Chapter 3 Cont d Present Value Helps us answer the question: What s the value in today s dollars of a sum of money to be received in the future? It lets us strip away the effects
More informationI = Prt. = P(1+i) n. A = Pe rt
11 Chapte 6 Matheatcs of Fnance We wll look at the atheatcs of fnance. 6.1 Sple and Copound Inteest We wll look at two ways nteest calculated on oney. If pncpal pesent value) aount P nvested at nteest
More informationKey Concepts and Skills. Multiple Cash Flows Future Value Example 6.1. Chapter Outline. Multiple Cash Flows Example 2 Continued
6 Calculators Discounted Cash Flow Valuation Key Concepts and Skills Be able to compute the future value of multiple cash flows Be able to compute the present value of multiple cash flows Be able to compute
More informationChapter 4. Time Value of Money
Chapter 4 Time Value of Money Learning Goals 1. Discuss the role of time value in finance, the use of computational aids, and the basic patterns of cash flow. 2. Understand the concept of future value
More informationReal estate investment & Appraisal Dr. Ahmed Y. Dashti. Sample Exam Questions
Real estate investment & Appraisal Dr. Ahmed Y. Dashti Sample Exam Questions Problem 31 a) Future Value = $12,000 (FVIF, 9%, 7 years) = $12,000 (1.82804) = $21,936 (annual compounding) b) Future Value
More informationTopics. Chapter 5. Future Value. Future Value  Compounding. Time Value of Money. 0 r = 5% 1
Chapter 5 Time Value of Money Topics 1. Future Value of a Lump Sum 2. Present Value of a Lump Sum 3. Future Value of Cash Flow Streams 4. Present Value of Cash Flow Streams 5. Perpetuities 6. Uneven Series
More information3. Time value of money. We will review some tools for discounting cash flows.
1 3. Time value of money We will review some tools for discounting cash flows. Simple interest 2 With simple interest, the amount earned each period is always the same: i = rp o where i = interest earned
More informationChapter 4: Time Value of Money
FIN 301 Homework Solution Ch4 Chapter 4: Time Value of Money 1. a. 10,000/(1.10) 10 = 3,855.43 b. 10,000/(1.10) 20 = 1,486.44 c. 10,000/(1.05) 10 = 6,139.13 d. 10,000/(1.05) 20 = 3,768.89 2. a. $100 (1.10)
More information3. Time value of money
1 Simple interest 2 3. Time value of money With simple interest, the amount earned each period is always the same: i = rp o We will review some tools for discounting cash flows. where i = interest earned
More informationTime Value Conepts & Applications. Prof. Raad Jassim
Time Value Conepts & Applications Prof. Raad Jassim Chapter Outline Introduction to Valuation: The Time Value of Money 1 2 3 4 5 6 7 8 Future Value and Compounding Present Value and Discounting More on
More informationChapter 4. The Time Value of Money
Chapter 4 The Time Value of Money 1 Learning Outcomes Chapter 4 Identify various types of cash flow patterns Compute the future value and the present value of different cash flow streams Compute the return
More informationCh. Ch. 5 Discounted Cash Flows & Valuation In Chapter 5,
Ch. 5 Discounted Cash Flows & Valuation In Chapter 5, we found the PV & FV of single cash flowseither payments or receipts. In this chapter, we will do the same for multiple cash flows. 2 Multiple Cash
More informationChapter 6. Learning Objectives Principles Used in This Chapter 1. Annuities 2. Perpetuities 3. Complex Cash Flow Streams
Chapter 6 Learning Objectives Principles Used in This Chapter 1. Annuities 2. Perpetuities 3. Complex Cash Flow Streams 1. Distinguish between an ordinary annuity and an annuity due, and calculate present
More informationChapter 15 Debt and Taxes
hapter 15 Debt and Taxes 151. Pelamed Pharmaceutcals has EBIT of $325 mllon n 2006. In addton, Pelamed has nterest expenses of $125 mllon and a corporate tax rate of 40%. a. What s Pelamed s 2006 net
More informationCHAPTER 9 Time Value Analysis
Copyright 2008 by the Foundation of the American College of Healthcare Executives 6/11/07 Version 91 CHAPTER 9 Time Value Analysis Future and present values Lump sums Annuities Uneven cash flow streams
More informationInterest Rate Futures
Interest Rate Futures Chapter 6 6.1 Day Count Conventons n the U.S. (Page 129) Treasury Bonds: Corporate Bonds: Money Market Instruments: Actual/Actual (n perod) 30/360 Actual/360 The day count conventon
More informationJoe Pimbley, unpublished, 2005. Yield Curve Calculations
Joe Pmbley, unpublshed, 005. Yeld Curve Calculatons Background: Everythng s dscount factors Yeld curve calculatons nclude valuaton of forward rate agreements (FRAs), swaps, nterest rate optons, and forward
More informationKey Concepts and Skills
McGrawHill/Irwin Copyright 2014 by the McGrawHill Companies, Inc. All rights reserved. Key Concepts and Skills Be able to compute: The future value of an investment made today The present value of cash
More informationTime Value of Money (TVM) A dollar today is more valuable than a dollar sometime in the future...
Lecture: II 1 Time Value of Money (TVM) A dollar today is more valuable than a dollar sometime in the future...! The intuitive basis for present value what determines the effect of timing on the value
More informationPowerPoint. to accompany. Chapter 5. Interest Rates
PowerPoint to accompany Chapter 5 Interest Rates 5.1 Interest Rate Quotes and Adjustments To understand interest rates, it s important to think of interest rates as a price the price of using money. When
More informationFINANCIAL MATHEMATICS 12 MARCH 2014
FINNCIL MTHEMTICS 12 MRCH 2014 I ths lesso we: Lesso Descrpto Make use of logarthms to calculate the value of, the tme perod, the equato P1 or P1. Solve problems volvg preset value ad future value autes.
More informationFinQuiz Notes 2 0 1 4
Reading 5 The Time Value of Money Money has a time value because a unit of money received today is worth more than a unit of money to be received tomorrow. Interest rates can be interpreted in three ways.
More informationOklahoma State University Spears School of Business. Time Value of Money
Oklahoma State University Spears School of Business Time Value of Money Slide 2 Time Value of Money Which would you rather receive as a signin bonus for your new job? 1. $15,000 cash upon signing the
More informationThe time value of money: Part II
The time value of money: Part II A reading prepared by Pamela Peterson Drake O U T L I E 1. Introduction 2. Annuities 3. Determining the unknown interest rate 4. Determining the number of compounding periods
More informationChapter 4 Discounted Cash Flow Valuation
University of Science and Technology Beijing Dongling School of Economics and management Chapter 4 Discounted Cash Flow Valuation Sep. 2012 Dr. Xiao Ming USTB 1 Key Concepts and Skills Be able to compute
More informationEXAM 2 OVERVIEW. Binay Adhikari
EXAM 2 OVERVIEW Binay Adhikari FEDERAL RESERVE & MARKET ACTIVITY (BS38) Definition 4.1 Discount Rate The discount rate is the periodic percentage return subtracted from the future cash flow for computing
More informationProblem Set: Annuities and Perpetuities (Solutions Below)
Problem Set: Annuities and Perpetuities (Solutions Below) 1. If you plan to save $300 annually for 10 years and the discount rate is 15%, what is the future value? 2. If you want to buy a boat in 6 years
More informationSolutions to Problems
Solutions to Problems P41. LG 1: Using a time line Basic a. b. and c. d. Financial managers rely more on present value than future value because they typically make decisions before the start of a project,
More informationUsing Financial Calculators
Chapter 4 Discounted Cash Flow Valuation 4B1 Appendix 4B Using Financial Calculators This appendix is intended to help you use your HewlettPackard or Texas Instruments BA II Plus financial calculator
More informationChapter 4 Time Value of Money
Chapter 4 Time Value of Money Solutions to Problems P41. LG 1: Using a Time Line Basic (a), (b), and (c) Compounding Future Value $25,000 $3,000 $6,000 $6,000 $10,000 $8,000 $7,000 > 0 1 2 3 4 5 6 End
More information