TVM Applications Chapter


 Candice Morris
 6 years ago
 Views:
Transcription
1 Chapter 6 Time of Money UPS, Walgreens, Costco, American Air, Dreamworks Intel (note 10 page 28) TVM Applications Accounting issue Chapter Notes receivable (longterm receivables) 7 Longterm assets 10 Longterm intangibles (patents, copyrights) 12 Notes payable (longterm liabilities) 14 Investments 17 Installment contracts 18 Pensions and other postretirement benefits (OPEB) 20 Leases 21 TVM calculations used in many fair value calculations Use of fair value increasing, TVM more important 1 2 Ch 6: TVM Calculator Chapter Overview TI83 Plus, TI84 Plus (Int. Algebra) TI BA II Plus HP 10B, HP 17B, HP 12C Casio FC200V, Sharp EL733A RiteAid FV ( ) and PV ( ) 3 Explain time value of money concept Differentiate simple, compound interest Solve future and present value of $1 problems Solve future and present value of annuities (ordinary, annuity due) Solve deferred annuities, bonds, and expected cash flows problems 4 Learning Objectives Learning Objectives Identify topics using time value of money (TVM) Distinguish between simple and compound interest Use appropriate compound interest tables. Identify variables needed to solve TVM problems Solve future and present value of $1 problems Solve future value of ordinary, annuity due problems Solve present value ordinary, annuity due problems Solve deferred annuities and bonds problems Solve expected cash flows problems Identify topics using time value of money (TVM) Distinguish between simple and compound interest Identify variables needed to solve TVM problems 5 6 1
2 Time Of Money Required by GAAP Many applications in accounting assets and liabilities Any amount more due > 1 year Longterm budgeting Basis for all finance TVM Applications In life Saving for retirement: 401(k), IRA, 529 Mortgage payments See WebAccess sample problems and website In general, time value of money calculations must be made whenever a dollar amount will change hands more than one year from today. 7 8 Time Of Money All money earns interest over time $1 today $1 tomorrow Every dollar in the future is part principal and part interest Time Of Money Amount of cash is small = Principal Rate Time = $10 3% 30/360 = $ Time Of Money Amount of cash is large = Principal Rate Time = $10,000,000,000 3% 30/360 = $25,000,000 = $10,000,000,000 3% 1 = $300,000,000 Payment to rent money Compensation to lender for use of $ Compensation for risk Inflation Risk of default Compensation for profit See Intel Annual Report, note 10, page
3 Difference between Beginning balance = $100 Ending balance = $106 To lender, interest revenue To borrower, interest expense Simple = Principal Rate Time rate per period Time is number of periods Rate and time must be same periods Year, semiannual, quarter, month 13 rate usually stated as rate per year, must convert to rate per period 14 Rate Per Period Number of Periods Compounding Annual Rate Periods per Year Rate per Period Annual 12% 1 = 12% Semiannual 12% 2 = 6% Quarterly 12% 4 = 3% Monthly 12% 12 = 1% Compounding Years Periods per Year Periods Annual 20 1 = 20 Semiannual 20 2 = 40 Quarterly 20 4 = 80 Monthly = rate per period = rate per year / periods per year Compounding Annual Rate Periods per Year Rate per Period Annual 12% 1 = 12% Simple : Yearly Semiannual 12% 2 = 6% Quarterly 12% 4 = 3% Monthly 12% 12 = 1% Number of periods = Number of years periods per year Compounding Years Periods per Year Periods Annual 20 1 = 20 Semiannual 20 2 = 40 Quarterly 20 4 = 80 Monthly = Borrow $100,000 For 20 years Annual interest rate of 12% = Principal Rate Time = $100,000 12% 20 = $240,000 calculated on original principal only 18 3
4 Simple : Monthly Borrow $100,000 For 20 years Annual interest rate of 12% = Principal Rate Time = $100,000 1% 240 = $240,000 Same total interest 19 Simple value (PV) $1,000 rate per year 10% Number of years 3 Compounding periods per year None Period Principal Ending 1 1, , , , , ,300 calculated on original principal only 20 Compound Earn interest on Initial investment accumulated in previous periods 21 One compounding interval per year value (PV) $1,000 rate per year 10% Number of years 3 Compounding periods per year 1 rate period 10% Number of periods 3 Period Beg Ending 1 1, , , , , , Two compounding intervals per year value (PV) $1,000 rate per year 10% Number of years 3 Compounding periods per year 2 rate period 5% Number of periods 6 Simple and Compound value (PV) $1,000 rate per year 10% Number of years 3 Period Beg Ending 1 1, , , , , , , , , , , , Calculation Amount Simple $1,300 Compounded annually $1,331 Compounded semiannually $1,
5 Simple interest compared to compound interest Principal $100,000 Rate 12% per period Time 3 periods Simple and Compound Simple ($100,000, 12% per period, 3 periods) Period Beg Bal Rate End Bal 1 100,000 12% 12, , ,000 12% 12, , ,000 12% 12, ,000 Principal Rate Time Simple $100,000 12% 20 $240,000 Simple $100,000 1% 240 $240,000 same regardless of time periods Total interest 36,000 Compound Period Beg Bal Rate End Bal 1 100,000 12% 12, , ,000 12% 13, , ,440 12% 15, ,493 Total interest 40, Compounding Interval Annually $864,629 Semiannually $928,572 Quarterly $964,089 Monthly $989,255 different for each compounding interval 26 Five Tables in Textbook Time Of Money 1. of $1 2. of $1 3. : Ordinary Annuity of $1 4. : Ordinary Annuity of $1 5. : Annuity Due of $1 Money variables value value Annuity Other variables rate (per period) Time (number of periods) Annuity timing (beginning or end of period) Problem Solving Memorize These Formulas What are you given? What do you need to compute? Draw a timeline Carefully count periods Write down formulas (FV=PV FV$1) Solve for unknowns Double check what you need to calc Ask: Does answer make sense? 29 value PV$1 factor = value Annuity PVAnnuity$1 factor = value value FV$1 factor = value Annuity FVAnnuity$1 factor = value 30 5
6 Learning Objectives Time Of Money Compute future value of single amount Time Of Money Given PV Calculate FV Single amount value Single amount value value Principal Original investment value Principal + interest Maturity value Principal 33 Accumulating interest 34 Given PV Calculate FV If we make an investment today, how much will it grow to in the future? Given PV Calculate FV Invest $10,000 today and earn 20% compounded quarterly for three years Calculate future value compounding periods Today $10,000 Unknown Unknown
7 Given PV Calculate FV Invest $10,000 today and earn 20% compounded quarterly for three years Calculate future value Data Given value $10,000 rate per year 20% Number of years 3 Compounding periods per year 4 rate per period 5% Number of periods Data Given value $10,000 rate per year 20% Number of years 3 Compounding periods per year 4 rate per period 5% Number of periods 12 of $1 Periods 4% 5% 6% See TVM tables on WebAccess 38 of $1 Periods 4% 5% 6% value value FV$1 factor = Calculation of PV FV$1 = FV $10, = FV $17,960 = FV value Given PV Calculate FV How Does it Work? Invest $10,000 today and earn 20% compounded quarterly for three years Calculate future value Given present value calculate future value Given: value (PV) $4,000 rate per year (R) 10% Years of investment (Y) 3 Compounding periods per year (c) 2 Calculate: rate per period (i = R / c) 5% Number of periods (n = Y c) 6 value of $1 factor $10,000 $7,960 $17,960 value $5,
8 Period Given present value calculate future value Given: value (PV) $4,000 rate per year (R) 10% Years of investment (Y) 3 Compounding periods per year (c) 2 Calculate: rate per period (i = R / c) 5% Number of periods (n = Y c) 6 value of $1 factor value $5,360 Beginning Ending 1 4, , , , , , , , , , , ,360 Given PV Calculate FV value FV$1 factor = value value = value FV$1 factor FV$1 factor = value value 44 Learning Objectives Compute present value of single amount Given FV Calculate PV How much of future amount is original investment (principal)? Today Principal compounding periods 45 Discounting interest 46 Given FV Calculate PV Need $90,000 at end of five years, earn 12% compounded semiannually Calculate present value Given FV Calculate PV Need $90,000 at end of five years, earn 12% compounded semiannually Calculate present value Unknown Unknown $90, Data Given value $90,000 rate per year 12% Number of years 5 Compounding periods per year 2 rate per period 6% Number of periods
9 Data Given value $90,000 rate per year 12% Number of years 5 Compounding periods per year 2 rate per period 6% Number of periods 10 of $1 Periods 5% 6% 7% of $1 Periods 5% 6% 7% value PV$1 factor = value Calculation of FV PV$1 = PV $90, = PV $50,220 = PV Given FV Calculate PV value Need $90,000 at end of five years, earn 12% compounded semiannually Calculate present value value $50,220 $39,780 $90, How Does it Work? Given future value calculate present value Given: value (FV) $100,000 rate per year (R) 14% Years of investment (Y) 6 Compounding periods per year (c) 1 Calculate: rate per period (i = R / c) 14% Number of periods (n = Y c) 6 value of $1 factor value $45, Period Given future value calculate present value Given: value (FV) $100,000 rate per year (R) 14% Years of investment (Y) 6 Compounding periods per year (c) 1 Calculate: rate per period (i = R / c) 14% Number of periods (n = Y c) 6 value of $1 factor value $45,600 Beginning Ending 1 45,600 6,384 51, ,984 7,278 59, ,262 8,297 67, ,559 9,458 77, ,017 10,782 87, ,799 12, ,000 9
10 Given FV Calculate PV Learning Objectives PV$1 factor = value value = PV$1 factor Given present value and future value, solve for interest rate or number of periods PV$1 factor = value Solving for Other s Four variables in time value of money Given three calculate fourth Manipulating Equation value FV$1 factor = value FV = PV (1 + i) n Rate Number of Compounding Periods value FV$1 factor = = value FV$1 factor value value Calculate Rate: FV$1 Table Borrow $1,000 today and repay $1,082 at end of two periods Calculate interest rate per period $1,000 $82 $1, Calculate Rate: FV$1 Table Borrow $1,000 today and repay $1,082 at end of two periods Calculate interest rate per period Calculation of FV$1 Factor PV FV$1 = FV $1,000 FV $1 = $1,082 FV$1 = $1,082 $1,000 FV$1 = See row 2 of FV$1 table 60 10
11 of $1 Table PV FV$1 = FV $1,000 FV $1 = $1,082 FV$1 = $1,082 $1,000 FV$1 = See row 2 of FV$1 table of $1 Periods 3% 4% 5% Manipulating Equation PV$1 factor = value value = PV$1 factor PV$1 factor = value Solve this question using TVM calculator, not TVM table Calculate Rate: PV$1 Table Borrow $1,000 today and repay $1,082 at end of two periods Calculate interest rate per period of $1 Table FV PV$1 = PV $1,082 PV $1 = $1,000 PV$1 = $1,000 $1,082 PV$1 = See row 2 of PV$1 table 63 of $1 Table FV PV$1 = PV $1,092 PV $1 = $1,000 PV$1 = $1,000 $1,082 PV$1 = See row 2 of PV$1 table of $1 Periods 3% 4% 5% Solve this question using TVM calculator, not TVM table 64 Calculate Periods: FV$1 Table Calculate Periods: FV$1 Table Deposit $47,811 today and accumulate $70,000 at 10% compounded annually Calculate number of periods $47,811 $22,189 $70, Deposit $47,811 today and accumulate $70,000 at 10% compounded annually Calculate number of periods using FV of $1 Table PV FV$1 = FV $47,811 FV $1 = $70,000 FV$1 = $70,000 $47,811 FV$1 = See 10% column of FV$1 table 66 11
12 of $1 Table PV FV$1 = FV $47,811 FV $1 = $70,000 FV$1 = $70,000 $47,811 FV$1 = See 10% column of FV$1 table of $1 Periods 9% 10% 11% Solve this question using TVM calculator, not TVM table 67 Calculate Periods: PV$1 Table Deposit $47,811 today and accumulate $70,000 at 10% compounded annually Calculate number of periods using PV of $1 Table FV PV$1 = PV $70,000 PV $1 = $47,811 PV$1 = $47,811 $70,000 PV$1 = See 10% column of PV$1 table 68 of $1 Table FV PV$1 = PV $70,000 PV $1 = $47,811 PV$1 = $47,811 $70,000 PV$1 = See 10% column of PV$1 table of $1 Periods 9% 10% 11% Solve this question using TVM calculator, not TVM table 69 Learning Objectives Explain the difference between an ordinary annuity and an annuity due Compute the future value of both an ordinary annuity and an annuity due 70 Annuities Ordinary Annuity Series of equal periodic payments Equal amounts Equal time periods Defined period of time Payments made at end of period compounding periods Pay $2,500 at the end of each quarter for five years Financial calculators: PMT key, specify END or BEG Payments are called Rents No payment Payment 1 Payment 2 Payment By default use ordinary annuity unless told otherwise 72 12
13 Annuity Due (in Advance) Payments made at beginning of period compounding periods Payment 1 Payment 2 Payment No payment Only use annuity due when specifically stated 73 Annuity amount: $10,000 rate per period: 4% Ordinary Annuity Period Beginning Payment Ending ,000 10, , ,000 20, , ,000 31,216 Annuity Due Period Payment Beginning Ending 1 10,000 10, , ,000 20, , ,000 31,216 1,249 32, Ordinary Annuity Make regular principal investments Calculate future value Ordinary Annuity Equal payments made each period Payments, interest accumulate compounding periods Principal 75 Today Payment 1 Payment 2 Payment of Ordinary Annuity of $1 Periods 14% 15% 16% Given Annuity Calculate FV Invest $5,000 at end of each quarter, at 16% compounded quarterly, for 5 years Calculate future value Annuity FVAnnuity$1 factor = value Calculation of FV of Ordinary Annuity Annuity FVAnnuity$1 factor = FV $1, = FV $4,993 = FV 77 Data Given Annuity $5,000 rate per year 16% Number of years 5 Compounding periods per year 4 rate per period 4% Number of periods
14 Data Given Annuity $5,000 rate per year 16% Number of years 5 Compounding periods per year 4 rate per period 4% Number of periods 20 of Ordinary Annuity of $1 Periods 3% 4% 5% of Ordinary Annuity of $1 Periods 3% 4% 5% Annuity FVAnnuity$1 factor = value Calculation of FV of Ordinary Annuity Annuity FVAnnuity$1 factor = FV $5, = FV $148,890 = FV 80 Ordinary Annuity How Does it Work? value Annuity (Amount number) 81 Given ordinary annuity calculate future value Given: Annuity [also called PMT] $10,000 rate per year (R) 8% Years of investment (Y) 3 Payments / compounding periods per year (c) 2 Calculate: rate per period (i = R / c) 4% Number of periods (n = Y c) 6 value of ordinary annuity of $1 factor value of ordinary annuity $66, Period Given ordinary annuity calculate future value Given: Annuity [also called PMT] $10,000 rate per year (R) 8% Years of investment (Y) 3 Payments / compounding periods per year (c) 2 Calculate: rate per period (i = R / c) 4% Number of periods (n = Y c) 6 value of ordinary annuity of $1 factor value of ordinary annuity $66,330 Beginning Payment Ending ,000 10, , ,000 20, , ,000 31, ,216 1,249 10,000 42, ,465 1,699 10,000 54, ,164 2,166 10,000 66,330 Ordinary Annuity Annuity FVAnnuity$1 factor = value Annuity = value FVAnnuity$1 factor FVAnnuity$1 factor = value Annuity 84 14
15 Annuity Due Similar calculations Use FV annuity due table Use FV ordinary ann table (1 + rate) of Ordinary Annuity of $1 Periods 3% 4% 5% Calculation of FV of Ordinary Annuity Annuity FVAnnuity$1 factor = FV $5, = FV $148,890 = FV Calculation of FV of Annuity Due FV Ordinary Annuity (1 + rate) = FV Annuity Due $148,890 ( ) = FV Annuity Due 85 $154,846 = FV Annuity Due 86 Annuity amount: $10,000 rate per period: 4% Ordinary Annuity Period Beginning Payment Ending ,000 10, , ,000 20, , ,000 31,216 Annuity Due Period Payment Beginning Ending 1 10,000 10, , ,000 20, , ,000 31,216 1,249 32, Learning Objectives Compute the present value of an ordinary annuity and an annuity due 88 PV Ordinary Annuity What amount today is equivalent to a series of payments in the future? PV Ordinary Annuity Withdraw $10,000 at end of each year For 4 years Earn 10% compounded annually How much do you need to invest today? Today Payment 1 Payment 2 Payment 3 Principal
16 Given Annuity Calculate PV Pay $7,000 at end of each six months, 10% compounded semiannually,7years Calculate present value Data Given Annuity $7,000 rate per year 10% Number of years 7 Compounding periods per year 2 rate per period 5% Number of periods Data Given Annuity $7,000 rate per year 10% Number of years 7 Compounding periods per year 2 rate per period 5% Number of periods 14 of Ordinary Annuity of $1 Periods 4% 5% 6% of Ordinary Annuity of $1 Periods 4% 5% 6% PV Ordinary Annuity Annuity (Amount number) Annuity PVAnnuity$1 factor = value value Calculation of PV of Ordinary Annuity Annuity PVAnnuity$1 factor = PV $7, = PV $69,293 = PV How Does it Work? Given ordinary annuity calculate present value Given: Annuity [also called PMT] $2,500 rate per year (R) 7% Years of investment (Y) 6 Payments / compounding periods per year (c) 1 Calculate: rate per period (i = R / c) 7% Number of periods (n = Y c) 6 value of ordinary annuity of $1 factor value of ordinary annuity $11, Period Given ordinary annuity calculate present value Given: Annuity [also called PMT] $2,500 rate per year (R) 7% Years of investment (Y) 6 Payments / compounding periods per year (c) 1 Calculate: rate per period (i = R / c) 7% Number of periods (n = Y c) 6 value of ordinary annuity of $1 factor value of ordinary annuity $11,918 Beginning Payment Reduction Ending 1 11, ,500 1,666 10, , ,500 1,782 8, , ,500 1,907 6, , ,500 2,041 4, , ,500 2,183 2, , ,500 2,
17 PV Ordinary Annuity Annuity Due Annuity PVAnnuity$1 factor = value value Annuity = PVAnnuity$1 factor Similar calculations Use PV annuity due table Use PV ordinary ann table (1 + rate) PVAnnuity$1 factor = value Annuity Learning Objectives Annuity problems: Solving for annuity amount, interest rate, number of periods Manipulating Equation Annuity PVAnnuity$1 factor = value value of ordinary annuity used as example Annuity = value PVAnnuity$1 factor PVAnnuity$1 factor = value Annuity Calculate Annuity Borrow $39,550 for 5 years at 24% interest, compounded semiannually Calculate semiannual annuity amount of Annuity of $1 Periods 11% 12% 13% of Annuity of $1 Periods 11% 12% 13% of Annuity of $1 Annuity PVAnnuity$1 factor = PV Annuity = $39,550 Annuity = $39, Annuity = $7,
18 Calculate Rate Borrow $20,442 today and pay $3,000 at end of each period for 12 periods Calculate interest rate per period of Annuity of $1 Annuity PVAnnuity$1 factor = PV $3,000 PVAnnuity$1 = $20,442 PVAnnuity$1 = $20,442 $3,000 PVAnnuity$1 = See row 12 of PVAnnuity$1 table 103 of Annuity of $1 Annuity PVAnnuity$1 factor = PV $3,000 PVAnnuity$1 = $20,442 PVAnnuity$1 = $20,442 $3,000 PVAnnuity$1 = See row 12 of PVAnnuity$1 table of Annuity of $1 Periods 9% 10% 11% Solve this question using TVM calculator, not TVM table 104 Calculate Periods Borrow $17,118 today and pay $2,000 at end of each period at 8% per period Calculate number of periods of Annuity of $1 Annuity PVAnnuity$1 factor = PV $2,000 PVAnnuity$1 = $17,118 PVAnnuity$1 = $17,118 $2,000 PVAnnuity$1 = See 8% column of PVAnnuity$1 table 105 of Annuity of $1 Annuity PVAnnuity$1 factor = PV $2,000 PVAnnuity$1 = $17,118 PVAnnuity$1 = $17,118 $2,000 PVAnnuity$1 = See 8% column of PVAnnuity$1 table of Annuity of $1 Periods 7% 8% 9% Solve this question using TVM calculator, not TVM table 106 Learning Objectives Compute the present value of a deferred annuity PV of Deferred Annuity First cash flow of annuity occurs more than one period in future
19 PV of Deferred Annuity Today: January 1, 2010 Beginning: December 31, 2012 Annuity will pay $12,500 a year At end of each year for 2 years? $12,500 $12,500 Rate of return, 12% Calculate PV 1/1/06 12/31/06 12/31/07 12/31/08 12/31/09 12/31/ $12,500 $12,500 PV of Deferred Annuity: #1? $12,500 $12,500 1/1/10 12/31/10 12/31/11 12/31/12 12/31/13 Two Step Process 1. Calculate PV of annuity as of beginning of annuity period 2. Discount single value to its present value at time zero 1/1/10 12/31/10 12/31/11 12/31/12 12/31/ PV of Deferred Annuity: #1? $12,500 $12,500 1/1/10 12/31/10 12/31/11 12/31/12 12/31/13 PV of Deferred Annuity: #2 PV annuity for period with no payments = $12,500 $12,500 1/1/10 12/31/10 12/31/11 12/31/12 12/31/13 PV single amount n = 2, i = 12% FV = $21,126 PV factor = PV = $16,841 PV ordinary annuity n = 2, i = 12% Annuity = $12,500 PV factor = PV = $21, PV annuity for entire period = $12,500 ( ) = $16, Learning Objectives Application of time value of money Notes receivable / Notes payable Bonds Effective interest amortization Expected cash flow Monetary Assets, Liabilities Monetary assets Cash and claims to receive cash Amount fixed or determinable Monetary liabilities Obligations to pay cash Amount fixed or determinable
20 Monetary Assets, Liabilities Time frame important Cash exchanged one year or less at face value Use simple interest (if interest rate stated) Cost of using PV > benefit Monetary Assets, Liabilities Time frame important Cash exchanged more than one year Use compound interest at present value of future cash flows Receive utility bill, $500; pay in 30 days Made sale on account, $1,000; collect in 60 days Loan $15,000 to vendor, 8% interest, due in 90 days Note With Rate Purchase equipment Sign note, face value, $1,000 rate, 4.5% Market rate, 4.5% Due in two years Pay $1,092 in two years (FV) Jan 1 Equipment 1, Note payable 1, Note With Rate Dec 31 expense (1, %) payable 45 Dec 31 expense (1, %) payable 47 Dec 31 Note payable 1, payable 92 Cash 1, Unreasonable Stated Rate Exchanging cash for noncash asset Time frame greater than one year Discount future amount at market rate Stated rate on note 15%, market rate for borrower 6% Differing Rates 1 Purchase inventory on January 2, 2011 FMV inventory unknown Seller accepts note Face value, $100,000 Stated interest rate, 2% Term, 4 years (due 12/31/2014) Buyer s interest rate from bank, 10%
21 Differing Rates 1 Differing Rates 1 1/2/11 12/31/11 12/31/12 12/31/13 12/31/14 1/2/11 12/31/11 12/31/12 12/31/13 12/31/14 Calculation of i = 2% (stated rate), n=4 PV FV$1 = FV $100, = FV $108,243 = FV 121 Calculation of i = 10% (market rate), n=4 FV PV$1 = PV $108, = PV $73,931 = PV 122 Differing Rates 1 1/2/11 Inventory 73,931 Discount on note payable 34,312 Note payable 108,243 Differing Rates 1 Recognize interest expense for period 1/2/11 Inventory 73,931 Discount on note payable 34,312 Note payable 108,243 Dec 31 expense (73,931 10%) 7, Discount on note payable 7,393 Dec 31 Int exp ((73, ,393) 10%) 8, Discount on note payable 8, Differing Rates 2 Purchase inventory on January 2, 2011 FMV inventory unknown Seller accepts note Face value, $100,000 Stated interest rate, 8% Term, 4 years (due 12/31/2014) Buyer s interest rate from bank, 5% Differing Rates 2 1/2/11 12/31/11 12/31/12 12/31/13 12/31/14 Calculation of i = 8% (stated rate), n=4 PV FV$1 = FV $100, = FV 125 $136,049 = FV
22 Differing Rates 2 Differing Rates 2 1/2/11 12/31/11 12/31/12 12/31/13 12/31/14 Calculation of i = 5% (market rate), n=4 FV PV$1 = PV $136, = PV $111,928 = PV 127 1/2/11 Inventory 111,928 Discount on note payable 24,121 Note payable 136,049 Dec 31 expense (111,928 5%) 5, Discount on note payable 5,596 Dec 31 Int exp ((111, ,596) 5%) 5, Discount on note payable 5, Learning Objectives Bonds issued at discounts, premiums Effective interest amortization Need Two Billion Dollars Intel needs cash to build new factory Large debt broken into small pieces $2,000,000, Sell 2,000,000 $1,000 bonds 130 Bonds Receive cash when issued Promise to pay Face value on maturity date (future value) semiannually (ordinary annuity) Issue price of bond is PV of future value + PV of ordinary annuity 131 Issued At Par General Electric issued bonds Face value of $50 million Mature in five years Coupon interest rate of 9% Issued par, market rate = coupon rate Cash 50,000,000 Bonds payable 50,000,
23 Calculate Annuity Coupon rate used to compute annuity (periodic interest payments) payment = Face value Coupon rate Time Payments Semiannual interest payments I = P R T I = $50,000, /12 I = $2,250,000 only loan 133 expense 2,250,000 Cash 2,250, Payment At Maturity Make last interest payment expense 2,250,000 Cash 2,250,000 Pay principal (face value) in full Bonds payable 50,000,000 Two Rates Rate printed on bond called Coupon rate Stated rate Contract rate Market interest rate called Effectiverate Yieldtomaturity Cash 50,000, Two Rates Coupon interest rate Determines semiannual payment Market interest rate Determines bond market price (PV) Effective interest expense Market rate > coupon rate, bond issued at discount Coupon rate > market rate, bond issued at premium 137 Issued At Discount A $1,000 bond issued at a discount Market rate > coupon rate Bond sells for less than face value For example Quoted at 88 3/8 Sells for 88 3/8% of face value Bought or sold for $
24 Bond issued at discount Face value $5,000 Term 3 years Coupon interest rate 7% Market interest rate 10% Compounded semiannually Market interest rate per period 5% Number of periods 6 Bond Principal payment = Face value Coupon rate Time $175 = $5, /2 Issue price $4,618 Discount $ Payment 1 Payment 2 Payment 3 Single amt 140 Bond Issue Price Of Bond $3,730 Discount at market rate, 10%, semiannually $5,000 of the Face (a single amount) + of the Payments (an annuity) = value of Bond (Issue Price of the Bond) $888 $175 $175 $175 $4,618 Payment 1 Payment 2 Payment 3 Single amt 141 Use market rate of interest to calculate present value 142 Issue Price Of Bond $ 3,730 of the Face of the Annuity = $ 4,618 of the Bonds Bond discount effectiveinterest amortization schedule (A) Beginning A*MR*1/2= (B) Effective (C) Annuity Payment B C= (D) Discount Amortized F(up) D= (F) Discount Remaining A+D= (G) Ending , , , , , , , , , , , , ,000 Also called issue price of bonds, or market value of bonds 143 Effective interest expense Beg Bal Market Rate Time $4,618 10% 1/2 = $231 payment Face value Coupon rate time $5,000 7% 1/2 = $
25 Zero Coupon Bond Zero Coupon Bond Principal of the Face (a single payment) + of the Payments (an annuity) = Issue Price of the Bond Payment 1 Payment 2 Payment 3 Single amt Issued At Premium A $1,000 bond issued at a premium Market rate < coupon rate Bond sells for more than face value For example Quoted at 110 ¼ Sells for % of face value Bought or sold for $1, Bond issued at premium Face value $6,000 Term 3 years Coupon interest rate 12% Market interest rate 8% Compounded semiannually Market interest rate per period 6% Number of periods 6 payment = Face value Coupon rate Time $360 = $6, /2 Issue price $6,627 Discount $ Of Bond $ 4,740 of the Face + 1,887 of the Annuity = $ 6,627 of the Bonds $6,627 is greater than face amount of $6,000, bonds are issued at premium of $ Bond premium effectiveinterest amortization schedule (A) Beginning A*MR*1/2= (B) Effective (C) Annuity Payment C B= (D) Premium Amortized F(up) D= (F) Premium Remaining A D= (G) Ending , , , , , , , , , , , , ,000 Effective interest expense Beg Bal Market Rate Time $6,627 8% 1/2 = $265 payment Face value Coupon rate time $6,000 12% 1/2 = $
26 Learning Objectives Expected cash flow Amount Timing Uncertainty Cash Flow Issues Expected Cash Flows Concepts Statement No. 7 requires expected cash flow approach that uses a range of cash flows and incorporates the probabilities of those cash flows FASB states a company should discount expected cash flows by the riskfree rate of return Expected Cash Flows Pure Rate (2% to 4%) No possibility of default No expectation of inflation Expected Inflation Rate (0% or more) Credit Risk Rate ( 0% or more) RiskFree Rate of Return Pure rate + Expected inflation rate = Risk Free Rate Expected Cash Flows Expected Cash Flows cash flow uncertain Estimate amount using expected value Discount to PV using riskfree rate Expected value paid at end of 5 years Assume risk free rate of 5% Calculate present value Amount Probability Expected Amount Probability Expected $100,000 10% $10,000 $100,000 10% $10,000 $200,000 60% $120,000 $200,000 60% $120,000 $300,000 30% $90,000 $300,000 30% $90,000 Expected value $220, Expected value $220,
CHAPTER 6. Accounting and the Time Value of Money. 2. Use of tables. 13, 14 8 1. a. Unknown future amount. 7, 19 1, 5, 13 2, 3, 4, 7
CHAPTER 6 Accounting and the Time Value of Money ASSIGNMENT CLASSIFICATION TABLE (BY TOPIC) Topics Questions Brief Exercises Exercises Problems 1. Present value concepts. 1, 2, 3, 4, 5, 9, 17 2. Use of
More informationCHAPTER 6. Accounting and the Time Value of Money. 2. Use of tables. 13, 14 8 1. a. Unknown future amount. 7, 19 1, 5, 13 2, 3, 4, 6
CHAPTER 6 Accounting and the Time Value of Money ASSIGNMENT CLASSIFICATION TABLE (BY TOPIC) Topics Questions Brief Exercises Exercises Problems 1. Present value concepts. 1, 2, 3, 4, 5, 9, 17, 19 2. Use
More informationTIME VALUE OF MONEY (TVM)
TIME VALUE OF MONEY (TVM) INTEREST Rate of Return When we know the Present Value (amount today), Future Value (amount to which the investment will grow), and Number of Periods, we can calculate the rate
More informationChapter 6. Time Value of Money Concepts. Simple Interest 61. Interest amount = P i n. Assume you invest $1,000 at 6% simple interest for 3 years.
61 Chapter 6 Time Value of Money Concepts 62 Time Value of Money Interest is the rent paid for the use of money over time. That s right! A dollar today is more valuable than a dollar to be received in
More informationDick Schwanke Finite Math 111 Harford Community College Fall 2013
Annuities and Amortization Finite Mathematics 111 Dick Schwanke Session #3 1 In the Previous Two Sessions Calculating Simple Interest Finding the Amount Owed Computing Discounted Loans Quick Review of
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 informationPresent Value Concepts
Present Value Concepts Present value concepts are widely used by accountants in the preparation of financial statements. In fact, under International Financial Reporting Standards (IFRS), these concepts
More informationTime Value of Money Concepts
BASIC ANNUITIES There are many accounting transactions that require the payment of a specific amount each period. A payment for a auto loan or a mortgage payment are examples of this type of transaction.
More information2 The Mathematics. of Finance. Copyright Cengage Learning. All rights reserved.
2 The Mathematics of Finance Copyright Cengage Learning. All rights reserved. 2.3 Annuities, Loans, and Bonds Copyright Cengage Learning. All rights reserved. Annuities, Loans, and Bonds A typical definedcontribution
More informationBond valuation. Present value of a bond = present value of interest payments + present value of maturity value
Bond valuation A reading prepared by Pamela Peterson Drake O U T L I N E 1. Valuation of longterm debt securities 2. Issues 3. Summary 1. Valuation of longterm debt securities Debt securities are obligations
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 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 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 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 informationThe Time Value of Money
The following is a review of the Quantitative Methods: Basic Concepts principles designed to address the learning outcome statements set forth by CFA Institute. This topic is also covered in: The Time
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 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 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 Synopsis
CHAPTER 4 The Time Value of Money Chapter Synopsis Many financial problems require the valuation of cash flows occurring at different times. However, money received in the future is worth less than money
More informationHow To Read The Book \"Financial Planning\"
Time Value of Money Reading 5 IFT Notes for the 2015 Level 1 CFA exam Contents 1. Introduction... 2 2. Interest Rates: Interpretation... 2 3. The Future Value of a Single Cash Flow... 4 4. The Future Value
More informationChapter The Time Value of Money
Chapter The Time Value of Money PPT 92 Chapter 9  Outline Time Value of Money Future Value and Present Value Annuities TimeValueofMoney Formulas Adjusting for NonAnnual Compounding Compound Interest
More informationBasic financial arithmetic
2 Basic financial arithmetic Simple interest Compound interest Nominal and effective rates Continuous discounting Conversions and comparisons Exercise Summary File: MFME2_02.xls 13 This chapter deals
More informationYou just paid $350,000 for a policy that will pay you and your heirs $12,000 a year forever. What rate of return are you earning on this policy?
1 You estimate that you will have $24,500 in student loans by the time you graduate. The interest rate is 6.5%. If you want to have this debt paid in full within five years, how much must you pay each
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 informationAppendix C 1. Time Value of Money. Appendix C 2. Financial Accounting, Fifth Edition
C 1 Time Value of Money C 2 Financial Accounting, Fifth Edition Study Objectives 1. Distinguish between simple and compound interest. 2. Solve for future value of a single amount. 3. Solve for future
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 informationModule 5: Interest concepts of future and present value
file:///f /Courses/201011/CGA/FA2/06course/m05intro.htm Module 5: Interest concepts of future and present value Overview In this module, you learn about the fundamental concepts of interest and present
More informationLongTerm Debt. Objectives: simple present value calculations. Understand the terminology of longterm debt Par value Discount vs.
Objectives: LongTerm Debt! Extend our understanding of valuation methods beyond simple present value calculations. Understand the terminology of longterm debt Par value Discount vs. Premium Mortgages!
More informationSolutions to Time value of money practice problems
Solutions to Time value of money practice problems Prepared by Pamela Peterson Drake 1. What is the balance in an account at the end of 10 years if $2,500 is deposited today and the account earns 4% interest,
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 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 informationTime Value of Money. 2014 Level I Quantitative Methods. IFT Notes for the CFA exam
Time Value of Money 2014 Level I Quantitative Methods IFT Notes for the CFA exam Contents 1. Introduction... 2 2. Interest Rates: Interpretation... 2 3. The Future Value of a Single Cash Flow... 4 4. The
More informationPREVIEW OF CHAPTER 62
61 PREVIEW OF CHAPTER 6 62 Intermediate Accounting IFRS 2nd Edition Kieso, Weygandt, and Warfield 6 Accounting and the Time Value of Money LEARNING OBJECTIVES After studying this chapter, you should
More informationPractice Problems. Use the following information extracted from present and future value tables to answer question 1 to 4.
PROBLEM 1 MULTIPLE CHOICE Practice Problems Use the following information extracted from present and future value tables to answer question 1 to 4. Type of Table Number of Periods Interest Rate Factor
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 informationPrepared by: Dalia A. Marafi Version 2.0
Kuwait University College of Business Administration Department of Finance and Financial Institutions Using )Casio FC200V( for Fundamentals of Financial Management (220) Prepared by: Dalia A. Marafi Version
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 informationTimeValueofMoney and Amortization Worksheets
2 TimeValueofMoney and Amortization Worksheets The TimeValueofMoney and Amortization worksheets are useful in applications where the cash flows are equal, evenly spaced, and either all inflows or
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 informationTime Value of Money. 15.511 Corporate Accounting Summer 2004. Professor S. P. Kothari Sloan School of Management Massachusetts Institute of Technology
Time Value of Money 15.511 Corporate Accounting Summer 2004 Professor S. P. Kothari Sloan School of Management Massachusetts Institute of Technology July 2, 2004 1 LIABILITIES: Current Liabilities Obligations
More informationModule 5: Interest concepts of future and present value
Page 1 of 23 Module 5: Interest concepts of future and present value Overview In this module, you learn about the fundamental concepts of interest and present and future values, as well as ordinary annuities
More informationSample Examination Questions CHAPTER 6 ACCOUNTING AND THE TIME VALUE OF MONEY MULTIPLE CHOICE Conceptual Answer No. Description d 1. Definition of present value. c 2. Understanding compound interest tables.
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 informationfirst complete "prior knowlegde"  to refresh knowledge of Simple and Compound Interest.
ORDINARY SIMPLE ANNUITIES first complete "prior knowlegde"  to refresh knowledge of Simple and Compound Interest. LESSON OBJECTIVES: students will learn how to determine the Accumulated Value of Regular
More informationFin 3312 Sample Exam 1 Questions
Fin 3312 Sample Exam 1 Questions Here are some representative type questions. This review is intended to give you an idea of the types of questions that may appear on the exam, and how the questions might
More informationCHAPTER 6 DISCOUNTED CASH FLOW VALUATION
CHAPTER 6 DISCOUNTED CASH FLOW VALUATION Answers to Concepts Review and Critical Thinking Questions 1. The four pieces are the present value (PV), the periodic cash flow (C), the discount rate (r), and
More informationCALCULATOR TUTORIAL. Because most students that use Understanding Healthcare Financial Management will be conducting time
CALCULATOR TUTORIAL INTRODUCTION Because most students that use Understanding Healthcare Financial Management will be conducting time value analyses on spreadsheets, most of the text discussion focuses
More informationTime Value of Money. Work book Section I True, False type questions. State whether the following statements are true (T) or False (F)
Time Value of Money Work book Section I True, False type questions State whether the following statements are true (T) or False (F) 1.1 Money has time value because you forgo something certain today for
More informationRegular Annuities: Determining Present Value
8.6 Regular Annuities: Determining Present Value GOAL Find the present value when payments or deposits are made at regular intervals. LEARN ABOUT the Math Harry has money in an account that pays 9%/a compounded
More informationMathematics. Rosella Castellano. Rome, University of Tor Vergata
and Loans Mathematics Rome, University of Tor Vergata and Loans Future Value for Simple Interest Present Value for Simple Interest You deposit E. 1,000, called the principal or present value, into a savings
More informationCHAPTER 6. Accounting and the Time Value of Money. 2. Use of tables. 13, 14 8 1. a. Unknown future amount. 7, 19 1, 5, 13 2, 4, 6, 7, 11
CHAPTER 6 Accounting and the Time Value of Money ASSIGNMENT CLASSIFICATION TABLE (BY TOPIC) Topics Questions Brief Exercises Exercises Problems 1. Present value concepts. 1, 2, 3, 4, 5, 9, 17 2. Use of
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 informationAppendix. Time Value of Money. Financial Accounting, IFRS Edition Weygandt Kimmel Kieso. Appendix C 1
C Time Value of Money C 1 Financial Accounting, IFRS Edition Weygandt Kimmel Kieso C 2 Study Objectives 1. Distinguish between simple and compound interest. 2. Solve for future value of a single amount.
More informationThe explanations below will make it easier for you to use the calculator. The ON/OFF key is used to turn the calculator on and off.
USER GUIDE Texas Instrument BA II Plus Calculator April 2007 GENERAL INFORMATION The Texas Instrument BA II Plus financial calculator was designed to support the many possible applications in the areas
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 informationFoundation review. Introduction. Learning objectives
Foundation review: Introduction Foundation review Introduction Throughout FN1, you will be expected to apply techniques and concepts that you learned in prerequisite courses. The purpose of this foundation
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 informationMAT116 Project 2 Chapters 8 & 9
MAT116 Project 2 Chapters 8 & 9 1 81: The Project In Project 1 we made a loan workout decision based only on data from three banks that had merged into one. We did not consider issues like: What was the
More informationClick Here to Buy the Tutorial
FIN 534 Week 4 Quiz 3 (Str) Click Here to Buy the Tutorial http://www.tutorialoutlet.com/fin534/fin534week4quiz3 str/ For more course tutorials visit www.tutorialoutlet.com Which of the following
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 informationIntegrated Case. 542 First National Bank Time Value of Money Analysis
Integrated Case 542 First National Bank Time Value of Money Analysis You have applied for a job with a local bank. As part of its evaluation process, you must take an examination on time value of money
More informationFINA 351 Managerial Finance, Ch.45, TimeValueofMoney (TVM), Notes
FINA 351 Managerial Finance, Ch.45, TimeValueofMoney (TVM), Notes The concept of timevalueofmoney is important to know, not only for this class, but for your own financial planning. It is a critical
More informationIn October 1997, HewlettPackard issued zero coupon bonds with a face value of $1.8 million, due in 2017, for proceeds of $968 million.
BE112 In October 1997, HewlettPackard issued zero coupon bonds with a face value of $1.8 million, due in 2017, for proceeds of $968 million. (a) What is the life of these bonds? The life of the bonds
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 11. LongTerm Liabilities Notes, Bonds, and Leases
1 Chapter 11 LongTerm Liabilities Notes, Bonds, and Leases 2 LongTerm Liabilities 3 Economic Consequences of Reporting LongTerm Liabilities Improved credit ratings can lead to lower borrowing costs
More informationPresent Value (PV) Tutorial
EYK 151 Present Value (PV) Tutorial The concepts of present value are described and applied in Chapter 15. This supplement provides added explanations, illustrations, calculations, present value tables,
More informationCHAPTER 6 Accounting and the Time Value of Money
CHAPTER 6 Accounting and the Time Value of Money 61 LECTURE OUTLINE This chapter can be covered in two to three class sessions. Most students have had previous exposure to single sum problems and ordinary
More informationA) 1.8% B) 1.9% C) 2.0% D) 2.1% E) 2.2%
1 Exam FM Questions Practice Exam 1 1. Consider the following yield curve: Year Spot Rate 1 5.5% 2 5.0% 3 5.0% 4 4.5% 5 4.0% Find the four year forward rate. A) 1.8% B) 1.9% C) 2.0% D) 2.1% E) 2.2% 2.
More informationANALYSIS OF FIXED INCOME SECURITIES
ANALYSIS OF FIXED INCOME SECURITIES Valuation of Fixed Income Securities Page 1 VALUATION Valuation is the process of determining the fair value of a financial asset. The fair value of an asset is its
More informationChapter 5: Valuing Bonds
FIN 302 Class Notes Chapter 5: Valuing Bonds What is a bond? A longterm debt instrument A contract where a borrower agrees to make interest and principal payments on specific dates Corporate Bond Quotations
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 informationCHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY
CHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY 1. The simple interest per year is: $5,000.08 = $400 So after 10 years you will have: $400 10 = $4,000 in interest. The total balance will be
More informationTime Value of Money. 2014 Level I Quantitative Methods. IFT Notes for the CFA exam
Time Value of Money 2014 Level I Quantitative Methods IFT Notes for the CFA exam Contents 1. Introduction...2 2. Interest Rates: Interpretation...2 3. The Future Value of a Single Cash Flow...4 4. The
More informationFixed Income: Practice Problems with Solutions
Fixed Income: Practice Problems with Solutions Directions: Unless otherwise stated, assume semiannual payment on bonds.. A 6.0 percent bond matures in exactly 8 years and has a par value of 000 dollars.
More informationTIME VALUE OF MONEY #6: TREASURY BOND. Professor Peter Harris Mathematics by Dr. Sharon Petrushka. Introduction
TIME VALUE OF MONEY #6: TREASURY BOND Professor Peter Harris Mathematics by Dr. Sharon Petrushka Introduction This problem assumes that you have mastered problems 15, which are prerequisites. In this
More informationCHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY
CHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY Answers to Concepts Review and Critical Thinking Questions 1. The four parts are the present value (PV), the future value (FV), the discount
More informationAPPENDIX. Interest Concepts of Future and Present Value. Concept of Interest TIME VALUE OF MONEY BASIC INTEREST CONCEPTS
CHAPTER 8 Current Monetary Balances 395 APPENDIX Interest Concepts of Future and Present Value TIME VALUE OF MONEY In general business terms, interest is defined as the cost of using money over time. Economists
More informationBond Price Arithmetic
1 Bond Price Arithmetic The purpose of this chapter is: To review the basics of the time value of money. This involves reviewing discounting guaranteed future cash flows at annual, semiannual and continuously
More informationsubstantially more powerful. The internal rate of return feature is one of the most useful of the additions. Using the TI BA II Plus
for Actuarial Finance Calculations Introduction. This manual is being written to help actuarial students become more efficient problem solvers for the Part II examination of the Casualty Actuarial Society
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 informationFinQuiz Notes 2 0 1 5
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 informationCHAPTER 8 INTEREST RATES AND BOND VALUATION
CHAPTER 8 INTEREST RATES AND BOND VALUATION Answers to Concept Questions 1. No. As interest rates fluctuate, the value of a Treasury security will fluctuate. Longterm Treasury securities have substantial
More informationBonds. Accounting for LongTerm Debt. Agenda LongTerm Debt. 15.501/516 Accounting Spring 2004
Accounting for LongTerm Debt 15.501/516 Accounting Spring 2004 Professor S. Roychowdhury Sloan School of Management Massachusetts Institute of Technology April 5, 2004 1 Agenda LongTerm Debt Extend our
More informationWalk Through Balance Sheet. Chapter 7. Learning Objectives. Learning Objectives 1, 2. Learning Objectives 1, 2. Cash and Receivables.
Chapter 7 Walk Through Balance Sheet Cash and Receivables Chapters 1 6 Accounting cycle: JE, AJE, financial stmts Conceptual framework, GAAP, revenue Time value of money concepts Remaining chapters (ACTG
More informationCHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES
CHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES 1. Expectations hypothesis. The yields on longterm bonds are geometric averages of present and expected future short rates. An upward sloping curve is
More informationHewlettPackard 10BII Tutorial
This tutorial has been developed to be used in conjunction with Brigham and Houston s Fundamentals of Financial Management 11 th edition and Fundamentals of Financial Management: Concise Edition. In particular,
More informationThe Time Value of Money C H A P T E R N I N E
The Time Value of Money C H A P T E R N I N E Figure 91 Relationship of present value and future value PPT 91 $1,000 present value $ 10% interest $1,464.10 future value 0 1 2 3 4 Number of periods Figure
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 informationLO.a: Interpret interest rates as required rates of return, discount rates, or opportunity costs.
LO.a: Interpret interest rates as required rates of return, discount rates, or opportunity costs. 1. The minimum rate of return that an investor must receive in order to invest in a project is most likely
More informationFinancial Math on Spreadsheet and Calculator Version 4.0
Financial Math on Spreadsheet and Calculator Version 4.0 2002 Kent L. Womack and Andrew Brownell Tuck School of Business Dartmouth College Table of Contents INTRODUCTION...1 PERFORMING TVM CALCULATIONS
More informationCompound Interest Formula
Mathematics of Finance Interest is the rental fee charged by a lender to a business or individual for the use of money. charged is determined by Principle, rate and time Interest Formula I = Prt $100 At
More informationDick Schwanke Finite Math 111 Harford Community College Fall 2015
Using Technology to Assist in Financial Calculations Calculators: TI83 and HP12C Software: Microsoft Excel 2007/2010 Session #4 of Finite Mathematics 1 TI83 / 84 Graphing Calculator Section 5.5 of textbook
More information300 Chapter 5 Finance
300 Chapter 5 Finance 17. House Mortgage A couple wish to purchase a house for $200,000 with a down payment of $40,000. They can amortize the balance either at 8% for 20 years or at 9% for 25 years. Which
More informationCompounding Assumptions. Compounding Assumptions. Financial Calculations on the Texas Instruments BAII Plus. Compounding Assumptions.
Compounding Assumptions Financial Calculations on the Texas Instruments BAII Plus This is a first draft, and may contain errors. Feedback is appreciated The TI BAII Plus has builtin preset assumptions
More informationCHAPTER 5. Interest Rates. Chapter Synopsis
CHAPTER 5 Interest Rates Chapter Synopsis 5.1 Interest Rate Quotes and Adjustments Interest rates can compound more than once per year, such as monthly or semiannually. An annual percentage rate (APR)
More informationIntroduction to the HewlettPackard (HP) 10BII Calculator and Review of Mortgage Finance Calculations
Introduction to the HewlettPackard (HP) 10BII Calculator and Review of Mortgage Finance Calculations Real Estate Division Sauder School of Business University of British Columbia Introduction to the HewlettPackard
More informationChapter 10 Expectations. NOTE: Whenever you see the word communicate, it is implied that it means to communicate both verbally and in writing!
Chapter 10 Expectations NOTE: Whenever you see the word communicate, it is implied that it means to communicate both verbally and in writing! Section 1: Expectations for Interest 1. Communicate to your
More informationCorporate Finance Fundamentals [FN1]
Page 1 of 32 Foundation review Introduction Throughout FN1, you encounter important techniques and concepts that you learned in previous courses in the CGA program of professional studies. The purpose
More informationFINANCIAL CALCULATIONS
FINANCIAL CALCULATIONS 1 Main function is to calculate payments, determine interest rates and to solve for the present or future value of a loan or an annuity 5 common keys on financial calculators: N
More informationLOS 56.a: Explain steps in the bond valuation process.
The following is a review of the Analysis of Fixed Income Investments principles designed to address the learning outcome statements set forth by CFA Institute. This topic is also covered in: Introduction
More information