UB MGF 401 - chap004 (35 pages)

4 1 Chapter 4 Topics Covered Future Values and Compound Interest Present Values Multiple Cash Flows Level Cash Flows Perpetuities and Annuities Inflation Time Value Effective Annual Interest Rate McGraw Hill Irwin Copyright 2007 by The McGraw Hill Companies Inc All rights 4 2 Future Values Future Value Amount to which an investment will grow after earning interest Compound Interest Interest earned on interest Simple Interest Interest earned only on the original investment McGraw Hill Irwin Copyright 2007 by The McGraw Hill Companies Inc All rights 4 3 Future Values Example Simple Interest Interest earned at a rate of 6 for five years on a principal balance of 100 Interest Earned Per Year 100 x 06 6 McGraw Hill Irwin Copyright 2007 by The McGraw Hill Companies Inc All rights 4 4 Future Values Example Simple Interest Interest earned at a rate of 6 for five years on a principal balance of 100 Today Future Years 1 2 3 4 5 Interest Earned 6 6 Value 100 106 112 6 118 6 124 6 130 Value at the end of Year 5 130 McGraw Hill Irwin Copyright 2007 by The McGraw Hill Companies Inc All rights 4 5 Future Values Example Compound Interest Interest earned at a rate of 6 for five years on the previous year s balance Interest Earned Per Year Prior Year Balance x 06 McGraw Hill Irwin Copyright 2007 by The McGraw Hill Companies Inc All rights 4 6 Future Values Example Compound Interest Interest earned at a rate of 6 for five years on the previous year s balance Today Interest Earned Value 100 Future Years 1 2 3 4 5 6 6 36 6 74 7 15 7 57 106 112 36 119 10 126 25 133 82 Value at the end of Year 5 133 82 McGraw Hill Irwin Copyright 2007 by The McGraw Hill Companies Inc All rights 4 7 Future Values Future Value of 100 FV FV 100 1 r McGraw Hill Irwin t Copyright 2007 by The McGraw Hill Companies Inc All rights 4 8 Future Values FV 100 1 r t Example FV What is the future value of 100 if interest is compounded annually at a rate of 6 for five years 5 FV 100 1 06 133 82 McGraw Hill Irwin Copyright 2007 by The McGraw Hill Companies Inc All rights 4 9 Future Values with Compounding Interest Rates McGraw Hill Irwin Copyright 2007 by The McGraw Hill Companies Inc All rights 4 10 Manhattan Island Sale Peter Minuit bought Manhattan Island for 24 in 1626 Was this a good deal To answer determine 24 is worth in the year 2006 compounded at 8 380 FV 24 1 08 120 57 trillion FYI The value of Manhattan Island land is well below this figure McGraw Hill Irwin Copyright 2007 by The McGraw Hill Companies Inc All rights 4 11 Present Values Present Value Discount Factor Value today of a future cash flow Present value of a 1 future payment Discount Rate Interest rate used to compute present values of future cash flows McGraw Hill Irwin Copyright 2007 by The McGraw Hill Companies Inc All rights 4 12 Present Values Present Value PV PV McGraw Hill Irwin Future Value after t periods 1 r t Copyright 2007 by The McGraw Hill Companies Inc All rights 4 13 Present Values Example You just bought a new computer for 3 000 The payment terms are 2 years same as cash If you can earn 8 on your money how much money should you set aside today in order to make the payment when due in two years PV McGraw Hill Irwin 3000 1 08 2 2 572 Copyright 2007 by The McGraw Hill Companies Inc All rights 4 14 Present Values Discount Factor DF PV of 1 DF 1 t 1 r Discount Factors can be used to compute the present value of any cash flow McGraw Hill Irwin Copyright 2007 by The McGraw Hill Companies Inc All rights 4 15 Time Value of Money applications The PV formula has many applications Given any variables in the equation you can solve for the remaining variable PV FV McGraw Hill Irwin 1 1 r t Copyright 2007 by The McGraw Hill Companies Inc All rights 4 16 Present Values with Compounding Interest Rates McGraw Hill Irwin Copyright 2007 by The McGraw Hill Companies Inc All rights 4 17 Time Value of Money applications Value of Free Credit Implied Interest Rates Internal Rate of Return Time necessary to accumulate funds McGraw Hill Irwin Copyright 2007 by The McGraw Hill Companies Inc All rights 4 18 PV of Multiple Cash Flows Example Your auto dealer gives you the choice to pay 15 500 cash now or make three payments 8 000 now and 4 000 at the end of the following two years If your cost of money is 8 which do you prefer Immediate payment 8 000 00 PV1 14 000 1 3 703 70 08 PV2 14 000 3 429 36 08 2 Total PV McGraw Hill Irwin 15 133 06 Copyright 2007 by The McGraw Hill Companies Inc All rights 4 19 PV of Multiple Cash Flows Finding the present value of multiple cash flows by using a spreadsheet Time until CF Cash flow Present value 0 8000 8 000 00 1 4000 3 703 70 2 4000 3 429 36 SUM Discount rate McGraw Hill Irwin Formula in Column C PV B 11 A4 0 B4 PV B 11 A5 0 B5 PV B 11 A6 0 B6 15 133 06 SUM C4 C6 0 08 Copyright 2007 by The McGraw Hill Companies Inc All rights 4 20 PV of Multiple Cash Flows PVs can be added together to evaluate multiple cash flows C1 C2 PV 1 r 1 1 r 2 McGraw Hill Irwin Copyright 2007 by The McGraw Hill Companies Inc All rights 4 21 Perpetuities Annuities Perpetuity A stream of level cash payments that never ends Annuity Equally spaced level stream of cash flows for a limited period of time McGraw Hill Irwin Copyright 2007 by The McGraw Hill Companies Inc All rights 4 22 Perpetuities Annuities PV of Perpetuity Formula PV C r C cash payment r interest rate McGraw Hill Irwin Copyright 2007 by The McGraw Hill Companies Inc All rights 4 23 Perpetuities Annuities Example Perpetuity In order to create an endowment which pays 100 000 per year at the end of each year forever how much money must be set aside today in the rate of interest is 10 PV McGraw Hill Irwin 100 000 10 1 000 000 Copyright 2007 by The McGraw Hill Companies Inc All rights 4 24 Perpetuities Annuities Example continued If the first perpetuity payment will not be received until four years from today how much money needs to be set aside today PV McGraw Hill Irwin 1 000 000 1 10 3 751 315 Copyright 2007 by The McGraw Hill Companies Inc All rights 4 25 Perpetuities Annuities PV of Annuity Formula PV C 1 r 1 t r 1 r C cash payment r interest rate t Number of years cash payment is received McGraw …