Copyright © 2011 Nelson Education Limited Finance for Non-Financial Managers, 6 th edition PowerPoint Slides to accompany Prepared by Pierre Bergeron, University of Ottawa

Copyright © 2011 Nelson Education Limited Finance for Non-Financial Managers, 6 th edition CHAPTER 10 TIME-VALUE-OF-MONEY CONCEPT

Copyright © 2011 Nelson Education Limited Time Value of Money 1.Differentiate between time value of money versus inflation and risk. 2. Explain the financial tools that can be used to solve time-value-of-money problems. 3. Differentiate between future value of single sums and future values of annuities. 4. Make the distinction between present values of single sums and present values of annuities 5. Solve capital investment decisions using time-value- of money decision-making tools. Chapter Reference Chapter 10: Time Value of Money Chapter Objectives

Copyright © 2011 Nelson Education Limited Why Money Has a Time Value A dollar earned today will be worth more tomorrow This is called compounding. A dollar earned tomorrow is worth less today This is called discounting. Money has a time value because of the existence of interest $1,000 $1,100 $1,000 $1,100

Copyright © 2011 Nelson Education Limited An Example – 10 10% $5,000 Single sum Compounding IRR $ 12,970 Table A (2.594) Table C (15.937) Discounting -$5,000 Single sum +$5,000 0 Table D (6.1446) PV NPV $ Annuity $ Annuity $ 12, % IRR Table D (4.1925) $ 1, % Table D (3.0915) $ 1,617.33

Copyright © 2011 Nelson Education Limited Compounding versus Discounting companies Years 120 Yearly premiums (cash inflows) $1,000 Money is worth 10% ($1,000 x___________)$_______ Death benefit (cash outflow)$ - 50,000 Net cash flow of NFV$________ _____________companies Years 120 A company invests $150,000 (cash outflow) to modernize a plant. As a result, the company saves $20,000 (cash inflows) each year. -$ 150,000 cash outflow present value of the savings if money is worth 10% +$______ $20,000 X __________ +$______ net cash flow or net present value (NPV) Insurance ,275 7,275 Industrial ,272 20,272 12% , IRR is 11.9%

Copyright © 2011 Nelson Education Limited 1. Time Value of Money and Inflation Years Projected statement of income Revenue (with inflation) Cost of sales (with inflation) Gross profit Expenses (with inflation) Profit before taxes Income tax expense Profit for the year Add back depreciation Cash flow (with inflation) 1 $ $ 7 2 $ $ 9 3 $ $ 10 Inflation is included in the forecast (ex. revenue, costs, etc.). Once the cash flow has been determined, then this amount is discounted.

Copyright © 2011 Nelson Education Limited Factors to consider 1. Time value of money 2. Inflation 3. Risk  Modernization  Expansion  New facility  New equipment/machinery/vehicle  New product  Anti-pollution equipment  Research and development Types of projects: High risk, medium risk, low risk, compulsory ____ LR/C LR MR HR C HR/C Time value of Money and Risk

Copyright © 2011 Nelson Education Limited Investment Decisions in Capital Budgeting TIME Lotto 649 win of $100,000 Two options Option 1 Option 2 Cash Outflows (disbursements) Cash Inflows (receipts) CASH $10,000 $10,000 $10,000 $10,000 $10,000 $12,000 $12,000 $12,000 $12,000 $12,000 $14,000 $14,000 $14,000 $14,000 $14,000 $16,000 $16,000 $16,000 $16,000 $16,000 $100,000 today

Copyright © 2011 Nelson Education Limited 2. Tools For Solving Time-Value-of-Money Problems Algebraic Notations Interest Tables Financial Calculators and Spreadsheets Time Lines

Copyright © 2011 Nelson Education Limited 3. Effect of Compounding F = Future amount P = Principal or initial amount i = Interest rate n = Number of years F = P (1 + i) n F = $1,000 (1.10) 3 F = $1,000 X F = $1,331 If you invest $1,000 in the bank bearing a 10% compound interest, what is the future value of the investment at the end of three years? Problem: Year Beginning amount $1,000 $1,100 $1,210 Interest rate.10 Amount of interest $100 $110 $121 Beginning amount $1,000 $1,100 $1,210 Ending amount $1,100 $1,210 $1,331

Copyright © 2011 Nelson Education Limited CompoundingDiscounting Single sum A B Annuity C D Future Value of a Single Sum – Table A N 9% 10% 11% 12% 14% 16% 18% 20%

Copyright © 2011 Nelson Education Limited Future Value of an Annuity An annuity is defined as a series of payments of fixed amount for a specified number of years. Examples of annuities are mortgages, RRSPs, whole-life insurance premiums. Problem:If you were to receive $1,000 at the end of each year, for the next five years, what would be the value of the receipts if the interest rate is compounded annually at 10%? AmountInterest Future Year received factorsInterest value 1$1, $464$1,464 2$1, $331$1,331 3$1, $210$1,210 4$1, $100$1,100 5$1, $1,000 $5,000$1,105$6,105 W = Value of annuity R = Sum of receipts i = Interest rate n = Number of years W = R (1 + i) n - 1 i W = $1,000 X F = $6,105

Copyright © 2011 Nelson Education Limited CompoundingDiscounting Single sum A B Annuity C D Future Value of an Annuity – Table C N 9% 10% 11% 12% 14% 16% 18% 20%

Copyright © 2011 Nelson Education Limited 4. Effect of Discounting P = Present value F = Sum to be received i = Interest rate n = Number of years P = F 1 (1 + i) n P = $1,000 1 (1 +.10) 3 F = $1, P = $1,000 x P = $ Year 3 Beginning amount $1,000 Discount rate Present value $751.3 If you were to receive $1,000 in three years from now, what would be the present value of that amount if you were to discount it at 10%? Problem:

Copyright © 2011 Nelson Education Limited CompoundingDiscounting Single sum A B Annuity C D Present Value of a Single Sum – Table B N 9% 10% 11% 12% 13% 14% 15% 16%

Copyright © 2011 Nelson Education Limited Present Value of an Annuity BeginningInterest Present Year amount factors value 1$1, $909 2$1, $826 3$1, $751 4$1, $683 5$1, $621 $5,000 $3,790 B = Present value of annuity R = Fixed annuity i = Interest rate n = Number of years B = R 1- (1 + i) -n i W = $1,000 X F = $3, Suppose your company deposits $1,000 in your bank account at the end of each year during the next five years, what is the present value of that gift if the interest rate is 10%? Problem:

Copyright © 2011 Nelson Education Limited CompoundingDiscounting Single sum A B Annuity C D Present Value of an Annuity – Table D N 9% 10% 11% 12% 13% 14% 15% 16%

Copyright © 2011 Nelson Education Limited 5. Using Interest Tables in Capital Budgeting 1.You invest $25,000 in an asset. 2.It generates $1,000 in savings each year. 3.The expected life of the asset is 25 years. 4.Your cost of capital is 10%. How much must you save each year if you want to make 10% on your asset? 1.Investment 2.Annual savings: $1,000 3.Total savings: $25,000 4.Present value of savings (_________ X $_______) Net present value 1.Investment 2.Annual savings: 3.Total savings: 4.Present value of savings (_________ X $_______) Net present value When the discount rate makes the inflows (savings) equal to the outflow (investment), it is called the_________. In this case, the IRR is ______. -$ 25, ,000 25, $______ +$_______ ,754 68,850 15,923 9,077 +$______ +$_______ +$______ $______ IRR 10%.

Copyright © 2011 Nelson Education Limited An Example of a Capital Project But, if you want to make 16% on the $25,000 asset, how much must your asset generate in savings or cash each year? 1.Investment 2.Annual savings: $ _______ 3.Total savings: $________ 4.Present value of savings (________ x $________ ) Net present value Here, the discount rate that makes your savings equal to your investment is__________. Therefore this is your_______. The hurdle rate is... 1.The cost of capital _____ 2.Adjusted for the project’s risk _____ 3.Hurdle rate _____ 4, , ,100 - $ 25,000 +$________ 25, % 10 % 6 % 16 % IRR

Copyright © 2011 Nelson Education Limited The Statement of Financial Position Assets$25,000 Loan$25,000 Savings $ ________ Payments $ _________ Gives _________% Costs __________% Per year The company earns ______% or $ _____ each year after paying the loan. 4,100 2, ,346

Copyright © 2011 Nelson Education Limited How to Use the Interest Tables To compoundTo discount Single sumTable ATable B AnnuityTable CTable D These two tables are used in capital budgeting