© 2008 by Nelson, a division of Thomson Canada Limited Transparency 10.1 Finance for Non-Financial Managers Fifth Edition Slides prepared by Pierre G. Bergeron University of Ottawa

© 2008 by Nelson, a division of Thomson Canada Limited Transparency 10.2 Time Value of Money 1.Differentiate between time value of money versus inflation and risk. 2. Explain financial tools that can be used to solve time- value-of-money problems. 3. Differentiate between future values 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

© 2008 by Nelson, a division of Thomson Canada Limited Transparency 10.3 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

© 2008 by Nelson, a division of Thomson Canada Limited Transparency 10.4 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

© 2008 by Nelson, a division of Thomson Canada Limited Transparency 10.5 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%

© 2008 by Nelson, a division of Thomson Canada Limited Transparency Time Value of Money and Inflation Years Projected income statement Sales revenue (with inflation) Cost of sales (with inflation) Gross profit Administrative expenses (with inflation) Income before taxes Income taxes Net income Add back amortization 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.

© 2008 by Nelson, a division of Thomson Canada Limited Transparency 10.7 Things 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 1. Time value of Money and Risk

© 2008 by Nelson, a division of Thomson Canada Limited Transparency 10.8 Investment Decisions in Capital Budgeting TIME 6-49 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

© 2008 by Nelson, a division of Thomson Canada Limited Transparency Tools For Solving Time-Value-of-Money Problems Algebraic Notations Interest Tables Financial Calculators and Spreadsheets Time Lines

© 2008 by Nelson, a division of Thomson Canada Limited Transparency Effect of Compounding Problem: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? Beginning Interest Amount Beginning Ending Year amount rateof interest amountamount 1 $1, $100$1,000$1,100 2 $1, $110$1,100$1,210 3 $1, $121$1,210$1,331 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

© 2008 by Nelson, a division of Thomson Canada Limited Transparency 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%

© 2008 by Nelson, a division of Thomson Canada Limited Transparency 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

© 2008 by Nelson, a division of Thomson Canada Limited Transparency CompoundingDiscounting Single sum A B Annuity C D Future Value of an Annuity – Table C N 9% 10% 11% 12% 14% 16% 18% 20%

© 2008 by Nelson, a division of Thomson Canada Limited Transparency Effect of Discounting Problem: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%? Beginning DiscountPresent Year amount rate value 3 $1, $ 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 = $751.31

© 2008 by Nelson, a division of Thomson Canada Limited Transparency CompoundingDiscounting Single sum A B Annuity C D O Present Value of a Single Sum – Table B N 9% 10% 11% 12% 13% 14% 15% 16%

© 2008 by Nelson, a division of Thomson Canada Limited Transparency Present Value of an Annuity Problem: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%? 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 = $3,790.80

© 2008 by Nelson, a division of Thomson Canada Limited Transparency CompoundingDiscounting Single sum A B Annuity C D Present Value of an Annuity – Table D N 9% 10% 11% 12% 13% 14% 15% 16%

© 2008 by Nelson, a division of Thomson Canada Limited Transparency 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%.

© 2008 by Nelson, a division of Thomson Canada Limited Transparency 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

© 2008 by Nelson, a division of Thomson Canada Limited Transparency The Balance Sheet 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

© 2008 by Nelson, a division of Thomson Canada Limited Transparency How to Use the Interest Tables To compoundTo discount Single sumTable ATable B AnnuityTable CTable D These two tables are used in capital budgeting