PowerPoint to accompany Chapter Time Value Of Money Learning Goals: • Discuss the role of time value in finance and the basic patterns of cash flows • Understand present and future value • Describe annuities, and perpetuities • Find future/present values of a stream of cash flows • Understand the effect of frequently compounding interest • Determine amortisation parameters Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Pty Ltd) – 9781442518193/ Gitman et al / Principles of Managerial Finance / 6th edition The Role Of Time Value • The “time value of money” principle says that all things being equal, a dollar today is worth more than a dollar that will be received at some future date  Financial values and decisions can be assessed by considering:  Future Value  Present Value Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Pty Ltd) – 9781442518193/ Gitman et al / Principles of Managerial Finance / 6th edition The Role Of Time Value • Future cash flows are best depicted through the use of a timeline: Cash Flows On Top Time On Bottom Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Pty Ltd) – 9781442518193/ Gitman et al / Principles of Managerial Finance / 6th edition Compounding & Discounting Page 147 Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Pty Ltd) – 9781442518193/ Gitman et al / Principles of Managerial Finance / 6th edition Useful Calculation Tools  Formulas Formula Sheet.pdf  Financial Tables – Appendix AFinancial Tables.pdf  Electronic SpreadsheetsAnnuity.xls  Financial Calculators Page 147 Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Pty Ltd) – 9781442518193/ Gitman et al / Principles of Managerial Finance / 6th edition Financial TablesFinancial Tables.pdf Page 148 Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Pty Ltd) – 9781442518193/ Gitman et al / Principles of Managerial Finance / 6th edition Basic Cash Flow Patterns  Single Amount: One lump sum  Annuity: Series of cash flows of equal amount, received at equal time intervals  Mixed Stream: Series of cash flows that are not equal or a series of cash flows that are not received at equal time intervals Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Pty Ltd) – 9781442518193/ Gitman et al / Principles of Managerial Finance / 6th edition Future Value Of A Single Amount  Future Value: the value of a present amount at a future date (Go to excel sheet)  Calculated by applying compound interest over a specified period of time  FVn = PV x (1 + i)n [Equation 4.4] Where:  FVn = Future value at the end of period n    PV = Present value i = Annual interest rate n = Number of periods Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Pty Ltd) – 9781442518193/ Gitman et al / Principles of Managerial Finance / 6th edition Future Value Of A Single Amount  Future Value Interest Factor (FVIF): the multiplier used to calculate FV at a given discount rate • Written as FVIFi,n • FVIFi,n = (1 + i)n [Equation 4.5] Financial Tables.pdf • FVn = PV x FVIFi,n [Equation 4.6] Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Pty Ltd) – 9781442518193/ Gitman et al / Principles of Managerial Finance / 6th edition Future Value Of A Mixed Stream  Example: Shrell Industries, a cabinet manufacturer, expects to receive the following mixed stream of cash flows over the next five years from one of its small customers: Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Pty Ltd) – 9781442518193/ Gitman et al / Principles of Managerial Finance / 6th edition Future Value Of A Mixed Stream If Shrell expects to earn 8% on its investments, how much will accumulate by the end of year if it immediately invests the cash flows when they are received?  Financial Calculator: i = 8, C1 = 11,500, C2 = 14,000, C3 = 12,900, C4 = 16,000, C5 = 18,000 FV = $83,608.15 Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Pty Ltd) – 9781442518193/ Gitman et al / Principles of Managerial Finance / 6th edition Future Value Of A Mixed Stream  Financial Tables: (Using Appendix A-1) FVn = PV x FVIFi,n Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Pty Ltd) – 9781442518193/ Gitman et al / Principles of Managerial Finance / 6th edition Present Value Of A Mixed Stream  Example: Frey Ltd, a shoe manufacturer, has been offered an opportunity to receive the following mixed stream of cash flows over the next five years: Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Pty Ltd) – 9781442518193/ Gitman et al / Principles of Managerial Finance / 6th edition Present Value Of A Mixed Stream If the firm must earn at least 9% on its investments, what is the most it should pay for this opportunity?  Financial Calculator: i = 9, C0 = 0, C1 = 400, C2 = 800, C3 = 500, C4 = 400, C5 = 300 PV = $1,904.76 Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Pty Ltd) – 9781442518193/ Gitman et al / Principles of Managerial Finance / 6th edition Present Value Of A Mixed Stream  Financial Tables: (Using Appendix A-3) PVn = PMT x PVIFi,n Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Pty Ltd) – 9781442518193/ Gitman et al / Principles of Managerial Finance / 6th edition Compounding More Frequently  Compounding can be done:   Semi Annually  Quarterly  Monthly  Daily   Annually Continuously The more frequent the compounding the larger the amount of money accumulated Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Pty Ltd) – 9781442518193/ Gitman et al / Principles of Managerial Finance / 6th edition Compounding More Frequently  Is calculated with the following formula:  Where m is the number of times per year interest is compounded Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Pty Ltd) – 9781442518193/ Gitman et al / Principles of Managerial Finance / 6th edition Continuous Compounding  Involves compounding over every instant  Future value of a sum that is subject to continuous compounding can be calculated by: FV n (Continuous Compounding) = PV x (e i x n ) [Equation 4.21] Where: e = exponential function e=2.718281828 Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Pty Ltd) – 9781442518193/ Gitman et al / Principles of Managerial Finance / 6th edition Continuous Compounding  Example: Fred Moore wished to find the future value at the end of two years of $100 invested at 8% interest compounded continuously FV n (Continuous Compounding) = 100 x (e 0.08 x ) FV = 100 x 1.1735 FV = $117.35 Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Pty Ltd) – 9781442518193/ Gitman et al / Principles of Managerial Finance / 6th edition Nominal & Effective Rates Of Interest  Used to put interest rates on a common basis to allow comparison  Nominal Interest Rate: The contractual annual rate of interest charged by the lender or promised by a borrower Must be disclosed by financial providers to consumers on credit cards and loans Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Pty Ltd) – 9781442518193/ Gitman et al / Principles of Managerial Finance / 6th edition Nominal & Effective Rates Of Interest  Effective Annual Rate (EAR): The annual rate of interest actually paid or earned Must be disclosed by financial providers on savings products  Annual Percentage Rate (APR): the nominal annual rate charged on loan products  Annual Percentage Yield (APY): the effective annual rate a savings product pays Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Pty Ltd) – 9781442518193/ Gitman et al / Principles of Managerial Finance / 6th edition Applications Of Time Value Deposits needed to accumulate a future sum: Finding the deposit/s need to accumulate a specified future sum e.g house deposit PMT = FVA n FVIFAi, n [Equation 4.25] Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Pty Ltd) – 9781442518193/ Gitman et al / Principles of Managerial Finance / 6th edition Applications Of Time Value Loan amortisation: Finding the equal periodic loan payments needed to meet the lender’s required interest rate and repayment date A loan amortisation schedule shows the allocation of each payment to principal and interest PMT = PVA n PVIFAi, n [Equation 4.27] Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Pty Ltd) – 9781442518193/ Gitman et al / Principles of Managerial Finance / 6th edition Applications Of Time Value Interest rate determination: Finding the compound annual interest/growth rate of a series of cash flows PVIFAi, n = PVAn PMT [Equation 4.28] Period determination: Finding an unknown number of periods needed to generate a given amount of cash flow from an initial amount PVIFAi, n = PVAn PMT Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Pty Ltd) – 9781442518193/ Gitman et al / Principles of Managerial Finance / 6th edition ... division of Pearson Australia Group Pty Ltd) – 978 144 2518193/ Gitman et al / Principles of Managerial Finance / 6th edition Future Value Of A Single Amount  Future Value: the value of a present... division of Pearson Australia Group Pty Ltd) – 978 144 2518193/ Gitman et al / Principles of Managerial Finance / 6th edition Present Value Of A Single Amount  Present Value: the current value of a... role of time value in finance and the basic patterns of cash flows • Understand present and future value • Describe annuities, and perpetuities • Find future/present values of a stream of cash