G-1 Appendix G Time Value of Money Accounting in Action Learning Objectives After studying this chapter, you should be able to: [1] Distinguish between simple and compound interest [2] Solve for future value of a single amount [3] Solve for future value of an annuity [4] Identify the variables fundamental to solving present value problems [5] Solve for present value of a single amount [6] Solve for present value of an annuity [7] Compute the present value of notes and bonds [8] Compute the present values in capital budgeting situations [9] Use a financial calculator to solve time value of money problems G-2 Basic Time Value Concepts Time Value of Money Would you rather receive $1,000 today or in a year from now? Today! “Interest Factor” G-3 Nature of Interest  Payment for the use of money  Difference between amount borrowed or invested (principal) and amount repaid or collected Elements involved in financing transaction: G-4 Principal (p): Amount borrowed or invested Interest Rate (i): An annual percentage Time (n): Number of years or portion of a year that the principal is borrowed or invested LO Nature of Interest Simple Interest  Interest computed on the principal only Illustration: Assume you borrow $5,000 for years at a simple interest rate of 12% annually Calculate the annual interest cost Illustration G-1 Interest computations FULL YEARS G-5 Interest = p x i x n = $5,000 x 12 x = $1,200 LO Nature of Interest Compound Interest   G-6 Computes interest on ► the principal and ► any interest earned that has not been paid or withdrawn Most business situations use compound interest LO Nature of Interest - Compound Interest Illustration: Assume that you deposit $1,000 in Bank Two, where it will earn simple interest of 9% per year, and you deposit another $1,000 in Citizens Bank, where it will earn compound interest of 9% per year compounded annually Also assume that in both cases you will not withdraw any interest until three years from the date of deposit Illustration G-2 Simple versus compound interest G-7 Year $1,000.00 x 9% $ 90.00 $ 1,090.00 Year $1,090.00 x 9% $ 98.10 $ 1,188.10 Year $1,188.10 x 9% $106.93 $ 1,295.03 LO Appendix G Time Value of Money Accounting in Action Learning Objectives After studying this chapter, you should be able to: [1] Distinguish between simple and compound interest [2] Solve for future value of a single amount [3] Solve for future value of an annuity [4] Identify the variables fundamental to solving present value problems [5] Solve for present value of a single amount [6] Solve for present value of an annuity [7] Compute the present value of notes and bonds [8] Compute the present values in capital budgeting situations [9] Use a financial calculator to solve time value of money problems G-8 Future Value Concepts Future Value of a Single Amount Future value of a single amount is the value at a future date of a given amount invested, assuming compound interest Illustration G-3 Formula for future value FV = future value of a single amount p i n G-9 = principal (or present value; the value today) = interest rate for one period = number of periods LO Future Value of a Single Amount Illustration: If you want a 9% rate of return, you would compute the future value of a $1,000 investment for three years as follows: Illustration G-4 Time diagram G-10 LO Present Value of a Long-term Note or Bond Illustration: Now assume that the investor’s required rate of return is 12%, not 10% The future amounts are again $100,000 and $5,000, respectively, but now a discount rate of 6% (12% ÷ 2) must be used Calculate the present value of the principal and interest payments Illustration G-20 Present value of principal and interest—discount G-44 LO Present Value of a Long-term Note or Bond Illustration: Now assume that the investor’s required rate of return is 8% The future amounts are again $100,000 and $5,000, respectively, but now a discount rate of 4% (8% ÷ 2) must be used Calculate the present value of the principal and interest payments Illustration G-21 Present value of principal and interest—premium G-45 LO Appendix G Time Value of Money Accounting in Action Learning Objectives After studying this chapter, you should be able to: [1] Distinguish between simple and compound interest [2] Solve for future value of a single amount [3] Solve for future value of an annuity [4] Identify the variables fundamental to solving present value problems [5] Solve for present value of a single amount [6] Solve for present value of an annuity [7] Compute the present value of notes and bonds [8] Compute the present values in capital budgeting situations [9] Use a financial calculator to solve time value of money problems G-46 Present Value Concepts Computing the Present Values in a Capital Budgeting Decision Illustration: Nagel-Siebert Trucking Company, a cross-country freight carrier in Montgomery, Illinois, is considering adding another truck to its fleet because of a purchasing opportunity Navistar Inc., Nagel-Siebert’s primary supplier of overland rigs, is overstocked and offers to sell its biggest rig for $154,000 cash payable upon delivery Nagel-Siebert knows that the rig will produce a net cash flow per year of $40,000 for five years (received at the end of each year), at which time it will be sold for an estimated salvage value of $35,000 Nagel-Siebert’s discount rate in evaluating capital expenditures is 10% Should Nagel-Siebert commit to the purchase of this rig? G-47 LO Present Value in a Capital Budgeting Decision The cash flows that must be discounted to present value by Nagel-Siebert are as follows  Cash payable on delivery (today): $154,000  Net cash flow from operating the rig: $40,000 for years (at the end of each year)  Cash received from sale of rig at the end of years: $35,000 The time diagrams for the latter two cash flows are shown in Illustration G-22 which follows G-48 LO Present Value in a Capital Budgeting Decision The time diagrams for the latter two cash are as follows: Illustration G-22 Time diagrams for NagelSiebert Trucking Company G-49 LO Present Value in a Capital Budgeting Decision The computation of these present values are as follows: Illustration G-23 Present value computations at 10% The decision to invest should be accepted G-50 Advance slide in presentation mode to reveal answer LO Present Value in a Capital Budgeting Decision Assume Nagle-Siegert uses a discount rate of 15%, not 10% Illustration G-24 Present value computations at 15% The decision to invest should be rejected G-51 Advance slide in presentation mode to reveal answer LO Appendix G Time Value of Money Accounting in Action Learning Objectives After studying this chapter, you should be able to: [1] Distinguish between simple and compound interest [2] Solve for future value of a single amount [3] Solve for future value of an annuity [4] Identify the variables fundamental to solving present value problems [5] Solve for present value of a single amount [6] Solve for present value of an annuity [7] Compute the present value of notes and bonds [8] Compute the present values in capital budgeting situations [9] Use a financial calculator to solve time value of money problems G-52 Using Financial Calculators N = number of periods I = interest rate per period PV = present value Illustration G-25 Financial calculator keys PMT = payment FV G-53 = future value LO Using Financial Calculators Present Value of a Single Sum Assume that you want to know the present value of $84,253 to be received in five years, discounted at 11% compounded annually Illustration G-26 Calculator solution for present value of a single sum G-54 LO Using Financial Calculators Present Value of an Annuity Assume that you are asked to determine the present value of rental receipts of $6,000 each to be received at the end of each of the next five years, when discounted at 12% Illustration G-27 Calculator solution for present value of an annuity G-55 LO Using Financial Calculators Useful Applications – Auto Loan The loan has a 9.5% nominal annual interest rate, compounded monthly The price of the car is $6,000, and you want to determine the monthly payments, assuming that the payments start one month after the purchase Illustration G-28 Calculator solution for auto loan payments G-56 LO Using Financial Calculators Useful Applications – Mortgage Loan Amount You decide that the maximum mortgage payment you can afford is $700 per month The annual interest rate is 8.4% If you get a mortgage that requires you to make monthly payments over a 15-year period, what is the maximum Illustration G-29 purchase price you can afford? Calculator solution for mortgage amount G-57 LO Copyright “Copyright © 2014 John Wiley & Sons, Inc All rights reserved Reproduction or translation of this work beyond that permitted in Section 117 of the 1976 United States Copyright Act without the express written permission of the copyright owner is unlawful Request for further information should be addressed to the Permissions Department, John Wiley & Sons, Inc The purchaser may make back-up copies for his/her own use only and not for distribution or resale The Publisher assumes no responsibility for errors, omissions, or damages, caused by the use of these programs or from the use of the information contained herein.” G-58 ... Payment G- 20 x 4.37462 Factor = $10,936.55 Future Value LO Appendix G Time Value of Money Accounting in Action Learning Objectives After studying this chapter, you should be able to: [1] Distinguish.. .Appendix G Time Value of Money Accounting in Action Learning Objectives After studying this chapter, you should be able to: [1] Distinguish between simple and compound... (the discount rate) G- 22 LO Appendix G Time Value of Money Accounting in Action Learning Objectives After studying this chapter, you should be able to: [1] Distinguish between simple and compound