Accounting Principles Thirteenth Edition Weygandt Kimmel Kieso Appendix G Time Value of Money Prepared by Coby Harmon University of California, Santa Barbara Westmont College Chapter Outline Learning Objectives LO Compute interest and future values LO Compute present values LO Compute the present value in capital budgeting situations LO Use a financial calculator to solve time value of money problems Copyright ©2018 John Wiley & Son, Inc Interest and Future Values 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: 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 Copyright ©2018 John Wiley & Son, Inc Nature of Interest Simple Interest Interest computed on 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 Principal Interest LO = p = $5,000 = $1,200 Rate x Time x i x Copyright ©2018 John Wiley & Son, Inc 0.12 n x Nature of Interest Compound Interest Computes interest on principal interest earned that has not been paid or withdrawn Most business situations use compound interest LO Copyright ©2018 John Wiley & Son, Inc Compound Interest Illustration: Assume you deposit $1,000 in Bank Two,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 cash until three years from the date of deposit Compute the interest to be received and the accumulated year-end balances for Citizens Bank LO Copyright ©2018 John Wiley & Son, Inc ILLUSTRATION G.2 Compound Interest Simple versus compound interest Bank Two Simple Interest Simple Accumulated Calculation Interest Year-End Balance Year $1,000 x 9% $ 90.00 $1,090.00 Year $1,000 x 9% 90.00 $1,180.00 Year $1,000 x 9% 90.00 $1,270.00 $270.00 Citizens Bank Compound Compound Accumulated Interest Calculation Interest Year-End Balance Year $1,000 x 9% $ 90.00 $1,090.00 Year $1,090 x 9% 98.10 $1,188.10 Year $1,188 x 9% 106.93 $1,295.03 $25.03 $295.03 LO Copyright ©2018 John Wiley & Son, Inc Future Value of a Single Amount Value at a future date of a given amount invested, assuming compound interest FV = p × (1 + i) LO n FV = future value of a single amount p = principal (or present value; the value today) i = interest rate for one period n = number of periods Copyright ©2018 John Wiley & Son, Inc Future Value of a Single Amount Illustration: The future value of a $1,000 investment earning 9% for three years is $1,295.03 FV = p n × (1 + i) = $1,000 × (1 + 09) = $1,000 × 1.29503 = $1,295.03 ILLUSTRATION G.4 Time diagram Present Value (p) $1,000 LO Future i = 9% Value n = years Copyright ©2018 John Wiley & Son, Inc $1,295.03 Future Value of a Single Amount Another method to compute the future value of a single amount involves a compound interest table Table Future Value of (n) Periods 5% 6% 7% 8% 9% 10% 1.05000 1.06000 1.07000 1.08000 1.09000 1.10000 1.10250 1.12360 1.14490 1.16640 1.18810 1.21000 1.15763 1.19102 1.22504 1.25971 1.29503 1.33100 1.21551 1.26248 1.31080 1.36049 1.41158 1.46410 1.27628 1.33823 1.40255 1.46933 1.53862 1.61051 $1,000 Present Value LO x 1.29503 Factor Copyright ©2018 John Wiley & Son, Inc = $1,295.03 Future Value 10 Present Value Long-Term Note or Bond Assume the investor’s required rate of return is 4%, not 5% 5% Contractual Rate—4% Discount Rate Present value of principal to be received at maturity $100,000 × 67556 (Table 3) $ 67,556 Present value of interest to be received periodically over the term of the bonds $5,000 × 8.11090 (Table 4) 40,555* Present value of bonds $108,111 LO Copyright ©2018 John Wiley & Son, Inc 40 Capital Budgeting Situations 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 NagelSiebert’s discount rate in evaluating capital expenditures is 10% Should Nagel-Siebert commit to the purchase of this rig? LO Copyright ©2018 John Wiley & Son, Inc 41 Capital Budgeting Situations The cash flows that must be discounted to present value by Nagel-Siebert are as follows a Cash payable on delivery (today): $154,000 b Net cash flow from operating the rig: $40,000 for years (at the end of each year) c Cash received from sale of rig at the end of years: $35,000 The time diagrams for the latter two cash flows are shown as follows LO Copyright ©2018 John Wiley & Son, Inc 42 Capital Budgeting Situations Time diagrams for latter two cash flows are as follows: i = 10% Net Operating Cash Flows PV (?) $40,000 $40,000 $40,000 $40,000 $40,000 years n=5 Today Cash from Sale i = 10% PV (?) years n=5 Today LO $35,000 ILLUSTRATION G.22 Copyright ©2018 John Wiley & Son, Inc 43 Capital Budgeting Situations Computation of these present values are as follows: Present Values—10% Discount Rate Present value of net operating cash flows received annually over years $40,000 × PV of received annually for years at 10% $40,000 × 3.79079 $ 151,631.60 Present value of salvage value to be received in years $35,000 × PV of received in years at 10% $35,000 × 62092 21,732.20 Present value of cash inflows 173,363.80 Present value of cash outflows (price due today at 10%) $154,000 × PV of due today $154,000 × 1.00000 (154,000.00) Net present value LO $ 19,363.80 Copyright ©2018 John Wiley & Son, Inc 44 Capital Budgeting Situations Assume Nagle-Siegert uses a discount rate of 15%, not 10%: Present Values—15% Discount Rate Present value of net operating cash flows received annually over years at 15% $40,000 × 3.35216 $ 134,086.40 Present value of salvage value to be received in years at 15% $35,000 × 49718 17,401.30 Present value of cash inflows 151,487.70 Present value of cash outflows (price due today at 15%) $154,000 × 1.00000 (154,000.00) Net present value LO $ (2,512.30) Copyright ©2018 John Wiley & Son, Inc 45 Using Financial Calculators ILLUSTRATION G.25 Financial calculator keys LO N = number of periods I = interest rate per period PV = present value PMT = payment FV future value = Copyright ©2018 John Wiley & Son, Inc 46 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 Inputs: Answer: 11 ? 84,253 N I PV PMT FV -50,000 ILLUSTRATION G.26 Calculator solution for present value of a single sum LO Copyright ©2018 John Wiley & Son, Inc 47 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% Inputs: Answer: 12 ? 6,000 N I PV PMT FV -21,628.66 ILLUSTRATION G.27 Calculator solution for present value of an annuity LO Copyright ©2018 John Wiley & Son, Inc 48 Future Value of a Single Sum Assume you will invest $20,000 today into a fund and you intend to leave it there for 15 years The fund earns 7% interest Compute the future value at the end of year 15 Inputs: 15 20,000 ? N I PV PMT FV Answer: -55,180.63 ILLUSTRATION G.28 Calculator solution for future value of a single sum LO Copyright ©2018 John Wiley & Son, Inc 49 Future Value of an Annuity Assume you will invest $8,000 into a fund at the end of each of the next eight years The fund earns 9% interest Compute the future value of the fund at the end of the eighth year Inputs: 8,000 ? N I PV PMT FV Answer: -88,227.79 ILLUSTRATION G.29 Calculator solution for future value of an annuity LO Copyright ©2018 John Wiley & Son, Inc 50 Internal Rate of Return A purchase of a piece of equipment with a seven-year life requires an initial investment of $54,000, has positive cash flows of $7,800 per year, and has an estimated salvage value of $11,000 Compute the internal rate of return Inputs: ? -54,000 7,800 11,000 N I PV PMT FV Answer: 4.52% ILLUSTRATION G.30 Calculator solution for internal rate of return LO Copyright ©2018 John Wiley & Son, Inc 51 Useful Applications – Auto Loan You are financing the purchase of a car with a three-year loan The annual interest rate is 9.5%, compounded monthly The price of the car is $6,000 Calculate the monthly payments, assuming payments start one month after purchase Inputs: 36 9.5 6,000 ? N I PV PMT FV Answer: -192.2 ILLUSTRATION G.31 Calculator solution for auto loan payments LO Copyright ©2018 John Wiley & Son, Inc 52 Useful Applications – Mortgage Loan You decide the maximum mortgage payment you can afford is $700 per month The annual interest rate is 8.4% What is the maximum purchase price you can afford if the mortgage requires you to make monthly payments over a 15 years? Inputs: 180 8.4 ? -700 N I PV PMT FV Answer: 71,509.81 ILLUSTRATION G.32 Calculator solution for mortgage amount LO Copyright ©2018 John Wiley & Son, Inc 53 Copyright Copyright © 2018 John Wiley & Sons, Inc All rights reserved Reproduction or translation of this work beyond that permitted in Section 117 of the 1976 United States 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 Copyright ©2018 John Wiley & Son, Inc 54