Gíao trình kế toán bằng tiếng anh appendix a

Appendix A Time Value of Money Learning Objectives After studying this chapter, you should be able to: A- 1 Distinguish between simple and compound interest Solve for future value of a single amount Solve for future value of an annuity Identify the variables fundamental to solving present value problems Solve for present value of a single amount Solve for present value of an annuity Compute the present value of notes and bonds Compute the present values in capital budgeting situations Use a financial calculator to solve time value of money problems Basic Time Value Concepts Time Value of Money Would you rather receive $1,000 today or in a year from now? Today! “Interest Factor” A- Nature of Interest Interest  Payment for the use of money  Excess cash received or repaid over the amount borrowed (principal) Variables involved in financing transaction: Principal (p) - Amount borrowed or invested Interest Rate (i) – An annual percentage Time (n) - The number of years or portion of a year that the principal is borrowed or invested A- LO Distinguish between simple and compound interest Nature of Interest Simple Interest  Interest computed on the principal only Illustration: Assume you borrow $5,000 for years at a simple interest of 12% annually Calculate the annual interest cost Illustration A-1 Interest = p x i x n FULL YEAR = $5,000 x 12 x = $1,200 A- LO Distinguish between simple and compound interest Nature of Interest Compound Interest   A- Computes interest on ► the principal and ► any interest earned that has not been paid or withdrawn Most business situations use compound interest LO Distinguish between simple and compound interest Nature of Interest Illustration: Assume that you deposit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 A-2 Simple versus compound interest A- 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 Distinguish between simple and compound interest 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 FV = p x (1 + i )n FV = p = i = n = A- Illustration A-3 Formula for future value future value of a single amount principal (or present value; the value today) interest rate for one period number of periods LO Solve for a future value of a single amount 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 A-4 A- LO Solve for a future value of a single amount Future Value of a Single Amount Alternate Method 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 A-4 What table we use? A- LO Solve for a future value of a single amount Future Value of a Single Amount What factor we use? $1,000 Present Value A- 10 x 1.29503 Factor = $1,295.03 Future Value LO Solve for a future value of a single amount Present Value of a Long-Term Note or Bond PV of Principal $100,000 Principal A- 34 x 61391 Factor = $61,391 Present Value LO Compute the present value of notes and bonds Present Value of a Long-Term Note or Bond PV of Interest $5,000 Principal A- 35 x 7.72173 Factor = $38,609 Present Value LO Compute the present value of notes and bonds Present Value of a Long-Term Note or Bond Illustration: Assume a bond issue of 10%, five-year bonds with a face value of $100,000 with interest payable semiannually on January and July Present value of Principal $61,391 Present value of Interest 38,609 Bond current market value A- 36 $100,000 LO Compute the present value of notes and bonds 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 A-20 A- 37 LO Compute the present value of notes and bonds 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 A-21 A- 38 LO Compute the present value of notes and bonds PV in a Capital Budgeting Decisions The decision to make long-term capital investments is best evaluated using discounting techniques that recognize the time value of money To this, many companies calculate the present value of the cash flows involved in a capital investment A- 39 SO Compute the present values in capital budgeting situations PV in a Capital Budgeting Decisions 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 NagelSiebert commit to the purchase of this rig? A- 40 SO Compute the present values in capital budgeting situations PV in a Capital Budgeting Decisions Cash flows that must be discounted to present value are:  Cash payable on delivery (today): $154,000  Net cash flow from operating the rig: $40,000 for years  Cash received from sale of rig at the end of years: $35,000 Illustration A-22 A- 41 SO Compute the present values in capital budgeting situations PV in a Capital Budgeting Decisions Notice the present value of the net operating cash flows is discounting an annuity, while computing the present value of the $35,000 salvage value is discounting a single sum Illustration A-23 Accepted A- 42 SO Using Financial Calculators N = number of periods I Illustration A-25 Financial calculator keys = interest rate per period PV = present value PMT = payment FV = future value A- 43 LO Use a financial calculator to solve time value of money problems 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 A-23 Calculator solution for present value of a single sum A- 44 LO Use a financial calculator to solve time value of money problems 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 A-27 Calculator solution for present value of an annuity A- 45 LO Use a financial calculator to solve time value of money problems 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 A-28 A- 46 LO Use a financial calculator to solve time value of money problems Using Financial Calculators Useful Applications – Mortgage Loan 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 purchase price you can afford? Illustration A-29 A- 47 LO Use a financial calculator to solve time value of money problems Copyright Copyright © 2012 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 A- 48 ... Value A- 29 x 2.48685 Factor = $2,484.85 Present Value LO Solve for present value of an annuity Present Value of an Annuity Illustration: Kildare Company has just signed a capitalizable lease... same in each period, the future value can be computed by using a future value of an annuity of table Illustration: A- 16 Illustration A- 8 LO Solve for a future value of an annuity Future Value... Value of a Single Amount Illustration A- 10 Illustration: If you want a 10% rate of return, you can also compute the present value of $1,000 for one year by using a present value table What table