Intermediate Accounting, 10th edition, Chapter 6 (Kieso et al.) Weygandt , and Warfield Chapter 6: The Time Value of Money Prepared by Krishnan Ranganathan , Angelo State University, San Angelo, Texas 11/8/2018 Intermediate Accounting, 10th edition, Chapter 6 (Kieso et al.)

Basic Time Value Concepts The time value of money is the relationship between time and money. According to the present value of money concept, a dollar earned today is worth more than a dollar earned in the future. This concept is used to choose among alternative investment proposals. 11/8/2018 Intermediate Accounting, 10th edition, Chapter 6 (Kieso et al.)

Accounting Applications The following are some of the applications of time value of money concept: Valuing non-current receivables and payables Valuing assets and obligations to be capitalized under long term leases Measuring post retirement obligations and pension expense Measuring the value of future cash flows from oil and gas reserves 11/8/2018 Intermediate Accounting, 10th edition, Chapter 6 (Kieso et al.)

Choosing an Interest Rate in Time Value Measurements The relevance and reliability of accounting information depend on the selection of appropriate interest rates. The interest rate in turn depends on: the pure rate of interest (2% - 4%) credit risk rate of interest (0% - 5%) expected inflation rate of interest (0% - ?) The higher the credit risk, the higher the interest rate. 11/8/2018 Intermediate Accounting, 10th edition, Chapter 6 (Kieso et al.)

Simple and Compound Interests Simple interest is determined on the principal only. principal * interest rate (%) * time Compound interest is determined on: the principal, and any interest earned (and not withdrawn) Compound interest is the typical computation applied in most time value applications. 11/8/2018 Intermediate Accounting, 10th edition, Chapter 6 (Kieso et al.)

Intermediate Accounting, 10th edition, Chapter 6 (Kieso et al.) Compound Interest Tables (5) in Time Value of Money Measurements (1 of 2) Future value of $1: $1 deposited today and left to accumulate for a specified number of periods till a future date Present value of $1: Amount to be deposited today to yield $1 at some specified future date Future value of an ordinary annuity of $1: $1 deposited end of each period and left to accumulate until a specified future date. 11/8/2018 Intermediate Accounting, 10th edition, Chapter 6 (Kieso et al.)

Compound Interest Tables in Time Value Measurements (2 of 2) Present value of an ordinary annuity of $1: Amount to be deposited today to permit withdrawals of $1 at the end of each period for a specified number of periods Present value of an annuity due of $1: Amount to be deposited today to permit withdrawals of $1 at the beginning of each period for a specified number of periods 11/8/2018 Intermediate Accounting, 10th edition, Chapter 6 (Kieso et al.)

Interest Rates and Frequency of Compounding Interest rate per year: 12% Frequency of Compounding Interest rate per compounding Number of compounding periods Annual 12% One (1) Semi-annual 6% Two (2) Quarterly 3% Four (4) Monthly 1% Twelve (12) 11/8/2018 Intermediate Accounting, 10th edition, Chapter 6 (Kieso et al.)

Single Sum Problems - Future Value of a Single Sum Given: Amount of deposit today: $50,000 Interest rate 11% Frequency of compounding: Annual Number of periods (5 years): 5 periods Determine the future value of this single sum. $50,000 * (1.68506) = $84,253 11/8/2018 Intermediate Accounting, 10th edition, Chapter 6 (Kieso et al.)

Single Sum Problems - Present Value of a Single Sum Given: Amount of deposit end of 5 years: $84,253 Interest rate (discount) rate 11% Frequency of compounding: Annual Number of periods (5 years): 5 periods Determine the present value of this single sum. $84,253 * (0.59345) = $50,000 11/8/2018 Intermediate Accounting, 10th edition, Chapter 6 (Kieso et al.)

Intermediate Accounting, 10th edition, Chapter 6 (Kieso et al.) Annuity Computations An annuity requires that: the periodic payments or receipts always be of the same amount, the interval between such payments or receipts be the same, and the interest be compounded once each interval 11/8/2018 Intermediate Accounting, 10th edition, Chapter 6 (Kieso et al.)

Annuities - Future Value of an Ordinary Annuity Given: Deposit made at the end of each period: $5,000 Compounding: Annual Number of periods: Five Interest rate 12% Determine the future value of these deposits. $5,000 * (6.35285) = $ 31,764.25 11/8/2018 Intermediate Accounting, 10th edition, Chapter 6 (Kieso et al.)

Annuities - Present Value of an Ordinary Annuity Given: Rental receipts at the end of each period: $6,000 Compounding: Annual Number of periods (years): 5 Interest rate 12% Determine the present value of these receipts. $6,000 * (3.60478) = $ 21,268.68 11/8/2018 Intermediate Accounting, 10th edition, Chapter 6 (Kieso et al.)

Annuities - Future Value of an Annuity Due Given: Deposit made at the beginning of each period: $ 800 Compounding: Annual Number of periods: Eight Interest rate 12% Determine the future value of these deposits. 11/8/2018 Intermediate Accounting, 10th edition, Chapter 6 (Kieso et al.)

Annuities - Future Value of an Annuity Due 1 2 3 4 5 6 7 8 R = $800 $800 $800 $800 $800 $800 $800 $800 End of period, no receipt. Interest rate = 12% N= 1. Ordinary annuity factor: 8 periods, 12% : 12.29969 2. Convert to annuity due factor: 12.29969 * 1.12 : 13.77565 3. Future value of annuity due: $800 * 13.77565 : $ 11,020.52 11/8/2018 Intermediate Accounting, 10th edition, Chapter 6 (Kieso et al.)

Annuities - Present Value of an Annuity Due Given: Payment made at the beginning of each period: $ 4.8M Compounding: Annual Number of periods: Four Interest rate 11% Determine the present value of these payments. 11/8/2018 Intermediate Accounting, 10th edition, Chapter 6 (Kieso et al.)

Annuities - Present Value of an Annuity Due 1 R = $4.8M $4.8M $4.8M $4.8M Interest rate = 11% N= 4 3 2 1. Ordinary annuity factor: 4 periods, 11% : 3.10245 2. Convert to annuity due factor: 3.10245 * 1.11 : 3.44372 3. Present value of annuity due: $4.8M * 3.44372 : $ 16,529,856 11/8/2018 Intermediate Accounting, 10th edition, Chapter 6 (Kieso et al.)

Annuities - Future Value of a Deferred Annuity Given: Deposit made at end of fourth, fifth, and sixth period: $80,000 each period No deposits were made at end of the first, second, or the third periods. Compounding: Annual Interest rate: 12% Number of periods: 6 Determine the future value of the deferred annuity. 11/8/2018 Intermediate Accounting, 10th edition, Chapter 6 (Kieso et al.)

Annuities - Future Value of a Deferred Annuity 1 6 5 3 4 2 R= $0 $0 $0 $80,000 $80,000 $80,000 Interest rate = 12% 1. Deferred annuity is calculated like ordinary annuity. 2. $80,000 * (3.37440) = $269,952 11/8/2018 Intermediate Accounting, 10th edition, Chapter 6 (Kieso et al.)

Annuities - Present Value of a Deferred Annuity Given: Payments made at end of fifth through tenth period (6 payments): $5,000 each period No payments were made at end of the first through the fourth periods (deferred periods = 4). Compounding: Annual Interest rate: 8% Number of periods: 10 total Determine the present value of the deferred annuity. 11/8/2018 Intermediate Accounting, 10th edition, Chapter 6 (Kieso et al.)

Annuities - Present Value of a Deferred Annuity 1 2 3 4 5 6 7 8 R = $5,000 5,000 5,000 5,000 5,000 5,000 Interest rate = 8% 9 10 Deferred period 1. Present value of an ordinary annuity (10 periods): 6.71008 2. Less: P.V. of an ordinary annuity (deferred 4 periods):(3.31213) 3. Present value of an annuity (6 periods): 3.39795 4. Present value of the deferred annuity = $5,000 * 3.39795 = $16,989.75 11/8/2018 Intermediate Accounting, 10th edition, Chapter 6 (Kieso et al.)

Intermediate Accounting, 10th edition, Chapter 6 (Kieso et al.) COPYRIGHT Copyright © 2001 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. 11/8/2018 Intermediate Accounting, 10th edition, Chapter 6 (Kieso et al.)