- - - - - - Cover Page - - - - - - Lesson TVM-10-040-xx Present Value Ordinary Annuity Clip 01 This workbook contains notes and worksheets to accompany the corresponding video lesson available online at: Permission is granted for educators and students to make copies and redistribute this document without fee provided the copyright notice and page footer is retained. All other intellectual property rights are reserved by the copyright holder. Copyright 2011 by Rocky Spears Enterprises LLC, All Rights Reserved Page 1 of 7
Corrections Subsequent to the production of these videos in July 2010, we re-structured and renumbered them to be consistent with a structure that emerged from our later work in which the last two digits of our numbering scheme represents part 1, part 2, part3, etc. of a lesson. This allows us to break lessons into shorter related subsets easier for you as viewer to manage. We re-edited the videos to refer to the new number structure. However, there may be some references to lesson numbers in the videos that still refer to the old numbering scheme. If so, please alert us so that we can correct that in a future release. For your convenience, the numbering systems are as follows: OLD NUMBER SCHEME NEW NUMBER SCHEME TOPIC TVM-10-010-01 TVM-10-010-xx TVM-10-010-01 Part 1 TVM-10-010-02 Part 2 Future Value of a Single Sum TVM-10-010-02 TVM-10-020-xx TVM-10-020-01 Part 1 TVM-10-020-02 Part 2 Future Value of an Ordinary Annuity TVM-10-010-03 TVM-10-030-xx TVM-10-030-01 Part 1 TVM-10-030-02 Part 2 Present Value of a Single Sum TVM-10-010-04 TVM-10-040-xx TVM-10-040-01 Part 1 TVM-10-040-02 Part 2 Present Value of an Ordinary Annuity TVM-10-010-05 TVM-10-050-xx TVM-10-050-01 Part 1 TVM-10-050-02 Part 2 Future Value of an Annuity Due TVM-10-010-06 TVM-10-060-xx TVM-10-060-01 Part 1 TVM-10-060-02 Part 2 Present Value of an Annuity Due We apologize for any confusion this may cause. Copyright 2011 by Rocky Spears Enterprises LLC, All Rights Reserved Page 2 of 7
Time Value of Money - Present Value Ordinary Annuity - Part 1 [Clip 01] Ordinary Annuity Concept Pre-requisites Understand the concepts of future value of a single sum and present value of a single sum. These are covered in Lesson TVM-10-030 Present Value Single Sum. We will assume you understand the concepts and problems from this earlier lesson and we will refer to prior examples as we study the present value of an Annuity Due. Objectives: 1. Ordinary Annuity concept 2. Present value of an Ordinary Annuity formula, tables, financial calculator 3. Solve present value of an Ordinary Annuity problems 4. Solve combination problems involving present value of a single sum and present value of an ordinary annuity Copyright 2011 by Rocky Spears Enterprises LLC, All Rights Reserved Page 3 of 7
Concept of an Ordinary Annuity In this lesson we study how to determine the present value of an ordinary annuity. An annuity is a cash payment or a cash receipt that occurs at equal intervals (periods) for a number of intervals (periods). The intervals can be years, semiannual periods, quarterly periods, monthly periods, etc. An annuity amount can be fixed, that is, the same each period, or it can be variable. Our interest in this lesson is a fixed annuity amount, because we have special procedures to determine the present value of a fixed annuity. A variable annuity problem is solved using a combination of ordinary fixed annuity and single sum procedures. An ordinary annuity is one in which the cash payment or cash receipt occurs at the end of a period. This lesson will deal with that situation. Examples of ordinary annuities include: 1. Installment loans such as your car payment. Typically such payments occur at the end of each month from the point of view of the inception of the loan. 2. Long term debt issued by corporations such as coupon bonds which typically pay the investor/lender interest at the end of each semi-annual period. When the cash payment or cash receipt occurs at the beginning of each period, it is called an annuity due. We study the present value of annuity due in Lesson TVM-10-060. An example of an annuity due is rent or lease payments. Most rent or lease payments are due at the beginning of the period covered by the lease. Copyright 2011 by Rocky Spears Enterprises LLC, All Rights Reserved Page 4 of 7
Comparison of Time Value of Money Situations Period FV SS PV SS FV OA PV OA FV AD PV AD 0 - Today -PMT 0 or -PV 0 -PV 0? -PV 0? -PMT 1 -PV 0? +PMT 1 Period 1 -PMT 1 +PMT 1 -PMT 2 +PMT 2 Period 2 -PMT 2 +PMT 2 -PMT 3 +PMT 3 Period 3 -PMT 3 +PMT 3 +PMT n +FV n? or +FV n -PMT n-1 +PMT n-1 Period N -PMT n +FV n? +PMT n FV n? This table compares the cash flows streams for different time value of money situations. Notice how the column for present value of an ordinary annuity (PV OA ) differs from present value of a single sum (PV SS ). In present value of a single sum, we typically know a future amount at the end of some future period, call it PMT n or FV n. We want to know the present value of that amount today at some discount rate, call it r. We are asking How much are we willing to pay today for a future amount? In present value of an ordinary annuity, we know a future amount that occurs at the end of every period from period 1 through period n. We want to know the present value of those amounts today at some discount rate, call it r. We are Copyright 2011 by Rocky Spears Enterprises LLC, All Rights Reserved Page 5 of 7
asking How much are we willing to pay today for a stream of future amounts that are the same each period? We can also turn this around a bit and ask If we have an amount today, call it PV 0, invested at a certain rate of return, r, what is the amount of the future payments we could receive at the end of each period starting at period 1 through period n? Another question we might ask is If we have an amount today, call it PV 0, and we want to have a certain periodic payment at the end of each period for a certain number of periods n, what rate of return is required on that amount today? A final variation is If we have an amount today, call it PV 0, and we want to have a certain periodic payment at the end of each period given a certain rate of return, for how many periods can the payment be made? Copyright 2011 by Rocky Spears Enterprises LLC, All Rights Reserved Page 6 of 7
Present Value of an Ordinary Annuity Example In the remainder of this clip we use examples from Lesson TVM-10-030 Present Value of a Single Sum to show that the Present Value of an Ordinary Annuity is the sum of the single sum present value factors for the annuity term. The sample problems reviewed are shown below. Copyright 2011 by Rocky Spears Enterprises LLC, All Rights Reserved Page 7 of 7