J. K. Dietrich - GSBA 548 – MBA.PM Spring 2007 Present Value: Calculations and Interpretation Classes 3 & 4: March 5 and 7 (LA) and March 1 and 6 (OCC)

J. K. Dietrich - GSBA 548 – MBA.PM Spring 2007 From last classes... u What should be the goal of financial managers? u What do we need to know to pursue goal? u How can we assess progress towards that goal? u What is a firm’s market value? Market cap? How do we compute them?

J. K. Dietrich - GSBA 548 – MBA.PM Spring 2007 Overview: Classes 3 to 6 u Discounted present value: basic tool given projections of cash flows and discount rate –Present value and wealth creation –One and multi-period cash flows –Patterns in cash flows = formulas –Applications to valuation: bonds –Application to valuation: stocks u To be addressed later: projecting cash flows, choosing a discount rate (Class 3 & 4) (Class 5 & 6)

J. K. Dietrich - GSBA 548 – MBA.PM Spring 2007 Determinants of Value u Cash, Time, Risk determine value u Present value analysis deals with the effect of time or timing on value u Cash flow estimation is the subject of the next part of the course (classes 5 to 8) u Risk is incorporated in the discount rate that we discuss in Part 3 of the course u In discussing present value analysis now, we assume that cash flows and discount rates are given

J. K. Dietrich - GSBA 548 – MBA.PM Spring 2007 Emphasis on Present Values u Chapter 4 raises a number of topics relevant to the calculation of present values: –Simple versus compound interest –Compounding interval –Continuous compounding –Future values –Calculation of number of periods of cash flows to achieve a given present or future value u We will not emphasize these issues, we concentrate on basic present value calculations

J. K. Dietrich - GSBA 548 – MBA.PM Spring 2007 Present Value of Cash Flows u Calculation of present values is key technique to assign values u Present value calculations are applications or simplications of two basic formulas: PV of single cash flow = PV of multiple cash flows =

J. K. Dietrich - GSBA 548 – MBA.PM Spring 2007 Calculation of Present Values

J. K. Dietrich - GSBA 548 – MBA.PM Spring 2007 Examples / Applications u U. S. Treasury strip prices are examples of market determined discount factors for default-risk free cash flows u The structure of present value tables like those in the text (A.1 and A.2) are very straightforward u Time in discounting in in terms of periods, usually one year, but often shorter intervals u Compounding interval will affect present or future values

J. K. Dietrich - GSBA 548 – MBA.PM Spring 2007 Present Value Calculations u Present values can be calculated using present value tables and paper, calculators and paper, routines programmed into calculators, and spreadsheets u All correct methods produce the same answers u There is often more than one way to calculate the answers using formulas or individual cash flows but, if correct, they are all mathematically equivalent

J. K. Dietrich - GSBA 548 – MBA.PM Spring 2007 Example of Three Approaches u Present value of $1000 received at the end of each year for five years discounted at 10% u Three (at least) ways produce same answer: (Using Appendix Table A.1) (Using Appendix Table A.2) (Using Perpetuity formula and Appendix Table A.1 discussed later)

J. K. Dietrich - GSBA 548 – MBA.PM Spring 2007 Characteristics of Present Value u Present value calculations are non-linear in the discount rate and growth rates, means changes in present values are not proportional to changes in the discount rate u Changes in timing or patterns of growth must always be calculated, relying on intuition is dangerous u Terminology may be confusing: discount rate, discount factor, interest rate, cost of capital, opportunity cost, and yield all can mean the same thing in a calculation

J. K. Dietrich - GSBA 548 – MBA.PM Spring 2007 Example of Dangers u Change discount rate in previous example to 20% from 10%, PV becomes $2,991, reduced to 78.9% of $3,791 at 10%, not half. u Change times to $1,000 for ten years at 10%, PV becomes $6,146, not double. u Delay first cash flow by one year, PV reduced by about 10%, or if by three years, PV reduced by about 25%, difference between delay of one or three years is not three times greater.

J. K. Dietrich - GSBA 548 – MBA.PM Spring 2007 Meaning of Present Value and Equality of Present Values u Present Value of $1,000 for five years at 10 percent (Table A.2) u $3, is equivalent to $1,000 at the end of every year for five years at 10 percent u Future value of $3, at end of five years is $3,790.80x(1.10) 5 =$6, u This is also future value of $1,000 for five years at 10 percent (see Table A.4)

J. K. Dietrich - GSBA 548 – MBA.PM Spring 2007 Equivalence of Present Value to Annual Cash Flows

J. K. Dietrich - GSBA 548 – MBA.PM Spring 2007 Example of Future Value

J. K. Dietrich - GSBA 548 – MBA.PM Spring 2007 Summary of PV/FV Examples u Present value is the amount that can replicate cash flows if discount rate is the future interest rate u Maximizing present values also maximizes future values if interest rates do not change (in this case, they are equivalent) u Present values and future values of different patterns of cash flows will differ from calculations using constant discount rate if interest-rates vary through time

J. K. Dietrich - GSBA 548 – MBA.PM Spring 2007 Net Present Value u Net present value (NPV) is the difference between the present value of the future cash flows and the cost of acquiring the cash flows u In most examples, costs are immediate and are not discounted, while cash flows are in the future and must be discounted u More generally, costs and benefits may both be discounted if some costs occur in the future u Net present value is a measure of how much more something is worth than it costs, or a wealth increase, as we discuss and illustrate later

J. K. Dietrich - GSBA 548 – MBA.PM Spring 2007 Positive Net Present Values u A positive net present value means that future cash flows represent earnings higher than the discount rate u Net present value represents the excess returns (returns above the discount or opportunity rate) represented by the future cash flows u Net present values represent value added relative to the opportunity rate

J. K. Dietrich - GSBA 548 – MBA.PM Spring 2007 Seek Simplifying Patterns in Cash Flows for Short-cuts u Can always evaluate individual annual cash flows but this is cumbersome u Simplest pattern is constant cash flow each year -- u First formula to memorize is time Cash flow

J. K. Dietrich - GSBA 548 – MBA.PM Spring 2007 Useful Present Value Formulas u Perpetuity: u Growing Perpetuity: u Annuity: u Growing Annuity:

J. K. Dietrich - GSBA 548 – MBA.PM Spring 2007 Simple Patterns in Cash Flows u Perpetuity = Preferred dividend u Growing perpetuity = Approximate cash flows from new products or stock earnings u Annuity = Retirement fund or car or mortgage loan payments u Growing annuity = Approximate cash flows from investment with limited life or lifetime earnings

J. K. Dietrich - GSBA 548 – MBA.PM Spring 2007 Graphical Representations u Perpetuity: u Growing Perpetuity: Time Cash Flow 0 0 Time Cash Flow

J. K. Dietrich - GSBA 548 – MBA.PM Spring 2007 Graphical Representations u Annuity: u Growing Annuity: 0 0 Cash Flow TimeT Cash Flow Time T

J. K. Dietrich - GSBA 548 – MBA.PM Spring 2007 Sources of Present Values u Present value of $1 perpetuity at 20% is $5 u Present value of $1 annuity for five years at 20% is $2.99 u Therefore, present values of $1 from years six to infinity at 20% is $5 minus $2.99 = $2.01 (less than half of $5) u Present value of perpetuity growing at 10% starting at $1 and at 20% is $10 u Growing over infinite life is valued at $10 minus $5 or $5

J. K. Dietrich - GSBA 548 – MBA.PM Spring 2007 Graphical Presentation of Four Present Value Formulas time 0 AB D C Cash Flow E T

J. K. Dietrich - GSBA 548 – MBA.PM Spring 2007 Graphical representation of the four important formulas u Areas in graph represent parts of future cash flows - Perpetuity = A+B u Growing Perpetuity = A+B+C+D+E u Annuity = A u Growing Annuity = A+C u You can solve for value added by a piece of cash flows, for example cash flows after T, by subtracting A from A+B

J. K. Dietrich - GSBA 548 – MBA.PM Spring 2007 Example: $1 growing at 10% Discounted at 20% 5 0 A =$ 2.99B = $ 2.01 D = 1.23 $ 1 E = $ 3.23 C = $.54 PV = $ 10.00

J. K. Dietrich - GSBA 548 – MBA.PM Spring 2007 Present Value and Net PV (NPV) u Present values are calculations assuming expected cash flows and required discount rates u Each may differ for different analysts –Knowledge and skill about future cash flows –Assessment of risk and alternative investments u Net present value = Present value - cost u Contrast present value with intrinsic value, market value, under-valued and over-valued

J. K. Dietrich - GSBA 548 – MBA.PM Spring 2007 Use of Present Value Formulas u Familiarity with PV formulas important u For example, what is future value of constant annual cash flow? Using annuity obtaining (see. p. 840) u Relations between present value formulas are really simple

J. K. Dietrich - GSBA 548 – MBA.PM Spring 2007 Using PV Formulas to Find Rates u You can solve for r given PV, in simplest case of perpetuity r = C / PV u With a value for g and PV in growth formula, find r also easy and common in stock analysis (we will use later) u With annuities and other formulas you can also solve for r although the equations are non-linear requiring searches

J. K. Dietrich - GSBA 548 – MBA.PM Spring 2007 Present Value and Wealth u Wealth = Present value of consumption u Wealth = Present value of cash income   Wealth = Change in value of consumption = Change in present value of cash income   Wealth => Increase in utility from consumption   Wealth = Net present value u Net present value > 0 => Wealth increased

J. K. Dietrich - GSBA 548 – MBA.PM Spring 2007 Present Value and MVA/EVA (I) u Market value added is how much more assets are worth than they cost u MVA is in part the present value of returns above the opportunity rate on investments thus represents management’s ability to find investments better than alternatives u EVA represents the returns above the opportunity rate and is a measure of management’s superior investment strategy

J. K. Dietrich - GSBA 548 – MBA.PM Spring 2007 Present Value and MVA/EVA (II) u Market values represent present value of expected future cash flows u If market value is above acquisition cost (MVA), management is expect to produce cash flows are above opportunity rate levels u Excess returns (EVA) can be from existing investments and future growth opportunities or growth options

J. K. Dietrich - GSBA 548 – MBA.PM Spring 2007 Present Value Summary u Present values represent cash amounts that can reproduce a pattern of cash flows in the future given the discount rate u Two equal present values can represent different patterns of future cash flows u Future values and present values are equivalent measures of value given the discount rate u Net present values are measures of the increase in wealth representing increased utility from increases in present and future consumption

J. K. Dietrich - GSBA 548 – MBA.PM Spring 2007 Present Value Analysis: Review u Objectives u Vocabulary u Problem Assignments u Relation to syllabus and requirements

J. K. Dietrich - GSBA 548 – MBA.PM Spring 2007 Basic Steps to Valuation in Finance u Estimate cash flows (CASH, TIME) –Easy or hard depending on asset –Look for patterns in cash flows u Choose a discount rate (TIME, RISK) –Risk adjusted –Opportunity cost u Calculate present value and net present value

J. K. Dietrich - GSBA 548 – MBA.PM Spring 2007 Valuation in Finance u Applies to all investment opportunities, including –investments in fixed plant and equipment –starting a new business –selling a line of business (spin-off) –buying an existing business –values of bonds and stocks –real estate investments u Used by financial managers, stock and bond analysts, real estate investors

J. K. Dietrich - GSBA 548 – MBA.PM Spring 2007 For Next Classes u Read Chapter 5, 14 and 20 u Do problems as assigned u Download or call or write for annual report, 10K, and proxy statement, and any other disclosures, for the group project firm u Bring Value Line Investment Survey and Standard and Poor’s reports for the company to class u Look for analysts’ reports and press coverage of the group firm