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# Present Value: Calculations and Interpretation PowerPoint PPT Presentation

Present Value: Calculations and Interpretation. Classes 3 & 4: March 5 and 7 (LA) and March 1 and 6 (OCC). From last classes . . . . What should be the goal of financial managers? What do we need to know to pursue goal? How can we assess progress towards that goal?

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Present Value: Calculations and Interpretation

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## Present Value: Calculations and Interpretation

Classes 3 & 4:

March 5 and 7 (LA) and

March 1 and 6 (OCC)

### From last classes . . .

• What should be the goal of financial managers?

• What do we need to know to pursue goal?

• How can we assess progress towards that goal?

• What is a firm’s market value? Market cap? How do we compute them?

### Overview: Classes 3 to 6

• 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

• To be addressed later: projecting cash flows, choosing a discount rate

(Class 3 & 4)

(Class 5 & 6)

### Determinants of Value

• Cash, Time, Riskdetermine value

• Present value analysis deals with the effect of time or timing on value

• Cash flow estimation is the subject of the next part of the course (classes 5 to 8)

• Risk is incorporated in the discount ratethat we discuss in Part 3 of the course

• In discussing present value analysis now, we assume that cash flows and discount rates are given

### Emphasis on Present Values

• 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

• We will not emphasize these issues, we concentrate on basic present value calculations

### Present Value of Cash Flows

• Calculation of present values is key technique to assign values

• Present value calculations are applications or simplications of two basic formulas: PV of single cash flow = PV of multiple cash flows =

### Examples / Applications

• U. S. Treasury strip prices are examples of market determined discount factors for default-risk free cash flows

• The structure of present value tables like those in the text (A.1 and A.2) are very straightforward

• Time in discounting in in terms of periods, usually one year, but often shorter intervals

• Compounding interval will affect present or future values

### Present Value Calculations

• Present values can be calculated using present value tables and paper, calculators and paper, routines programmed into calculators, and spreadsheets

• All correct methods produce the same answers

• 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

### Example of Three Approaches

• Present value of \$1000 received at the end of each year for five years discounted at 10%

• 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)

### Characteristics of Present Value

• 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

• Changes in timing or patterns of growth must always be calculated, relying on intuition is dangerous

• 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

### Example of Dangers

• 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.

• Change times to \$1,000 for ten years at 10%, PV becomes \$6,146, not double.

• 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.

### Meaning of Present Value and Equality of Present Values

• Present Value of \$1,000 for five years at 10 percent (Table A.2)

• \$3,790.80 is equivalent to \$1,000 at the end of every year for five years at 10 percent

• Future value of \$3,790.80 at end of five years is \$3,790.80x(1.10)5=\$6,105.12

• This is also future value of \$1,000 for five years at 10 percent (see Table A.4)

### Summary of PV/FV Examples

• Present value is the amount that can replicatecash flows if discount rate is the future interest rate

• Maximizing present values also maximizes future values if interest rates do not change (in this case, they are equivalent)

• 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

### Net Present Value

• Net present value (NPV) is the difference between the present value of the future cash flows and the cost of acquiring the cash flows

• In most examples, costs are immediate and are not discounted, while cash flows are in the future and must be discounted

• More generally, costs and benefits may both be discounted if some costs occur in the future

• 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

### Positive Net Present Values

• A positive net present value means that future cash flows represent earnings higher than the discount rate

• Net present value represents the excess returns (returns above the discount or opportunity rate) represented by the future cash flows

• Net present values represent value added relative to the opportunity rate

### Seek Simplifying Patterns in Cash Flows for Short-cuts

• Can always evaluate individual annual cash flows but this is cumbersome

• Simplest pattern is constant cash flow each year --

• First formula to memorize is

Cash flow

time

### Useful Present Value Formulas

• Perpetuity:

• Growing Perpetuity:

• Annuity:

• Growing Annuity:

### Simple Patterns in Cash Flows

• Perpetuity = Preferred dividend

• Growing perpetuity = Approximate cash flows from new products or stock earnings

• Annuity = Retirement fund or car or mortgage loan payments

• Growing annuity = Approximate cash flows from investment with limited life or lifetime earnings

### Graphical Representations

• Perpetuity:

• Growing Perpetuity:

Cash Flow

0

Time

Cash Flow

0

Time

### Graphical Representations

• Annuity:

• Growing Annuity:

Cash Flow

0

T

Time

Cash Flow

0

T

Time

### Sources of Present Values

• Present value of \$1 perpetuity at 20% is \$5

• Present value of \$1 annuity for five years at 20% is \$2.99

• Therefore, present values of \$1 from years six to infinity at 20% is \$5 minus \$2.99 = \$2.01 (less than half of \$5)

• Present value of perpetuity growing at 10% starting at \$1 and at 20% is \$10

• Growing over infinite life is valued at \$10 minus \$5 or \$5

E

D

C

Cash

Flow

A

B

T

time

0

### Graphical representation of the four important formulas

• Areas in graph represent parts of future cash flows - Perpetuity = A+B

• Growing Perpetuity = A+B+C+D+E

• Annuity = A

• Growing Annuity = A+C

• You can solve for value added by a piece of cash flows, for example cash flows after T, by subtracting A from A+B

PV = \$ 10.00

E = \$ 3.23

D = 1.23

C = \$ .54

\$ 1

A =\$ 2.99

B = \$ 2.01

0

5

### Present Value and Net PV (NPV)

• Present values are calculations assuming expected cash flows and required discount rates

• Each may differ for different analysts

• Knowledge and skill about future cash flows

• Assessment of risk and alternative investments

• Net present value = Present value - cost

• Contrast present value with intrinsic value, market value, under-valued and over-valued

### Use of Present Value Formulas

• Familiarity with PV formulas important

• For example, what is future value of constant annual cash flow? Using annuityobtaining (see. p. 840)

• Relations between present value formulas are really simple

### Using PV Formulas to Find Rates

• You can solve for r given PV, in simplest case of perpetuity r = C / PV

• With a value for g and PV in growth formula, find r also easy and common in stock analysis (we will use later)

• With annuities and other formulas you can also solve for r although the equations are non-linear requiring searches

### Present Value and Wealth

• Wealth = Present value of consumption

• Wealth = Present value of cash income

• DWealth = Change in value of consumption = Change in present value of cash income

• DWealth => Increase in utility from consumption

• DWealth = Net present value

• Net present value > 0 => Wealth increased

### Present Value and MVA/EVA (I)

• Market value added is how much more assets are worth than they cost

• 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

• EVA represents the returns above the opportunity rate and is a measure of management’s superior investment strategy

### Present Value and MVA/EVA (II)

• Market values represent present value of expected future cash flows

• If market value is above acquisition cost (MVA), management is expect to produce cash flows are above opportunity rate levels

• Excess returns (EVA) can be from existing investments and future growth opportunities or growth options

### Present Value Summary

• Present values represent cash amounts that can reproduce a pattern of cash flows in the future given the discount rate

• Two equal present values can represent different patterns of future cash flows

• Future values and present values are equivalent measures of value given the discount rate

• Net present values are measures of the increase in wealth representing increased utility from increases in present and future consumption

### Present Value Analysis: Review

• Objectives

• Vocabulary

• Problem Assignments

• Relation to syllabus and requirements

### Basic Steps to Valuation in Finance

• Estimate cash flows (CASH, TIME)

• Easy or hard depending on asset

• Look for patterns in cash flows

• Choose a discount rate (TIME, RISK)

• Opportunity cost

• Calculate present value and net present value

### Valuation in Finance

• Applies to all investment opportunities, including

• investments in fixed plant and equipment

• selling a line of business (spin-off)

• values of bonds and stocks

• real estate investments

• Used by financial managers, stock and bond analysts, real estate investors

### For Next Classes

• Read Chapter 5, 14 and 20

• Do problems as assigned

• Download or call or write for annual report, 10K, and proxy statement, and any other disclosures, for the group project firm

• Bring Value Line Investment Survey and Standard and Poor’s reports for the company to class

• Look for analysts’ reports and press coverage of the group firm