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## PowerPoint Slideshow about 'Chapter 2 The Two Key Concepts in Finance' - Mia_John

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It’s what we learn after we think we know it all that counts.

- Kin Hubbard

Outline

- Introduction
- Time value of money
- Safe dollars and risky dollars
- Relationship between risk and return

Introduction

- The occasional reading of basic material in your chosen field is an excellent philosophical exercise
- Do not be tempted to include that you “know it all”
- E.g., what is the present value of a growing perpetuity that begins payments in five years

Time Value of Money

- Introduction
- Present and future values
- Present and future value factors
- Compounding
- Growing income streams

Introduction

- Time has a value
- If we owe, we would prefer to pay money later
- If we are owed, we would prefer to receive money sooner
- The longer the term of a single-payment loan, the higher the amount the borrower must repay

Present and Future Values

- Basic time value of money relationships:

Present and Future Values (cont’d)

- A present value is the discounted value of one or more future cash flows
- A future value is the compounded value of a present value
- The discount factor is the present value of a dollar invested in the future
- The compounding factor is the future value of a dollar invested today

Present and Future Values (cont’d)

- Why is a dollar today worth more than a dollar tomorrow?
- The discount factor:
- Decreases as time increases
- The farther away a cash flow is, the more we discount it
- Decreases as interest rates increase
- When interest rates are high, a dollar today is worth much more than that same dollar will be in the future

Present and Future Values (cont’d)

- Situations:
- Know the future value and the discount factor
- Like solving for the theoretical price of a bond
- Know the future value and present value
- Like finding the yield to maturity on a bond
- Know the present value and the discount rate
- Like solving for an account balance in the future

Present and Future Value Factors

- Single sum factors
- How we get present and future value tables
- Ordinary annuities and annuities due

Single Sum Factors

- Present value interest factor and future value interest factor:

Single Sum Factors (cont’d)

Example

You just invested $2,000 in a three-year bank certificate of deposit (CD) with a 9 percent interest rate.

How much will you receive at maturity?

How We Get Present and Future Value Tables

- Standard time value of money tables present factors for:
- Present value of a single sum
- Present value of an annuity
- Future value of a single sum
- Future value of an annuity

How We Get Present and Future Value Tables (cont’d)

- Relationships:
- You can use the present value of a single sum to obtain:
- The present value of an annuity factor (a running total of the single sum factors)
- The future value of a single sum factor (the inverse of the present value of a single sum factor)

Ordinary Annuities and Annuities Due

- An annuity is a series of payments at equal time intervals
- An ordinary annuity assumes the first payment occurs at the end of the first year
- An annuity due assumes the first payment occurs at the beginning of the first year

Ordinary Annuities and Annuities Due (cont’d)

Example

You have just won the lottery! You will receive $1 million in ten installments of $100,000 each. You think you can invest the $1 million at an 8 percent interest rate.

What is the present value of the $1 million if the first $100,000 payment occurs one year from today? What is the present value if the first payment occurs today?

Ordinary Annuities and Annuities Due (cont’d)

Example (cont’d)

Solution: These questions treat the cash flows as an ordinary annuity and an annuity due, respectively:

Compounding

- Definition
- Discrete versus continuous intervals
- Nominal versus effective yields

Definition

- Compounding refers to the frequency with which interest is computed and added to the principal balance
- The more frequent the compounding, the higher the interest earned

Discrete Versus Continuous Intervals

- Discrete compounding means we can count the number of compounding periods per year
- E.g., once a year, twice a year, quarterly, monthly, or daily
- Continuous compounding results when there is an infinite number of compounding periods

Discrete Versus Continuous Intervals (cont’d)

- Mathematical adjustment for discrete compounding:

Discrete Versus Continuous Intervals (cont’d)

- Mathematical equation for continuous compounding:

Discrete Versus Continuous Intervals (cont’d)

Example

Your bank pays you 3 percent per year on your savings account. You just deposited $100.00 in your savings account.

What is the future value of the $100.00 in one year if interest is compounded quarterly? If interest is compounded continuously?

Discrete Versus Continuous Intervals (cont’d)

Example (cont’d)

Solution (cont’d): For continuous compounding:

Nominal Versus Effective Yields

- The stated rate of interest is the simple rate or nominal rate
- 3.00% in the example
- The interest rate that relates present and future values is the effective rate
- $3.03/$100 = 3.03% for quarterly compounding
- $3.05/$100 = 3.05% for continuous compounding

Growing Income Streams

- Definition
- Growing annuity
- Growing perpetuity

Definition

- A growing stream is one in which each successive cash flow is larger than the previous one
- A common problem is one in which the cash flows grow by some fixed percentage

Growing Annuity

- A growing annuity is an annuity in which the cash flows grow at a constant rate g:

Growing Perpetuity

- A growing perpetuity is an annuity where the cash flows continue indefinitely:

Safe Dollars and Risky Dollars

- Introduction
- Choosing among risky alternatives
- Defining risk

Introduction

- A safe dollar is worth more than a risky dollar
- Investing in the stock market is exchanging bird-in-the-hand safe dollars for a chance at a higher number of dollars in the future

Introduction (cont’d)

- Most investors are risk averse
- People will take a risk only if they expect to be adequately rewarded for taking it
- People have different degrees of risk aversion
- Some people are more willing to take a chance than others

Choosing Among Risky Alternatives

Example

You have won the right to spin a lottery wheel one time. The wheel contains numbers 1 through 100, and a pointer selects one number when the wheel stops. The payoff alternatives are on the next slide.

Which alternative would you choose?

Choosing Among Risky Alternatives (cont’d)

Example (cont’d)

Solution:

- Most people would think Choice A is “safe.”
- Choice B has an opportunity cost of $90 relative to Choice A.
- People who get utility from playing a game pick Choice C.
- People who cannot tolerate the chance of any loss would avoid Choice D.

Choosing Among Risky Alternatives (cont’d)

Example (cont’d)

Solution (cont’d):

- Choice A is like buying shares of a utility stock.
- Choice B is like purchasing a stock option.
- Choice C is like a convertible bond.
- Choice D is like writing out-of-the-money call options.

Defining Risk

- Risk versus uncertainty
- Dispersion and chance of loss
- Types of risk

Risk Versus Uncertainty

- Uncertainty involves a doubtful outcome
- What you will get for your birthday
- If a particular horse will win at the track
- Risk involves the chance of loss
- If a particular horse will win at the track if you made a bet

Dispersion and Chance of Loss

- There are two material factors we use in judging risk:
- The average outcome
- The scattering of the other possibilities around the average

Dispersion and Chance of Loss (cont’d)

- Investments A and B have the same arithmetic mean
- Investment B is riskier than Investment A

Types of Risk

- Total risk refers to the overall variability of the returns of financial assets
- Undiversifiable risk is risk that must be borne by virtue of being in the market
- Arises from systematic factors that affect all securities of a particular type

Types of Risk (cont’d)

- Diversifiable risk can be removed by proper portfolio diversification
- The ups and down of individual securities due to company-specific events will cancel each other out
- The only return variability that remains will be due to economic events affecting all stocks

Relationship Between Risk and Return

- Direct relationship
- Concept of utility
- Diminishing marginal utility of money
- St. Petersburg paradox
- Fair bets
- The consumption decision
- Other considerations

Direct Relationship

- The more risk someone bears, the higher the expected return
- The appropriate discount rate depends on the risk level of the investment
- The risk-less rate of interest can be earned without bearing any risk

Direct Relationship (cont’d)

- The expected return is the weighted average of all possible returns
- The weights reflect the relative likelihood of each possible return
- The risk is undiversifiable risk
- A person is not rewarded for bearing risk that could have been diversified away

Concept of Utility

- Utility measures the satisfaction people get out of something
- Different individuals get different amounts of utility from the same source
- Casino gambling
- Pizza parties
- CDs
- Etc.

Diminishing Marginal Utility of Money

- Rational people prefer more money to less
- Money provides utility
- Diminishing marginal utility of money
- The relationship between more money and added utility is not linear
- “I hate to lose more than I like to win”

St. Petersburg Paradox

- Assume the following game:
- A coin is flipped until a head appears
- The payoff is based on the number of tails observed (n) before the first head
- The payoff is calculated as $2n
- What is the expected payoff?

St. Petersburg Paradox (cont’d)

- In the limit, the expected payoff is infinite
- How much would you be willing to play the game?
- Most people would only pay a couple of dollars
- The marginal utility for each additional $0.50 declines

Fair Bets

- A fair bet is a lottery in which the expected payoff is equal to the cost of playing
- E.g., matching quarters
- E.g., matching serial numbers on $100 bills
- Most people will not take a fair bet unless the dollar amount involved is small
- Utility lost is greater than utility gained

The Consumption Decision

- The consumption decision is the choice to save or to borrow
- If interest rates are high, we are inclined to save
- E.g., open a new savings account
- If interest rates are low, borrowing looks attractive
- E.g., a higher home mortgage

The Consumption Decision (cont’d)

- The equilibrium interest rate causes savers to deposit a sufficient amount of money to satisfy the borrowing needs of the economy

Other Considerations

- Psychic return
- Price risk versus convenience risk

Psychic Return

- Psychic return comes from an individual disposition about something
- People get utility from more expensive things, even if the quality is not higher than cheaper alternatives
- E.g., Rolex watches, designer jeans

Price Risk Versus Convenience Risk

- Price risk refers to the possibility of adverse changes in the value of an investment due to:
- A change in market conditions
- A change in the financial situation
- A change in public attitude
- E.g., rising interest rates and stock prices, a change in the price of gold and the value of the dollar

Price Risk Versus Convenience Risk (cont’d)

- Convenience risk refers to a loss of managerial time rather than a loss of dollars
- E.g., a bond’s call provision
- Allows the issuer to call in the debt early, meaning the investor has to look for other investments

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