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Introduction To Business Finance

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

-Benjamin Franklin

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Outline – Mauneel Desai Introduction Time value of money Safe dollars and risky dollars Relationship between risk and return

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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”

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Time Value of Money Introduction Present and future values Present and future value factors Compounding Growing income streams

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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

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Present and Future Values Basic time value of money relationships:

1/(1 )

(1 )

t

t

PV FV DFFV PV CF

where PV = present value; FV = future value;

DF = discount factor = R

CF = compounding factor = R R = interest rate per perio

d; and

t = time in periods

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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

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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

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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

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Present and Future Value Factors

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

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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

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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)

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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

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

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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

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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

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Dispersion and Chance of Loss (cont’d)

Investment A Investment B

Time

Investment value

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Dispersion and Chance of Loss (cont’d)

Investments A and B have the same arithmetic mean

Investment B is riskier than Investment A

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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

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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

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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

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Direct Relationship (cont’d)

Risk

Expected return

Rf

0

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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

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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

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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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Thank You – Mauneel Desai