FINA 3000 (POPE): Exam 2

Risk

the probability that actual future returns will deviate from expected returns; represents the variability of returns, so ___ implies a chance for some unfavorable event to occur

With a finance perspective, risk could then be any of the following examples:

sales, labor cost, material cost, inventory, exchange rates; impacts net income and dividends

Historical Risk and Return

what has our investment done historically... we know what the prices and dividends were

Average Return

(performance) average % return on investment over a sample time period

Variance

(votality) How far do returns fall from the mean or average

The greater the variance,

then the greater the volatility or risk of the investment

Return

the interest or % that we earn over a time period (typically a year or month)

Average of Return

the total % gain or loss divided by the number of returns

Holding Period Return (HP)

compounded return over life of investment

Random Variable

is some measurement that can have a number of possible future outcomes (it varies)

Example: Business {Sales, expenses , etc.} ; returns are random variables

Probability Distribution

is a function that assigns probabilities to the various possible outcomes that a random variable can have

there are two forms: discrete and continuous

For either the continuous or discrete probability function, the probabilities must add to 1

Discrete Probability Distribution

the outcomes can only take on a finite number of values

Continuous Probability Distribution

the outcomes can take on infinitely many values over a continuous range of values

Expected Value

the measure of central tendency of the distribution (the average value); (similar to average)

Variance Expected Value

measures the spread of the distribution or the variation in possible outcomes about the expected value

The normal distribution

is often used with financial variables such as returns or cash flows. The ____ is symmetric around a mean. _______ calculates a z-score or z-stat that measures how many standard deviations a specific value falls from the mean.

The normal curve

creates confidence intervals for where a random observation will fall. Standard deviation drives the _____ distribution.

Confidence Interval

chance that our outcome falls in a specific range

68% confidence interval = E(r) +/- std dev.

95% confidence interval = E(r) =/- 2 x std dev.

The return on a stock comes from two sources:

the gain in price (capital gain) and any dividends paid by the firm to the investor

The standard deviation is the variation in returns. It is also known as...

the stand-alone risk. ____ simply implies the risk associated with only investing in that stock

Std. Dev. = volatility = stand-alone risk

How can we compare two stocks?

It depends on the expected returns. If the two stocks have the same expected return, then we can look at the standard deviation and make a decision.

For most of us, we are risk

...averse. Standard deviation percentage higher same return for less risk

If the two stocks have different expected returns, we can use...

the coefficient of variation to determine which stock offers the most return per unit of risk

Coefficient of variation = std. dev./ E(r)

A portfolio...

is a collection of two or more assets. Allows you to lower your overall risk. "Don't put all your eggs in one basket"

A typical stock will have an expected return of _____ and a stand-alone risk of ___.

E(r) ; Std. Dev.

The correlation between two variables...

is a measure that indicates how much the two variables move or vary together

That is, both variables may vary and have outcomes different than their means, but when variable A has an outcome above its mean, will variable B tend to also have an outcome above its mean ... or below?

Correlation falls between...

-1 and 1

Positive Correlation

0< correlation (P) =<1

returns tend to move together

Negative Correlation

-1 =< correlation < 0

returns tend to be opposites

Zero Correlation

Correlation = no relationship

What does correlation capture?

It really identifies that stand-alone risk for a firm can be divided into components: market-wide risk and firm-specific risk

Market Wide Risk (Macroeconomic Risk)

There are economic events that have broad implications and cause all stocks to move up or down together.

Events such as economic recessions or booms, interest rate changes, taxes, political development, or oil prices will generally impact all firms and thus stock prices similarly

This is market risk also known as...

non-diversifiable risk. "A rising tide raises all boats"

these events tend to affect all stock returns in same Direction, BUT NOT THE SAME MAGNITUDE

Firm Specific Risk

systematic risk; non-diversifiable risk; there are economic and business events that impact only one or a few firms at a time

events unique to firm

product release, expansion, merger lawsuit, competition, CEO change

HIGH non diversifiable risk

HIGH return

The Market Portfolio...

is a portfolio that contains all assets in existence. Each asset is held in the same proportion as its value is to the total value in the economy

Risk of the market portfolio:

the stand-alone risk of the market portfolio is entirely nondiversifiable risk. It is entirely relevant risk

Investors have some _____ to hold the market portfolio. Using this return, we can determine the market risk premium.

expected return, E(r)

Market risk premium

the excess return required for the investor to buy the market portfolio

Market portfolio

reference point: risk of average investment; a benchmark that I will compare it to specific investment

A Stock's Relevant Risk

a stock's relevant or market risk equals its stand-alone times the correlation coefficient that exists between the stock's returns and the market portfolio

P(i,m)

correlation b/w returns on stock and the market portfolio

what % of time do stock "i" returns more with overall economy

% of a stock's volatility that can't be Diversified

A stock's Beta

we use beta to compare our stock vs. average investment

Beta

is a risk index. It is a ratio of a stock's relevant risk divided by the relevant risk of the market portfolio

=relevant risk of stock/risk of market portfolio

=Non-diversifiable risk of stock/risk of average investment

regression coefficient

how do market portfolio returns (x) explain the returns on my stocks (y)

slope: how does the market explain out stock

KEY POINT: Beta predicts...

the EXPECTED relationship between the market return and the return on the individual stock

Beta=1.50

riskier than average investment; if market is up 1%, stock is up by 1.5%; more volatile

Beta=0.75

safer than the average investment; if market is up by 1%, stock up 0.75%; smaller Beta smaller return

Beta=1.00

same risk as average investment; moves the same as market on average

The CAPM Formula

this relates a stock's market risk to its required return

r(i)

required return to invest today (based on risk)

r(f)

risk free return (guaranteed return; std. dev. = 0, Beta =0)

Beta

risk index (scales my required return); "multiplier"

Depends on BOTH correlation and std. dev.

E(rm)

expected return on market portfolio (average investment)

E(rm)-r(f)

market portfolio risk PREMIUM

Bonus return for average investment

How do we apply the CAPM formula?

r(f) = return or YTM on U.S. government debt (zero risk); 90 T-bill

E(rm)=return on market index (S&P 500 index return: 500 largest firms in our economy; fully diversified)

What weaknesses do you see in its calculations?

Beta= regression coefficient

x: returns on S&P 500

y: returns on individual stock

Historical spread b/w market returns and debt

Problem: using the past to predict the future

Security Market Line

graphical representation of CAPM

plot the required return as a function of Beta

Stock Valuation (One period model)

the investor plans to purchase a common stock and hold it for one period

P0

selling price today per share

P1

selling price per share in one year

D1

Dividend paid in exactly one year

r

Return on investment

Finite Holding Periods: Multiple Periods

investors will seek to estimate all the cash flows that the stock will generate

Once an investor has estimated all the cash flows, they can then discount or "capitalize" all the flows to arrive at their personal estimation of the present value of the stock OR their INTRINSIC VALUE for the stock

Weaknesses of Finite Model

1) Assume a future selling price **

2) Predicting future dividends is a challenge

Fundamental Analysis

the whole process of finding a stock's price. One has to examine ____ information on the firm's operations and management to make accurate estimations of the firm's earning and ultimately its dividends, future price, and r.

Infinite Holding Periods

stock is not sold in the future; assume that the stock is to be valued as a perpetual stream of dividends... no future selling price is to be considered in the pricing formula

Why is this reasonable?

Po=stock price=PV of all future dividends

and corporations have unlimited life

so the current price of a stock really just capitalizes all future dividend payments

How can we solve this equation?

We need to relate the dividends

Simpler solution is to assume that dividends grow at a constant annual rate

Gordon-Growth Model

Can we make the Infinite Model more realistic?

Pro: no assumed selling price

Cons: assuming constant growth forever, price is very sensitive to "g"

There are three basic types of stock market transactions:

1) Primary

2) Secondary

3) IPO: Initial Public Offering

Primary stock market transactions

when an existing public company issues new share for a project

Secondary stock market transactions

when investors trade shares of an existing public firms

IPO: Initial Public Offering

higher success in a Bull Market (everything sells for higher prices) ; market high, the amount of of IPO's increase

Two Phase Growth Model

Non-constant growth; while researching a firm, you may be able to arrive at a decent estimates of dividends for a few years in the future. After a certain point, your estimates may become quite uncertain. For this uncertain period, you may want to assume a constant growth rate in dividends

What are a few basic events that can affect a stock's price and how does this relate to our basic models?

1)Increase in Net Income for the firm

-income exceeds expectations (currently banks)

-↑income, ↑ dividends, ↑ stock price

2)Increase in Sales

-sales exceed expectations

↑ sales, ↑ N/I, ↑ Dividends, ↑stock price

3) Risk associated with a stock increases

-↑risk, ↑return, ↓stock price

-Ex: Verizon and Dunkin Donuts (wheat)

Stock Market Equilibrium

Required Return=CAPM=r

-Based on Risk

Expected Return=Actual Return

-Based on Price

Capital Budgeting

is the process of planning for purchases of assets whose returns are expected to continue beyond 1 year. Firms undertake ___capital budgeting decisions for the purchase of machinery, plant construction or expansion, new product development, merger decisions, and many other projects

The purpose of capital budgeting

is to plot a course of action for the firm. The firm should only take on projects that expand shareholder value

Invest in projects that meet or exceed my investor's required return.

We got multiple investors: debt investors, shareholder - discount rate of capital

The key component to capital budgeting

is to estimate the project cash flows associated with a project

Debt Investors (D) + Shareholders (r(E)) = Discount rate cost of capital

NPV

-Net present Value

-Dollars created today for our shareholders

-extra value created after we pay investors their required return

-values a project in today's dollars

Decision Rule (NPV)

accept if NPV is greater than 0

reject is NPV is less than 0 (doesn't give required return)

NPV greater than 0

-Gave investors their required return plus extra for shareholders

-Investing in positive NPV projects should cause an ↑ in share price

-+NPV = we created value for our shareholders

↑ risk, ↓NPV

What is we are uncertain about our cost of capital?

NPV profile

NPV Profile

x-y graph or NPV(y) vs r(x); shows what is the largest r before project is a bad investment

NPV=0 maximum cost of capital

0 if r less than x%, accept project

0 is r greater x%, reject Project

x% = IRR

Internal Rate of Return (IRR)

the internal rate of return sets the NPV of a project equal to zero. While NPV give you a dollar measure of a project, the ___ give your a percentage return.

Mathematically,

-IRR is 9%

-IRR is rate that sets NPV=o

-Breakeven %

-Profit rate: IRR is return earned on each $ invested

Decision Rule (IRR)

accept if r is less than IRR, r is financing, IRR=profitable

reject is r is greater than IRR

NPV(Pros/Cons)

Pros:

-Direct measure of shareholder wealth

-use cost of capital

Cons:

-Difficult to explain

-Need accurate measure for r

IRR (Pros/Cons)

Pros:

-Easy to explain

Cons:

-Doesn't use cost of capital

-Assume a cash flows are reinvested at IRR rate (unrealistic)

There are three basic types of projects

1) Independent

2) Mutually exclusive

3) Contingent

Independent Projects

investing in one opportunity doesn't prevent me from investing in another

Mutually Exclusive Projects

investing in one project prevents me from investing in another (take best project)

Ex: choosing the best choice for land

Contingent Projects

if you invest in one project, you have to invest in another (all or none)

Project Selection Rules for NPV and IRR

One Project

-NPV: invest is NPV is greater than 0

-IRR: invest if r is less than IRR

Comparing One Time Projects

-Project A + B

Independent Projects: Project A and Project B

-take all good projects

-NPV: take projects with highest NPV (if NPV is greater than 0)

-IRR: take project with largest IRR (r is less than IRR)

Can IRR and NPV lead you to a different project choice when projects are mutually exclusive?

B/c they use different interest rates

r ≠IRR

Reasons for the NPV and IRR Rule to Differ

1) Scale: size of cash flows

-Always defer to NPV

2) Timing of Cash Flows - when you get the cash impacts your project decision

3) Multiple IRR - for every negative cash flow there is one IRR

Contingent Projects

-all or nothing

-NPV: Take all if combined NPV greater than 0

-IRR: Take all if combined IRR are greater than r

each and every profit doesn't have to be good as long as combined yes

Payback Method

-Time

-How long to recover initial investment

-liquidity measure

-more important to small business owners

Two ways to calculate:

1) Repeated project cash flows (annuity)

=initial cost/annual cash flow

2) uneven cash flows

(table with cash flow and N/I)

Major weaknesses of this approach

1) does not use time value of money

2) No set rule on good payback

3) Ignores the time after payback

Secondary Rule

Profitability Index

this rule allows projects to be ranked by efficiency

we use this rules when we have a budget or resource constraint

PI=NPV/Amt. of Resource Used

rank projects from most efficient to least efficient

Modified Internal Rate of Return or MIRR

this rule addresses weaknesses in IRR rule

-IRR: assumes all cash flows are re-invested at IRR%

ALL CASH FLOWS ARE REINVESTED AT THE COST OF CAPITAL