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8. Stock Valuation. Discrete versus continuous time. While we value the bonds assuming ½, 1 years time difference between coupon payments, in reality the bond is traded every day.

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stock valuation

8

Stock Valuation

discrete versus continuous time
Discrete versus continuous time.
  • While we value the bonds assuming ½, 1 years time difference between coupon payments, in reality the bond is traded every day.
  • Assume a perpetuity that pays an annual coupon C with a required return of R. Show a graph that illustrates how the price of the perpetuity changes over time.
differences between debt and equity
Differences Between Debt and Equity
  • Equity
    • Ownership interest
    • Common stockholders vote for the board of directors and other issues
    • Dividends are not considered a cost of doing business and are not tax deductible
    • Dividends are not a liability of the firm and stockholders have no legal recourse if dividends are not paid
    • An all equity firm can not go bankrupt merely due to debt since it has no debt
  • Debt
    • Not an ownership interest
    • Creditors do not have voting rights
    • Interest is considered a cost of doing business and is tax deductible
    • Creditors have legal recourse if interest or principal payments are missed
    • Excess debt can lead to financial distress and bankruptcy
key concepts and skills
Key Concepts and Skills
  • Understand how stock prices depend on future dividends and dividend growth
  • Be able to compute stock prices using the dividend growth model
  • Understand how corporate directors are elected
  • Understand how stock markets work
  • Understand how stock prices are quoted
cash flows for stockholders
Cash Flows for Stockholders
  • If you buy a share of stock, you can receive cash in two ways
    • The company pays dividends
    • You sell your shares, either to another investor in the market or back to the company
  • As with bonds, the price of the stock is the present value of these expected cash flows
one period example
One-Period Example
  • Suppose you are thinking of purchasing the stock of Moore Oil, Inc. and you expect it to pay a $2 dividend in one year and you believe that you can sell the stock for $14 at that time. If you require a return of 20% on investments of this risk, what is the maximum you would be willing to pay?
    • Compute the PV of the expected cash flows
two period example
Two-Period Example
  • Now what if you decide to hold the stock for two years? In addition to the dividend in one year, you expect a dividend of $2.10 in two years and a stock price of $14.70 at the end of year 2. Now how much would you be willing to pay?
three period example
Three-Period Example
  • Finally, what if you decide to hold the stock for three years? In addition to the dividends at the end of years 1 and 2, you expect to receive a dividend of $2.205 at the end of year 3 and the stock price is expected to be $15.435. Now how much would you be willing to pay?
developing the model
Developing The Model
  • You could continue to push back the year in which you will sell the stock
  • You would find that the price of the stock is really just the present value of all expected future dividends –why?
estimating dividends special cases
Estimating Dividends: Special Cases
  • Constant dividend
    • The firm will pay a constant dividend forever
    • This is like preferred stock
    • The price is computed using the perpetuity formula
  • Constant dividend growth
    • The firm will increase the dividend by a constant percent every period
  • Supernormal growth
    • Dividend growth is not consistent initially, but settles down to constant growth eventually
zero growth
Zero Growth
  • Suppose stock is expected to pay a $0.50 dividend every quarter and the required return is 10% with quarterly compounding. What is the price?
dgm example 1
DGM – Example 1
  • Suppose Big D, Inc. just paid a dividend of $.50. It is expected to increase its dividend by 2% per year. If the market requires a return of 15% on assets of this risk, how much should the stock be selling for?
dgm example 2
DGM – Example 2
  • Suppose TB Pirates, Inc. is expected to pay a $2 dividend in one year. If the dividend is expected to grow at 5% per year and the required return is 20%, what is the price?
example 8 3 gordon growth company i
Example 8.3 Gordon Growth Company - I
  • Gordon Growth Company is expected to pay a dividend of $4 next period and dividends are expected to grow at 6% per year. The required return is 16%.
  • What is the current price?
example 8 3 gordon growth company ii
Example 8.3 – Gordon Growth Company - II
  • What is the price expected to be in year 4?
  • What is the implied return given the change in price during the four year period?
nonconstant growth problem statement
Nonconstant Growth Problem Statement
  • Suppose a firm is expected to increase dividends by 20% in one year and by 15% in two years. After that dividends will increase at a rate of 5% per year indefinitely. If the last dividend was $1 and the required return is 20%, what is the price of the stock?
  • Remember that we have to find the PV of all expected future dividends.
quick quiz part i
Quick Quiz – Part I
  • What is the value of a stock that is expected to pay a constant dividend of $2 per year if the required return is 15%?
  • What if the company starts increasing dividends by 3% per year, beginning with the next dividend? The required return stays at 15%.
finding the required return example
Finding the Required Return - Example
  • Suppose a firm’s stock is selling for $10.50. They just paid a $1 dividend and dividends are expected to grow at 5% per year. What is the required return?
  • What is the dividend yield?
  • What is the capital gains yield?
features of common stock
Features of Common Stock
  • Voting Rights
  • Proxy voting
  • Classes of stock
  • Other Rights
    • Share proportionally in declared dividends
    • Share proportionally in remaining assets during liquidation
    • Preemptive right – first shot at new stock issue to maintain proportional ownership if desired
dividend characteristics
Dividend Characteristics
  • Dividends are not a liability of the firm until a dividend has been declared by the Board
  • Consequently, a firm cannot go bankrupt for not declaring dividends
  • Dividends and Taxes
    • Dividend payments are not considered a business expense; therefore, they are not tax deductible
    • The taxation of dividends received by individuals depends on the holding period and specific country rules.
features of preferred stock
Features of Preferred Stock
  • Dividends
    • Stated dividend that must be paid before dividends can be paid to common stockholders
    • Dividends are not a liability of the firm and preferred dividends can be deferred indefinitely
    • Most preferred dividends are cumulative – any missed preferred dividends have to be paid before common dividends can be paid
  • Preferred stock generally does not carry voting rights
stock market
Stock Market
  • Dealers vs. Brokers
  • New York Stock Exchange (NYSE)
  • NASDAQ
reading stock quotes
Reading Stock Quotes
  • There are a many websites that provide real-time quote information. The most popular are Bloomberg, Google Finance, and Yahoo Finance. What type of information can we gather?
quick quiz part ii
Quick Quiz – Part II
  • You observe a stock price of $18.75. You expect a dividend growth rate of 5% and the most recent dividend was $1.50. What is the required return?
  • What are some of the major characteristics of common stock?
  • What are some of the major characteristics of preferred stock?
comprehensive problem
Comprehensive Problem
  • XYZ stock currently sells for $50 per share. The next expected annual dividend is $2, and the growth rate is 6%. What is the expected rate of return on this stock?
  • What price is expected a year from now?
  • If the required rate of return on this stock were 12%, what would the stock price be, and what would the dividend yield be?
last problem
Last problem
  • Suppose a stock has just paid a $5 per share dividend. The dividend is projected to grow at 10% for the next two years, then 8% for one year, and then 6% indefinitely. The required return is 12%. What is the stock’s value?
a few words on the ipo process
A few words on the IPO process
  • IPO stands for initial public offering.
  • Important players - SEC, Auditors (accounting firms), Underwriters
  • Due-diligence process
  • The “road show” and setting the offering price
  • Google – a unique example.
net present value and other investment criteria

9

Net Present Value and Other Investment Criteria

net present value

-$400,000

0

1

2

Net Present Value
  • Capital Budgeting Decision
    • Suppose you had the opportunity to buy a tbill which would be worth $400,000 one year from today.
      • Interest rates on tbills are a risk free 7%.
    • What would you be willing to pay for this investment?

PV today:

$400,000 / (1.07) = $373,832

net present value1
Net Present Value
  • Capital Budgeting Decision
    • You would be willing to pay $ 373,832 for a risk free $400,000 a year from today.
    • Suppose this were, instead, an opportunity to construct a building, which you could sell in a year for $400,000 (guaranteed).
    • Since this investment has the same risk and cash flows as the tbill, it is also worth the same amount to you:

$373,832

net present value2
Net Present Value
  • Capital Budgeting Decision
    • Now, assume you could buy the land for $50,000 and construct the building for $300,000.
      • Is this a good deal?
    • If you would be willing to pay $ 373,832 for this investment and can acquire it for only $350,000, you have found a very good deal!
    • You are better off by:

$373,832 - $350,000 = $23,832

net present value3
Net Present Value
  • Valuing long lived projects
    • The NPV rule works for projects of any duration:
      • Simply discount the cash flows at the appropriate opportunity cost of capital and then subtract the cost of the initial investment.
    • The critical problems in any NPV problem are to determine:
      • The amount and timing of the cash flows.
      • The appropriate discount rate.
good decision criteria
Good Decision Criteria
  • We need to ask ourselves the following questions when evaluating capital budgeting decision rules
    • Does the decision rule adjust for the time value of money?
    • Does the decision rule adjust for risk?
    • Does the decision rule provide information on whether we are creating value for the firm?
project example information
Project Example Information
  • You are looking at a new project and you have estimated the following cash flows:
    • Year 0: CF = -165,000
    • Year 1: CF = 63,120
    • Year 2: CF = 70,800
    • Year 3: CF = 91,080
  • Your required return for assets of this risk is 12%.
net present value4
Net Present Value
  • The difference between the market value of a project and its cost
  • How much value is created from undertaking an investment?
    • The first step is to estimate the expected future cash flows.
    • The second step is to estimate the required return for projects of this risk level.
    • The third step is to find the present value of the cash flows and subtract the initial investment.
npv decision rule
NPV – Decision Rule
  • If the NPV is positive, accept the project
  • A positive NPV means that the project is expected to add value to the firm and will therefore increase the wealth of the owners.
  • Since our goal is to increase owner wealth, NPV is a direct measure of how well this project will meet our goal.
decision criteria test npv
Decision Criteria Test - NPV
  • Does the NPV rule account for the time value of money?
  • Does the NPV rule account for the risk of the cash flows?
  • Does the NPV rule provide an indication about the increase in value?
  • Should we consider the NPV rule for our primary decision rule?
calculating npvs with a spreadsheet
Calculating NPVs with a Spreadsheet
  • Spreadsheets are an excellent way to compute NPVs, especially when you have to compute the cash flows as well.
  • Using the NPV function
    • The first component is the required return entered as a decimal
    • The second component is the range of cash flows beginning with year 1
    • Subtract the initial investment after computing the NPV
payback period
Payback Period
  • How long does it take to get the initial cost back in a nominal sense?
  • Computation
    • Estimate the cash flows
    • Subtract the future cash flows from the initial cost until the initial investment has been recovered
  • Decision Rule – Accept if the payback period is less than some preset limit
computing payback for the project
Computing Payback for the Project
  • Assume we will accept the project if it pays back within two years.
    • Year 1: 165,000 – 63,120 = 101,880 still to recover
    • Year 2: 101,880 – 70,800 = 31,080 still to recover
    • Year 3: 31,080 – 91,080 = -60,000 project pays back in year 3
  • Do we accept or reject the project? What do you think about this decision rule.
payback investment criteria

Cash Flows in Dollars

Project: C0 C1 C2 C3

A -2,000 +1,000 +$1,000 +10,000

B -2,000 +1,000 +$1,000 -

C -2,000 - +$2,000 -

Payback Investment Criteria
  • Payback
    • Payback is a very poor way of determining a project’s acceptability:
      • It often leads to nonsensical decisions.
    • Calculate the payback and NPV for the following projects if the discount rate is 10%:

a

payback investment criteria1

Project: Payback (years) NPV @ 10%

A 2 $7,249

B 2 - 264

C 2 - 347

Payback Investment Criteria
  • Payback vs NPV … what to do?
      • Under NPV, only project A is acceptable. B and C have negative NPV’s and are thus both unacceptable.
      • But if your payback period is 2 years, then all the projects are acceptable.
  • NPV and payback disagree … what is the correct answer?
decision criteria test payback
Decision Criteria Test - Payback
  • Does the payback rule account for the time value of money?
  • Does the payback rule account for the risk of the cash flows?
  • Does the payback rule provide an indication about the increase in value?
  • Should we consider the payback rule for our primary decision rule?
advantages and disadvantages of payback
Advantages and Disadvantages of Payback
  • Disadvantages
    • Ignores the time value of money
    • Requires an arbitrary cutoff point
    • Ignores cash flows beyond the cutoff date
    • Biased against long-term projects, such as research and development, and new projects
  • Advantages
    • Easy to understand
    • Adjusts for uncertainty of later cash flows
    • Biased toward liquidity
discounted payback period
Discounted Payback Period
  • Compute the present value of each cash flow and then determine how long it takes to pay back on a discounted basis
  • Compare to a specified required period
  • Decision Rule - Accept the project if it pays back on a discounted basis within the specified time
computing discounted payback for the project
Computing Discounted Payback for the Project
  • Assume we will accept the project if it pays back on a discounted basis in 2 years.
  • Compute the PV for each cash flow and determine the payback period using discounted cash flows
    • Year 1: 165,000 – 63,120/1.121 = 108,643
    • Year 2: 108,643 – 70,800/1.122 = 52,202
    • Year 3: 52,202 – 91,080/1.123 = -12,627 project pays back in year 3
  • Do we accept or reject the project?
decision criteria test discounted payback
Decision Criteria Test – Discounted Payback
  • Does the discounted payback rule account for the time value of money?
  • Does the discounted payback rule account for the risk of the cash flows?
  • Does the discounted payback rule provide an indication about the increase in value?
  • Should we consider the discounted payback rule for our primary decision rule?
advantages and disadvantages of discounted payback
Advantages and Disadvantages of Discounted Payback
  • Disadvantages
    • May reject positive NPV investments
    • Requires an arbitrary cutoff point
    • Ignores cash flows beyond the cutoff point
    • Biased against long-term projects, such as R&D and new products
  • Advantages
    • Includes time value of money
    • Easy to understand
    • Does not accept negative estimated NPV investments when all future cash flows are positive
    • Biased towards liquidity