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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.
- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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?

Stock Price Sensitivity to Dividend Growth, g

D1 = $2; R = 20%

Stock Price Sensitivity to Required Return, R

D1 = $2; g = 5%

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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- Dealers vs. Brokers
- New York Stock Exchange (NYSE)
- NASDAQ

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

- 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

- 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

- 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

- 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

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 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 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 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

- 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

- 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 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

- 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

- 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

- 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

- 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

- 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.

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

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

- 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

- 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

- 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

- 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

- 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

- 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

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