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FIN 400 Class Notes Set 1: Detailed Review and Extension of FIN 300

Dr. Chanwit Phengpis California State University, Long Beach

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The Roles of Financial Managers Real Assets VS Financial Assets Real Assets: Financial Assets: Diagram: Two Basic Decisions Faced by Financial Managers: 1. Investment or Capital Budgeting Decision: What real assets should a firm obtain? Thus, capital budgeting decision is the process of evaluating investment proposals. 2. Capital Structure Choice or Financing Decision: How should cash be raised to finance real assets? Thus, financing decision identifies the appropriate source or mixture of financial assets (stocks, bonds and/or bank loans) that support the firms existing operations as well as the firms new investments.

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The Goal of the corporation is to maximize the current market value of shareholders' equity or wealth: Current market value of shareholders' equity = # of shares outstanding current stock price Related implications: - A good project or real asset results in an increase stock price and thus the current market value of shareholders equity, thereby consistent with the goal of the corporation. - Two crucial elements that determine how good or valuable the project is:

- Size and timing of the projects cash flows: Due to the "time value of money" concept, today's values of two cash flows occurring at two different points in time differ. - The riskiness or uncertainty of the projects cash flows: This should not be too high because investors are risk averse and they require at least a fair return to compensate the level of risk they are taking.

- Capital budgeting decision and financing decision are typically separated or independent of each other. What does this statement mean?

- How valuable the project or real asset is (i.e., capital budgeting decision) should not depend on how we raise the money to finance it (i.e., financing decision). Example: Machine A financed with equity versus Machine A financed with equity + debt Should the value of Machine A change a result of different sources or mixtures of financing? No. The value of Machine A should not change as a result of equity financing versus equity + debt financing because, apparently, the same machine is being obtained. The value of this machine should depend on whether or not it will produce goods that consumers want and hence will bring significant cash flows to the firm, not on how it is financed. - Separation of capital budgeting and financing decisions should motivate managers to focus on identifying a truly valuable project (based on cash flows expected from the project and the risk of these cash flows) rather than on seeking the "right" mixture of financing (e.g., cheap financing) to support a mediocre or bad project (e.g., one with poor cash flows). - We will learn in class that, in many cases, the "right" mixture of financing in fact does not exist. That is the value of the project is independent of how it is financed.

- However, in many cases as well, capital budgeting decision and financing decision have some interaction.

- We will learn later in class that the mixture or choice of financing can impact value. Using the same example as above, Machine A financed with equity + debt may be more valuable than Machine A financed only with equity. Despite the fact the same machine is being acquired, financing partly with debt leads to interest expenses (which are tax deductible), lower taxable income and hence tax savings that add value to the firm. - Thus, in these cases, both a truly valuable project and an appropriate mixture of financing help increase value. That is the value of the project is not entirely independent of how it is financed.

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Time Value of Money Future Value of Money Refers to the amount an investment will grow to after one or more periods. Example: Suppose you invest $100 in an account paying 10% each year. How much will you have at the end of Year 2? Future Value Calculation In general, the future value of a $X dollars invested today at an interest rate of r, (10% implies r = 0.1) for t periods is

The expression (1 + r)t is called the future value factor. This formula assumes that all interest is reinvested at the interest rate r. Example: What would your $100 investment be worth after 5 years if the interest rate is 10% per year?

)r + $X(1 = FV t

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Future Values of Multiple Uneven Cash Flows Calculate the future value of each cash flow and then sum these future values to find total FV. Example: Suppose your rich uncle offers to help pay for your business school education by giving you $15,000 now, $10,000 one year from now and $5,000 two years from now. You plan to deposit this money into an interest-bearing account so that you can attend business school six-years from today. Assume you earn 4.25% per year on your account. How much will you have saved in total in six years?

Year

Cash Flow

Future Value

0

15,000

1

10,000

2

5,000

Total Future Value

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Future Value of Annuity An annuity is a stream of fixed cash flows for a finite period of time. Timeline for annuity: Three methods: 1. Long approach 2. Compact formula

3. Direct financial calculator keystrokes Example: Suppose you plan to retire ten years from today. You plan to invest $2,000 a year at the end of each of the next ten years. You can earn 8% per year on your money. How much will your investment be worth at the end of the tenth year?

[ ]1 - )r + (1rC = )FV(Annuity t

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Present Value of Money How much is the value today of cash flows expected in the future? How much money is needed today to generate the predetermined future value of money? Present value calculations are important in: - evaluation of investment projects - capital budgeting - pricing of bonds and stocks which are main sources of financing for the firm - firm valuation Why so? Because present value of future cash flows produced by the asset is the fair price of that asset, thereby allowing us to evaluate if we should invest in it.

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Present Value of Money Calculation

The expression 1/(1 + r)t is called the present value factor or discount factor. Calculating the present value of a future cash flow to determine its worth is commonly called discount cash flow valuation. Three different wordings for the same "r" in present value calculation:

- "discount rate" (because the process of finding the present value is called discounting) - "opportunity cost of capital" (the highest return available in capital markets on the investment with similar risk. This is based on the "law of one price". Same risk, same return. Similar risk, similar return.) - "required return" (because it is the rate of return that should be received by investors given the risk of an investment. If the investment provides less than the required return, investors will instead invest in a similar risk investment that provides at least the required return.)

t t1 $XPV = $X =

(1 + r (1 + r) )

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Example: What is the present value of the cash flow of $5,000 to be received 4 years from now with the discount rate of 10%? Net Present Value The present value of future cash flows (i.e., benefits) net of the initial investment (i.e., cost) NPV = - Initial investment + PV(future cash flows)

= - Cost + PV(benefits) A positive NPV project is attractive because it implies that PV(benefits) is greater than cost, resulting in value addition to the firm in the amount of $NPV. Also, NPV = - Cost + Fair price Thus, a positive NPV project also implies that the cost paid is less than the fair price. We love the bargain! Example: Your manager proposes to buy an asset for $350 million. You expect to sell the asset in four years for $520 million. Assume that the asset generates no income between the time you buy the asset and the time you sell the asset. You also know that you could invest the $350 million elsewhere and earn 10%. How much is the NPV and should you buy this asset?

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Example: Purchase this office building? - Project cost = $350,000 - Expect sale next year = $400,000 - Return on similar risk projects = 7% Thus, ____________________ and ________________ are also 7%. Using NPV, What if using rates comparison instead of NPV,

lienHighlightopportunity cost of capitaldiscount rate and required return are also 7%

lienSticky NoteNPV = - initial cost + PV of official cash flow

lienSticky NoteRequired return = 7%Expected return based on CF estimation = [(400,000 - 350,000)/350000]x100 = 14.29 %

Yes, expected return is greater than required returnThis evaluation is the IRR criterion learned FIN300

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Present Value of Multiple Uneven Cash Flows Example: Suppose your firm is evaluating if it should buy an asset. The asset is expected to generate the following cash flows: Year CF 1 $2,400 2 $3,200 3 $6,800 4 $8,100 Similar assets earn 8% per year. How much is the present value of future cash flows generated by the asset? Further, if the asset costs $14,000, should the firm invest in this asset?

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Present Value of an Annuity Again, an annuity is a stream of fixed cash flows for a finite period of time. Timeline for annuity: Three methods: 1. Long approach 2. Compact formula

3. Direct financial calculator keystrokes Example: You are considering purchasing a contract offered by an insurance company for your parents. It promises to pay them $20,000 a year for the rest of their life. If their life expectancy is 25 more years from now and the interest rate is 8%, what is the fair price of this contract?

)r + (1

1 - 1 rC = )PV(Annuity t

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Present Value of Growing Annuity Growing annuity is a stream of cash flows which grow at the rate of g for a finite period of time.

t

11 1 1 gPV(GrowingAnnuity) C

r g r g 1 r +

= +

Example: Walter Maxwell, a second-year MBA student, has just been offered a job at $50,000 a year. He anticipates his salary to increase by 9% a year until his retirement 40 years from now. Given an interest rate of 20%, what is the present value of his lifetime salary? For simplicity, assume that his first salary will be received at the end of each year and the first one occurs one year from today. Example: You have recently purchased an oil well at $700,000. Just prior to your purchase, the well has generated a cash flow (C0) of $100,000 which will grow at the rate of 5% a year. This well will last for only 10 years. Did you make the right decision? (r = 12%) C0 = $100,000 C1 =

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Present Value of Growing Perpetuity Growing perpetuity is a stream of cash flows that grow at the rate of g for an indefinite period of time (i.e., forever).

Example: Suppose an investment offers the cash flow next year of $800 which will grow at the rate of 4% every year. The return you require on such an investment is 6%. What is the value of this investment? Example: Valuing Common Stock as Growing Perpetuity - ABC Corp. has just paid the dividend of $4.50. - Required return on ABC equity = 12% - Historical dividend growth = 2% How much is the ABC share price?

1 0(1 )+ C C gPV(GrowingPerpetuity) = =

r g r g

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Present Value of Perpetuity Perpetuity is a stream of cash flows that grow at the rate of g = 0 for an indefinite period of time. That is the perpetuity is a stream of cash flows that are constant each period forever.

Example: Suppose an investment offers some perpetual cash flows of $800 every year. The return you require on such an investment is 6%. What is the value of this investment? Example: Valuing Preferred Stock as Perpetuity Preferred stock is an example of perpetuity. The holder of preferred stock is promised a fixed cash dividend every period (quarter). It is called preferred because the dividend is paid before common stock dividends. Suppose Fillini Co. wants to sell preferred stock at $100 per share. A very similar issue of preferred stock outstanding has a price of $40 per share and offers a dividend of $1 every quarter. What dividend will Fillini have to offer if the preferred stock is to sell for $100?

rC = ity)PV(Perpetu

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Special Cases of Cash Flow Timing Delayed Annuity: The first cash flow of annuity starts at t >1 What is the present value of a $100, 4-yr annuity which starts 5 year from now, given r = 10%? Delayed Growing Perpetuity: The first cash flow of growing perpetuity starts at t > 1 What is the present value of a growing perpetuity which starts 6 yrs from now at $100 and grows at the 5% rate, given r = 10%? Delayed Perpetuity: The first cash flow of perpetuity starts at t >1 What is the present value of a $100 perpetuity which starts 10 year from now, given r = 10%?

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Another Application Example: An insurance company is offering a new policy to its customers. Its target customers for this policy are parents of the newly born babies. The purchaser is expected to make the following six payments to the insurance company: First birthday $800 Second birthday $800 Third birthday $900 Fourth birthday $900 Fifth birthday $1,000 Sixth birthday $1,000 After the childs sixth birthday, no more payments are made. When the child reaches the age of 65, he/she receives $350,000. If the relevant interest rates are 11% for the first six years and 7% for all subsequent years, is the policy worth buying?

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Relationship between Present Value and Future Value

and:

Determining the Discount Rate Solving for r:

Example: What interest rate makes $100 today grow to $180 in 5 years?

)r + (1

1FV = PV t

)r + PV(1 = FV t

1 - PVFV = r

t1

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Finding the number of periods Solving for t:

Example: How long would it take to double your money at 5%?

[ ]ln lnln

ln

t

t

FV = PV(1 + r )FV = (1 + r )PV

FV = t (1 + r)PV

FVPVt =

(1 + r)

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When an interest rate is evaluated more than once per year (compounded interest)

and/or when cash flows occur more than once per year, we must be very careful! Effective Annual Rates and Compounding Stated rate or quoted rate or Annual Percentage Rate (APR): The rate before considering any compounding effects, such as 10% compounded semiannually. Effective Annual Rate (EAR): The rate, on an annual basis, that reflects compounding effects, such as 10% compounded semiannually gives an effective rate of 10.25%. Why?

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Calculating EAR An investment of $1 at a rate of r per year compounded m times a year will result in the total amount of:

mr 1 + m

at the end of one year and thus:

Examples: 1. What is the EAR for 12% compounded monthly? 2. What is the EAR for 12% compounded quarterly? 3. What is the EAR for 12% compounded yearly or annually? 4. What is the EAR for 15% compounded weekly? 5. What is the EAR for the quoted rate of "15% compounded every 65 days"?

mrEAR = 1 + - 1m

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Computing Present Value with Compounded Interest Rates What is the present value of $100 to be received at the end of two years at 10% compounded quarterly? Computing Future Value with Compounded Interest Rates What is the future value of todays money of $50 to be deposited in an investment trust for 5 years if the interest rate earned is 10% compounded monthly?

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Example: Equal-Installment Loan Contracts A finance company quotes a 13% interest rate on a one-year loan. If you borrow $10,000, the interest for the year will be $1,300 so that the total amount you will have to pay is $11,300. However, the company requires you to pay $11,300 in 12 monthly installments of $941.67 each. What is the quoted rate? What is the EAR?

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Example: Auto Loan Payments You have decided to buy a new four-wheel drive sports vehicle and finance the purchase with a 5-year loan. The loan is for $33,500. The first loan payment is one month after the loan is initiated. The interest rate on the loan (APR) is 8.5% per year for the 5-year period. How much will your monthly payment be? Example: You decided to set up a scholarship for students at a high school you once attended. The plan is for the scholarship to award $20,000 per quarter in perpetuity. The first scholarship is to be paid 5 years from today. How much money do you have to deposit to set up the fund today given the quoted interest of 6% per year? Example: You decided to set up a scholarship for students at a high school you once attended. The plan is for the scholarship to award $20,000 per year in perpetuity. The first scholarship is to be paid 5 years from today. How much money do you have to deposit to set up the fund today given the quoted interest rate of 6% per year compounded quarterly?

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Example: Annual Percentage Yield (APY) What is the APY for a savings account with 4.93% interest rate to be compounded daily? Example: APY revisited What is the quoted rate for a savings account with the APY of 6%? Example: Retirement Planning Your individual retirement account with an average return of 10% per year has the current balance of $50,000. You expect to put $240 each month in the account until you retire. How much can you expect to have at the time of your retirement 40 years from now?

( \ o r f l n ( ' n d f f ^ o t t t ) ' , t 1 i V ar LA

$mortizing. f;oan,,Consider a 4-yer amortizing loan.,You bolrow $1,000 initially, and repayit in four equal annual.year-end payments.

' . r ' . . : . ,

'

a. If the interest rate is 8 percent; ihow that the annual paymeni is $30t.92.b. Fill in the followingtable, which showq how:druch of each payment'is interest.versus prin-

cipal repayment (that is, amortizatibn), and the outstanding balance on the loan at each date.

Year BeginningLoan Balance

Payment InterestPortion

PrincipalPortion

EndingLoan Balance

I 1.000.0000)34

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Additional Example: You just bought a home for $600,000 in which you made a down payment of $200,000. You obtained a 30-year mortgage at a 5% annual rate to finance the balance. If you make fixed monthly payments, what loan balance will remain immediately after the 60th payment?

Some observations

Page 23 Example: Equal-Installment Loan Contracts Initial Quoted Rate / APR < True Quoted Rate / APR < EAR

_______% _______% _______%

|___________________Why?______________| |______________Why?___________|

Page 26 First Example: Mortgage with Points

Initial Quoted Rate / APR < True Quoted Rate / APR < EAR

_______% _______% _______%

|___________________Why?______________| |______________Why?___________|

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Nominal and Real Rates of Interest So far, the rate of return used is the nominal rate of return. To calculate the real rate of return which incorporates an adjustment for the change in purchasing power, the following relationship is used:

(1 + nominal rate of return) = (1 + real rate of return)(1 + inflation rate) Thus, (1 + real rate of return) = (1 + nominal rate of return)/ (1 + inflation rate) Example: If the nominal rate of return is 10% and the inflation rate is 5%, what is the real rate of return? Further, we may wish to adjust the cash flow at time t to reflect the change in purchasing power until time t. The following relationship is used: real cash flowt = nominal cash flowt (1 + inflation rate)t Example: How much would you accumulate in real terms if you invest $1,000 for 20 years at 10% with the inflation rate of 6% per year? Nominal Approach: nominal input, nominal rate, nominal output Real Approach: real input, real rate, real output

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Example: CF0 = $500 which will grow at the rate of 10%, inflation rate = 10%. What is the real CF at time 15?

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Example: Your real estate company is considering the purchase of an apartment complex that currently generates a cash flow of $400,000 per year. The cash flow is expected to grow with the inflation rate of 4% a year. The nominal required return is 10% a year. How much would your company be willing to pay for the complex if it will produce the cash flows forever?

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Example: Your real estate company is considering the purchase of an apartment complex that currently generates a cash flow of $400,000 per year. The cash flow is expected to grow with the inflation rate of 4% a year. The nominal required return is 10% a year. How much would your company be willing to pay for the complex if it will be torn down in 20 years? Assume that, net of demolition costs, the site will be worth $5 million in nominal terms at that time.

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Basic Valuation of Common Stocks and Bonds

Two basic sources of financing of the firm are stocks and bonds. We need to understand how they are valued so that: (1) we know how much money we can raise by issuing them and (2) we can estimate the fair returns required by stockholders and bondholders and hence know if the proposed project at least provides sufficient returns to these investors.

Common Stocks

The price of stock today is equal to the present value of all expected future dividends.

The above formula is a general formula, but impractical since, say, we cannot predict dividend payments 20-30 years from now. To overcome this complication, we need to simplify and make some assumptions about future stock prices, dividends and/or patterns of dividends. 1. Assuming that dividends over the investment horizon and stock price at the end of investment horizon is known

1 20 1 2 ...(1 ) (1 ) (1 )

+= + + ++ + +H H

H

DIV DIV DIV PPr r r

where H = Time horizon for your investment. Example: Current forecasts are for XYZ Company to pay dividends of $3, $3.24, and $3.50 over the next three years, respectively. At the end of three years you anticipate selling your stock at a market price of $94.48. What is the price of the stock given a 12% expected return?

1 2 30 1 2 3

D I V D IV D I V = + + + . . . P( 1 + r ( 1 + r (1 + r) ) )

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2. Zero Growth Dividend Model This implies that all the dividends are the same and equal to a constant perpetual cash flow.

DIV1 = DIV2 = DIV3 = DIV4 =..= DIV

Example: Suppose a firm's annual dividend is expected to remain constant at $1 per share forever. The discount rate appropriate for the risk of the dividends is 10% per year. What is the current price of a share? 3. Constant Growth Dividend Model In this case, a firm's dividends are expected to increase at a g% annual rate. Applying the future value concept, the value of a dividend at year t is: DIVt =DIV0(1 + g)t This is an example of a growing perpetuity. As long as g < r, the price of a share with the rate of dividends growing at the rate of g is:

Example: Suppose a firm just paid an annual dividend of $10 per share. Future dividends are expected to increase at a 5% annual rate. The expected rate of return is 10% per year. What is the current price per share of the firm? Example: Suppose a firm is expected to pay an annual dividend of $10 per share starting next year. Future dividends are expected to increase at a 5% annual rate. The expected rate of return is 10% per year. What is the current price per share of the firm?

0DIV = P r

1 00

(1 + g)DIV DIV= P (r - g) (r - g)=

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Estimating Required Return or Expected Rate of Return Thus far, we have taken the discount factor or the required rate of return or the expected return as given.

Recall, 10DIV = P (r - g)

Solve for r,

1

0

DIVr = + gP

This tells use the required rate of return or the expected rate of return on a firm's stock has two components: 1. The dividend yield, DIV1/P0 2. The growth rate g (the capital gain yield). Example: Suppose a stock has just paid an annual dividend of $1, and g = 10% per year. Suppose we observe a price of $10. If you forecasted the growth rate correctly, what rate of return can you expect from this stock? Example: Suppose a stock is expected to an annual dividend of $1 next year, and g = 10% per year. Suppose we observe a price of $10. If you forecasted the growth rate correctly, what rate of return does this stock offer you?

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Proof that the growth rate g is the same as capital gain yield Capital gain yield is the percentage change in stock prices over one period = (P1 - P0)/P0. Sometimes this yield is called "capital appreciation". Let's assume that you buy a stock today. One year from now, the stock pays the dividend DIV1 and you sell the stock at the expected price P1. Thus, Thus, the fair price of stock today (P0) must equal to the present value of future cash flows (DIV1 and P1) to be received.

1 10 (1 )

DIV PPr+= +

1 1

0

(1 ) DIV PrP++ =

1 1

0 0

(1 ) DIV PrP P

+ = +

1 1

0 0

1DIV PrP P

= +

01 1

0 0 0

PDIV PrP P P

= +

1 01

0 0

P PDIVrP P

= + ****** That is r = dividend yield + capital gain yield.

Also, from the previous page, 10

DIVr gP

= + . That is r = dividend yield + growth rate g.

Hence, we have two equivalent formulae for r, implying that the capital gain yield must be the same as the growth rate g.

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Example: The expected dividend one year from now is $2. The dividend growth rate is 4%. The current price of stock is $20. What is the required return on stock (based on r is equal to dividend yield + growth rate g)? What is the expected price one year from now? Also show that the capital gain yield is the same as the growth rate g

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Additional insight into dividend growth (g) If a firm elects to pay lower dividends out of its given earnings and reinvest the funds, the stock price may increase because future dividends may be higher due to growth. Payout Ratio - Fraction of earnings paid out as dividends Plowback Ratio - Fraction of earnings retained or reinvested by the firm. Growth can be derived from applying the return on equity to the percentage of earnings plowed back into operations. g = return on equity x plowback ratio Example: Our company forecasts to have a $5.00 EPS next year. Given a 12% expected return, how much is the stock price if we decide not to plow back any earnings? In contrast, how much is the stock price if we decide to plow back 40% of the earnings at the firms current return on equity of 20%? No plowing back; all earnings are paid as dividends; growth is zero. g = ROE * Plowback Ratio = DIV1 = Price = Plowing back some earnings; only portion of earnings is paid as dividends; growth is non-zero. g = ROE * Plowback Ratio = DIV1 = Price = Present value of growth opportunities (PVGO) = Price with growth Price with no growth

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4. Varying Growth Rates A single constant growth assumption may be unrealistic. Examples of more realistic approaches: - Forecast dividends for each period for some initial periods and then assume a constant growth afterwards. - Assume initial growth of g1 for some initial periods and g2 afterwards, where g2 < g1. Example: Dividends are forecasted to be $0, $0.31, $0.65 and $0.67 in years 1, 2, 3 and 4, respectively. After year 4, dividends are expected to grow at a constant rate of 4%. What should be the stock price if the required return is 10%? Example: A stock has just paid a $1 dividend which is expected to grow at the rate of 10% for the next 3 years and at the rate of 5% onwards. How much is this stock worth per share if the required return is 20%?

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Example: Put everything together Assume now we are at the end of 2002. Earnings for Raytheon Corp. are forecasted to be 2.67, 3.10, 3.53 and 4.00 for years 2003-2006, respectively. The dividend payout ratio is expected to be 30% for this 4-year period and thereafter. The long-run sustainable ROE is expected to be 13%. The required return on Raytheons common stocks is 11.40%. How much is the fair price of stock? If the stock is currently trading at $29, is it being fairly priced, overvalued or undervalued?

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Additional insight into valuation: Using free cash flows to value stocks Free cash flow available for investors = Operating cash flow - Investment expenditures necessary for growth Since investors in the firm comprise stockholders and bond/debt holders, Free cash flow available = Free cash flow - interest expense(1-tc) + increase in to equity/ stock holders available net debt (FCFE) for investors Example: Free cash flows available to stockholders are forecasted to be $30.5088M and $38.7492M for the next two years, respectively. Afterwards, these free cash flows will converge on the industry growth rate of 13%. The required return on equity is 14%. If there are 84M shares outstanding, what is the current fair price of stock?

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Bonds

The current price of bond is the present value of the expected coupon or interest payments each period until the maturity date on which the principal or par value is also received. The relevant discount rate for bond pricing is specifically called yield to maturity. It is the required return or expected return for bond investors who hold the bonds until maturity. Example: Bond Pricing--Annual Coupon Paying Bond - 20 year XYZ Corporation bond - $1,000 face value - 8% annual coupon payments - Yield to maturity = 6% How much is the price of this bond? Example: Bond Pricing--Semi Annual Coupon Paying Bond - 20 year XYZ Corporation bond - $1,000 face value - 8% semi-annual coupon payments - Yield to maturity 6% How much is the price of this bond?

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Example: Yield to Maturity Calculation--Annual Coupon Paying Bond Bond with $1000 Face Value, 6% coupon rate, 14 years to maturity. Price is $835.12. What is the YTM? Example: Yield to Maturity Calculation--Semi-Annual Coupon Paying Bond Bond with $1000 Face Value, 6% coupon rate, 14 years to maturity. Price is $835.12. What is the YTM if the bond pays coupons semi-annually?

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Further issues on bond returns Current Yield: Annual coupon payments divided by the bond price. It is not an appropriate measure of required or expected return for bond investors because it reflects only the current annual interest income relative to initial investment. Example: What is the current yield of the bond in the previous example? Expected or Realized Returns over Investment Horizons: Sometimes investors do not hold bonds until maturity for various reasons. Hence, by definition, YTM is not an appropriate measure of returns investors really receive. Example: Today you have just purchased a semi-annual coupon paying bond at $1,050. This bond has a par value of $1,000 and an 8% coupon rate. It is expected that in three years you will be able to see the bond at $1,025. How much is your expected return per year? Example: Four years ago, you purchased a semi-annual coupon paying bond with a 10% coupon rate at the price of $950. You can sell the bond now for $1,025. What is your realized rate of return per year?

$0 .Aside: working with an HB-108 Financiar calculator

L Clear your financial calculator's memory.

El,\-f orrrlr i l i{f boilen2. Set Payment/Year_ t

_

, r:l irL=-, l@3. set cash flows to occur at the end of each period or yearIf you set step 3 incorrectly, the word "BEGIN" will appear on the screen.

milD4. Set four decimal places to be displayed.

Caution:

l. Clear your financial calculator's memory every time before beginning new calculation.

2. Financial calculator reads the interest rate in the "o/o" format, not in the "decimal" format.

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Application example: FV of multiple uneven cash flows and compound interest John Doe will deposit the following into his retirement account: End of month amount 1 $1,000 2 $1,500 3 $2,000 After 3 months, he will not add any more money. How much money will he have in his retirement account 20 years or 240 months from now? The interest rate is 10% per year. Another example: APY is 3.30%. What is the quoted rate? If you deposit $1,000 today, how much money will you have 120 days or 4 months from now?

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