BSAD 180 Exam 3

Using the DGM to Find R

R = D1/P0 + g = dividend/ stock price + capital gain the bigger the g, the bigger the stock price P0 = D1/(R-g)

Disadvantages of the Profitability Index

Problems with mutually exclusive investments

The Nearside Co. just paid a dividend of $2.07 per share on its stock. The dividends are expected to grow at a constant rate of 4.3% per year, indefinitely. If the investors require a return of 11% on the stock, what is the current price? What will the price be in 3 years? In 15 years?

$2.07(1.043)/(.11-.043) =$32.22 ($2.07(1.043)^4)/(.11-.043) =$36.56 ($2.07(1.043)^16)/(.11-.043) =$60.60

Fifth National Bank just issued some new preferred stock. The issue will pay an annual dividend of $4 in perpetuity, beginning five years from now. If the market requires a return of 4.3% on this investment, how much does a share of preferred stock cost today?

$4/.043=$93.02 FV = 93.02, N=4, i =4.3% PV =78.60

•Suppose Michael's Mopeds is currently priced at $22.25. They have announced next year's dividend to be $1.25. The most recent dividend was $1.19. What is the required return based on this information? How much is capital gains growth? How much is dividend yield?

( $1.25/$1.19 ) - 1 = g the capital gains yield, g = 5.04% •Dividend yield = D1 / P0 = $1.25/$22.25 = 5.62% •Required Return = Dividend yield + capital gains = 10.66%

Types of DCF models

(1) those that value equity directly and (2) those that value the firm as a whole

An increase in the retention rate will:

-reduce the dividend paid to shareholders -increase the firm's growth rate

Estimating NPV

1. Estimate future cash flows: how much? and when? 2. Estimate discount rate 3. Estimate initial costs

To value a differential growth stock, we need to:

1. Estimate future dividends in the foreseeable future. 2. Estimate the future stock price when the stock becomes a Constant Growth Stock (case 2). 3. Compute the total present value of the estimated future dividends and future stock price at the appropriate discount rate.

If you buy a share of stock, you can receive cash in two ways

1. the company pays dividends 2. You sell your shares, either to another investor in the market or back to the company

The discount rate can be broken up into 2 parts

1. the dividend yield 2. The growth rate (in dividends)

Valuation models for equity

DCF, Relative Valuation, Portfolio Theory, Real Option Method, Technical Analysis

•Tomas Tea and Toffees (TTT) just paid a dividend of $4. TTT has been doing well recently and expects the dividends to grow at 20% for the next two years. After that, analysts expect dividends to grow at a more modest 2% per year. If the required rate of return for TTT is 15%, what is the maximum you should be willing to pay for the stock today?

Create a time line of dividends! $4 * (1.20) = $4.80 or PV = -4, i=20, N=1 calculate FV = $4.80 $4 * (1.20)2 = $5.76 or using TVM: PV = -4, i=20, N=2 calculate FV = $5.76 = $4 * (1.20)2 * (1.02) = $5.88 using TVM from D2 : PV = -5.76, i=2, N=1 calculate FV = $5.88 Once the dividends are projected to growth at a constant rate we can use the "Constant Growth Formula" = $5.88/(.15-.02) = $45.23 CF0 = 0 CF1 =$4.80 CF2 = 50.99 (5.76 + 45.23) i =15 NPV = $42.73

Disadvantages of IRR

Does not distinguish between investing and borrowing IRR may not exist, or there may be multiple IRRs Problems with mutually exclusive investments

Advantages of IRR

Easy to understand and communicate

Upton Corporation is expected to pay the following dividends over the next four years $9, $7, $5.75, and $2.55. Afterwards, the company pledges to maintain a constant 4.5% growth rate in dividends forever. If the required return on the stock is 10%, what is the current share price?

Find D5: PV = -2.55, i =4.5 , N =1 , FV= 2.6648 P4 = (2.6648)/(.1-.045) = $48.45 Put into calculator: CF0 = 0 CF1= 9 CF2 = 7 CF3 = 5.75 CF4 = 2.55 + 48.45 i =10 NPV = 53.12

Disadvantages of the payback period method

Ignores the time value of money Ignores cash flows after the payback period Biased against long-term projects Requires an arbitrary acceptance criteria A project accepted based on the payback criteria may not have a positive NPV

•Tomas Tea and Toffees (TTT) has a preferred stock that pays $5 dividends, and is currently priced at $64.19. What is the required return?

P0 = D / R •Therefore R = D / P0 = $5 / $64.19 = 7.79%

Michael's, Inc., just paid $2.45 to its shareholders as the annual dividend. Simultaneously, the company announced that future dividends will be increasing by 5.3 percent. If you require a rate of return of 9.5 percent, how much are you willing to pay today to purchase one share of the company's stock?

P0 = [$2.45 × (1 + .053)]/(.095 - .053) = $61.43

Constant dividend

The firm will pay a constant dividend forever This is like preferred stock The price is computed using the perpetuity formula

discounted cash flow (DCF) valuation

The intrinsic value of an investment equals the sum of the present value of future cash flows associated with this investment

How to determine which project you should pick and/or if the extra amount is worth it?

The project with the bigger NPV is better. It does not matter if IRR is smaller than the other project, however, it should be greater than the required return. IRR may be smaller due to larger-scale or larger cash flows. To determine if an extra amount is better, NPV > 0 and incremental IRR>R to accept project

Relative Valuation

The value of an asset equals the average prices of comparable assets

NPV

Total PV of future CF's + Initial Investment

The value of a firm depends on its

growth rate, g, and its discount rate, R.

Offer (or Ask)

price someone is willing to sell at.

If ROE > R

then increased retention increases firm value since reinvested capital earns more than the cost of capital

Why Use Net Present Value?

•Accepting positive NPV projects benefits shareholders. NPV uses cash flows NPV uses all the cash flows of the project NPV discounts the cash flows properly

Modified IRR

•Benefits: single answer and specific rates for borrowing and reinvestment

Zero Growth

•If dividends are expected at regular intervals forever, then this is like preferred stock and is valued as a perpetuity •P0 = D / R Example: •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? •P0 = .50 / (.1 / 4) = $20

Advantages of Profitability Index

•May be useful when available investment funds are limited •Easy to understand and communicate Correct decision when evaluating independent projects

Problems with IRR

•Multiple IRRs •Are We Borrowing or Lending •Mutually Exclusive Projects •The Scale Problem and/or •The Timing Problem

Mutually Exclusive vs. Independent

•Mutually Exclusive Projects: only ONE of several potential projects can be chosen, e.g., acquiring an accounting system. •RANK all alternatives, and select the best one. • •Independent Projects: accepting or rejecting one project does not affect the decision of the other projects. •Must exceed a MINIMUM acceptance criteria

Constant Dividend Growth

•The firm will increase the dividend by a constant percent every period

IRR and Non-conventional cash flows

•When the cash flows change sign more than once, there is more than one IRR •When you solve for IRR you are solving for the root of an equation and when you cross the x-axis more than once, there will be more than one return that solves the equation

•Suppose XYZ stock is currently 105.50 for 1000 shares bid, 1000 shares at 105.60 offered. •If you place a market sell order for 300 shares what price do you get? •If you put a limit bid order 105.55 for 300 shares, what happens? 105.65?

•You sell 300 shares at 105.50 •Your order stands and becomes the best bid At 106.65, you get 300 shares at 105.60

Market Orders

•You specify ticker and quantity •Immediate execution at best available price •Market buy will be executed at lowest ask •Market sell will be executed at highest bid

Limit Orders

•You specify ticker, quantity, and price •The order will be executed only if trade can be made at the limit price or better •Limit Buy can only be executed at limit price or lower •Limit Sell can only be executed at limit price or higher

Bid

•price someone is willing to buy at (may be a market maker, an institution or individual)

Incremental IRR

•projects of different size we can view the crossover rate as the value to the additional (incremental investment) investment. •To calculate the crossover / incremental IRR we need to subtract the smaller projects (smaller initial investment) cash flows from the larger projects. •If IRR > R the additional investment is justified.

The Profitability Index (PI)

PI = Total PV of future cash flows/ Initial Investment •Minimum Acceptance Criteria: •Accept if PI > 1 •Ranking Criteria: Selecting alternative with the highest PI may cause misranking

•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?

•R = [1(1.05)/10.50] + .05 = 15% •What is the dividend yield? •1(1.05) / 10.50 = 10% •What is the capital gains yield? •g =5%

DCF Model

•The main distinction between different DCF models is whether cash flows to equity or the whole firm are valued

Real-option Valuation

•The value of an assets equals the present value of cash flows plus the value of built-in options

Feature 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

•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 •Price = (14 + 2) / (1.2) = $13.33 •Or FV = 16; I/Y = 20; N = 1; CPT PV = -13.33

Where does g come from?

•Consider a business whose earnings are constant unless they increase their "net" investment. •Net investment is positive if the firm does not pay out all of NI as dividends. •g = Retention ratio × Return on retained earnings Earnings next year = Earnings this year + Retained earnings this year x Return on Retained Earnings ** If you divided by earnings this year it becomes: 1+g = 1 + plowback x return on Retained Earnings

differential growth

•Dividend growth is not consistent initially, but settles down to constant growth eventually

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

Dividend Growth Model

•Dividends are expected to grow at a constant percent per period. P0 = D1/ (r-g) or Pt = D(t+1)/(R-g)

Good Decision Criteria

•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?

Advantages of the payback period method

•Easy to understand •Biased toward liquidity

The Discounted Payback Period

•How long does it take the project to "pay back" its initial investment, taking the time value of money into account? •Decision rule: Accept the project if it pays back on a discounted basis within the specified time. •By the time you have discounted the cash flows, you might as well calculate the NPV.

The Payback Period Method

•How long does it take the project to "pay back" its initial investment? •Payback Period = number of years to recover initial costs •Minimum Acceptance Criteria: •Set by management •Ranking Criteria: •Set by management

The Internal Rate of Return

•IRR: the discount rate that sets NPV to zero •Minimum Acceptance Criteria: •Accept if the IRR exceeds the required return •Ranking Criteria: •Selecting alternative with the highest IRR may cause misranking •Reinvestment assumption: •All future cash flows are assumed to be reinvested at the IRR

•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?

•P0 = .50(1+.02) / (.15 - .02) = $3.92

•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?

•P0 = 2 / (.2 - .05) = $13.33

•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 and a stock price of $14.70 at the end of year 2. Now how much would you be willing to pay?

•PV = 2 / (1.2) + (2.10 + 14.70) / (1.2)2 = 13.33 •Or CF0 = 0; CF1 = 2; CF2 = 16.80; NPV; I = 20; CPT NPV = 13.33

•what if you decide to hold the stock for three periods? 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 a stock price of $15.435. Now how much would you be willing to pay?

•PV = 2 / 1.2 + 2.10 / (1.2)2 + (2.205 + 15.435) / (1.2)3 = 13.33 •Or CF0 = 0; CF1 = 2; CF2 = 2.10; CF3 = 17.64; NPV; I = 20; CPT NPV = 13.33

Investing or Borrowing

•Project 1 (Investing): cash flows CF(0)=-100, CF(1)=110. IRR = 10% • if R<IRR accept •Project 2 (Borrowing): cash flows CF(0)=100, CF(1)=-110. IRR = 10% •NPV > 0 when R is above 10% •if R>IRR accept.