Finance 3332 Exam 2 Prep Sheet PDF

Summary

This document is a review sheet for Finance 3332 Exam 2, providing information on stock valuation, preferred stock, and corporate governance. It details the theory and calculation concepts.

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Finance 3332 Review Material EXAM 2 Equity = Stock = Ownership in a Firm \| A broader term for equity in general is **variable-return securities** Stock holders have a residual claim common stock (which constitutes over 90% of variable-return securities), some real estate equities, limited partn...

Finance 3332 Review Material EXAM 2 Equity = Stock = Ownership in a Firm \| A broader term for equity in general is **variable-return securities** Stock holders have a residual claim common stock (which constitutes over 90% of variable-return securities), some real estate equities, limited partnership exposures, and others. The control issues involved in running a company are collectively known as **corporate governance**. **Valuing Preferred Stock** =========================== Preferred stock is a **hybrid security**, meaning that it has some elements that resemble equity and others that resemble debt. preferred stock is almost always nonvoting and nonparticipating (with the exception of venture capitalists) Preferred stock pays the same dividend year after year UNLESS THE COMPANY DECIDES TO SKIP IT, NO EXPLANATION IS NECESSARY\-\-\-- the reason they don't skip all the time is because if your preferred stock isn't paid out then you can pay out your common stock, which would cause shareholders to sell off their stock if they aren't getting their share\-\-\--This feature of preferred stock is known as holding the **dividends in arrears**. PREFFERED STOCK IS CUMULATIVE, SO IF THE COMPANY SKIPS A DIVIDEND THEY ARE STILL REQUIRED TO PAY IT AT SOME POINT BEFORE PAYING COMMON STOCK Companies issue preferred stock to increase company value by decreasing the denominator of the discounted cash flows **the fixed annual dividend = the par value X the dividend rate aka the quoted percentage** For example, Xerox issued \$75 million of 8.25% preferred stock at \$50 per share par value. To calculate the fixed annual dividend, simply multiply the par value by the quoted percentage to get 0.0825 × \$50 = \$4.125 per year. Annually, Xerox will pay the owner of this share of stock \$4.125 per share forever. the value of any stock is equal to the present value of its future expected cash flows **Value of a preferred stock=D/K \| Value of a preferred stock= dividend/required rate** V*~ps~* = value of preferred stock \| *D* = annual fixed dividend \| *k~ps~* = discount rate or required rate of return Example We calculated earlier that each share of Xerox preferred stock pays an annual fixed dividend of \$4.125. Suppose our required rate of return on Xerox preferred stock is 9.50%. What would we pay for the stock today? 4.125/.095= 43.4211 **Rate of return=Annual Dividend payment / Stock value** The Single Holding Period Model ------------------------------- **The single holding period model** assumes that an investor buys a stock today, holds it for one year, and then sells it in the market. The value of the stock today is determined by estimating the future cash flows from these two sources and then discounting them back to the present. **While the single period holding model has the advantage of being easy to understand and use, it has one major limitation. It requires as one of its inputs the price of the stock in one year in order to calculate its price today (ITS not possible to predict that, so it may be inaccurate** A year from now we will receive \$120 from sale of the stock and \$5.50 in dividends for a total of \$125.50. The market requires a 15% return on the stock---as do we. To find today's value, we discount the cash flow in one year back to the present. In a financial calculator (with payments per year at one and in end mode), the inputs would be as follows: I/Y = 15 \| N = 1 \| FV = 125.50 This computation yields a present value (*V~0~*) of --109.13, which is the price of the stock that yields the market's required rate of return A picture containing font, white, design, typography Description automatically generated where: *V~0~* = value of the stock at time 0\ \ *V~1~* = value of the stock at time 1\ \ *D~1~* = dividend paid in time 1\ \ *k~cs~* = required rate of return **If you are looking for required rate of return** *Divide your dividend payment by your stock value and add your growth rate* *K=(D1/Vcs) +g \| Required rate= Dividend/ Stock Value + Growth rate* The Gordon Growth Model ----------------------- ***If Divided will be paid*** *Take your dividend payment. Take that number and divid it by your Required Rate of return- your dividend growth rate* *Value= (Dividend)/Required rate - Dividend growth rate* ***If a dividend is "being paid" "recently paid" "paid today"*** *Take your dividend payment, multiply it time your dividend growth rate +1. Take that number and divid it by your Required Rate of return - your dividend growth rate* *Value= (Dividend \* (Dividend growth rate + 1))/Required rate- Dividend growth rate* *USE IF IT IS **"being paid" "recently paid" "paid today"*** *Required Rate if growth is increasing= dividend(1+g)/ stock value+ growth rate* *Required Rate if growth is decreasing= dividend(1-g)/ stock value- growth rate* Growth rate= required rate- (D1/ Current price) ***If dividend payement Change*** *Take your dividend payment and divide it by your required rate + 1 to the power of the dividend( if it's the first one put it to the power of one, second to the power of 2, and so on...) then on your last one do the value of your stock in place of your dividend payement and put it to the highest power you used( ie your last dividend was the 3^rd^ year, put your stock value to the \^3) then add it all together.* ***HOLDING PERIOD MODEL-if there are multiple years, put it to the power of the year*** ***Holding period = D1/(1+I) + expected V/(1+I)*** *Value = Dividend/ (1 + required rate) + Expected value/ (1 + required rate)*  For Mature Firms A closed-form solution means that an infinite series can be expressed with a noninfinite equation. The closed-form solution, known as the **Gordon growth model** (or sometimes the **constant dividend growth model**) is written as follows: Full closed-form solution: ![A picture containing font, white, diagram, design Description automatically generated](media/image2.png) where: *V~0~* = value of the stock at time 0\ \ D~0~ = dividend paid in time 0\ \ *k~cs~* = required rate of return\ \ *g* = constant growth rate where: *D~1~* = *D~0~* (1 + *g*) = next period's annual dividend **Multiple Holding Period Models---The Two-Stage Growth Model** Estimate cash flows for two different growth stages: Stage 1: Dividends grow at above-average rates. \| Stage 2: Dividends grow at the industry average rate. **Value = PV(Stage 1) + PV(Stage 2)** **Information Needed for the Two-Stage Growth Model** 1. Growth rate during supernormal period **2.** Industry average growth rate **3.** Length of the supernormal period **4.** Required return **5.** Recent dividend **Return** ========== A **return** is the amount of money gained or lost on an investment over a certain period of time. As stated in the introduction, return is usually reported as an annualized percentage. **Nominal Rate= Real Rate + Interest Rate** **Holding Period Return= (P1-P0+CF)/P0 +** where: *P~0~* = price at the beginning \| *P~1~* = price at the end\ \ *CF* = value of cash flows received from the asset during the holding period ![A black text on a white background Description automatically generated with low confidence](media/image4.png) where: *P~0~* = price at the beginning \| *P~1~* = price at the end\ \ *CF* = value of cash flows received from the asset during the holding period A black text on a white background Description automatically generated with medium confidence where: *p~i~* = probability of outcome 1 X outcome 1\ \ R*~i~* = probability of outcome 2 X outcome 2 **Risk** ========  **Standard deviation** is a measure of dispersion of possible outcomes about the mean. It is the square root of the variance. Therefore, the greater a security's standard deviation, the greater the uncertainty and the greater the total risk of that security. **R*~mean=\ (Probability\ of\ outcome\ X\ Return)+\ (Probability\ of\ outcome\ X\ Return)+\ (Probability\ of\ outcome\ X\ Return).....=~*** ![A black text on a white background Description automatically generated with low confidence](media/image6.png) STD DEV= SQRT((R*~i~* - R*~mean~* ) \^2\* *P~i~* ) + ((R*~i~* - R*~mean~* )\^2\* *P~i~* )+ ((R*~i~* - R*~mean~* )\^2\* *P~i~* )+..... STD DEV= SQRT((Return-exp ret) \* Probability of outcome) + ((Return-exp ret) \* Probability of outcome)+..... where: *P~i~* = probability of outcome\ \ R*~i~* = return\ \ R*~mean~* = expected return or exp ret A screenshot of a computer Description automatically generated with medium confidence **Diversification: The Impact of Correlation** ============================================== Specifically, there are two kinds of risk: market risk and firm-specific risk. **Market risk** (also called **systematic risk** or **nondiversifiable risk**) is common to most securities and is the risk inherent in the economy as a whole. *Systematic risk cannot be diversified away*. Market Risk Factors: Unexpected changes in interest rates \| Unexpected changes in cash flows due to tax changes \| Business cycle changes **Firm-specific risk** (also called **nonsystematic risk** or **idiosyncratic risk**) can be defined as risk that results from factors at a particular firm or handful of firms. As we will discuss shortly, *firm-specific risk can be diversified away*. Firm-Specific Risk Factors: A company's labor force goes on strike. \| A company's top management dies in a plane crash. \| An oil tank bursts and floods a company's production area. ![A picture containing text, diagram, screenshot, line Description automatically generated](media/image8.png) **Diversification Through Portfolios** ====================================== For these you need to find your expected return for each stock using **R*~mean=\ (Probability\ of\ outcome\ X\ Return)+~ (Probability of outcome X Return)+ (Probability of outcome X Return).....=*** Once you have your expected return you multiply each one with its portfolio make up percentage and solve both of the standard deviations You will then calculate your covariance and your standard deviation of the correlation coeficient Oa,b Co variance is the relationship between two securities Pa,b correlation coeficienet = Oa,b/ (Oa \*Ob) A screenshot of a computer Description automatically generated ![A close-up of a document Description automatically generated with low confidence](media/image10.png) **Understanding Systematic Risk: Beta** ======================================= If risk is higher than one, its above market risk. The higher the number the higher the risk ie a beta of 2 is twice as risky or if the market goes up my 10% wed expect the stock to climb 20% If our stock has a beta of.5 its half as risky and growth will be half as much The Beta of the market is 1 BETAp= WEIGHT1 \* Bi 1 + WEIGHT2b \* Bi2 **Beta measures systematic risk not firm-specific risk.** **Required Rate of Return, SML, and CAPM** ========================================== Required rate of return = Risk-Free Rate + Risk Premium The **required rate of return** is defined as the return on an investment required by investors given the investment's risk. The **risk-free rate** is the rate of return on an investment with no risk and reflects the compensation for the time the investor is without his or her money AKA JUST MARKET RISK The **risk premium** is the compensation for the amount of risk taken on by investors. The **systematic risk principle**, that is, the notion that the size of the risk premium is based on market risk, leads us to one of the most significant insights in finance the **security market line (SML)**. The SML expresses required return as a function of the risk-free rate and a risk premium determined by beta. In other words, the SML quantifies the risk-return trade-off in terms of the asset\'s beta Ri=Rrf+βi(Rm−Rrf) CAPM=risk free rate + Beta (Return on market -- Risk free rate) where: *R~i~* = return on the *i*^ th^ security PEMDAS\ \ *R~rf~* = risk-free rate\ \ *R~m~* = return on the market\ \ β*~i~* = security's beta\ \ (*R~m~* − *R~rf~*) = market risk premium For example, suppose that a Treasury bond (our proxy for the risk-free rate) is yielding 6%, the expected return on the S&P 500 index is 12%, and Google has a beta of 1.7. According to the CAPM, what is Google's required rate of return? We have all the information needed to use the CAPM to find the expected rate of return. Here's how we would do it: E(RGoogle)=0.06+1.7(0.12−0.06)=0.162 or 16.2 IF THE SECURITY IS ABOVE THE SML LINE IT IS UNDERPRICED \| IF THE SECURITY IS BELOW THE SML LINE ITS OVERPRICED This means that the return on the security is too high for the amount of risk inherent in the security. If the return is too high, it means that the price is too low---the security is undervalued. **An Alternative to the CAPM: The Build-Up Method** =================================================== +-----------------------------------+-----------------------------------+ | | Bond yield | +===================================+===================================+ | \+ | Equity risk premium | +-----------------------------------+-----------------------------------+ | \+ | Micro-cap risk premium | +-----------------------------------+-----------------------------------+ | \+ | Start-up risk premium | +-----------------------------------+-----------------------------------+ | | **Required rate of return** | +-----------------------------------+-----------------------------------+ | | The bond yield and the equity | | | risk premium added together would | | | be the equivalent of the CAPM for | | | a security with a beta of | | | approximately 1. | | | | | | The micro-cap risk premium would | | | be added to the bond yield and | | | the equity risk premium if the | | | company is small (i.e., less | | | than, say, \$1 billion in sales). | | | | | | **Required rate= Bond yeild + | | | equity risk premium** | | | | | | **Well established small company | | | (Micro Cap equity rate) =Micro | | | cap risk premium + base equity | | | rate** | | | | | | **Start-up required rate of | | | return= Start up risk premium + | | | base equity** | +-----------------------------------+-----------------------------------+

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