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\author{deluded1}
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  /Title (fin-531-corporate-finance.pdf)
  /Creator (Cheatography)
  /Author (deluded1)
  /Subject (FIN 531 Corporate Finance Cheat Sheet)
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\noindent
\begin{multicols}{3}
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    {\parbox{\dimexpr\textwidth-2\fboxsep\relax}{\noindent
        \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}}
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    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{FIN 531 Corporate Finance Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{deluded1} via \textcolor{DarkBackground}{\uline{cheatography.com/42545/cs/12802/}}}
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\noindent
\begin{multicols}{3}
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  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}deluded1 \\
  \uline{cheatography.com/deluded1} \\
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Published 3rd October, 2017.\\
   Updated 3rd October, 2017.\\
   Page {\thepage} of \pageref{LastPage}.
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Sponsor}}  \\
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  \vspace{-5pt}
  %\includegraphics[width=48px,height=48px]{dave.jpeg}
  Measure your website readability!\\
  www.readability-score.com
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\end{multicols}}




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\begin{multicols*}{3}

\begin{tabularx}{5.377cm}{x{2.33919 cm} x{2.63781 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Calculating Portfolio Risk}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{σ\textasciicircum{}2\textasciicircum{}=W`a`\textasciicircum{}2\textasciicircum{}σ`a`\textasciicircum{}2\textasciicircum{}+W`b`\textasciicircum{}2\textasciicircum{}σ`b`\textasciicircum{}2\textasciicircum{}+2(W`a`W`b` Cor σ`a`σ`b`)} \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
σ`x`=standard deviation & σ\textasciicircum{}2\textasciicircum{}= variance of portfolio \tn 
% Row Count 4 (+ 2)
% Row 2
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W`x` = weight of stock in portfolio & Covariance of stocks = correlation *σ`a`*σ`b` \tn 
% Row Count 7 (+ 3)
% Row 3
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\mymulticolumn{2}{x{5.377cm}}{σ = risk of an individual stock} \tn 
% Row Count 8 (+ 1)
% Row 4
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\mymulticolumn{2}{x{5.377cm}}{{\ss} = Market risk} \tn 
% Row Count 9 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{If you need to find out the standard deviation, take the square root of the answer.  Variance, leave it squared.}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{2.33919 cm} x{2.63781 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Book Rate of Return}}  \tn
% Row 0
\SetRowColor{LightBackground}
Book Rate of Return= & Book income/book assets \tn 
% Row Count 2 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Payback \& Discounted Payback Period}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Payback = \# of years to payback investment (no NPV adjustment)} \tn 
% Row Count 2 (+ 2)
% Row 1
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\mymulticolumn{1}{x{5.377cm}}{Discounted = \# of years to payback investment NPV adjustment)} \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{NPV= \seqsplit{C`0`+(C`1`/(1+r`1`))+(C`2`/(1+r`2`))}..............(C`t`/(1+r`t`))} \tn 
% Row Count 6 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Non-constant growth valuation  stock}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{G1= 20\% for 2 years; G2=5\% for rest of time  \newline % Row Count 1 (+ 1)
D0=1.25  \newline % Row Count 2 (+ 1)
D1=1.25(1.20) = 1.50 \newline % Row Count 3 (+ 1)
D2=1.25(1.20)\textasciicircum{}2\textasciicircum{}=1.80 \newline % Row Count 4 (+ 1)
D3=1.25(1.20)\textasciicircum{}2\textasciicircum{}(1.05) =1.89 \newline % Row Count 5 (+ 1)
D4=1.25(1.20)\textasciicircum{}2\textasciicircum{}(1.05)\textasciicircum{}2\textasciicircum{}=1.98% Row Count 6 (+ 1)
} \tn 
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\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Internal rate of return | IRR}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{NPV must =0 to calculate} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{NPV=C`0`+C`1`/(1+IRR)\textasciicircum{}1\textasciicircum{}+C`2`/(1+IRR)\textasciicircum{}2\textasciicircum{}=0} \tn 
% Row Count 2 (+ 1)
% Row 2
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\mymulticolumn{1}{x{5.377cm}}{Must use Excel to calculate} \tn 
% Row Count 3 (+ 1)
% Row 3
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\mymulticolumn{1}{x{5.377cm}}{Pitfall 1 = Lending or borrowing?} \tn 
% Row Count 4 (+ 1)
% Row 4
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\mymulticolumn{1}{x{5.377cm}}{Pitfall 2 = Multiple rates of return (when cash goes from + to -)} \tn 
% Row Count 6 (+ 2)
% Row 5
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\mymulticolumn{1}{x{5.377cm}}{Pitfall 3 = Mutually exclusive projects- IRR sometimes ignores magnitude of a project} \tn 
% Row Count 8 (+ 2)
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\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Pitfall 4 – What Happens When There is More than One Opportunity Cost of Capital \newline  \newline Term Structure Assumption \newline We assume that discount rates are stable during the term of the project.   \newline This assumption implies that all funds are reinvested at the IRR.   \newline This is a false assumption.}  \tn 
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\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Covariance of multiple stocks}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{With 100 securities, the box is    100 by 100.The variance terms are the diagonal terms, and thus there are 100 variance terms.  The rest are the covariance terms.  Because the box has(100 ×   100) terms altogether, the number of covariance terms is:Number of covariance terms = 1002–   100 = 9,900Half of these terms (i.e., 4,950) are different. \newline % Row Count 7 (+ 7)
bWith 50 stocks, all with the same standard deviation (.30), the same weight in the portfolio (.02), and all pairs having the same correlation coefficient (.40), the portfolio variance is \newline % Row Count 11 (+ 4)
:σ2=   50(.02)2(.30)2+   {[}(50)2–   50{]}(.02)2(.40)(.30)2= .03708σ   =   .193, or 19.3\% \newline % Row Count 13 (+ 2)
c.For a fully diversified portfolio, portfolio variance equals the average covariance:σ2=   (.30)(.30)(.40) = .036σ   =   .190, or 19.0\%% Row Count 16 (+ 3)
} \tn 
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\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Efficient Frontier}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/deluded1_1507065175_Markowitz_frontier.jpg}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
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\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Present Value of a Growing Perpetuity}}  \tn
% Row 0
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\mymulticolumn{1}{x{5.377cm}}{PV = CF1 / r - g r \textgreater{} g} \tn 
% Row Count 1 (+ 1)
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\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Bond Valuation}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{PV=C1/(1+r)\textasciicircum{}1\textasciicircum{}+C2/(1+r)\textasciicircum{}2\textasciicircum{}...+(Par+Cn)/(1+r)\textasciicircum{}n\textasciicircum{}} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Duration = {[}1xPV (c1){]}/PV+{[}2xPV (c2){]}/ PV...+(TxPV(CT){]}/PV} \tn 
% Row Count 3 (+ 2)
% Row 2
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\mymulticolumn{1}{x{5.377cm}}{Modified Duration = volatitliy (\%)=duration/(1+yield)} \tn 
% Row Count 5 (+ 2)
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\end{tabularx}
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\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{DPS Calculation}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{D0=1.50 \newline % Row Count 1 (+ 1)
D1=1.50(1.07) \newline % Row Count 2 (+ 1)
D2=1.50(1.07)\textasciicircum{}2\textasciicircum{} \newline % Row Count 3 (+ 1)
D3=1.50(1.07)\textasciicircum{}3\textasciicircum{} \newline % Row Count 4 (+ 1)
D4=1.50(1.07)\textasciicircum{}3\textasciicircum{}(1.05) \newline % Row Count 5 (+ 1)
D5=1.50(1.07)\textasciicircum{}3\textasciicircum{}(1.05)\textasciicircum{}2\textasciicircum{}% Row Count 6 (+ 1)
} \tn 
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\begin{tabularx}{5.377cm}{x{3.73275 cm} p{1.24425 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Sharpe Ratio = (r-r`f`)/(σ)}}  \tn
% Row 0
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Risk premium & r-r`f` \tn 
% Row Count 1 (+ 1)
% Row 1
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Standard Deviation & σ \tn 
% Row Count 2 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{Ratio of risk premium to standard deviation.  Measures risk-adjusted performance of investment managers}  \tn 
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\end{tabularx}
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\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{SML}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/deluded1_1507059284_SML-chart (1).png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{The Y-intercept of the SML is equal to the risk-free interest rate. The slope of the SML is equal to the market risk premium and reflects the risk return trade off at a given time. \newline where: \newline  \newline E(Ri) is an expected return on security \newline E(RM) is an expected return on market portfolio M \newline β is a nondiversifiable or systematic risk \newline RM is a market rate of return \newline Rf is a risk-free rate}  \tn 
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\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Efficient Frontier}}  \tn
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\mymulticolumn{1}{x{5.377cm}}{The efficient frontier is the set of optimal portfolios that offers the highest expected return for a defined level of risk or the lowest risk for a given level of expected return. Portfolios that lie below the efficient frontier are sub-optimal, because they do not provide enough return for the level of risk.% Row Count 7 (+ 7)
} \tn 
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\begin{tabularx}{5.377cm}{p{1.09494 cm} x{3.88206 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Stock Returns}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{R=(P`t+1`-P`t`+D)/(P`t`)} \tn 
% Row Count 1 (+ 1)
% Row 1
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R= & Return \tn 
% Row Count 2 (+ 1)
% Row 2
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P`t`= & Stock Price @ time \tn 
% Row Count 3 (+ 1)
% Row 3
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D = & Dividend \tn 
% Row Count 4 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
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\begin{tabularx}{5.377cm}{x{2.23965 cm} x{2.73735 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{CAPM = Capital Asset Pricing Model}}  \tn
% Row 0
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r`i`=r`f`+{\ss}(r`m`-r`f`) & {\ss}=Beta \tn 
% Row Count 2 (+ 2)
% Row 1
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r`f`= risk free rate & r`m` = market rate \tn 
% Row Count 4 (+ 2)
% Row 2
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i = investment & E(r) = expected return \tn 
% Row Count 5 (+ 1)
% Row 3
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Expected risk premium on stock= & beta x expected risk premium on market \tn 
% Row Count 7 (+ 2)
% Row 4
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\mymulticolumn{2}{x{5.377cm}}{r-r`f`={\ss}(r`m`-r`f`)} \tn 
% Row Count 8 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{Beta is the extent to which a stock moves with the market.  CAPM says that the higher the Beta, the higher the risk}  \tn 
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\end{tabularx}
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\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Market Efficiency}}  \tn
% Row 0
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\mymulticolumn{1}{x{5.377cm}}{1.) Weak = Market reflects past info} \tn 
% Row Count 1 (+ 1)
% Row 1
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\mymulticolumn{1}{x{5.377cm}}{2.) Semi-Strong = Past \& Current public info is reflected} \tn 
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% Row 2
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\mymulticolumn{1}{x{5.377cm}}{3.) All information is reflected in the stock price (public \& private)} \tn 
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\mymulticolumn{1}{x{5.377cm}}{Efficient Market - Market in which information is reflected in stock prices quickly + correctly}  \tn 
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\begin{tabularx}{5.377cm}{p{0.4977 cm} p{0.4977 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Profitability Index}}  \tn
% Row 0
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\mymulticolumn{2}{x{5.377cm}}{PI = NPV/Investment} \tn 
% Row Count 1 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{Another Example - continued \newline Proj	NPV 		Investment	PI \newline A		230,000	200,000	1.15 \newline B		141,250	125,000	1.13 \newline C		194,250	175,000	1.11 \newline D		162,000	150,000	1.08 \newline  \newline Select projects with highest Weighted Avg PI \newline WAPI (BD) = 1.13(125) + 1.08(150) + 0.0 (25) \newline                                (300)           (300)         (300) \newline                      = 1.01}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
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\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Captal Rationing}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Capital Rationing - Limit set on the amount of funds available for investment. \newline % Row Count 2 (+ 2)
Soft Rationing - Limits on available funds imposed by management. \newline % Row Count 4 (+ 2)
Hard Rationing - Limits on available funds imposed by the unavailability of funds in the capital market.% Row Count 7 (+ 3)
} \tn 
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\end{tabularx}
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\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Market Risk premium}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{=r`m`-r`f`} \tn 
% Row Count 1 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{For any investment, we can find the opportunity cost of capital using the security market line.  With  = 0.8, the opportunity cost of capital is: \newline r = rf + B(rm – rf) \newline r = 0.04 + {[}0.8 B (0.12 – 0.04){]} = 0.104 = 10.4\% \newline  \newline The opportunity cost of capital is 10.4\% and the investment is expected to earn 9.8\%.  Therefore, the investment has a negative NPV. \newline  \newline If return is 11.2\% What is Beta? \newline r = rf + (rm – rf) \newline 0.112 = 0.04 + (0.12 – 0.04)   = 0.9}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
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% That's all folks
\end{multicols*}

\end{document}