Recently, in my financial statements analysis class, I had to perform a valuation of Apple Inc. with a number of different valuation methods. One of the things that made valuation simpler is the lack of long-term debt on Apple's balance sheet. This simple fact means that Apple's WACC is equal to the cost of equity.

To find the cost of equity, I use CAPM, which states

where is the expected return on capital, after accounting for the market risk premium. To find the component pieces , , and , I will use R with the quantmod package, and I will also use the PerformanceAnalytics Package, although I will show you how to avoid using it if you choose.

The sourcecode for the project:

^{?}Download betacalc.r

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 | #Packages required require(PerformanceAnalytics) require(quantmod) require(car) #Here we get the symbols for the SP500 (GSPC), AAPL, and 5yr Treasuries (GS5) getSymbols("^GSPC", src = "yahoo", from = as.Date("2008-01-01"), to = as.Date("2011-12-31")) getSymbols("AAPL", src = "yahoo", from = as.Date("2009-01-01"), to = as.Date("2011-12-31")) getSymbols("GS5", src = "FRED", from = as.Date("2008-12-01"), to = as.Date("2011-12-31")) #Market risk R_m is the arithmetic mean of SP500 from 2009 through 2011 #Riskfree rate is arithmetic mean of 5yr treasuries marketRisk<- mean(yearlyReturn(GSPC['2009::2011'])) riskFree <- mean(GS5['2009::2011']) #My professor advised us to use weekly returns taken on wednesday #so I take a subset of wednesdays and use the quantmod function #weeklyReturn() AAPL.weekly <- subset(AAPL,weekdays(time(AAPL))=='Wednesday') AAPL.weekly <- weeklyReturn(AAPL['2009::2011']) GSPC.weekly <- subset(GSPC,weekdays(time(GSPC))=='Wednesday') GSPC.weekly <- weeklyReturn(GSPC['2009::2011']) #Here I use PerformanceAnalytics functions for alpha+beta #Then we calculate Cost of equity using our calculated figures AAPL.beta <- CAPM.beta(AAPL.weekly,GSPC.weekly) AAPL.alpha <- CAPM.alpha(AAPL.weekly,GSPC.weekly) AAPL.expectedReturn <- riskFree + AAPL.beta * (marketRisk-riskFree) #For my graph, I want to show R^2, so we get it from the #lm object AAPL.reg AAPL.reg<-lm(AAPL.weekly~GSPC.weekly) AAPL.rsquared<-summary(AAPL.reg)$r.squared #Lastly, we graph the returns and fit line, along with info scatterplot(100*as.vector(GSPC.weekly),100*as.vector(AAPL.weekly), smooth=FALSE, main='Apple Inc. vs. S&P 500 2009-2011',xlab='S&P500 Returns', ylab='Apple Returns',boxplots=FALSE) text(5,-10,paste('y = ',signif(AAPL.alpha,digits=4),' + ',signif(AAPL.beta,digits=5),'x \n R^2 = ',signif(AAPL.rsquared,digits=6),'\nn=',length(as.vector(AAPL.weekly)),sep=''),font=2) |

The code is commented, but I will make some additional comments on specific sections to explain the process for those unsure. I apologize for my unstandardized variable names as well!

First of all, I use the getQuotes() function, which has a few sources. In this example, I use Yahoo data for equity data and FRED for information on 5yr Treasuries. For reference, the ticker for retrieving the SP500 on Yahoo is "^GSPC", and the FRED code for 5yr treasuries is "GS5". Other symbols should be self explanatory.

Next is the issue of regression parameters. To find alpha and beta, I use the capm functions of PerformanceAnalytics, but to find I read it out of the the regression object using

^{?}View Code RSPLUS

1 2 | AAPL.reg <- lm(AAPL.weekly~GSPC.weekly) AAPL.rsquared <- summary(AAPL.reg)$r.squared |

It is possible to do this with beta and alpha, however, I did not do this because I did not originally did not start out to find , and turned to PerformanceAnalytics out of convenience.

Finally, I graphed the results and regression line for the benefit of my teacher, the results of which can be seen here:

Thank you for providing this code. I used it as a starting point. I'm not sure the formula in the regression is correct. It doesn't appear to be incorporate the risk free rate. The regression should be based on each security's excess returns over the expected return of a riskless assest.

[WORDPRESS HASHCASH] The poster sent us '358469740 which is not a hashcash value.

Haha thanks, I will check out the code tonight and see what I did wrong