Forecasting P/S for Magna

Auto parts maker Magna (MGA) started the month of November trading around $53 and then, wham!, it lost $5 in one day on the announcement of the Trans Pacific Partnership (TPP). The TPP is
a proposed partnership agreement that would establish terms of trade between 12 Pacific Rim countries: Australia, Brunei, Canada, Chile, Japan, Malaysia, Mexico, New Zealand, Peru, Singapore, the U.S., and Vietnam. One of  the concerns for auto parts maker Magna is that under NAFTA, only auto parts containing 60% North American content could move duty free between Canada, Mexico, and the US. The TPP reduces the local content threshold to something in the range of 35% to 40%.




Here is a plot of Magna's quarterly sales. The Great Recession had a huge impact on slowing Magna's sales, but afterward, sales climbed steadily until late 2014.

One interesting question is how does Magna currently compare on a standard valuation measure like price to sales (P/S). The P/S ratio, like P/E, P/B, and P/CF, is a measure of valuation. Lower values are preferred (generally less than 1 for P/S), but it is important to take into account industry effects. Also, like other valuation measures, a low P/S could indicate a value stock or it could indicate something else is wrong with the company.

My approach is to compare price to trailing 12 month sales with price to forward 12 month sales. If the forward P/S is less than the trailing P/S the company may be undervalued. For this comparison I will need forecasts of future sales.

I use a variety of different uni-variate models to forecast Magna's quarterly sales.  Forecasting approaches include  simple averages, Holt, Holt-Winters, ETS, ARIMA, and ANN. Data from the first quarter of 2001 to the fourth quarter of 2012 are used for training. Models are tested on out-of-sample forecasts over the period 2013:1 to 2015:3.

Here is table of forecast accuracy measures ranked on MASE.

	ME	RMSE	MAE	MPE	MAPE	MASE
Holt Winters training	10.3605	416.6794	272.9042	-0.1470	5.7363	0.3097
ETS training	101.3534	432.8289	308.9523	1.6208	6.4568	0.3506
STL training	112.1135	451.0617	310.0710	1.9976	6.5669	0.3519
ARIMA training	-0.1629	447.0967	321.3737	-0.3155	6.3713	0.3647
ANN2 training	0.9323	498.2682	385.9291	-0.9804	7.5023	0.4379
ANN training	-0.3573	501.1293	387.6661	-1.0337	7.5453	0.4399
Holt linear training	3.4478	516.7124	389.2279	-0.4852	7.8051	0.4417
Holt ES training	32.4932	522.0256	394.1387	0.2721	7.8724	0.4472
Holt dampled training	49.4785	519.0834	396.3995	0.3593	7.8883	0.4498
ES training	107.7185	527.2579	408.3396	1.5849	7.9818	0.4634
Naive training	110.0000	532.8356	417.0213	1.6185	8.1515	0.4732
Holt linear test	-151.2323	765.2259	576.4225	-2.2910	6.9925	0.6541
Holt damped test	297.9467	656.7112	583.8959	3.0695	6.7486	0.6626
Holt Winters test	24.8474	691.3100	601.4257	-0.1406	7.1852	0.6825
Holt ES test	-274.5440	859.5667	625.6039	-3.7699	7.6591	0.7099
Naive test	510.9091	739.0499	626.0000	5.6066	7.1001	0.7104
ES test	510.9714	739.0929	626.0396	5.6074	7.1005	0.7104
ARIMA test	-298.4399	823.3481	638.6404	-4.0160	7.7919	0.7247
STL test	578.2432	789.4180	648.2347	6.4402	7.3382	0.7356
ETS test	649.8151	815.6195	685.7139	7.2909	7.7528	0.7781
S. Naive test	864.0909	966.5054	864.0909	9.8515	9.8515	0.9805
S. Naive training	450.2500	1132.3782	881.2500	6.6540	17.4009	1.0000
ANN test	1073.7787	1149.9015	1073.7787	12.3361	12.3361	1.2185
ANN2 test	1105.4155	1178.8549	1105.4155	12.7111	12.7111	1.2544
Mean training	0.0000	1550.3499	1302.3281	-11.0193	29.8710	1.4778
Mean test	3184.2841	3228.7508	3184.2841	37.0207	37.0207	3.6134

Based on the MASE for the test measures, Holt linear trend ranks lowest. Notice, however, that Holt-Winters has the lowest absolute ME among the test measures. I will estimate the Holt-Winters approach on data from 2001:1 to 2015:3, and then forecast 6 quarters ahead.

Here is a plot of the forecasts.

Here are the forecasted values in table form.

         Qtr1     Qtr2     Qtr3     Qtr4
2015                            8385.564
2016 8185.603 8534.537 8029.078 8783.678
2017 8569.665 

Here is a comparison between the trailing P/S and the forward P/S.

     P/S ttm    P/S forward
[1,]  0.5509724   0.5480994

The forward P/S ratio is slightly less than the trailing P/S ratio indicating slight undervaluation.

It is important to compare company P/S ratios to industry averages. For this I use the auto parts P/S value of  0.69 from Damodaran, indicating that based on P/S, Magna is undervalued relative to the industry average.

As with any valuation exercise, it is important to compare these results for P/S with those of other valuation ratios like P/E, P/B, and P/CF.


The R code and data are posted below.

#########################################################
#  Economic forecasting and analysis
#  Fall 2015
#  Perry Sadorsky
#  Forecasting sales of Magna
#  with smoothing methods, ARIMA, and ANN
##########################################################


# load libraries
library(fpp)


# import data
as1_data <- read.csv("C:/econ 6210/6210f15/week 10/as1_data.csv")
View(as1_data)

df = as1_data


# define as time series
df = ts(df, start=2000, frequency=4)
df

# extract sales
 y = df[,"MGA"]
# y = df[,"SPLS"]
y

                      
# some graphs
par(font.axis = 2)
par(font.lab = 2)
plot(y, main = "MGA quarterly sales ($ millions)", xlab="", ylab="" , col ="blue", lwd=2)
tsdisplay(y)
par(mfrow = c(1,1))


# generate some returns
y.ret = diff(log(y)) * 100
tsdisplay(y.ret)
par(mfrow = c(1,1))                    


# training period
train <- window(y,start=c(2001, 1),end=c(2012, 4))
train

# test period
test <- window(y, start=2013)

# number of steps to forecast
h = length(test)

# out of sample forecast
y5 <- window(y,start=c(2001, 1)  )
h2 = 6

##########################################################
# forecast using simple methods
##########################################################


yfit1 <- meanf(train, h=h)
yfit2 <- naive(train, h=h)
yfit3 <- snaive(train, h=h)

plot(yfit1)
plot(yfit2)
plot(yfit3)

# make a nice plot showing the forecasts
plot(yfit1, plot.conf=FALSE,
main="Forecasts for quarterly TGT sales")
lines(yfit2$mean,col=2)
lines(yfit3$mean,col=3)
legend("topleft",lty=1,col=c(4,2,3),
legend=c("Mean method","Naive method","Seasonal naive method"))


# plot with forecasts and actual values
plot(yfit1, plot.conf=FALSE,
     main="Forecasts for quarterly TGT sales")
lines(yfit2$mean,col=2)
lines(yfit3$mean,col=3)
lines(y)
legend("topleft",lty=1,col=c(4,2,3),
       legend=c("Mean method","Naive method","Seasonal naive method"),bty="n")



##########################################################
# exponential smoothing approaches
##########################################################

# simple exponential moving averages
yfit4 <- ses(train, h = h)
summary(yfit4)
plot(yfit4)


# holt's linear trend method
yfit5 <- holt(train,  h=h)
summary(yfit5)
plot(yfit5)


# holt's exponential trend method
yfit6 <- holt(train, exponential=TRUE, h=h)
summary(yfit6)
plot(yfit6)


# holt's damped trend method
yfit7 <- holt(train, damped=TRUE, h=h)
summary(yfit7)
plot(yfit7)


# holt winter's  method
yfit8 <- hw(train, seasonal="multiplicative", h=h)
summary(yfit8)
plot(yfit8)


# ETS  method
y.ets <- ets(train, model="ZZZ")
summary(y.ets)
yfit9 <- forecast(y.ets, h=h)
summary(yfit9)
plot(yfit9)


# STL  method
y.stl <- stl(train, t.window=15, s.window="periodic", robust=TRUE)
summary(y.stl)
yfit10 <- forecast(y.stl, method="naive",h=h)
summary(yfit10)
plot(yfit10)


##########################################################
# arima method
##########################################################

y.arima <- auto.arima(train)
yfit11 <- forecast(y.arima, h=h)
plot(yfit11)


##########################################################
# ANN
##########################################################

fit.ann <- nnetar(train)
yfit12 = forecast(fit.ann,h=h)
plot(yfit12)


fit.ann2 <- nnetar(train, repeats= 100)
yfit13 = forecast(fit.ann2,h=h)
plot(yfit13)



##########################################################
# accuracy measures
##########################################################


a1 = accuracy(yfit1, test)
a2 = accuracy(yfit2, test)
a3 = accuracy(yfit3, test)
a4 = accuracy(yfit4, test)
a5 = accuracy(yfit5, test)
a6 = accuracy(yfit6, test)
a7 = accuracy(yfit7, test)
a8 = accuracy(yfit8, test)
a9 = accuracy(yfit9, test)
a10 = accuracy(yfit10, test)
a11 = accuracy(yfit11, test)
a12 = accuracy(yfit12, test)
a13 = accuracy(yfit13, test)


#Combining forecast summary statistics into a table with row names
a.table<-rbind(a1, a2, a3, a4, a5, a6, a7, a8, a9, a10, a11, a12, a13)

row.names(a.table)<-c('Mean training','Mean test', 'Naive training', 'Naive test', 'S. Naive training', 'S. Naive test' ,
                      'ES training','ES test', 'Holt linear training', 'Holt linear test', 'Holt ES training', 'Holt ES test' ,
                      'Holt dampled training','Holt damped test', 'Holt Winters training', 'Holt Winters test', 'ETS training', 'ETS test' ,     
                  'STL training','STL test', 'ARIMA training','ARIMA test', 'ANN training', 'ANN test','ANN2 training', 'ANN2 test' )

# order the table according to MASE
a.table<-as.data.frame(a.table)
a.table<-a.table[order(a.table$MASE),]
a.table

# write table to csv file
# write.csv(a.table, "C:/econ 6210/6210f15/week 10/atable.csv")


## forecast 6 periods into the future

plot(hw(y5, seasonal="multiplicative", h=h2))
par(mfrow = c(1,1))

y_forc =hw(y5, seasonal="multiplicative", h=h2)$mean
# y_forc = holt(y5, h=h2)$mean


# forecasted sales for 2016
# sales_f = y_forc[3] + y_forc[4] + y_forc[5] + y_forc[6]

sales_f = 0
for (i in 1:4){
sales_f = sales_f + y_forc[i]
  }
sales_f





# calculate price to forward sales
# data on November 21, 2015
price  = 44.94    # current stock prices
shares = 404.12   # millions of shares outstanding


ptos_f = price/(sales_f/shares)
ptos_f




# calculate price to trailing sales
last = tail(y,4)
sales_t = 0
for (i in 1:4){
  sales_t = sales_t + last[i]
}
sales_t


ptos_t = price/( sales_t /shares)
ptos_t

ps = cbind(ptos_t, ptos_f)
colnames(ps) = cbind("P/S ttm   ", "P/S forward")
ps

# compare with industry average
# http://pages.stern.nyu.edu/~adamodar/New_Home_Page/datafile/psdata.html
# auto parts 0.69


Data

datacqtr MGA 1 2000Q1 2808 2 2000Q2 2610 3 2000Q3 2354 4 2000Q4 2741 5 2001Q1 2863 6 2001Q2 2817 7 2001Q3 2517 8 2001Q4 2829 9 2002Q1 3121 10 2002Q2 2896 11 2002Q3 2962 12 2002Q4 3443 13 2003Q1 3496 14 2003Q2 3660 15 2003Q3 3566 16 2003Q4 4623 17 2004Q1 5103 18 2004Q2 5113 19 2004Q3 4784 20 2004Q4 5653 21 2005Q1 5718 22 2005Q2 5858 23 2005Q3 5381 24 2005Q4 5854 25 2006Q1 6019 26 2006Q2 6369 27 2006Q3 5424 28 2006Q4 6368 29 2007Q1 6423 30 2007Q2 6731 31 2007Q3 6077 32 2007Q4 6836 33 2008Q1 6622 34 2008Q2 6713 35 2008Q3 5533 36 2008Q4 4836 37 2009Q1 3574 38 2009Q2 3705 39 2009Q3 4669 40 2009Q4 5419 41 2010Q1 5512 42 2010Q2 6050 43 2010Q3 5942 44 2010Q4 6598 45 2011Q1 7189 46 2011Q2 7338 47 2011Q3 6970 48 2011Q4 7251 49 2012Q1 7666 50 2012Q2 7727 51 2012Q3 7411 52 2012Q4 8033 53 2013Q1 8361 54 2013Q2 8962 55 2013Q3 8338 56 2013Q4 9174 57 2014Q1 8455 58 2014Q2 8911 59 2014Q3 8820 60 2014Q4 9396 61 2015Q1 7772 62 2015Q2 8133 63 2015Q3 7661

US Airline Woes

More travelers are flying than ever before and yet airlines have a difficult time making money. The airline industry is a tough business to be in. Airplanes, fuel and people are the three biggest costs to airlines. New airplanes cost money and borrowed money is vulnerable to interest rate fluctuations. The price of jet fuel fluctuates with movements in the petroleum markets. Airlines require lots of people to make your flight as smooth as possible. The difficulties of running a profitable airline have pushed some US  carriers into bankruptcy and created incentives to merge. US Airways has been through Chapter 11 bankruptcy proceedings twice and United and Delta each once. American recently filed for Chapter 11 and now it looks like a merger with US Airways is in the works. Mergers, however, often do not work out as planned with the anticipated  managerial efficiencies and scale effects failing to materialize.

How efficient are US airlines? Using data published in a recent Economist article, I investigate the efficiency of US airlines.

To calculate technical efficiency I use data envelope analysis (DEA).  DEA is a non-parametric approach to the estimation of production functions. I use four inputs (global capacity, domestic market share, employees, delayed/cancelled flights)  and two outputs (market capitalization, operating profits).  For those interested in the technical details, I use the 2 stage input approach with variable returns to scale (VRS).

The DEA results are presented in the above table. Total technical efficiency (CRS_TE) can be broken down into pure technical efficiency (VRS_TE) and a scale effect. The total technical efficiency measures indicate that US Airways, Delta, Southwest, and Alaska are efficient since their CRS_TE measures are equal to one. These companies are operating on the boundary of the production possibility frontier. The other companies are inefficient with American being the least efficient. American for example, can reduce its inputs by 99% and still produce the same output (measured by market capitalization and operating profits). This really shows the extent of American's problems. Pure technical efficiency (VRS_TE) is a measure of manager effectiveness. American's inefficiency is coming from a combination of managerial inefficiency (VRS_TE) and a scale effect inefficiency. American has the least effective management and the largest scale inefficiency. The unity value in the RTS column indicates that American is operating with increasing returns to scale. American needs to get bigger and become more efficient. I wonder if US Airways knows the extent of these inefficiencies and how difficult it is going to be to get the merger to work.

A Shake Up at CP

Canadian Pacific (CP) railroad recently announced substantial job cuts. The plan is for a one quarter cut in its work force by 2016.The job cuts will be achieved through attrition and not filling jobs when people quit or retire. CP has been the subject of much discussion lately with claims that the company is inefficient.

From the CBC:

"The strategic moves are the latest for the railway since a new board of directors installed CEO Hunter Harrison in the summer following a bitter proxy fight with the company's largest shareholder."


CP can be compared with its competitors to see how efficient it is. To calculate technical efficiency I use data envelope analysis (DEA).  DEA is a non-parametric approach to the estimation of production functions. I use three inputs (employees, total assets, total operating costs) and one output (total revenues). Data are averages over the years 2005 - 2011. For those interested in the technical details, I use the 2 stage input approach with variable returns to scale (VRS).

The DEA results are presented in the above table. Total technical efficiency (CRS_TE) can be broken down into pure technical efficiency (VRS_TE) and a scale effect. The total technical efficiency measures indicate that only Canadian National and Union Pacific are efficient since their CRS_TE measure are equal to one. The other companies are inefficient. CP for example, can reduce its inputs by 6% and still produce the same output. Kansas City Southern in even more inefficient because it can reduce its inputs by 10% and produce the same output. In the case of Kansas City Southern, the pure technical efficiency measure of 1 indicates that allocation of inputs to output is efficient and the inefficiencies are coming from the scale effect which measures the size of the company. Four companies have increasing returns to scale (IRS). CP suffers from a technical efficiency effect and a scale effect.  CP needs to get bigger and use its inputs more efficiently. CP's recent announcement on job cuts is a move in the right direction.

CP's share price suffered through 2011, but has recovered nicely since this summer when new management took over.

HP Needs a New Way

I have a particular fondness for HP because I remember reading "The HP Way" when it first came out in 1995. The book is written by David Packard and tells the story of HP from the beginning. In the book Packard explains that he is not a big fan of the MBA degree but is more interested in the MBWA (Management By Walking Around). HP's success was built on excellent products, technological innovation, knowing the customers, and adapting to change.After reading the book, I though, "wow! what an amazing company". HP was admired by many people and many business cases were written about it. HP is after all, credited as the founder of Silicon Valley.
 
In the 2000s HP pursued an aggressive expansion strategy that involved buying big companies (the merger with Compaq in 2002, the acquisition of EDS in 2008, the acquisition of 3Com in 2009 and the buyout of Palm in 2010). With this many big deals in such a relatively short period of time, critics wondered where the synergies were coming from. Along the way, HP had a number of product issues and accounting issues.
 
Now the company is in a death spiral. The stock is now trading at a 10 year low after recently announcing a $8.8 billion write-down and poor quarterly results (see here). HP is reeling from its $11 billion purchase of Autonomy. This was a move designed to help HP move farther into software and services (something that IBM has successfully done).

Over the past 2 years HP is down almost 70%. DELL has also had a difficult past 2 years, while  MSFT is holding steady.

HP can be compared with its competitors to see how efficient it is. To calculate technical efficiency I use data envelope analysis (DEA).  DEA is a non-parametric approach to the estimation of production functions. I use three inputs (employees, total assets, total operating costs) and one output (total revenues). Data are averages over the years 2004 - 2011. For those interested in the technical details, I use the 2 stage input approach with variable returns to scale (VRS).

The DEA results are presented in the above table. Total technical efficiency (CRS_TE) can be broken down into pure technical efficiency (VRS_TE) and a scale effect. The total technical efficiency measures indicate that Apple, Google, Dell, Microsoft and Accenture are efficient since their CRS_TE measures are equal to one. Cisco and HP are inefficient. HP. for example, can reduce its inputs by 1% and still produce the same output. In the case of HP, the pure technical efficiency measure of 1 indicates that allocation of inputs to output is efficient and the inefficiencies are coming from the scale effect which measures the size of the company. HP exhibits decreasing returns to scale (RTS) which means that given its production possibility frontier it is producing too much output. Value creation under decreasing returns to scale is difficult because decreasing returns to scale means that HP needs to get smaller.

How Efficient is Reseach in Motion?

Watching Research in Motion's (RIMM) stock price fall over the past few years has been difficult. While RIMM gets singled out for its poor stock price performance and Apple becomes the most valuable company in the world by stock market capitalization, it is important to point out that some of RIMM's competitors have not been doing so well. Over the past year, Apple has been the clear winner, but Ericson, Nokia and Research in Motion have each underperformed.

One thing to remember about companies based on cutting edge technologies is that no company can be the leader forever. The product landscape changes. What is new today becomes common place in the future. Think about the cutting edge technology companies of 15 years ago (Microsoft, Cisco, Dell). These companies are still in business but now they are no longer considered young dynamic upstarts but rather established mature companies. In my view, handset makers are entering a more mature phase in which the explosive growth in hand sets is going  to slow considerably. A new United Nations report reveals that there are now 6 billion cellphone users in the world. That means that 86 out of every 100 people now have a cellphone.

A different way to compare RIMM with its competitors is to calculate how efficient it is. To calculate technical efficiency I use data envelope analysis (DEA).  DEA is a non-parametric approach to the estimation of production functions. I use three inputs (employees, total assets, total operating costs) and one output (total revenues). Data are for the year 2011. Samsung is omitted from the comparison because it is a huge multi-product conglomerate. For those interested in the technical details, I use the 2 stage input approach with variable returns to scale (VRS).

The DEA results are presented in the above table. Total technical efficiency (CRS_TE) can be broken down into pure technical efficiency (VRS_TE) and a  scale effect. The total technical efficiency measures indicate that Apple, Google and Research in Motion are efficient since their CRS_TE measures are equal to one. Ericsson, Motorola are Nokia are inefficient. Nokia. for example, can reduce its inputs by 29% and still produce the same output. In the case of Motorola, the pure technical efficiency measure of 1 indicates that management is efficient and the inefficiencies are coming from the scale effect which measures the size of the company. So, while Research in Motion's stock price has suffered over the past year, it is, at least by these calculations, an efficient company.