Center for Freelance Writing: February 2012

Wednesday, February 29, 2012

LinkedIn Corporation (NYSE: LNKD)

Launched in 2003, LinkedIn has grown to be world's largest professional network with over 150 million users, with the majority located outside of the United States. In 2011, LinkedIn members performed over 4.2 billion "professionally-oriented searches" on the platform, on which over 2 million companies have public profiles. Remarkable, considering that it is almost nearing a decade in operation, is the continuous growth. For 2011, annual revenue was up 155% and stood at $522 million. This follows performances in 2009 and 2010, which saw revenue grow annually at 52% and 102%, respectively. Members, unique users, and page views in 2011 all increased around 60%.

LinkedIn still trumps Twitter and Facebook when it comes to use from recruitment companies. While the latter two are experiencing rises in the use for recruitment, LinkedIn maintains its edge as it is "geared up as a professional networking facility." The internal news section, LinkedIn Today, is filled with business- or career-oriented stories, and have Wall Street Journal, CNN Money, and Bloomberg as some of its top sources. This is a wide contrast to Facebook and Twitter, which are social networks without any specific categorizations.

This past week, Linked acquired the start-up Rapportive for 15 million in cash. Rapportive is a Gmail plugin that shows users the latest social network updates from others that the user corresponds with. CEO of Rapportive has mentioned that the services will be supported by LinkedIn. The service will allow users to skip the Google search of names, thereby "cutting off Google+’s opportunity to steal the click."

At the closing of trading on February 28, LinkedIn traded at 86.95. With a market cap of $8.38 billion and annual net income of $11.9 million in 2011, the P/E ratio is at a whopping value greater than 700. Google and Yahoo both have values at or around 20. In terms of price-to-sales ratio, the value of 16 is still significantly high, but is lower than Facebook's projected value. One reason for the high price ratios of LinkedIn is its relatively low profit margin. At 2.28% for 2011, it is drastically lower than Google's 25.69%. However, looking at the 2011 income statements, an amount of $132 million, or about 25% of the total revenue, was spent on research and development, nearly doubling Google's figure of 13.6%. Whether or not LinkedIn can sustain the recent growth, and whether or not the heavy research and development can lead to continuously innovative services will ultimately decide the trajectory of LinkedIn.

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Monday, February 27, 2012

Binomial vs. Poisson vs. Normal Distribution

Consider this scenario: Given 100 bottles, each of which independently has 10% chance of being defected, what's the chance that up to 0 will be defected? Up to 1 will be defected? Up to 2? 3? ... Change to a general case, given (n) samples, each of which independently has probability (p) of returning true, what's the probability that up to (k) of the samples will return true? The binomial distribution gives an exact answer, while Poisson and normal distribution help to approximate an answer, with varying accuracy depending on the scenario.

Write MATLAB code as follows. In this case, n = 100, p = 0.05, and k = 0 to 10, but all of those values can be easily changed manually. The first column of the vector were manually-chosen (k) values for which the cumulative probability values want to be calculated:

result = 0;
table = zeros(11,4);
table(:,1) = [0;1;2;3;4;5;6;7;8;9;10];
n = 100;
p = 0.05;

for i=1:11
    table(i,2) = binocdf(i,n,p);
    table(i,3) = poisscdf(i,n*p);
    table(i,4) = normcdf((i+0.5-n*p)/(n*p*(1-p))^0.5);
end
table

Now use and tweak the program (value of n, p, and table(:,1)) above to run through two cases. In case 1, n is big while p is small. In case 2, p is relatively large. The combination of MATLAB results and Excel calculations were used to produce this table:

Case 1: n = 200, p = 0.02, λ = 4

k	Binomial	Poisson	Normal	Pois Error	Norm Error
0	0.0176	0.0183	0.0385	3.98%	118.75%
1	0.0894	0.0916	0.1034	2.46%	15.66%
2	0.2351	0.2381	0.2243	1.28%	-4.59%
3	0.4315	0.4335	0.4003	0.46%	-7.23%
4	0.6288	0.6288	0.5997	0.00%	-4.63%
5	0.7867	0.7851	0.7757	-0.20%	-1.40%
6	0.8914	0.8893	0.8966	-0.24%	0.58%
7	0.9507	0.9489	0.9615	-0.19%	1.14%
8	0.9798	0.9786	0.9885	-0.12%	0.89%
9	0.9925	0.9919	0.9973	-0.06%	0.48%
10	0.9975	0.9972	0.9995	-0.03%	0.20%

Case 2: n = 100, p = 0.4, λ = 40

k	Binomial	Poisson	Normal	Pois Error	Norm Error
15	0	0	0	#DIV/0!	#DIV/0!
20	0	0.0004	0	#DIV/0!	#DIV/0!
25	0.0012	0.0076	0.0015	533.33%	25.00%
30	0.0248	0.0617	0.0262	148.79%	5.65%
35	0.1795	0.2424	0.1792	35.04%	-0.17%
40	0.5433	0.5419	0.5406	-0.26%	-0.50%
45	0.8689	0.8097	0.8692	-6.81%	0.03%
50	0.9832	0.9474	0.984	-3.64%	0.08%
55	0.9991	0.9903	0.9992	-0.88%	0.01%
60	1	0.9988	1	-0.12%	0.00%
65	1	0.9999	1	-0.01%	0.00%

These data show that Poisson distribution is a better approximation when p is small, while normal distribution is a better approximation when p is large. As the numbers here were copied from MATLAB onto Excel, rounding errors have be distorted the percentage error calculations a bit.

Sunday, February 26, 2012

Otis Elevator Company

While the frontier of transportation may focus on long-distance travel, it is the short-distance travel that is at the foundation. When it comes to elevators, Otis Elevator Company has been manufacturing, installing, and maintaining elevators since 1853. Today, approximately 2.4 million Otis elevators and escalators are in operation worldwide. In 2010, the company generated $11.6 billion in revenue, with the majority coming from services, and nearly fourth-fifth coming from outside of the United States. Business outlook of Otis correlates directly with global economic outlook. In 2011, Otis estimated that over two-thirds of the expected new units will be installed in China. At the same time though, it is engaging in high-profile projects domestically as well; it won a contract last June to replace 68 original lifts in Empire State building, on top of a 10-year maintenance contract.

Otis Elevator Company is wholly owned by United Technologies Corporation (NYSE: UTX). Based in Hartford, CT, United Technologies Corporation registered over $58 billion in revenue in 2011 and over $75 billion in market cap presently. UTX provides "high technology products and services to the building systems and aerospace industries" and employs over 200,000 people worldwide. Annual revenue fell over 10% in 2009, but has been consistently increasing for each of the past two years. In terms of prices, UTX has not gained back the losses since last July, but has gained nearly 10% year-to-date, closing most recently at 83.97.

Sources:

Tuesday, February 21, 2012

Madison Square Garden, Inc. (NASDAQ: MSG)

New York Knicks fans may have been disappointed at their team's loss to the rival New Jersey Nets on Monday night, particularly given that it marked the return of Carmelo Anthony. That said, the team is still currently riding on the momentum and sensations built by the rise of Jeremy Lin. While Lin and the Knicks have been on the headlines in ESPN or CNN, they have been featured in the Wall Street Journal as well. Most people may know Madison Square Garden, or simply MSG, as the iconic arena that is home to he Knicks. But it is also a $2.49 billion market cap publicly traded company on the NASDAQ.

As of Monday, February 13th, or about a week since Lin's rise in the Knicks, prices of MSG stock rose over 10% during the period, finishing at $32.32. As of Monday, February 20th, which didn't see trading due to President's Day, the price is still $32.85. With Knicks' recent success, it has meant more viewers: "MSG said its ratings for Knicks games are up 52 percent during Lin's four starts compared to the rest of the season." The recent spike has also put pressure on MSG and Time Warner Cable to settle their disputes, which has affected 2 million subscribers since Jan 1st; the dispute has recently been resolved.

As far as the company goes, MSG is divided into the business segments of MSG Sports, MSG Media and MSG Entertainment. With James Dolan as the CEO, MSG owns not only the Knicks, but also New York Rangers of NHL. As far as its financial statements go, the total equity has exceed total liability for each of the last 4 years. Revenue for Q4-2011 dropped from Q4-2010, but that is largely attributed to the NBA lockout. The success of the Knicks, with its new face of Jeremy Lin, will ultimately dictate the success of MSG.

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Monday, February 20, 2012

Starbucks Corporation (NASDAQ: SBUX)

Founded in 1971, Starbucks is now the largest coffeehouse company in the world with over 17,000 retail stores in 55 countries. During its lifetime, expansion and acquisition have defined the growth of Starbucks, which now has over $11 billion in annual sales and a market cap of $36.5 billion. In 1996, when the total store count was only around 1000, Starbucks opened its first store outside of North America, with branches in Japan and Singapore. In 2003, Starbucks acquired Seattle Coffee Company, which includes Seattle’s Best Coffee. In 2010, Starbucks began to offer customers with free, unlimited Wi-Fi.

Since going public in 1992 at $0.53 per share, after adjusting for stock splits, prices climbed until reaching a peak in 2006. After hitting a low below $8 in late 2008, the shares have bounced back up to the high 40s, closing most recently at 48.45. For Q4-2011, Starbucks reported net income of $382 million, up over 10% from the same quarter previous year. Total revenue saw 16% increase across the same time. Starbucks has benefited from consumer products business, including the sales of Starbucks ice cream. While the P/E ratio of 29.22 may initially seem high, it is far below that of Dunkin' Brands Group (NASDAQ: DNKN) at over 100. Caribou Coffee Company (NASDAQ: CBOU) has P/E at around 10.45, but its market cap size is about two orders of magnitude smaller than that of Starbucks.

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Monday, February 13, 2012

Apple (NASDAQ: AAPL) Pushes Above $500

Apple has toppled the $500-per-share mark for the first time, but the climb may be far from over. Since the January 24th announcement that Apple posted net income in excess of $13 billion and sales in excess of $46 billion, which is more than double, and up 73% from previous year, respectively, Apple's share has soared from around $420 to climb over $80, nearly 20% gain, in less than 3 weeks. Apple had been in contest with Exxon Mobil as the largest company, but with a market valuation of $465 billion, it is now the conspicuous spearhead.

What's next for Apple? While the release of iPad 3 will be highly anticipated in March, the prospect of dividends has certainly fueled the continual rise. Former CEO Steve Jobs was opposed to dividends, but that could begin to change in the shareholder meeting on February 23rd. A 2.5 dividend yield would translate currently to around $12.50 annual dividend a share. Given the current count of 932.37M stocks and 502.60 closing price, it would cost Apple 932.37M * 0.025 * 502.60 = around $11.7 billion. Even that would only be a fraction of the $17.5 Apple brought in Q4-2011 in cash flow from operations itself. That said, Apple has recently used much of its cash in investments. In the 52 weeks closing at end of Q3-2011, Apple actually saw negative net cash flows. However, with cash and short-term investments totaling over $30 billion as of end of Q4-2011, Apple would still have a solid current ratio of 1.24 if $11.7 billion of short-term investments were removed.

While the shareholder meeting is highly anticipated, analysts believe that the price will continue climbing. Yahoo Finance, through CNBC, quoted Shaw Wu, a Sterne Agee analyst, with a $550 price target on the shares. This meeting and the reception of new iPad 3 will ultimately dictate the direction of the world's most valuable company.

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Tuesday, February 7, 2012

Mixed Strategy Game

Two players A and B play a game, in which both has a red and a blue marble. They simultaneously present a marble to each other. If both present red, A wins $3. If both present blue, A wins $1. Otherwise, if the colors don't match, B wins $2. Who is in the better situation here?

		A
		Red	Blue
B	Red	A: $3	B: $2
B	Blue	B: $2	A: $1

If both players choose red or blue with equal probability, the expected payoff for both players is identical at $1. It's true that Player A has a greater variance in the results, and therefore Player B is better for risk-averse individuals. However, let p be the probability that the other player chooses red. Here in the mixed strategies:

3p = (1-p) --> A would be indifferent about the decision if B had 1/4 chance of choosing red
2p = 2*(1-p) --> B would be indifferent about the decision if A had 1/2 chance of choosing red

What does this mean? Although there is no dominant strategy, Player A clearly prefers playing red (expected payoff = 1.5, against 0.5 for blue), if Player B chooses randomly. However, knowing this, Player B would be more likely to choose blue. 3/4 chance of choosing blue for Player B finally would make Player A indifferent. What about the expected payoff in this mixed strategy?

Player A: (1/4)(1/2)(3) + (3/4)(1/2)(1) = 3/4
Player B: (1/2)(1/2)(2) + (1/2)(1/2)(2) = 1

So in this mixed strategy, whereby Player B recognizes that Player A prefers playing red, Player B plays blue more frequently. Although Player A had preferred red under random decisions from B, now Player A is better off playing blue if B also puts blue.

Finally, to simulate the game on MATLAB, this script was written. This case simulates the mixed strategy where B has 25% chance of choosing red. In the original consideration of random selection, simply change the value of the variable RedprobB.

trial = 1;
numTrials = 1000000;
payoffA = zeros(1,numTrials);
payoffB = zeros(1,numTrials);
RedprobA = 0.5;
RedprobB = 0.25;
while trial <= numTrials
    testA = rand;
    testB = rand;
    if(testA < RedprobA & testB < RedprobB)
        payoffA(trial) = 3;
    elseif(testA >= RedprobA & testB >= RedprobB)
        payoffA(trial) = 1;
    else
        payoffB(trial) = 2;
    end
    trial = trial + 1;
end

sumA = sum(payoffA);
sumB = sum(payoffB);
disp(sumA)
disp(sumB)

If both players choosing red and blue with 50% chance, here are some of the results of the sum of the payoff over 1,000,000 trials:

A: 999,425; B: 1,000,670
A: 999,662; B: 1,000,664
A: 1,001,261; B: 999,018

The results closely aligns with the expected payoff per trial of 1. Now, change back the code so that Player B has 25% chance of choosing red. Here are some of the results:

A: 749,312; B: 1,001,864
A: 751,635; B: 997,710
A: 749,364; B: 999,236

Again, the results closely aligns with the revised expected payoff per trial of 0.75 for Player A and 1 for Player B. Now, taking a step further, if Player A knows that Player B will play red 1/4 of the time, what can Player A do? By changing the value of the variable RedprobA, here are some observations:

RedprobA = 0.01: A earns about 0.75 per trial, B about 0.50
RedprobA = 0.25: both A and B earn about 0.75
RedprobA = 0.75: A earns about 0.75 per trial, B about 1.25
RedprobA = 0.99: A earns about 0.75 per trial, B about 1.50

So it looks like if Player B is fixed at 1/4 probability of picking red, Player A can't do much to improve its own expected payoff. This shouldn't come at a surprise, since back earlier when p=1/2 for A and p=1/4 for B were calculated, that was the Nash equilibrium. Neither player has an incentive to switch strategies, given that the other won't. However, Player A here is able to affect the payoff of B, but it was assumed for this problem that the payoff of the other player doesn't factor into any decisions.

Wednesday, February 1, 2012

Facebook Ready for IPO

Facebook is just about ready to file for IPO. Morgan Stanley is said to be hired to structure the offering that could see Facebook raise more than $5 billion and see the company formed in 2004 be valued at as much as $100 billion. Most of Facebook's revenue comes from advertising, and that figure was $3.8 billion in 2011. Research firm eMarketer estimates that revenues in 2012 will increase over 50% to $5.78 billion. In the days leading up to today's public filing, much talk has been centered on this $100 billion figure.

Facebook will be three times more expensive than Google was during its IPO. Given Facebook's $3.8 billion revenue and $100 billion valuation, that is a price-to-sales ratio of around 26. For comparison, a Market Watch article discussed valuations of 76 IPOs from companies with at least $3 billion in sales in the 12 trailing months up to IPO. The results reveal that their average price-to-sales ratio was around 0.7, meaning that Facebook's ratio is nearly 40 times that of comparable companies at the time of IPO. Google, to which Facebook is often compared to, had a price-to-sales ratio of 8.7 during its IPO, or nearly 1/3 that of Facebook. According to the latest financials, Google in 2011 had $37.9 billion in revenue. Its latest market capitalization value is $188.61 billion, or about 5 times its latest annual revenue. For Facebook, even with the 50% growth estimates from eMarketer for 2012 revenues, the $100 billion valuable will be over 17 times the annual revenue.

The high valuation of Facebook may rest on the anticipation of continual fast growth. However, the $3.8 billion revenue in 2011 missed the forecast of $4.3 billion from eMarketer. Zynga, one of the biggest advertiser on Facebook, began trading on NASDAQ last December. Up until this past week, its price was consistently below the initial pricing of $10; the recent spike may be attributed to the imminent IPO of Facebook itself. Finally, eMarketer forecasts that growth rates of Facebook's ad revenue worldwide will drastically decrease from 152% in 2010 to 21.1% in 2013.

In an article written by Business Insider and posted on Yahoo, the $100 billion valuation was defended on the basis of Facebook's control of traffic on Internet, personal identity data, and the biggest social platform. Based on these three criteria, the future cash-flow discounted to today's value makes $100 billion a plausible amount. Facebook's high valuation rests on its continual fast growth. That success will ultimately determine whether the $100 billion valuation is appropriate or not.

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Center for Freelance Writing