September 25 , 2012
CLASS 6: FINANCE 1
Read: the definition of “Time Value of Money” from Wikipedia:
• Value of money figuring in a given amount of interest earned over a given amount of
• The time value of money is the central concept in finance theory.
• For example, $100 of today's money invested for one year and earning 5% interest will
be worth $105 after one year. Therefore, $100 paid now or $105 paid exactly one year
from now both have the same value to the recipient who assumes 5% interest;
o using time value of money terminology, $100 invested for one year at 5% interest
has a future value of $105.
• Present value The current worth of a future sum of money or stream ocash flows given a
specified rate of return.
o Future cash flows are discounted at the discount rate, and the higher the discount rate,
the lower the present value of the future cash flows.
• Future value is the value of an asset or cash at a specified date in the future that is equivalent in
value to a specified sum today
Present value of a future sum
The present value formula is the core formula for the time value of money; each of the other formulae is
derived from this formula. For example, the annuity formula is the sum of a series of present value
The present value (PV) formula has four variables, each of which can be solved for:
1. PV is the value at time=0
2. FV is the value at time=n
3. i is the discount rate, or the interest rate at which the amount will be compounded each
4. n is the number of periods (not necessarily an integer) Read: “Apple rides iPhone wave to claim stock market crown. Omar El Akkad;
Marlow, Iain. The Globe and Mail [Toronto, Ont] 21 Aug 2012: B.1.
Apple Inc. has gone where no company has ever been before, nearing the $625billion (U.S.) mark in stock market value amid
a surge of optimism about its next wave of products.
The Cupertino, Calif., company broke Microsoft Corp.'s previous record, set in 1999 during the technology bubble, to become the
most valuable public company ever, in nominal terms. The latest rally, which has seen the stock rise about 16 per cent
since July 25, represents a turn in sentiment since it disclosed thirdquarter earnings that disappointed some investors.
Apple's recent performance has aided a market surge, propelling the Nasdaq composite index and the Standard & Poor's 500 to near their
2012 highs. The S & P closed the day at 1,418, one point shy of its April peak.
What's driving Apple shares upward, it appears, is the same thing that is damaging rivals such as Research In Motion Ltd: the prospect of a
sleek new version of the iPhone hitting the market next month.
"There have been plenty of leaked parts pictured on the Internet and Apple is expected to announce details of the new smartphone as early as
Sept. 12," said Kris Thompson, an analyst with National Bank Financial. "The iPhone 5 may be in my hands as early as Sept. 21."
While not unexpected, that is not good news for RIM, which has struggled to come up with a consumer smartphone that is
competitive with the iPhone and devices running Google Inc.'s Android software.
RIM's nextgeneration phones have been repeatedly delayed and will not be available until early 2013.
For a moment this summer, it seemed Apple might actually be coming down from six years of meteoric sales and profit growth. The company
missed analyst expectations when it reported its most recent quarterly earnings. As a result, Apple's share price took a shortterm hit, falling to
$574.97 the next day. It closed at $665.15 on Monday.
But Apple's disappointing earnings were largely due to the number of consumers holding off on buying a currentgeneration
iPhone because a new version of the phone is due out this fall. And instead of avoiding the stock, investors appear to be
jumping on Apple shares now in anticipation of a blockbuster end of the year once the new phone does come out.
And although Mr. Thompson notes that Apple has seen a recent surge of competition from Samsung, which has built a
technically more powerful device with the Samsung Galaxy S3, few on Wall or Bay Street are predicting that Apple's next phone will
be a failure even if expectations may be getting out of hand.
"Obviously Apple's going to have a lot of success with its iPhone 5, it's also widely expected that it's going to come this fall, so you just have to
be cautious of expectations getting ahead of reality," said Colin Gillis, senior technology analyst at BGC Financial LP in New York. "There's
already talk about the iPhone 5 selling 250 million units. ... In reality, it will probably be a little thinner, a little faster, a little bigger. It's not likely to
mow your lawn."
For Apple, the news couldn't be better. Not only does its share price continue to defy gravity, but the anticipated launch of the new iPhone, a
smaller iPad and a media storage and consumption product called iTV in the next few months means Apple's near future looks very bright.
THE BIGGER THEY ARE ...
There's little reason to believe Apple's fortunes will take a turn for the worse any time soon. But no company dominates forever. What could stop
the juggernaut? Here are a few risk factors:
For years, Android phones lagged far behind Apple's devices in popularity and quality. But in recent months, a number of highend Android
phones have received glowing reviews. Chief among those are a number of new phones from Samsung, which has emerged as Apple's most formidable opponent in the smartphone
market. By leveraging its massive size and scope, Samsung recently became the biggest smartphone vendor in the
world, and is posting faster growth rates than its chief rival (although Apple still generates far more profit every time it sells a phone). The
iPhone may still be the world's most recognized smartphone, but thanks to Android, it at least has a semblance of competition.
Microsoft's mobile push
Microsoft hasn't been a serious challenger to Apple in the mobile space since the beginning of the iPhone era. But this fall, the company behind
the most popular operating system on Earth will make a big push to change that. Microsoft's latest version of the Windows operating system is,
for the first time, built primarily for mobile devices. Coupled with its smartphone partnership with Nokia and its Surface tablet (due out this fall),
Microsoft will use the Windows launch to try to convince its existing desktop and laptop customers to put Windows on their mobile devices as
Endless patent lawsuits
For months, Apple and Samsung have been tied up in dozens of lawsuits in courtrooms across the globe, from South Korea to the U.S. to
Germany. Most of the legal wrangling centres on Apple's contention that rivals copied its designs in producing mobile
products. But increasingly, the lawsuits have become a public relations debacle and Apple has faced criticism for its decision to go
after competitors for patent infringement in areas that are considered fairly generic, such as the "slidetounlock" feature on touchscreens.
Read: “Zuckerberg's rocket, ready for lift‐off; Valuing Facebook”Anonymous.
The Economist 403. 8784 (May 12, 2012): 69‐70.
Despite the hype as it prepares to launch its IPO, the giant social network still has plenty to prove
OUTSIDE Facebook's vast new headquarters in Silicon Valley is a huge sign with an image of a hand on it giving a thumbsup sign. A tiny
digital version of the same hand sits on millions of websites and invites Facebook's 900m or so users to click on it to share content they have
found with their pals. Now Facebook is hoping to get another big thumbsup when it stages its eagerly awaited initial public offering
(IPO) of 12% of its equity on America's NASDAQ stockmarket on May 18th. Assuming all goes according to plan, the
flotation will be the largest yet undertaken by an internet company.
On a roadshow across America to promote the listing this week, Mark Zuckerberg, Facebook's 27yearold boss, and other executives were
treated like rock stars. Long queues snaked out of hotels where they were holding meetings, as investors lined up to hang on their every word.
Hordes of photographers rushed to take pictures of Mr Zuckerberg, in his trademark hoodie, as he and his colleagues were whisked off to
This frenzy is further proof, if any were needed, that Facebook has become a global internet idol. Facebulls reckon the flotation, which could
raise almost $12 billion (with about half going to shareholders selling up), will help transform the social network into a web powerhouse
in the same way that Google used the riches from its 2004 IPO to spread its tentacles across the web. And they confidently predict that
Facebook's shares will start trading well above the range of $2835 that the firm has set for thema range that would value Facebook at $77
Some financiers think it could command an even bigger price. If Facebook's valuation were to hit $100 billion, it would put the company roughly
on a par with, say, Amazon and give it