time value of money
what finance is really about (big picture)
finance is not about trading or “getting rich quick.” finance is about fair value.
financial markets exist to move money from people who have money now but don’t need it yet (households) to people who need money now but will have money later (firms)
this is no different from any other market
farmers have fruit → consumers want fruit
savers have money → firms want money
prices are set so both sides are willing to trade
no one is “getting ripped off” at the fair price
why stock prices move
stock prices change only because of news
prices do not move when something happens
prices move when expectations change
two sources of price changes
company-specific news: information that changes expectations about one particular company’s future cash flows
if a stock falls more than the index → firm-specific bad news
economy-wide news: information that affects many or all firms at the same time by changing the economic environment
if it falls roughly with the index → market-wide effect
prices reflect the present value of expected future cash flows
index
a stock index combines many stocks into one number
it moves when:
the overall market moves
economy-wide news arrives
it is used as a reference point, not an investment itself (conceptually)
market capitalization vs share price
share price
the price of one share → depends on how many shares the company has
can change due to stock splits without changing the company’s value
stock splits happen to make shares more accessible & liquid while leaving the firm’s total value unchanged.
if apple’s share price is $200, that’s just the price of one slice of apple.
market capitalization
total value of the firm
market cap = share price x number of shares
earnings, dividends, & growth
apple vs philip morris
two firms can earn similar earnings per share, but behave very differently:
growth firms (e.g. apple):
reinvest earnings
lower dividends now
higher expected future cash flows
mature firms (e.g. philip morris):
high dividends
low growth
stable but limited future cash flows
investors choose based on timing of cash flows, not just size
long run or short run profits?
time value of money example
assume interest rate ≈ 4%
$100 today vs $103 in one year
everyone prefers $100 today
why?
$100 today can become $104 in one year
the bank has a higher interest rate
therefore:
$100 today > $103 next year
future value (fv)
future value: how much money today will be worth in the future
money grows by multiplying by (1+r) each period
formula
example
$300 today
6% for 12 years
fv ≈ $603.66
present value (pv)
present value: how much money today is equivalent to a future cash flow
r: discount rate
present value as “happiness in dollars”
value is measured in today’s dollars
a deal can look better or worse depending on timing (time value of money)
money today ≠ money tomorrow
this is why finance uses present value by convention
present value (streams of cash flows)
present value of a stream of cash flows: when there are multiple future cash flows at different times
bond valuation
bond value = pv of all promised payments
coupons + face value
discount each payment separately
add them up
c = coupon
f = face value
r = discount rate
t = maturity
example
3-year bond:
coupon = $50/year
face value = $1,000
r = 4%
cash flows:
year 1: $50
year 2: $50
year 3: $1,050
net present value
value created or destroyed by doing the project
is this investment worth doing?
formula
pv of a stream, including the initial cost
initial is usually negative (money paid today)
npv decision rules
npv > 0 → creates value → accept
npv < 0 → destroys value → reject
choose highest npv among alternatives
why firms should maximize npv
short-term profit → reduces future cash flows
dividends → does not create value by themselves
total present value → present value of all future cash flows ( share price)
spending money now can be good if pv of future cash flows is higher