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An Application of Present
Value Arithmetic
       Basic Principle of

Financial assets (stocks and bonds, etc.)
 are valued for the cash flow that they
 will provide.

Value = PV of all future cash flows from
             the asset
Applying the Basic
 Principle to Bond
     What are Corporate

Securities that document a loan to the
The standard denomination of a bond is
 $1,000. This is called the face value or
 par value of the bond.
The corporation has agreed to pay back
 this amount at the maturity date of the
    Bonds have a coupon
       interest rate.

The coupon rate is the contracted rate of
 interest which the corporation has
 promised to pay the bond holder.
The coupon rate is expressed as a percent
 of the face value and doesn’t change.
The coupon rate multiplied by the face
 value gives the amount of cash paid to
 the bond holder each year.
     Most bonds pay the
   coupon interest in two
   semi-annual payments.

Thus, in summary, the total cash flow that
 a bond investor expects to receive from a
 bond are:
The semi-annual coupon payments (an
 annuity) from now until the maturity date,
AND the $1,000 face value at the maturity
           An example:

What cash flows will a bond pay if it is a
 7% coupon bond maturing 18 years from
Answer: $35 every six months for 18
 years (36 payments), and $1,000 one
 time only after 36 periods.
The Yield-to-maturity on a

The rate of return a bond investor actually earns
 depends on the bond price paid.
Note that bonds usually sell at market prices
 quite different from their face value, so
 investors can earn actual rates of return quite
 different from the bond’s coupon rate.
The rate of return that will actually be earned
 by buying a bond at a given price is called the
 yield-to-maturity, or simply the yield.
To find the value of a bond,
   calculate the present
value of all the future cash
 flows, using the yield-to-
maturity as the time value
          of money
   For the example bond:

Assume the bond is priced to yield 8%
 per year. (YTM = 8%)
Since the bond pays semi-annual
 coupons, the time value discount rate is
 8%/2= 4% per semi-annual period.
The present value of the $35 annuity is
 $661.79, and the present value of $1,000
 is $243.67.
Thus, the bond has a total
    value of $905.46.

We can say that the bond has a value of
 $905.46 when it is yielding 8%,

OR, we can say that the bond yields 8%
 when it sells at a price of $905.46.
   Bond prices change as
    interest rates in the
      economy change

Higher interest rates mean that investors
 will require higher yields on bond
Present value calculation methods imply
 higher yields mean lower bond prices.
Bond prices and interest rates always
 move in opposite directions.
If you read that the central
bank is raising interest
rates, what will happen to
bond prices?
Bond investors will require a higher yield
 to invest in bonds.
Bond prices will fall to increase the yield
 provided by a bond. (Price = PV of cash
Note: The face value and coupon rate do
 not change! Only the price (value) and
 the yield changes.
   Applying the Basic
Principle of valuation to
    Stock Valuation:
Common stocks pay only
one kind of cash flow to

 The value of a common
stock is the present value
of all future dividends the
stock is expected to pay.
           An example:

Assume a stock is expected to pay a
 dividend of $10 per share next year, and
 to increase the dividend payout by 3%
 per year every year thereafter.
Assume investors require a 15% rate of
 return on this stock.
The stock’s value is the present value of a
 growing perpetuity.
Using the formula: Value = $10/(.15-.03)
     = $83.33.
    Preferred stocks are
   stocks that pay a fixed

Preferred stock dividends must be paid
 before paying any dividends on common
 stock. Thus the name “preferred” stock.

Since the dividends don’t grow, the value
 of a preferred stock is simply the present
 value of an ordinary perpetuity.
A preferred stock valuation

What is the value of a preferred stock that
 pays a dividend of $20 per share every
 year, assuming investors require a 15%
 rate of return?

Answer:    Value = $20/.15 = $133.33
              per share.
  Since stock prices are
present values, they also
(like bonds) tend to move
 in the opposite direction
     as interest rates.
    However, the biggest
    factor affecting stock
   prices is the forecasted
  (and the dividend growth
Since investors differ in their expectations
 about the future dividends that a stock
 will pay, they also differ in their valuations
 of stocks. (This is why investors trade
 stocks in the market.)