Valuation of Financial Assets
Chapter 14
Capitalization-of-Income Method
• Financial asset: a security (e.g. a share of stock
or bond) that represents a claim against the
future income or assets of issuer
• Value of financial asset may be determined as
discounted present value of expected future
cash flows earned on that asset.
Capitalization-of-Income Method
• Two areas of concern
1. Determining appropriate earnings to be
capitalized
2. Determining appropriate capitalization rate
Selecting Appropriate Capitalization Rates
1. Given risk characteristics of a particular
investment opportunity or security, define
appropriate capitalization rate (K) as minimum
expected rate or return required to induce
investors to accept that investment
– Recall Ch. 13: According to capital asset pricing
model (CAPM), the higher the risk involved in
investing in asset, the higher will be minimum
expected rate of return necessary to induce investors
to invest in asset
– Appropriate capitalization rate for any financial asset
is function of riskiness of asset.
Selecting Appropriate Capitalization Rates
• Risk: standard deviation of expected future
returns
– Standard deviation measures expected variability
around expected future rate of return
– Higher variability  higher standard deviation 
higher risk
• Capital market line (CML): graphic
representation of risk/return trade-off line
Selecting Appropriate Capitalization
Rates
• See exhibit 14.1
• CAPM states that appropriate capitalization rate (K)
should be equal to risk-free rate (Rf) plus risk
premium
– Risk-free rate is intercept of CML, since this is return that
should be earned when standard deviation is zero (where
there is no risk)
– Risk premium is function of standard deviation of expected
future returns (S)
– M is slope of CML
K = Rf + MS
Selecting Appropriate Capitalization
Rates
• What determines risk-free rate?
– Recall Ch. 13: Rf is generally measured as shortterm Treasury bill rate, which is highly responsive
to inflation
– Increased inflation  intercept of CML curve
shifts upward
– Decreased inflation  intercept of CML shifts
downward
Selecting Appropriate Capitalization
Rates
• What determines slope of CML?
– Slope of CML reflects investors’ attitudes toward
risk
– Increased economic uncertainty  increase in
investors’ risk aversion  increase in M
• Greater risk aversion  steeper CML curve
• Decrease in economic uncertainty  flatter
CML curve
Selecting Appropriate Capitalization
Rates
• Capitalization rate depends on general level of
inflation and interest rates, risk involved in
particular investment being considered, and
investors’ attitudes toward risk.
• Find slope and intercept of CML in order to
determine K.
Selecting Appropriate Capitalization
Rates
• Use regression analysis to estimate CML empirically.
• Accept “going rate” for particular asset as
appropriate K.
– Ex. Consult Standard and Poor’s Bond Guide to determine
average rate of return being earned on 20-year, AAA-rated
corporate bonds. This rate can be used as appropriate K.
• Use “hurdle rate” for K: minimum rate of return
acceptable for particular investment as judged by
individual or organization doing valuation
• Once appropriate K is determined in valuation process,
determine discounted present value of expected future cash
flows.
Bond Valuation
• Two cash flows for regular, “bullet” bonds:
1. Cash flow provided by semiannual
interest payments
•
•
Discount rate used in valuing bond is one-half
appropriate annual-bond capitalization rate
Number of discount periods is twice number
of years to maturity
Bond Valuation
2. Cash flow provided by repayment of
bond par value at maturity
•
•
Value of bond is equal to present value of
future interest payments plus present value of
par value received at maturity.
Value of particular bond may be found by
using present-value tables (recall Ch. 11),
specially constructed bond-valuation tables,
or any business-oriented calculator
Bond Valuation
• Equation for value of bond:
V = C[((1-(1/(1+(K/2)2n)))/(K/2)] + P[1/(1+(K/2)2n)]
Where V = value of bond
C = semiannual coupon interest payments
K = annual capitalization rate, compounded semiannually
n = number of years to maturity
P = par value of bond received at maturity
• First term represents present value of annuity of n years’
duration discounted semiannually at rate of K/2. This figure is
present value of semiannual coupon-interest payments.
• Second term represents present value of par value of bond to
be received n years (n/2 periods) from now.
Bond Valuation
• Ex. Suppose appropriate capitalization rate for AAA-rated
corporate bonds is 12%, compounded semiannually.
What is value of seasoned AAA-rated bond with par value
of $1,000, and 8% coupon rate ($40 paid semiannually),
and 20 years to maturity?
V = $40[(1-1/(1+.06)40)/.06] + $1,000[1/(1+.06)40]
V = ($40)(15.0463) + ($1,000)(.0972)
V = $699.05
Bond Valuation
• Use same bond-valuation equation to determine
yield to maturity of bond that is available at known
price.
– Treat V, C, n, and P as given, but solve equation for K.
– Yield to maturity on bond is then effective annual yield at
K%, compounded semiannually.
– Ex. (continued) Yield to maturity is 12.36%, which is
effective rate of return form 12% compounded
semiannually ([1.06]2-1).
• Use calculators or computer spreadsheets to solve
bond-valuation equation for K.
Bond Valuation
Zero Coupon Bonds
• Zero coupon bonds (in contrast to bullet
bonds) are originally sold at discount from par
value and pay full par value at maturity.
– Have no coupons
– Pay no current interest
Bond Valuation
Zero Coupon Bonds
• From investor’s point of view, zero coupon bonds
are attractive because they eliminate reinvestment
risk.
– Reinvestment risk: risk that one may not be able to
reinvest coupon payments received from conventional
bond at same rate that bond is earning
– Ex. Investor buying newly issued 10% bond at par will not
actually earn 10% yield to maturity unless future cash
interest payments can be reinvested at 10%. Since there
are no cash interest payments to be reinvested on zero
coupon bond, risk is eliminated.
Bond Valuation
Zero Coupon Bonds
• Zero coupon bonds benefit issuer during periods of
high interest rates.
– Since bond eliminates reinvestment risk, investors will
accept lower rate of return on zero coupon bond than they
would accept on conventional bond.
– Zero coupon bond lowers issuer’s interest costs.
– Zero coupon bonds have sinking fund provision.
• In periods of low interest rates, rates on zero coupon
bonds tend to be higher than bullet bonds.
Bond Valuation
Zero Coupon Bonds
• According to IRS, discount on zero coupon
bond is taxable as if current interest were
being paid.
• Zero coupon bonds are generally suitable for
nontaxable investors (i.e. corporate pension
funds, individuals’ IRA or 401(k) plans)
Bond Valuation
Zero Coupon Bond
• Present value of zero coupon bond is present
value of par value paid at maturity.
• Ex. Present value of ten-year, $1,000 par, 12%
zero coupon bond:
V = ($1,000)[1/(1.12)10]
V = $322
Preferred Stock Valuation
• Preferred stock has no maturity date.
• Value of share of preferred stock is present value of
dividend payment from date of purchase to infinity.
• Consider two factors when discounting out to
infinity:
1. There are corporations that have existed for 50 or more
years and can be expected to survive for another 50 or
more years.
2. “Economic infinity” for discounting purposes is not as far
away as the word infinity implies.
Preferred Stock Valuation
• Assuming that dividends are paid annually,
value of share of preferred stock is:
V = D/(1+K) + D/(1+K)2 + D/(1+K)3 + … + D/(1+K)∞
Where V = value of preferred stock
D = annual dividend payment
K = appropriate capitalization rate
∞ = infinity
Preferred Stock Valuation
• Since present value of each year’s dividend
decreases each year, preferred-stock-valuation
equation is infinite series of decreasing
numbers.
• Sum of preferred-stock-dividend series:
V = D/K
Preferred Stock Valuation
• Ex. If K is 12%, value of share of preferred
stock paying an $8.00 annual dividend is:
V = $8.00/0.12
V = $66.67
• At price of $66.67, share of preferred stock
paying $8.00 dividend provides annual yield of
12% from now to infinity.
Preferred Stock Valuation
• Preferred stocks are riskier investments than
bonds.
– Unlike bond-interest payments, preferred stock is
not guaranteed.
– Preferred stock is junior to debt in priority.
• However, market-capitalization rates for
preferred stock are often lower than bondcapitalization rates. Why?
Preferred Stock Valuation
• Recall Ch. 2: 85% of stock dividends paid to corporation are
tax free.
– Dividends paid by corporations are subject to tax at long-term capital
gains rate, which is significantly lower than highest personal marginal
income tax rate.
– Bond interest is fully taxable at highest marginal rate.
• For corporation or individual investor, dollar’s worth of
preferred dividends is worth much more than dollar’s
worth of bond interest.
• Investors willing to accept lower pre-tax yield on preferred
stocks than on bonds.
• Market activities generally results in lower pre-tax
capitalization rates for preferred stocks than for bonds.
Common-Stock Valuation
• Two forms of expected cash flows from
common stocks:
1. Dividends received over investor’s stock holding
period
2. Price expected to be received when stock is
sold
Common-Stock Valuation
• Two major concerns for valuation:
1. Earnings and dividends per share are expected to
increase over time.
•
Cannot use annuity formulas for common-stock valuation
because calculating present vale of annuity requires that cash
flows be constant annual amount.
2. Uncertainty surrounding expected future dividend
payments and expected future stock price.
•
•
Common-stock dividends are never guaranteed and stock prices
fluctuate.
Account for uncertainty in valuation process by assigning higher
capitalization rate to common stocks than to bonds or preferred
stocks.
Common-Stock Valuation
• Most models are based on premise that common-stock values
are function of expected future cash flows from dividends and
expected future value of stock.
• Widely accepted model views common-stock values as
dependent on dividend-paying capacity of corporation.
– Explanation: Price at end of any year is always equal to present value
of following year’s dividend and price.
– As price approaches economic infinity, present value of terminal price
(price in final year) becomes zero for valuation purposes.
– Any financial asset is equal to present value of future cash flows.
– Since stock may exist until economic infinity, only cash flows that will
be received from share of common stocks are dividends.
– Present value of share of common stock is equal to present value of
future expected dividends from now until infinity.
Common-Stock Valuation
• Value of common stock is sum of infinite
series of growing dividends.
• Two assumptions must be made:
1. Dividends will grow at constant rate.
2. Constant growth rate will be less than
capitalization rate that will be applied to value
of stream of growing dividends.
Common-Stock Valuation
• Value of share of common stock:
P0 = D1/(K-g)
Where P0 = present value of share of common stock
D1 = expected dividend in year 1
K = appropriate capitalization rate
g = expected future growth rate of dividends
Common-Stock Valuation
• Ex. Suppose XYZ common stock is expected to pay
dividend of $2.16 in coming year. This dividend is
expected to increase at average annual rate of 8%
per year. Appropriate capitalization rate is 15%. What
is present value of XYZ’s common stock?
P0 = $2.16/(0.15-0.08)
P0 = 30.86
Common-Stock Valuation
• What if expected future growth rate is not
constant?
– Each year’s expected dividend must be discounted
separately out to year for which it is estimated that
dividend growth will “settle down” to some constant rate.
– Use dividend-capitalization model to determine value of
stock at end of last year of irregular growth.
– Present value of stock price at end of irregular growth
period plus present value of dividends received during
irregular growth period equals present value of stock.
Common-Stock Valuation
• What if growth rate exceeds capitalization
rate?
– For temporary supernormal growth, discount value of
dividends received during that period separately.
– Use dividend-capitalization model to determine value of
stock at end of supernormal growth period.
– Present value of stock equals present value of dividends
received during supernormal growth period plus present
value of stock price at end of same period.
Common-Stock Valuation
• What if stocks pay no dividends and sell for
positive prices (capitalizing dividends)?
– Estimate whether company will be able to start
paying dividends in future.
– Use dividend-capitalization model to determine
value of stock at time.
– Discount this value back to present to determine
present value of stock.
Common-Stock Valuation
• See Exhibit 15.2: Application of dividendcapitalization model to no-growth stock, normal
growth stock, and supernormal growth stock.
– High-growth stocks sell at higher multiples of earnings
than do lower-growth stocks because growing dividends
impart more value to stock price.
– High-growth stocks have much lower dividend yields than
low-growth stocks because value of growth potential of
high-growth stock drives up price of stock and thus drives
down dividend payment as percentage of stock price.
Common-Stock Valuation
Intrinsic Values and Market Values
• Intrinsic value: value of share of stock as determined
by a valuation model
• When market price equals intrinsic value, stock price
is in equilibrium.
– Remember, there are different common-stock valuation
methods!
– Changes in market-capitalization rates used by investors
and changes in growth outlook for stock cause intrinsic
value and market price to fluctuate, and thereby prevents
equilibrium.
Common-Stock Valuation
Intrinsic Values and Market Values
• If market price is less than intrinsic value,
stock is undervalued and should be
purchased.
• If market price is greater than intrinsic value,
stock is overvalued and should be sold.
• If market price equals intrinsic value, stock is
in equilibrium and may be held or purchased.
Common-Stock Valuation
Intrinsic Values and Market Values
• Efficient markets hypothesis (EMH):
– Large number of well-educated, professional market participants have
access to same databases
– All of these participants analyze these data in same way
– Most draw same conclusions about intrinsic value of most stocks
– Market activities cause most stocks to be priced at their intrinsic
values
• Price at which rate of return earned on common-stock investment
is commensurate with risk involved in investment
– It is not possible to “beat the market” by earning an
above-average rate of return.