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### 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
- Determining appropriate earnings to be capitalized
- Determining appropriate capitalization rate

Selecting Appropriate Capitalization Rates

- 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 short-term 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:
- 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:
- There are corporations that have existed for 50 or more years and can be expected to survive for another 50 or more years.
- “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 bond-capitalization 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:
- Dividends received over investor’s stock holding period
- Price expected to be received when stock is sold

Common-Stock Valuation

- Two major concerns for valuation:
- 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.
- 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:
- Dividends will grow at constant rate.
- 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 dividend-capitalization 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.

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