Valuation and Ratesof Return

Chapter 10

Chapter 10 - OutlineValuation of BondsRelationship Between Bond Prices and

YieldsPreferred StockValuation of Common StockValuation Using the Price-Earnings RatioFactors that Influence the Required Rate of

Return

Valuation of BondsThe value of a bond is made up of 2 parts

added together:– PV of the interest payments (an annuity) – PV of the principal payment (a lump sum)

The principal payment at maturity:– can also be called the par value or face value – is usually $1,000

The interest rate used: – is the yield to maturity or discount rate– is also the required rate of return

Relationship Between Bond Prices and YieldsBond prices are inversely related to bond yields

(move in opposite directions)The longer the maturity, the more sensitive the bond

prices are to interest rate changes.

As interest rates in the economy change, the price or value of an existing bond changes:– if the required rate of return increases, the price of

the bond will decrease– if the required rate of return decreases, the price of

the bond will increase

Valuing bonds

Some definitions: BOND Long-term debt issued by government or firms COUPON Regular interest payment on bond FACE VALUE Amount repaid at maturity (usually $1000)

Example: A Treasury 9% coupon bond matures in 1998. In 1993 each bond offered these cash flows:

1994 1995 1996 1997 1998 $90 $90 $90 $90 $1090

The interest rate on similar bonds was 5.3%.Therefore the value of 9% Treasuries was

$90 $90 $90 $90 $1090PV = + + + + (1 + r) (1 + r)2 (1 + r)3 (1 + r)4 (1 + r)5

$90 $90 $90 $90 $1090 = + + + + 1.053 (1.053)2 (1.053)3 (1.053)4 (1.053)5

= $1158.87

Calculating bond yields

If the price of the 9% Treasury bond is $1158.87,what return do investors expect? Return is usuallymeasured by the yield to maturity. This is the discountrate, r, that makes a bond's present value equal to price.

$90 $90 $90 $90 $1090PV = + + + + (1 + r) (1 + r)2 (1 + r)3 (1 + r)4 (1 + r)5

= $1158.87

Yield to maturity (r) = .053 or 5.3%.

Preferred StockPreferred stock:

– usually represents a perpetuity (something with no maturity date)

– has a fixed dividend payment– is valued without any principal payment since it has

no ending life– is considered a hybrid security (a mixture of a stock

and a bond)– owners have a higher priority than common

stockholders

Value = Pref. Div / Kp

Valuation of Common StockThe value of common stock is the present

value of a stream of future dividendsCommon stock dividends can vary, unlike

preferred stock dividendsThere are 3 possible cases:

– No growth in dividends (valued like preferred stock)

– Constant growth in dividends– Variable growth in dividends

Stock price (value) is equal to the present value of expected future cash flows (dividends)

DIV + P P = 1 + r

DIV + PSimilarly P = 1 + r

DIV DIV + PTherefore P = + 1 + r (1 + r)

We can also express P2 in terms of DIV3 & P3 etc. Thus

DIV DIV DIV3

P = + + + ...... 1 + r (1 + r)2 (1 + r)3

0

1 1

1

2 2

0

1 2 2

2

21

0

Constant-growth dividend discount model(the Gordon model)

If dividends are expected to grow at a constant rate (g), the value of the stock is DIV1

PV = r - g

Example:Blue Skies is expected to pay a $3 dividend next year (DIV1 = 3). Investors expect Blue Skies dividends to increase by 8% a year indefinitely (g = .08). The discount rate is 12% (r = .12).

DIV1 3PV = = = $75 r - g .12 - .08

Note: The formula works only if g is less than r

Estimating the required rate of return (a special case)

If dividends are expected to grow at a constant rate, g

DIV1

P0 = r - g

DIV1

r = + g P0

Note: This is a special case that only works for constant growth cases.

Valuation Using the Price-Earnings Ratio

The Price-Earnings (P/E) ratio can also be used to value stocks

The P/E ratio is influenced by:– the earnings and sales growth of the firm– the risk (or volatility in performance)– the debt-equity structure of the firm– the dividend policy– the quality of management– a number of other factors

High vs. Low P/Es

A stock with a high P/E ratio:– indicates positive expectations for the future of the

company– means the stock is more expensive relative to

earnings– typically represents a successful and fast-growing

company– is called a growth stock

A stock with a low P/E ratio:– indicates negative expectations for the future of the

company– may suggest that the stock is a better value or buy– is called a value stock

Factors that Influence the Required Rate of Return

Real Rate of Return:– represents the opportunity cost of the

investmentInflation Premium:

– a premium to compensate for the effects of inflation

Risk Premium:– a premium associated with business and

financial risk