© 2003 McGraw-Hill Ryerson Limited

1010Chapt

er

Chapt

er Valuation and Rates

of ReturnValuation and Rates

of Return

McGraw-Hill Ryerson ©2003 McGraw-Hill Ryerson Limited

Based on:Terry FegartyCarol Edwards,Lawrence J. Gitman

April 12, 2005

© 2003 McGraw-Hill Ryerson Limited

Chapter 10 - Outline Valuation Concepts

Importance of Valuation Basic Valuation Model 3 Factors that Influence

the Required Rate of Return Valuation of Bonds

Relationship Between Bond Prices and Yields Valuation Preferred Stock Valuation of Common Stock Valuation Using the Price-Earnings Ratio Summary and Conclusions

PPT 10-2

© 2003 McGraw-Hill Ryerson Limited

Valuation Concepts

The value or price of a stock or bond is based upon the present value of future expected cash flows to the investor

Key inputs to the valuation process include: Cash Flows (returns), Timing, and Required Return (risk).

Greater risk can be incorporated into an analysis by using a higher required return or discount rate.

PPT 10-4

© 2003 McGraw-Hill Ryerson Limited

Valuation Concepts - Importance of Asset Valuation Valuation is important to any firm for at least 2

reasons:1. A firm must continually assess its market value

if it satisfies its goal of share price maximization.2. It must accurately determine the worth or value

of its business when selling securities to raise long-term funds. Firms (Issuers) will lose money if they undervalue

their businesses Would-be investors would not want to pay more

than what the businesses are worth, so firms must not overvalue their businesses.

© 2003 McGraw-Hill Ryerson Limited

Valuation Concepts - Basic Valuation Model

The VALUE of any asset is the Present Value of all future cash flows it is expected to provide over the relevant time period.

V0 = value of the asset at time zero

CFt = cash flow expected at the end of year t

k = appropriate required rate of return (discount rate)

n = relevant time period

nn

k

CF

k

CF

k

CFV

)1(...

)1()1( 22

11

0

© 2003 McGraw-Hill Ryerson Limited

Definitions - Bonds Firms borrow money from lenders for the long term

by issuing securities which are called bonds:Firms collect the money when they issue the bond, or sell

it to the public.The money they collect is the amount of the loan.The amount of the loan may be known as the par value,

face value, maturity value, or the principal.The date on which the loan will be paid off is the

maturity date. For many bonds, its life or maturity could be for a term of 20 to 30 years.

Valuation of Bonds - Bond Characteristics

© 2003 McGraw-Hill Ryerson Limited

Valuation of Bonds - Bond Characteristics

Definitions - Coupon Rate The issuer (firm) promises to make specified fixed income

payments (interest) each year(or semi-annually) to the bondholders (lenders). These payments are known as the coupon (or interest) and are

based on the coupon rate stated in the issued bonds. Interest payment is usually made semi-annually.

The coupon rate is the annual interest payment divided by the face value of the bond.

This coupon rate on a bond is set at the time of issue and does not change for the life of the bond.

This coupon rate is based on the Government of Canada Bonds rate with the same maturity date plus a premium for risk.

© 2003 McGraw-Hill Ryerson Limited

Valuation of Bonds - Bond Characteristics

Definitions - Coupon Rate vs Yield to Maturity (YTM) After a bond is issued, two major factors can occur:

Economic conditions can changeA firm’s risk can change

These changes will be reflected on the issued bond in its interest rate (also known discount rate, rate of return) and more specifically, Yield to Maturity (YTM).

While the interest and principal payment will remain unchanged if the bond is re-issued, the price of the bond will change if the coupon rate deviates from the YTM.

Yield to Maturity is the rate of return investors earn if they buy the bond at the new price and hold it until maturity.

This is also the interest rate (or discount rate) at which the cash flows from the bond are discounted to determine its present value (New Price).

© 2003 McGraw-Hill Ryerson Limited

3 Factors that Influence the YTM (Required Rate of Return)

1. Real Rate of Return: represents the interest cost of the investment in the early 1990’s, 5-7%, but now about 3-4%

2. Inflation Premium: a premium to compensate for the effects of inflation lately, 2%

3. Risk Premium: a premium associated with business and financial risk typically, 2-6%

So, the Required Rate of Return equals:

Real Rate of Return + Inflation Premium + Risk Premium

© 2003 McGraw-Hill Ryerson Limited

Relationship Between Bond Prices and YTM

Bond prices are inversely related to YTM (Bond Yields), that is , they move in opposite directions

As interest rates in the economy change, the price or value of a 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

© 2003 McGraw-Hill Ryerson Limited

Table 10-1Bond price table

(10 Percent Interest Payment, 20 Years to Maturity)

Yield to Maturity Bond Price

2 4 6 7 8 91011121314162025

% . . . . . . . . . . . . . . . . . . . . . . $2,308.11. . . . . . . . . . . . . . . . . . . . . . . . 1,815.42. . . . . . . . . . . . . . . . . . . . . . . . 1,458.80. . . . . . . . . . . . . . . . . . . . . . . . 1,317.82. . . . . . . . . . . . . . . . . . . . . . . . 1,196.36. . . . . . . . . . . . . . . . . . . . . . . . 1,091.29. . . . . . . . . . . . . . . . . . . . . . . . 1,000.00. . . . . . . . . . . . . . . . . . . . . . . . 920.37. . . . . . . . . . . . . . . . . . . . . . . . 850.61. . . . . . . . . . . . . . . . . . . . . . . . 789.26. . . . . . . . . . . . . . . . . . . . . . . . 735.07. . . . . . . . . . . . . . . . . . . . . . . . 644.27. . . . . . . . . . . . . . . . . . . . . . . . 513.04. . . . . . . . . . . . . . . . . . . . . . . . 406.92

PPT 10-7

© 2003 McGraw-Hill Ryerson Limited

0 . . . . . . . . $1,000.00 $1,000.001 . . . . . . . . 1,018.52 982.145 . . . . . . . . 1,079.85 927.90

10 . . . . . . . . 1,134.20 887.0015 . . . . . . . . 1,171.19 863.7820 . . . . . . . . 1,196.36 850.61

25 . . . . . . . . 1,213.50 843.14

30 . . . . . . . . 1,225.16 838.90

Time Period Bond Price with Bond Price within Years 8 Percent Yield 12 Percent Yield

(of 10 percent bond) to Maturity to Maturity

PPT 10-9Table 10-2Impact of time to maturity on bond prices

© 2003 McGraw-Hill Ryerson Limited

1,300

1,200

1,100

1,000

900

800

700

Bond Price ($)

30 25 15Number of years to maturity

* The relationship in the graph is not symmetrical in nature.

10% bond, $1,000 par value

Assumes 12% yield to maturity

5 0

Assumes 8% yield to maturity

PPT 10-10Figure 10-2Relationship between time to maturity and bond price*

© 2003 McGraw-Hill Ryerson Limited

Your Daily Paper Issuer Coupon Maturity Price Yield Change

BC Tel 9.65 Apr 8-22 138.5 6.488 +1.118

CompanyCompany NameNameCouponCoupon(interest rate %)(interest rate %)

Maturity DateMaturity Date(April 8, 2022)(April 8, 2022)

PricePrice(Last transaction(Last transactionprice = $138.50/ $100price = $138.50/ $100of face value)of face value)

YieldYield((Annual interestAnnual interestMarket price)Market price)

ChangeChange(Closing (Closing price up $1.12/ price up $1.12/ $100 from$100 fromprevious day)previous day)

PPT 10-11

Reading Bond Quotations

© 2003 McGraw-Hill Ryerson Limited

Valuation of Bonds – Bond Example

par value = $1000 coupon = 6.5% of par value per year, paid semi-

annually. Interest Payment = $65 per year/2 = $32.50 every 6

months. maturity = 24 years (matures in 2029) x 2 = 48 periods. issued by AT&T.

0 1 2 3 4 5 ….. 48

$32.50 $32.50 $32.50 $32.50 $32.50 $32.50+$1000

© 2003 McGraw-Hill Ryerson Limited

Valuation of Bond Formula

Where: Pb = Price of the bond n = total number of periods It = Interest Payments Y = Yield to maturity (required rate of return) Pn = Principal payment at maturity t = number corresponding to a period; running from 1 to n

),,

2

2

1

1

1

()(

)1()1(

11

)1()1(....

)1()1(

)1()1(

nYnnY

n

nn

n

n

n

n

n

nn

tt

t

b

PVIFPPVIFAI

Y

P

YY

I

Y

P

Y

I

Y

I

Y

I

Y

P

Y

IP

© 2003 McGraw-Hill Ryerson Limited

Bond Example Problem

Suppose a firm decides to issue 20-year bonds with a par value of $1,000 and annual coupon payments. The return on other corporate bonds of similar risk is currently 12%, so we decide to offer a 12% coupon interest rate.

What would be a fair price for these bonds?

0 1 2 3 . . . 20

1000Pb=? 120 120 120 . . . 120

© 2003 McGraw-Hill Ryerson Limited

Bond Example Problem

N = 20 I/YR = 12

FV = 1,000 PMT = 120

Solve PV = -$1,000

Note: If the coupon rate = YTM (rate of return, discount rate) the bond will sell at par value.

© 2003 McGraw-Hill Ryerson Limited

Bond Example Problem

Mathematical Solution: Pb = I (PVIFA Y, n ) + Pn (PVIF Y, n )

= 120 (PVIFA .12, 20 ) + 1000 (PVIF .12, 20 )

= $1,000

n

nn

Y

P

YY

I)1(

)1(1

1

20

20

)12.01(

1000

12.0)12.01(

11

120

© 2003 McGraw-Hill Ryerson Limited

Bond Example Problem

Suppose interest rates fall immediately after we issue the bonds. The YTM (required return) on bonds of similar risk drops to 10%. What would happen to the bond’s price?

N = 20 I/YR = 10

FV = 1,000 PMT = 120

Solve PV = -$1,170.27 Note: If the coupon rate > YTM,

the bond will sell at a premium.

© 2003 McGraw-Hill Ryerson Limited

Bond Example Problem

Mathematical Solution: Pb = I (PVIFA Y, n ) + Pn (PVIF Y, n )

= 120 (PVIFA .10, 20 ) + 1000 (PVIF .10, 20 )

= $1,170.27

n

nn

Y

P

YY

I)1(

)1(1

1

20

20

)10.01(

1000

10.0)10.01(

11

120

© 2003 McGraw-Hill Ryerson Limited

Bond Example Problem

Suppose interest rates rise immediately after we issue the bonds. The YTM (required return) on bonds of similar risk rises to 14%. What would happen to the bond’s price?

N = 20 I/YR = 14

FV = 1,000 PMT = 120

Solve PV = -$867.54 Note: If the coupon rate < YTM,

the bond will sell at a discount.

© 2003 McGraw-Hill Ryerson Limited

Bond Example Problem

Mathematical Solution: Pb = I (PVIFA Y, n ) + Pn (PVIF Y, n )

= 120 (PVIFA .14, 20 ) + 1000 (PVIF .14, 20 )

= $867.54

n

nn

Y

P

YY

I)1(

)1(1

1

20

20

)14.01(

1000

14.0)14.01(

11

120

© 2003 McGraw-Hill Ryerson Limited

Valuation of Bonds

The value of a bond is made up of 2 parts: 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 (discount rate) also called the required rate of return

PPT 10-5

© 2003 McGraw-Hill Ryerson Limited

Semiannual Coupon Payments and Bond Values

The procedure to value bonds paying semiannual interest involved compounding interest more frequently than annually: Convert annual interest (coupon), I, to

semiannual by dividing I by 2. Convert number of years to maturity to number

of 6-month periods to maturity by multiplying n by 2.

Convert Yield to Maturity (required rate of return) from annual to semiannual by dividing Y by 2.

© 2003 McGraw-Hill Ryerson Limited

Valuation of Preferred Stock - Characteristics

Firms can also raise long term money by issuing and selling securities which are called preferred stocks or shares.

Investors who purchase these shares are called preferred shareholders

Preferred Stock is a hybrid security: it’s like common stock - no fixed maturity (perpetuity).

technically, it’s part of equity capital.

it’s like debt - preferred dividends are fixed. Usually sold for $25, $50, or $100 per share. Dividends are fixed either as a dollar amount or as a

percentage of par value.

© 2003 McGraw-Hill Ryerson Limited

Valuation of Preferred Stock - Characteristics

Example: In 1988, Xerox issued $75 million of 8.25% preferred stock at $50 per share. $4.125 is the fixed, annual dividend per share.

Is valued without any principal payment since it has no ending life.

Price is based upon PV of future dividends. Creditors have prior claim on earnings; interest on debt must be

paid before preferred stockholders can receive anything. Once creditor claims have been met, preferred stock has priority

over common stockholders in terms of claims on assets in liquidation, that is,dividends must be paid before common stockholders receive any payment.

© 2003 McGraw-Hill Ryerson Limited

Valuation of Preferred Stock

Failure to pay preferred dividend does not result in bankruptcy.To value a Preferred Stock, we use the following formula:

Where :

Pp= Price of Preferred Stock

Dp= Annual Dividend for Preferred Stock

Kp= Required Rate of Return or Discount Rate

p

ppk

DP

© 2003 McGraw-Hill Ryerson Limited

Valuation of Preferred Stock-Example

Xerox preferred pays an 8.25% dividend on a $50 par value. Suppose our required rate of return on Xerox preferred is 9.5%.

42.43$095.0

125.4

p

ppk

DP

© 2003 McGraw-Hill Ryerson Limited

Valuation of Common Stock - Characteristics

Common stock represents equity or ownership; includes voting rights.

Limited liability: liability is limited to the amount of owners’ investment.

Claims Priority: lower than debt and preferred. Unlike preferred stock, there is no pre-set dividend

rate. Instead, dividends are paid at the discretion of the firm’s board of directors.

Common Stock is a variable-income security. dividends may be increased or decreased,

depending on earnings.

© 2003 McGraw-Hill Ryerson Limited

Valuation of Common Stock - Characteristics

The value of common shares is equal to the present value of all future dividends the company is expected to pay over an infinite time horizon.

There are 3 possible cases: No growth in dividends (valued like preferred

stock) Constant growth in dividends Variable growth in dividends

Required rate of return reflects the dividend yield on the stock and the expected growth rate in the dividend

© 2003 McGraw-Hill Ryerson Limited

Valuation of Common Stock- No Growth Model

Under the no growth circumstance, the formula is similar to preferred stock:

Where : Po= Price of Common Stock today

D0= Current Annual Common Dividend (constant value)

Ke= Required Rate of Return on Common Stock

ek

DP

00

© 2003 McGraw-Hill Ryerson Limited

Valuation of Common Stock- Constant Growth Model

Under the Constant Growth Model, the formula is:

Where : Po= Price of Common Stock today

D1= Dividend at the end of the 1st year

Ke= Required Rate of Return on Common Stock g = constant growth rate in dividends

gk

DP

e

10

© 2003 McGraw-Hill Ryerson Limited

Valuation Using the Price-Earnings Ratio

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

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

The average P/E ratio for TSX Composite, excluding Nortel and JDS Uniphase, in early 2002 was 33 to 1

PPT 10-14

© 2003 McGraw-Hill Ryerson Limited

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

PPT 10-15

© 2003 McGraw-Hill Ryerson Limited

Table 10-4An example of stock quotations from the Globe and Mail

PPT 10-16

Source: ILX Systems, a division of Thomson Information Services Inc.

© 2003 McGraw-Hill Ryerson Limited

Your Daily Paper Company Volume High Low Close Change

Inco 3760 29.150 28.500 28.600 -.400

StockStockVolumeVolume(Total number of(Total number ofshares traded (100s)shares traded (100s)

CloseClose(Last price paid(Last price paidat close of trading)at close of trading)

HighHigh(Highest (Highest price paidprice paidper share per share for the for the day day was was $29.15)$29.15)

LowLow(Lowest price paid(Lowest price paidper share for the per share for the day day was $28.50)was $28.50)

ChangeChange(Difference (Difference betweenbetweentoday’s price andtoday’s price andprevious day’s. A previous day’s. A .40 decrease).40 decrease)

PPT 10-17

Reading Stock Quotations

© 2003 McGraw-Hill Ryerson Limited

Summary and Conclusions

The price of a bond reflects the present value of future payments of interest and principal, discounted at current market bond yieldsThe price of a preferred or common stock reflects the present value of future dividends, discounted at current market dividend yieldsAn alternative for valuing common stock is the price-earnings ratio

PPT 10-20

The value of securities is based upon the present value of expected future cash flows from the investment, discounted at the rate of return required by investorsThe required rate of return includes premiums for expected inflation and the perceived risk of the investment