Chap005

McGraw-Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved

CHAPTER

5 How to Value Bonds and Stocks

Slide 2

Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved

McGraw-Hill/Irwin

Chapter Outline5.1 Definitions and Example of a Bond5.2 How to Value Bonds5.3 Bond Concepts5.4 The Present Value of Common Stocks5.5 Estimates of Parameters in the Dividend-

Discount Model5.6 Growth Opportunities5.7 The Dividend Growth Model and the

NPVGO Model5.8 Price-Earnings Ratio

Slide 3


McGraw-Hill/Irwin

5.1 Definition of a Bond

• A bond is a legally binding agreement between a borrower and a lender that specifies the:– Par (face) value– Coupon rate– Coupon payment– Maturity Date

• The yield to maturity (YTM) is the required market interest rate on the bond.

Slide 4


McGraw-Hill/Irwin

5.2 How to Value Bonds

• Primary Principle:– Value of financial securities = PV of expected

future cash flows

• Bond value is, therefore, determined by the present value of the coupon payments and par value.

• Interest rates are inversely related to present (i.e., bond) values.

Slide 5


McGraw-Hill/Irwin

The Bond Pricing Equation

T

T

)(1

FV

RR)(1

1-1

C Value BondR

Slide 6


McGraw-Hill/Irwin

Pure Discount Bonds

• Make no periodic interest payments (coupon rate = 0%)

• The entire yield to maturity comes from the difference between the purchase price and the par value.

• Cannot sell for more than par value• Sometimes called zeroes, deep discount bonds,

or original issue discount bonds (OIDs)

Slide 7


McGraw-Hill/Irwin

Pure Discount BondsInformation needed for valuing pure discount bonds:

– Time to maturity (T) = Maturity date - today’s date– Face value (F)– Discount rate (r)

TR

FVPV

)1(

Present value of a pure discount bond at time 0:

0

0$

1

0$

2

0$

1T

F$

T

Slide 8


McGraw-Hill/Irwin

Pure Discount Bond: Example

Find the value of a 30-year zero-coupon bond with a $1,000 par value and a YTM of 6%.

11.174$)06.1(

000,1$

)1( 30

TR

FVPV

0

0$

1

0$

2

0$

29

000,1$

30

0

0$

1

0$

2

0$

29

000,1$

30

Slide 9


McGraw-Hill/Irwin

Level Coupon Bonds

• Make periodic coupon payments in addition to the maturity value

• The payments are equal each period. Therefore, the bond is just a combination of an annuity and a terminal (maturity) value.

• Coupon payments are typically semiannual.• Effective annual rate (EAR) =

(1 + R/m)m – 1

Slide 10


McGraw-Hill/Irwin

Level Coupon Bond: Example

Slide 11


McGraw-Hill/Irwin

Consols

• Not all bonds have a final maturity.• British consols pay a set amount (i.e., coupon)

every period forever.• These are examples of a perpetuity.

R

CPV

Slide 12


McGraw-Hill/Irwin

5.3 Bond Concepts

Bond prices and market interest rates move in opposite directions.

When coupon rate = YTM, price = par value

When coupon rate > YTM, price > par value (premium bond)

When coupon rate < YTM, price < par value (discount bond)

Slide 13


McGraw-Hill/Irwin

YTM and Bond Value

800

1000

1100

1200

1300

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

Discount Rate

Bon

d V

alu

e

6 3/8

When the YTM < coupon, the bond trades at a premium.

When the YTM = coupon, the bond trades at par.

When the YTM > coupon, the bond trades at a discount.

Slide 14


McGraw-Hill/Irwin

Bond Example Revisited (p.133)

Slide 15


McGraw-Hill/Irwin

Computing Yield to Maturity (p.134)

• Yield to maturity is the rate implied by the current bond price.

Slide 16


McGraw-Hill/Irwin

5.4 The Present Value of Common Stocks

• The value of any asset is the present value of its expected future cash flows.

• Stock ownership produces cash flows from: – Dividends – Capital Gains

• Valuation of Different Types of Stocks– Zero Growth– Constant Growth– Differential Growth

Slide 17


McGraw-Hill/Irwin

Case 1: Zero Growth

• Assume that dividends will remain at the same level forever

RP

RRRP

Div

)1(

Div

)1(

Div

)1(

Div

0

33

22

11

0

321 DivDivDiv Since future cash flows are constant, the value of a zero

growth stock is the present value of a perpetuity:

Slide 18


McGraw-Hill/Irwin

Case 2: Constant Growth

)1(DivDiv 01 g

Since future cash flows grow at a constant rate forever, the value of a constant growth stock is the present value of a growing perpetuity:

gRP

1

0

Div

Assume that dividends will grow at a constant rate, g, forever, i.e.,

2012 )1(Div)1(DivDiv gg

3023 )1(Div)1(DivDiv gg

.

..

Slide 19


McGraw-Hill/Irwin

Case 3: Differential Growth• Assume that dividends will grow at different

rates in the foreseeable future and then will grow at a constant rate thereafter.

• To value a Differential Growth Stock, we need to:– Estimate future dividends in the foreseeable future.– Estimate the future stock price when the stock

becomes a Constant Growth Stock (case 2).– Compute the total present value of the estimated

future dividends and future stock price at the appropriate discount rate.

Slide 20


McGraw-Hill/Irwin

5.5 Estimates of Parameters• The value of a firm depends upon its growth rate,

g, and its discount rate, R. – Where does g come from?

g = Retention ratio × Return on retained earnings (ROE)

Slide 21


McGraw-Hill/Irwin

Where does R come from?

• Start with the DGM:

gP

D g

P

g)1(D R

g-R

D

g - R

g)1(DP

0

1

0

0

100

Rearrange and solve for R:

Slide 22


McGraw-Hill/Irwin

Where does R come from?

R = Div1/P0 + g

The discount rate can be broken into two parts. – The dividend yield – The growth rate (in dividends) or capital gain

yield

In practice, there is a great deal of estimation error involved in estimating R.

Slide 23


McGraw-Hill/Irwin

• A Healthy Sense of Skepticism – Estimate of g is based on a number of

assumptions:• return on reinvestment• future retention ratio

– Some financial economists suggest calculating the average R for an entire industry.

Slide 24


McGraw-Hill/Irwin

Two polar cases

• Case1: A firm paying no dividend, and going from no dividends to a positive number of dividends

• Case2: An analyst whose estimate of g for a particular firm is equal to or above R must have made a mistake.

Slide 25


McGraw-Hill/Irwin

5.6 Growth Opportunities

• Imagine a company with a level stream of earnings per share in perpetuity

• The company pays off these earnings out to stockholders as dividends. Hence.

EPS = Div (Cash cow)

• It’s value equals

EPS/r = Div/r

Slide 26


McGraw-Hill/Irwin

• Growth opportunities are opportunities to invest in positive NPV projects.

• Suppose the firm retains the entire dividend at date 1 in order to invest in a particular capital budgeting project

• Stock Price after Firm Commits to the New Project: EPS/r + NPVGO

Slide 27


McGraw-Hill/Irwin

Example

EPS/r + NPVGO

= 【〔 $1,000,000/1.1 〕 + 〔 $1,000,000/(1.1)2 〕 +…+ 〔 $1,000,000/(1.1)n 〕】 + 【〔 -$1,000,000+($210,000/0.1) 〕 /1.1 】

= 〔 $1,000,000/0.1 〕 + 〔 -$1,000,000+ ($210,000/0.1) 〕 /1.1= $10,000,000+$1,000,000= $11,000,000The price per share:

$11,000,000/100,000 = $110

Slide 28


McGraw-Hill/Irwin

• Two conditions must be met in order to increase value: – Earnings must be retained so that projects

can be funded. – The projects must have positive net present

value.

Slide 29


McGraw-Hill/Irwin

Growth in Earnings and Dividends versus Growth Opportunities

• A policy of investing in projects with negative NPVs rather than paying out earnings as dividends will lead to growth in dividends and earnings, but will reduce value.

Slide 30


McGraw-Hill/Irwin

Dividends or Earnings: Which to discount?

• Dividends, or would ignore the investment that a firm must make today in order to generate future returns. (only a portion of earnings goes to the stockholders as dividends)

Slide 31


McGraw-Hill/Irwin

The No-Dividend Firm

• A firm with many growth opportunities faces two choices: pays out dividends now, or forgoes dividends now and makes investments.

• The actual application of the dividend discount model is difficult for firms of this type.

Slide 32


McGraw-Hill/Irwin

5.7 The Dividend Growth Model and the NPVGO Model

• A steady growth in dividends results from a continual investment in growth opportunities, not just in a single opportunity.

Slide 33


McGraw-Hill/Irwin

5.7 The Dividend Growth Model and the NPVGO Model

• We have two ways to value a stock:– The dividend discount model– The sum of its price as a “cash cow” plus the

per share value of its growth opportunities

Slide 34


McGraw-Hill/Irwin

Example

• C has EPS of $10 at the end of the first year, a dividend-payout ratio of 40%, a discount rate of 16%, and a return on its retained earnings of 20%.

Slide 35


McGraw-Hill/Irwin

Solution

• The Dividend-Growth Model

P0 = Div1/(R-g)

• The NPVGO Model

P0 = EPS/R + NPVGO (5.10)

Slide 36


McGraw-Hill/Irwin

The Dividend-Growth Model

• Div1/(R-g) = $4/(.16-.12)

=$100

Slide 37


McGraw-Hill/Irwin

Solution• The NPVGO Model

– Value Per Share of a Single Growth Opportunities -$6 + $1.20/0.16 = $1.5

– Value Per Share of All Opportunities NPVGO = $1.50/(0.16-0.12)=$37.50

– Value Per Share if Firm Is a Cash Cow Div/r = $10/0.16 = $62.50

– Summation P0 = EPS/r + NPVGO = $62.5 + $37.5 = $100.0

Slide 38


McGraw-Hill/Irwin

5.8 Price-Earnings Ratio

• Many analysts frequently relate earnings per share to price.

• The price-earnings ratio is calculated as the current stock price divided by annual EPS.

Slide 39


McGraw-Hill/Irwin

5.8 Price-Earnings Ratio (P/E ratio)

• P (Price per share) = EPS/r + NPVGO

• P/E = 1/r + NPVGO / EPS

• The market is merely pricing perceptions of the future, not the future itself.

• It implies that P/E ratio is a function of growth opportunities, risk, and the choice of accounting methods.

Chap005

Economy & Finance

discount rate bond value

maturity value

price par value discount

bond example

bond trades

price par value premium

bond values

ytm coupon