7-1 Copyright (C) 2000 by Harcourt, Inc. All rights reserved. Chapter 7 Valuation Concepts Bond Values Stock Values Rates of Return Market Equilibrium

7-1

Copyright (C) 2000 by Harcourt, Inc. All rights reserved.

Chapter 7Valuation Concepts

Bond ValuesStock ValuesRates of ReturnMarket Equilibrium

Copyright © 2000 by Harcourt, Inc.

All rights reserved. Requests for permission to make copies of any part of the work should be mailed to the following address: Permissions Department, Harcourt, Inc., 6277 Sea Harbor Drive, Orlando, Florida 32887-6777.

7-2


Basic Valuation

From “The Time Value of Money” we realize that the value of anything is based on the present value of the cash flows the asset is expected to produce in the future.

7-3


V CF1

1 k 1 CF2

1 k 2 CFN

1 k N

CFt

1 k tt1

N

^ ^ ^Asset value

^

Basic Valuation

k = the return investors consider appropriate for holding such an asset - usually referred to as the required return, based on riskiness and economic conditions

CFt = the cash flow expected to be generated by the asset in period t

^

7-4


Valuation of Financial Assets: Bonds - long term debt instruments

Principal Amount, Face Value, Maturity Principal Amount, Face Value, Maturity Value, Par Value:Value, Par Value: The amount of money the firm borrows and promises to repay at some future date, often at maturity.

Coupon Payment:Coupon Payment: The specified number of dollars of interest paid each period, generally each six months, on a bond.

Key Terms

7-5


Coupon Interest Rate:Coupon Interest Rate: The stated annual rate of interest paid on a bond.

Maturity Date:Maturity Date: A specified date on which the par value of a bond must be repaid.

Original Maturity:Original Maturity: The number of years to maturity at the time the bond is issued.

Call Provision:Call Provision: Gives the issuer right to pay off bonds prior to maturity.

Key Terms

7-6


The Basic Bond Valuation Model

kd = required rate of return on a debt instrument

N = number of years before the bond matures

INT = dollars of interest paid each year (Coupon rate x Par value)

M = par or face, value of the bond to be paid off at maturity

7-7


Bond Value

d

k1

MN

1tt

dk1

INT

Nd

k1

MN

dk1

INT...

2d

k1

INT1

dk1

INTd

V

INT(PVIFAkd,N) M(PVIFkd, N)

7-8


Genesco 15%, 15year, $1,000 bonds valued at 15% required rate of return

Vd = $150 (5.8474) + $1,000 (0.1229)

= $877.11 + $122.89 = $1,000

15

15

1.15

1000,1$

15.015.1

11

150$Bond value

Numerical solution:

7-9


Look up the PVIF and PVIFA values in Tables A-1 and A-2 and insert them in the equation

Vd = $150 (5.8474) + $1,000 (0.1229)

= $877.11 + $122.89 = $1,000


Tabular solution:

7-10



Financial calculator solution:

15 15 150 1000N I/YR PV PMT FV

- 1000

INPUTS

OUTPUT

7-11


Changes in Bond Values Over Time

If the market rate associated with a bond, kd, equals the coupon rate of interest, the bond will sell at its par value.

If interest rates in the economy fall after the bonds are issued, kd is below the coupon rate.

The interest payments and maturity payoff stay the same, but the PVIF and PVIFA values are based on the new kd increasing the bond value

7-12


Begind,

Begind,Endd,

d

V

VV

valuebond

Beginning

valuebond

Ending

valuebond

Beginning

V

INT

Current yield

Capital gains yield

Current yieldCurrent yield is the annual interest payment on a bond divided by its current market value


7-13


Discount BondDiscount Bond

A bond that sells below its par value, which occurs whenever the going rate of interest rises above the coupon rate

Premium BondPremium Bond

A bond that sells above its par value, which occurs whenever the going rate of interest falls below the coupon rate


7-14


An increase in interest rates will cause the price of an outstanding bond to fall

A decrease in interest rates will cause the price to rise

The market value of a bond will always approach its par value as its maturity date approaches, provided the firm does not go bankrupt


7-15


Time path of value of a 15% Coupon, $1000 par value bond when interest rates are 10%, 15%, and 20%

Year kd = 10% kd = 15% kd = 20%

0 $1,380.30 $1,000.00 $766.231 $1,368.33 $1,000.00 $769.472 $1,355.17 $1,000.00 $773.373 $1,340.68 $1,000.00 $778.044 $1,324.75 $1,000.00 $783.655 $1,307.23 $1,000.00 $790.386 $1,287.95 $1,000.00 $798.457 $1,266.75 $1,000.00 $808.148 $1,243.42 $1,000.00 $819.779 $1,217.76 $1,000.00 $833.7210 $1,189.54 $1,000.00 $850.4711 $1,158.49 $1,000.00 $870.5612 $1,124.34 $1,000.00 $894.6813 $1,086.78 $1,000.00 $923.6114 $1,045.45 $1,000.00 $958.3315 $1,000.00 $1,000.00 $1,000.00

7-16


Time path of value of a 15% Coupon, $1000 par value bond when interest rates are 10%, 15%, and 20%

$0

$250

$500

$750

$1,000

$1,250

$1,500

1 3 5 7 9 11 13 15

Kd = Coupon Rate

Kd < Coupon Rate

Kd > Coupon Rate

Years

Bond Value


7-17


Finding the Interest Rate on a Bond: Yield to Maturity

YTMYTM is the average rate of return earned on a bond if it is held to maturity

Approximate yield to maturity

(does not consider time value of money)

3

M V 2N

V-M INT

bond of valueAverage

gains capital interest

Accrued

Annual

d

d

7-18


Bond Values with Semiannual Compounding

,2N2

k

,2N2

k

2N

d

2N

1tt

d

d

dd

PVIFMPVIFA2

INT

2k

1

M

2k

1

2INT

V

7-19


Interest Rate Risk on a Bond

Interest Rate Price RiskInterest Rate Price Risk - the risk of changes in bond prices to which investors are exposed due to changing interest rates

Interest Rate Reinvestment Rate RiskInterest Rate Reinvestment Rate Risk - the risk that income from a bond portfolio will vary because cash flows have to be reinvested at current market rates

7-20


Current Market Interest Rate, kd

1-Year Bond 14-Year Bond

5% 1,095.24$ 1,989.86$ 10% 1,045.45$ 1,368.33$ 15% 1,000.00$ 1,000.00$ 20% 958.33$ 769.47$ 25% 920.00$ 617.59$

Value of

Value of Long and Short-Term15% Annual Coupon Rate Bonds

7-21


Interest Rate, kd (%)

BondValue

($) 2,000

1,500

1,000

500

0 5 10 15 20 25

14-Year Bond

1-Year Bond

Value of Long and Short-Term15% Annual Coupon Rate Bonds

7-22


Bond Prices in Recent Years

7-23


Valuation of Financial Assets - Equity (Stock)

Common StockCommon Stock Preferred StockPreferred Stock

– hybrid• similar to bonds with fixed

dividend amounts• similar to common stock as

dividends are not required and have no fixed maturity date

7-24


Stock Valuation Models

Terms: Expected DividendsExpected Dividends

investors amongdiffer may estimates

theso values,expected are dividends future All

years twoof end at the expected dividend theis D̂

year thisof end at the paid be it will and

paid, be toexpected dividendnext theis D̂

paidalready dividendrecent most theis D

Year t of end at the recieve

toexpectsr stockholde thedividendD̂

2

1

0

t


7-25


aymarket tod in the sells

stock aat which price theP0


Terms: Market PriceMarket Price


7-26


bothor ,book value its price,

market current sasset' thefrom

different bemay and facts by the

justified is investor,an of mind

in the ,asset thatan of value theP̂0


Terms: Intrinsic ValueIntrinsic Value


7-27


Year teach of end at the

stock theof price expected theP̂t


Terms: Expected PriceExpected Price


7-28


shareper dividendsin

change of rate expected theg


Terms: Growth RateGrowth Rate


7-29


sinvestmentother

on available returns and riskiness

itsgiven acceptableconsider

rsstockholde stock thatcommon

aon return of rate minimum theks


Terms: Required Rate of ReturnRequired Rate of Return


7-30


stock of

share a of pricecurrent by the

divided dividend expected theP

D̂

0

1


Terms: Dividend YieldDividend Yield


7-31


year theof beginning at the price

itsby dividedyear given a during

gain) (capital pricein change theP

PP

0

01


Terms: Capital Gain YieldCapital Gain Yield


7-32


ˆ k s the rate of return on a common

stock that an individual investor

expects to receive; equal to the

expected dividend yield plus the

expected capital gains yield


Terms: Expected Rate of ReturnExpected Rate of Return


7-33


yield gains capital the

plus yield dividend the toequal

fact; after the receives,actually

investor individualan stock that

common aon return of rate theks


Terms: Actual Rate of ReturnActual Rate of Return


7-34


Expected Dividends as the Basis for Stock Values

If you hold a stock forever, all you receive is the dividend payments

The value of the stock today is the present value of the future dividend payments

7-35


Value of Stock Vs ˆ P 0 PV of expected future dividends

ˆ D 1

1 k s 1

ˆ D 21 k s 2

ˆ D 1 ks

ˆ D t

1 k s tt1

Expected Dividends as the Basis for Stock Values

7-36


Stock Values with Zero Growth

A Zero Growth StockZero Growth Stock is a common stock whose future dividends are not expected to grow at all

02 DD̂ ...D̂D̂ and 0, g1

s2

s1

s

0k1

D...

k1

D

k1

D P̂

7-37


Normal, or Constant, Growth

Growth that is expected to continue into the foreseeable future at about the same rate as that of the economy as a whole

g = a constant

7-38


Normal, or Constant, Growth(Gordon ModelGordon Model)

ˆ P 0 D0 1 g 1

1 k s 1

D0 1 g 2

1 ks 2 D0 1 g

1 ks

gk

D̂

gk

g1D

s

1

s

0

7-39


Expected Rate of Return on a Constant Growth Stock

Dividend yield Expected growth rate, or capital gains yield

g D̂

k̂0

1s

P

7-40


Valuing Stocks with Nonconstant Growth

Nonconstant Growth:Nonconstant Growth: The part of the life cycle of a firm in which its growth is either much faster or much slower than that of the economy as a whole

7-41


1. Compute the value of the dividends that experience nonconstant growth, and then find the PV of these dividends

2. Find the price of the stock at the end of the nonconstant growth period, at which it has become a constant growth stock, and discount this price back to the present

3. Add these two components to find the intrinsic value of the stock, .

Valuing Stocks with Nonconstant Growth

ˆ P 0

7-42


Stock Market Equilibrium

1. The expected rate of return as seen by the marginal investor must equal the required rate of return,

2. The actual market price of the stock must equal its intrinsic value as estimated by the marginal investor,

k̂x = kx,

P0 = P0^

7-43


Changes in Stock Prices

Investors change the rates of return required to invest in stocks

Expectations about the cash flows associated with stocks change

7-44


The Efficient Markets Hypothesis

The weak formThe weak form of the EMH states that all information contained in the past price movements is fully reflected in current market prices.

The semistrong formThe semistrong form states that current market prices reflect all publicly available information

The strong formThe strong form states that current market prices reflect all pertinent information, whether publicly available or privately held.

7-45


Valuation of Real (Tangible) Assets

A company proposes to buy a machine so it can manufacture a new product. After five years the machine will be worthless, but during the five years it is used, the company will be able to increase its net cash flows by the following amounts:

7-46


Year Expected Cash Flow, CF 1 $120,000

2 $100,000 3 $150,000 4 $80,000 5 $50,000

To earn a 14% return on investments like this, what is the value of this machine?

Valuation of Real (Tangible) Assets

7-47


Cash Flow Time Lines

0 1 2 3 4 514%

$120,000 $100,000 $150,000 $80,000 $50,000

PV of $120,000

PV of $100,000

PV of $150,000

PV of $80,000

PF of $50,000

Asset Value =V0

54321 14.1

000,50$

14.1

000,80$

14.1

000,150$

14.1

000,100$

14.1

000,120$

7-48


End of Chapter 7 Valuation Concepts

Documents

7-1 Copyright (C) 2000 by Harcourt, Inc. All rights reserved. Chapter 7 Valuation Concepts Bond Values Stock Values Rates of Return Market Equilibrium