valuation concepts chapter 10. basic valuation ufrom the time value of money we realize that the...

Valuation ConceptsValuation Concepts

Chapter 10

Basic ValuationBasic 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


N

1tt

t

NN

22

11

k1

k1k1k1V

CF

CFCFCF

^ ^ ^

^

Asset value

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

^

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


Valuation of Financial Valuation of Financial Assets - BondsAssets - Bonds

Bond is a long term debt instrument Value is based on present value of:

stream of interest payments principal repayment at maturity


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 Par value)

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

Bond value

Nd

N

1t

td

Nd

Nd

2d

1d

d

k1

M

k1

INT

k1

M

k1

INT

k1

INT

k1

INTV



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

Numerical solution:

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

= $877.11 + $122.89 = $1,000

15

15

0001150151

11

1501.15

1,$

.

.$Bond

value


Financial Calculator Solution:

Inputs: N = 15; I = k = 15; PMT = INT = 150

M = FV = 1000; PV = ?

Output: PV = -1,000


Changes in Bond Values Changes in Bond Values over Timeover 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, causing the bond’s value to increase (investors demand lower returns, so they are willing to pay higher prices for bonds).

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

Begind,

Begind,Endd,

d

V

VV

value bondBeginning

value bondBeginning

value bondEnding

V

INT

Current yield

Capital gains yield



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

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


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

Time path of value of a 15% Coupon, Time path of value of a 15% Coupon, $1000 par value bond when interest $1000 par value bond when interest

rates are 10%, 15%, and 20%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


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 RateKd < Coupon Rate

Kd > Coupon Rate

Years

Bond Value

Yield to MaturityYield to Maturity

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

Approximate yield to maturity

3

M V 2

N

V-M INT

bond of value Average

gains capital interest d Accrue

Annual

d

d

2N

d

2N

1tt

d

d

2

k1

M

k1

2

INT

V

2

Bond Values with Bond Values with Semiannual CompoundingSemiannual Compounding

Interest Rate Risk Interest Rate Risk on a Bondon a Bond

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

Interest 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

Value of Long and Short-TermValue of Long and Short-Term15% Annual Coupon Rate Bonds15% Annual Coupon Rate Bonds

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

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-TermValue of Long and Short-Term15% Annual Coupon Rate Bonds15% Annual Coupon Rate Bonds

Valuation of Financial Valuation of Financial Assets - Equity (Stock)Assets - Equity (Stock)

Common stock Preferred stock

hybrid similar to bonds with fixed dividend amounts similar to common stock as dividends are not

required and have no fixed maturity date

Stock Valuation ModelsStock Valuation Models

Terms:


Terms: Expected 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

Terms: Market Price

aymarket tod in the sells

stock aat which price theP0



Terms: Intrinsic Value

bothor value, book its price, market current sasset' the from different be may and facts the by

justified is investor, an of mind the in that,asset an of value the P̂0

Terms: Expected Price

Year teach of end at the

stock theof price expected theP̂t



Terms: Growth Rate

g the expected rate of change

in dividends per share


Terms: Required Rate of Return

sinvestmentother on available returns and riskiness

its given ,acceptableconsider rsstockholdethat stock common

a on return of rate minimum the k s


Terms: Dividend Yield

stock of

share a of pricecurrent by the

divided dividend expected theP

D̂

0

1


Terms: Capital Gain Yield

year theof beginning at the price

itsby dividedyear given a during

gain) (capital pricein change theP

PP

0

01


Terms: Expected Rate of Return

yield gains capital expected yield dividend expected

receive to expects investor individual anthat stock

common a on return of rate the k̂ s

Terms: Actual Rate of Return

yield gains capital the

plus yield dividend the toequal

fact; after the receives,actually

investor individualan stock that

common aon return of rate theks



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


Expected Dividends as the Basis for Stock Values

1tt

s

t

s2

s

21

s

1

k1

D̂

k1

D̂

k1

D̂

k1

D̂

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

Stock Values with Zero GrowthA zero growth stock is a common stock

whose future dividends are not expected to grow at all

s2

s1

s

0k1

D

k1

D

k1

D P̂

s0 k

D P̂

0s P

D k̂



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

gk

D̂

gk

g1D

s

1

s

0


Normal, or Constant, Growth (Gordon Model)

s

02

s

20

1s

10

0k1

g1D

k1

g1D

k1

g1D P̂

Expected Rate of Return on Expected Rate of Return on a Constant Growth Stocka Constant Growth Stock

gain Capital yield Dividend

g P

D̂ k̂

0

1s

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

Nonconstant GrowthNonconstant Growth

Nonconstant GrowthNonconstant Growth

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 time it becomes 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, .

0P̂

Changes in Stock PricesChanges in Stock Prices

Investors change the rates of return required to invest in stocks

Expectations about the cash flows associated with stocks change

Valuation of Real Valuation of Real (Tangible) Assets(Tangible) Assets

Valuation is still based on expected cash flows of the asset

Valuation of Real Valuation of Real (Tangible) Assets(Tangible) Assets

Year Expected Cash Flow, CF

1 $120,000

2 100,000

3 150,000

4 80,000

5 50,000To earn a 14% return on investments like this, what is the value of this machine?

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 $50,000Asset Value = V0

54321 141

00050

141

00080

141

000150

141

000100

141

000120790356

.

,$

.

,$

.

,$

.

,$

.

,$,$

Cash Flow Time LinesCash Flow Time Lines

End of Chapter 10End of Chapter 10

ValuationConcepts

valuation concepts chapter 10. basic valuation ufrom the time value of money we realize that the...

Documents

par value bond

bond values

bond kd

bond maturesint

outstanding bond

bonds value

present value

coupon ratepremium bonda