Chapter 5

Valuation Concepts

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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.

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Basic Valuation

The Value of the Asset = the sum of the discounted cash flows the asset is expected

to generate over time

Required return = the rate you use to discount the cash flows back.= the rate of return investors consider appropriate for holding

such an asset= based on riskiness and economic conditions

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Key Terms for Bonds

Principal Amount = Face Value = Maturity Value,= Par Principal Amount = Face Value = Maturity Value,= Par Value:Value: The amount of money borrowed

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

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 the right to pay off bonds prior to maturity.

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Task: Find the present Value of Genesco’s 15%, 15-year, $1,000 bonds valued at 15% required rate of return

6

Financial calculator solution:Financial calculator solution:

Task: Find the present Value of Genesco’s 15%, 15-year, $1,000 bonds valued at 15% required rate of return

INPUTS

OUTPUT

15 15 ? 150 1000 N I/YR PV PMT FV

-1000

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Changes in Bond Values Over Time

Par Value BondPar Value Bond

Discount BondDiscount Bond

Premium BondPremium Bond

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Par Value Bonds

Par Value Bond:Par Value Bond:When the going interest rate = the

bond’s coupon interest rate The market value of a bond will

always approach its par value as its maturity date approaches, provided the firm does not go bankrupt.

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Discount Bonds

An increase in interest rates in the economy causes the price to fallDiscount Bond

= when a bond sells below its par value occurs whenever the going rate of

interest rises above the coupon rate

The bond value decreases so that the rate of return investors earn equates to the higher kd.

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Premium Bonds

A decrease in interest rates in the economy causes the bond price to risePremium

= when a bond sells above its par valueoccurs whenever the going rate of

interest falls below the coupon rate

The bond value increases so that the rate of return investors earn equates to the lower kd.

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dV

INTCurrent

yield

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

Calculating a Bond’s Current Yield

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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

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$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

Changes in Bond Values Over Time

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

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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.

Financial calculator solution:Financial calculator solution:

INPUTS

OUTPUT

15 ? -950 150 1000 N I/YR PV PMT FV

15.89

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Interest Rate Risk on 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 (presumably lower) market rates.

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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

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Valuation of Financial 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

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Stock Valuation Models

Term: Expected DividendsExpected Dividends

investors. amongdiffer may estimates

theso values,expected are dividends future All

years twoof end at the expected dividend theis 2D̂

year thisof end at the paid be it will and

paid, be toexpected dividendnext theis 1D̂

paidalready dividendrecent most theis 0D

Year t of end at the receive

toexpectsr stockholde thedividendtD̂

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ay.market tod in the sells

stock aat which price theP0

Term: Market PriceMarket Price

Stock Valuation Models

20both.or ,book value its price,

market current sasset' thefrom

differmay facts; by the

justified is investor,an of mind

in the ,asset thatan of value theP̂0

Term: Intrinsic ValueIntrinsic Value

Stock Valuation Models

21

Year t.each of end at the

stock theof price expected theP̂t

Term: Expected PriceExpected Price

Stock Valuation Models

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shareper dividendsin

change of rate expected theg

Term: Growth RateGrowth Rate

Stock Valuation Models

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s.investmentother

on available returns and riskiness

itsgiven acceptableconsider

rsstockholde stock thatcommon

aon return of rate minimum thek s

Term: Required Rate of ReturnRequired Rate of Return

Stock Valuation Models

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stock of

share a of pricecurrent by the

divided dividend expected theP

D̂

0

1

Term: Dividend YieldDividend Yield

Stock Valuation Models

25

year theof beginning at the price

itsby dividedyear given a during

gain) (capital pricein change theP

PP

0

01

Term: Capital Gain YieldCapital Gain Yield

Stock Valuation Models

260

01

0

1

s

P

PP

P

D̂

receive toexpects investor individualan stock that

common aon return of rate thek̂

Term: Expected Rate of ReturnExpected Rate of Return= Expected dividend yield + capital gains = Expected dividend yield + capital gains yieldyield

Stock Valuation Models

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yield. gains capital the

plus yield dividend the toequal

fact; after the receives,actually

investor individualan stock that

common aon return of rate thes k

Term: Actual Rate of ReturnActual Rate of Return

Stock Valuation Models

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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.

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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 = A PERPETUITY

02 DD̂D̂D̂ and 0, g1

s0 k

D P̂

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Normal, or Constant, Growth

Normal Growth is 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

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g

s

10

k

Div P̂

Normal, or Constant, Growth(Gordon Growth Model)

A Constant Growth StockConstant Growth Stock is a common stock whose future dividends are expected to grow at a constant rate = A GROWING PERPETUITY

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g P

D̂ k̂

0

1s

Expected Rate of Return on a Constant Growth Stock

Rearrange the formula for the price to get Dividend Yield

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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.

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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 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 P0.

Valuing Stocks with Nonconstant Growth

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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.^

Stock Market Equilibrium

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Changes in Stock Prices

Investors change the rates of return required to invest in stocks.

Expectations change about the cash flows associated with particular stocks.

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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.

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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:

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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

^

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In “CF” register:Type: 2nd, CE/C to clear information storedCF0 = 0

C01 = 120,000 F01 = 1C02 = 100,000 F02 = 1C03 = 120,000 F03 = 1C04 = 80,000 F04 = 1 C05 = 50,000 F05 = 1

In “NPV” Register:Type: I = 14, enter, down arrowSee: NPV = (varies)Type: CPTSee: NPV = 356,790.50

Calculator Solution:

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For Next Class

Review Chapter 5 materialsDo Chapter 5 homeworkPrepare for Quiz on Chapter 5Read Chapter 6 (Capital Budgeting)