Topic2 Valuation 6PG

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FINS1613: Business Finance

Semester 1, 2016

Topic 2: Valuation of a Firm’s securities

Contact Details

Emma Jincheng Zhang (Weeks 3-5)

[email protected]

Rm 302

Consultation hours: Wednesdays 10-12pm

Outline1. Capital structure2. Bond valuation

a) Bond terminologyb) Coupon bondsc) Zero coupon bondsd) Determinants of the yield to maturity

a) Inflation and interest ratesb) Interest rate risk

c) Term structure of interest rates

d) Credit ratings

3. Equity valuationa) Equity terminologyb) Dividend discount model

i. Estimating dividend growth

c) Total payout model

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1. Capital Structure

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Capital structure

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Capital structure: The relative proportions of debt, equityand other securities that a firm has outstanding

Common types of securities:

Bonds (debt)

Ordinary shares (equity)

Preference shares (equity)

=

V = PV of cash flows generated by the firm

D = PV of cash flows generated by debt securities

E = PV cash flows generated by equity securities

Capital structure: Debt

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When a corporation (or government) wishes to borrowmoney from the public on a long-term basis (at least 1 year), it

usually does so by selling bonds.

Government bonds are issued by the Australian Treasury

Considered ‘risk free’ in developed countries as there is no risk of thegovernment not making payments and defaulting.

E.g. Australian10-year bond

Corporate bonds are issued by corporations

Considered risky as corporations may default on payments. Thegreater the default risk, the higher the interest rate to attract buyers.

E.g. Woolworths Limited bonds

mailto:[email protected]:[email protected]


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Capital structure: Equity

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Equity financing includes ordinary shares (common stock)and preference shares (preferred stock)

Ordinary shares: Equity without priority for dividends; inbankruptcy it has a residual claim on the assets of thefirm.

E.g. Woolworths Limited (WOW) trading on the ASX

Preference shares: Share with dividend priority overordinary shares, normally with a fixed dividend rate,sometimes without voting rights.

E.g. ANZ convertible preference shares (ANZPA) trading onthe ASX

Residual value

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Primary and secondary markets

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Primary market transaction: the corporation is the sellerand the transaction raises money for the corporation.

Public offering: involves selling securities to the general public

Private placements: negotiated sale involving a specific buyer

Secondary market transaction: involves one owner orcreditor selling to another.

Secondary markets provide the means for transferringownership of corporate securities

2. Bond Valuation

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Bond terminology

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Coupon: The promised interest payments of a bond, paidperiodically until the maturity date of the bond.

Coupon rate: Determines the amount of each couponpayment; expressed as an APR

Face (par) value: The principle amount that is repaid atthe end of the term.

Maturity: Date on which the principal amount is paid.

Yield to maturity (yield): The market required rate ofreturn for bonds of similar risk and maturity; quoted as anAPR

Example: A six-year bond with $1,000 face value and 5%coupons paid semi-annually.

Bond terminology

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Coupon bonds

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Bond value = PV(coupons) + PV(face value)

Bond value = PV(annuity) + PV(single cash flow)

=

1

1

1

1

t = 0 t = 2 t = 3 t = 4 t = nt = 1

$C $C $C $C $C

$FV

C = Per-period coupon paymentr = Per-period yieldn = Number of periodsFV = Face value

Coupon bonds

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To calculate the per-period coupon payment:

= ×

Example: Annual coupons

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Consider a bond with a coupon rate of 10% andcoupons paid annually. The par value is $1000 and thebond has 5 years to maturity. The yield to maturity is11%. What is the value of the bond?

Solution: Number of coupon payments (n):

= 5

Per-period coupon payment (C): = 10% × $1,000= $100

Per-period yield (r): = 11%

Face value (FV): $1,000

Example: Annual coupons

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=

1

+

+

=100

0.11

1 1

1 0.11

1,000

1 0.11

= 369.59 593.45 = $963.04

t = 0 t = 2 t = 3 t = 4t = 1

$100

t = 5

$100 $100 $100 $100

$1,000


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Example: Semi-annual coupons

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Consider a bond with a coupon rate of 7% and coupons paidsemi-annually. The par value is $1000 and the bond has 7 yearsto maturity. The yield to maturity is 8%. What is the value ofthe bond?


= 2 × 7 = 14

Per-period coupon payment (C):

=% ×$,

= $35

Per-period yield (r):

=%

= 4%


Example: Semi-annual coupons

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=

1

+

+

=35

0.041

1

1 0.04

1,000

1 0.04

= 369.71 577.48 = $947.18

t = 0 t = 2 t = 3 t = 4 t = 14t = 1

$35 $35 $35 $35 $35

$1,000

Example: Solving for C

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Outback Corporation has bonds on the market with tenand a half years to maturity, a YTM of 6.9% and a currentprice of $1,070. The bonds have a face value of $1,000and make half-yearly payments. What is the semi-annualcoupon payment? What must the coupon rate be onOutback’s bonds?


= 2 × 10.5 = 21

Per-period yield (r):

=.%

= 3.45%



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t = 0 t = 2 t = 3 t = 4 t = 21t = 1

$C $C $C $C $C

$1,000

=

1

1

1

1

$1,070 =

0.03451

1

1 0.0345

1,000

1 0.0345

= $39.24


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Annual coupon rate:

= ×

$39.24 = × $1,000

2

=2 × $39.24

$1,000= 7.85%

Relationship between bond price, YTM and

coupon rate

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Bond trades

at

Price and Face

value

YTM and Coupon rate

Premium Price > Face value YTM < Coupon rate

Par Price = Face value YTM = Coupon rate

Discount Price < Face value YTM > Coupon rate


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Example: Relationship between bond price,

YTM and coupon rate

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The Barramundi fishing company is issuing a bond withten years to maturity. The Barramundi bond has a face

value of $1,000 and an annual coupon of $80. Similarbonds have a yield to maturity of 8%. Is the Barramundibond selling at par, premium or discount?

Since the yield to maturity = coupon rate, the bond is selling at

par.

=

1

1

1

1

=80

0.081

1

1 0.08

1,000

1 0.08

= 536.81 463.19 = $1,000


YTM and coupon rate

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Does your answer change if the Barramundi bond pays an annualcoupon of $60?

The coupon rate is 6%. Since yield to maturity > coupon rate, the bondis selling at a discount.

=

1

1

1

1

=60

0.081

1

1 0.08

1,000

1 0.08

= 402.60 463.19 = $865.79


YTM and coupon rate

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How about $100?

The coupon rate is 10%. Since yield to maturity < coupon rate, the bondis selling at a premium.

=

1

1

1

1

=

100

0.08 1

1

1 0.08

1,000

1 0.08

= 671.01 463.19 = $1,134.20

Discount, Par and Premium

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The coupon rate is fixed and simply determines what the bond’scoupon payments will be. The yield to maturity is what the marketdemands on the issue, and it will fluctuate through time.

You cannot determine if a bond is a good investment based onwhether it is selling at a discount, par or premium.

Example: Consider the following bonds. Each bond has 10 years tomaturity and pays coupons annually.

Bond A Bond B Bond C

YTM 10% 10% 10%

Coupon payment $80 $100 $120

Face value $1,000 $1,000 $1,000

Price $877.11 $1,000 $1122.89

Discount Par Premium

Zero-coupon bonds

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A bond that pays no coupons, and thus is initially pricedat a discount.

The price of an n-year zero-coupon bond is:

=

1

r = Per-period yield

n = Number of periods

FV = Face value

This is equivalent to finding the present value of a single cashflow.

Example: Zero-coupon bonds

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Suppose Digger Ltd issues a $1,000 face value, five-yearzero coupon bond. The initial price is set at $497. What isthe yield to maturity of the bond?

Solution:

We are solving for the yield to maturity, or r .

=

1

$497 =$1,000

1

= $1,000$497

/

1 = 1 5 %


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Inflation and interest rates

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Real rate of interest: change in purchasing power.

Nominal rate of interest: quoted rate of interest, changein purchasing power and inflation.

The ex ante nominal rate of interest includes our desiredreal rate of return plus an adjustment for expectedinflation.

Inflation and interest rates

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The Fisher effect: defines the relationship between realrates, nominal rates and inflation:

1 = 1 × (1 )

Approximation:

≈

Example: Inflation and interest rates

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If we require a 10% real return and we expect

inflation to be 8%, what is the nominal rate?

Nominal = (1.1)(1.08) – 1 = .188 = 18.8%

Approximation: Nominal = 10% + 8% = 18%

Because the real return and expected inflation are

relatively high, there is a significant difference betweenthe actual Fisher effect and the approximation.

Interest rate risk

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Interest rate risk: The risk that arises for bond

owners from fluctuating interest rates. Assuming allother things being equal,

1. The longer the time to maturity, the greater theinterest rate risk.

2. The lower the coupon rate, the greater the interestrate risk.

Example: Interest rate risk

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Both Bond Bill and Bond Ted have 8% coupons, make half-yearly payments, have a $1,000 face value, and are pricedat par value. Bond Bill has three years to maturity,whereas Bond Ted has twenty years to maturity. Whichbond has more interest rate risk?

Bond Ted (20-year bond) has more interest rate risk.

Bond YTM = 8% YTM = 10% YTM = 6%

3-year $1,000 $949.24 (-5.1%) $1,054.17 (+5.4%)

20-year $1,000 $828.41 (-17.2%) $1,231.15 (+23.1%)

Example: Interest rate risk

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Bond J is a 4% coupon bond. Bond S is a 10% couponbond. Both bonds have eight years to maturity, $1,000face value, make half-yearly payments, and have a YTM of7%. Which bond has more interest rate risk?

Bond J (4% coupon) has higher interest rate risk.

Bond YTM = 7% YTM = 9% YTM = 5%

4% coupon $818.59 $719.15 ( – 12.1%) $934.72 (+14.2%)

10% coupon $1,181.41 $1,056.17 ( – 10.6%) $1,326.38 (+12.3%)


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Term structure of interest rates

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The ‘term structure’ is the relationship between the

term to maturity and interest rate for securities in the

same risk class.

The term structure is illustrated by the yield curve,

which plots bond yield against term to maturity.

Determinants of term structure:

Market expectations hypothesis

Liquidity premium hypothesis


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Market expectations hypothesis

Interest rates are set so investors can expect to receive, onaverage, the same return over any future period, regardless ofthe security in which they invest.

Long and short-term rates are perfect substitutes.

The observed long-term rate is a function of today’s short

term rate and expected future short-term rates. If interest rates are expected to rise, long-term interest rates will be

higher than short-term rates to attract investors.

If interest rates are expected to drop, long-term interest rates will belower than short-term rates.


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Liquidity premium hypothesis (interest rate risk)

Although future interest rates are set by investorsexpectations, investors need to be given some reward (liquiditypremium) for taking the extra risk involved in longer termsecurities

May explain why yield curves generally upwards sloping

The yield curve has an upward bias built into the long-term ratesbecause of the risk premium

Forward rates are not equal to expected future short-termrates


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Credit risk and Credit ratings

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Australian Treasury securities are widely regardedto be risk free; it is highly unlikely that thegovernment will default on these bonds.

With corporate bonds, the bond issuer maydefault.

Credit risk: the risk of default by the issuer. Credit rating: the assessment by a credit rating

agency of the creditworthiness of the corporateissuer E.g. Standard & Poor’s (S&P), Moody’s Investors

Service, Fitch Ratings Encourages widespread investor participation


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Credit ratings

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High grade Moody’s Aaa, Fitch AAA and S&P AAA ─ capacity to pay is extremely

strong.

Moody’s Aa, Fitch AA and S&P AA ─

capacity to pay is very strong. Medium grade Moody’s A, Fitch A and S&P A ─ capacity to pay is strong, but more

susceptible to changes in circumstances. Moody’s Baa, Fitch BBB and S&P BBB ─ capacity to pay is adequate,

adverse conditions will have more impact on the firm’s ability to pay. Low grade

Moody’s Ba, B ,Caa and Ca Fitch BB, B, CCC and CC S&P BB, B, CCC Considered speculative with respect to capacity to pay. The ‘B’ ratings are the

lowest degree of speculation.

Very low grade Moody’s C , Fitch C and S&P C— income bonds with no interest being pa id. Moody’s D, Fitch DDD, DD and D, and S&P D— in default with principal and

interest in arrears.

Credit ratings

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3. Equity Valuation

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Equity valuation

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More difficult to value in practice than a bond:

1. Promised cash flows are not known in advance

2. Life of the investment is essentially forever; there is nomaturity for an ordinary share

3. No way to observe the rate of return required by the market

Equity terminology

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Return from an equity investment comes from twosources:

1. Dividend payments

Payment made to shareholders

Future dividends are uncertain and not guaranteed

2. Sale price

Cash flow occurs when the stock is sold

Market price on the stock exchange

Market price is not known with certainty before sale

Equity terminology

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Equity terminology

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Equity terminology

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Equity cost of capital (rE): The expected return of otherinvestments available in the market with equivalent risk to

the firm’s share.

This is the discount rate for equity

Equity terminology

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The expected total return of a share should equal itsequity cost of capital

Total return from equity ownership can be separated intotwo components:

Dividend yield: a share’s expected cash dividend divided by its

current price

Capital gain yield: the change in stock price as a percentage ofthe initial price

Total Return = Dividend yield + Capital gain rate

=

1 =

Equity valuation approach

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In general, we value an equity as follows:

1. Determine the expected cash flows

Consists of expected dividend payments and a final shareprice

2. Estimate a discount rate by comparison to a traded,benchmark asset with similar type of risk

Benchmark against the “market,” which does not have

idiosyncratic risk

Adjust the rate for each stock’s systematic risk relative

to the market

3. Compute the present value

Dividend Discount Model

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A one-year investor

Value of the stock today: P0

Expects to receive a dividend of Div1 in one year and sell thestock for P1

= 1

t = 0 t = 1 t = 2 t = 3 t = n

P0

Div1P1

Example: One-year investor

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Suppose you are thinking of purchasing the stock ofMoore Oil, Inc. and you expect it to pay a $2 dividend inone year and you believe that you can sell the stock for$14 at that time. If you require a return of 20% oninvestments of this risk, what is the maximum you wouldbe willing to pay?

=

1

= $+$+.

= $13.33

t = 0 t = 1 t = 2 t = 3 t = n

P0

Div1= $2P1= $14


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An n-year investor Value of the stock today: P0

Expects to receive a dividend of Div1 each year through to timen. At time n, will receive a final dividend and sell the stock forPn.

=

+

+ …

+

+

t = 0 t = 1 t = 2 t = 3 t = n

P0

DivnPn

Div3Div2Div1


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An infinite horizon investor

Value of the stock today: P0

Expects to receive a dividend each year in perpetuity.

t = 0 t = 1 t = 2 t = 3 t = ∞

P0

Div∞ Div3Div2Div1

=

1

1

1

⋯


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Dividend discount model: A model that values sharesaccording to the present value of the future dividends thefirm will pay.

The price of the share is equivalent to the present value of allof the expected future dividends it will pay

Estimating these dividends is difficult

We assume that in the long run, dividends grow at a constantrate.

Constant dividend growth model: A model for valuing a share

by viewing its dividends as a constant growth perpetuity

Example: Dividend Discount Model

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ACE is offering a constant dividend of $1. Your requiredrate of return is 10%. What is the value of a share?

=

=

$1

0.10= $10

t = 0 t = 1 t = 2 t = 3 t = ∞

P0

$1$1$1$1

Example: Dividend Discount Model

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BDF has just paid a dividend of $2.20 per share, whichis expected to grow at 4% per year in the future. Yourrequired rate of return is 11%. What is the value of ashare?

= = $2.20(1.04)

0.11 0.04= $32.69

t = 0 t = 1 t = 2 t = 3 t = ∞

P0

$2.20(1.04)3$2.20(1.04)2 $2.20(1.04)

Example: Solving for r

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CEG has a current share price of $46 and plans to pay$2.30 per share in dividends in the coming year. Ifdividends are expected to grow by 2% per year in thefuture, what is DFH’s equity cost of capital?

=

$46 =$2.30

0.02

=

$2.30

$46 0.02 = 7%


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Example: Two-stage model

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EGI will pay an annual dividend of $0.65 one year from now.Analysts expect this dividend to grow at 12% per year

thereafter until the fifth year. From year 6, the firm will pay adividend of $0.80 forever. What is the value of a EGI share ofthe firm’s equity cost of capital is 8%?

Solution:

=

1

1

1

1

=$0.65

0.08 0.121

1.12

1.08

$0.800.08

1 0.08

= $3.24 $6.81

= $10.05

Estimating dividend growth

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Earnings per share (EPS): Measures firm profitability. Itis total earnings normalised by the number of shares

outstanding.

Earnings can be used to pay out dividends or they can beretained within the firm for future investment

Dividend payout rate: The fraction of earnings that a firm pays asdividends

Retention rate:The fraction of earnings that a firm retains for newinvestment.

Return on new investment: Measures the ability of a firm to turninvestment into earnings. It is the ratio of new earnings to new investment.

= 1

How do dividends grow?

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EPS in the next period increases by 9.36c, which will beavailable for distribution as dividends or ploughed backinto the firm

EPS(153c)

Retainedprofit(52c)

EPSgrowth(9.36c)

Return on newinvestment = 18%

Retention rate = 34%

DPS

(101c)

Dividend payout rate = 66%


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Dividend per share can be computed as

=

×

= ×

Assume the dividend payout rate is constant, then

ℎ =−

=× −×

×

=−

An estimate for earnings growth is an estimate for

dividend growth.


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Assuming dividends are paid from earnings, estimating

dividend growth requires estimating earnings growth

Use accounting measures to:

Determine the amount of earnings retainedfor new investment

Determine the return on this newinvestment


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Assuming the dividend payout rate is constant, thedividend growth rate can be expressed as follows:

RONI: Return on new investment

ℎ = ×

= 1 ×


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Understanding dividend growth

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Assets Earnings DividendsAsset produceearnings

EPS EPS x Payout

Some earnings paidas dividends

Some earningsreinvested in the firm

Year

t

EPS x (1 - Payout )


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Assets Earnings Dividends

EPS EPS x Payout

Year

t

t + 1

EPS x (1 - Payout )

Assets in year t+1 compriseboth historical and new assetsHistorical

New Investment


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Assets Earnings Dividends

EPS EPS x Payout

Year

t

t + 1

Historical

New Investment

EPS x (1 - Payout )

Historical assetsproduce historical EPS

EPS EPS x Payout

EPS x (1 - Payout)x RONI

Historical assetshave return onnew investment EPS x (1 - Payout)

x RONI x Payout


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Analysing the example shows that the growth in

dividends is:

Example: Estimating dividend growth

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A company expects to have earnings in 2014 of $19.70when it will payout 67% of earnings. The firm reinvestsretained earnings in new projects with an expectedreturn on investment of 18% per year. What is theexpected dividend for 2015?

2014 2015

Earnings $19.70 $19.70 × (1.0594) = $20.87

Dividends (67%) $19.70 × 67% = $13.20 $20.87 × 67% = $13.98

Growth (1 – 67%) × 18% = 5.94%

ℎ = (1 ) ×

Limitations of the dividend-discount model

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Future dividends are uncertain

It is difficult to estimate the dividend growth rate

Some firms (especially young firms) pay no dividends

Growth rates change over time

Small changes in the estimate of the dividend growth rate can

lead to large changes in the estimated share price.


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Dividends and share repurchases

Firms have two ways to pay earnings to shareholders. They may pay dividends...

Payment made to each equity share’s owner.

or repurchase shares from existing shareholders.

Firm purchases and retires equity shares.

All shareholders benefit.

Selling shareholders: Receive cash for their shares resulting in a capital gain.

Remaining shareholders: Retain shares that represent a greater percent stake in

the firm.

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Dividends and share repurchasesAn illustrative problem.

A firm has enterprise value of $378 million and $22 million in cash. It would like to return

$8 million to investors. There are 10 million shares outstan ding. For simplicity, assumethere are no taxes on dividends or capital gains.

Option 1: Paying $8 million dividends

Each shareholder receives a dividends of ____80cent____, after which each share isworth __ ($378m+$22m-$8m)/10m=$39.2__

Option 2: Repurchase $8 million in shares at $40.0 each

It will purchase ___$8m/$40=0.2m___ shares

Retiring these shares will mean there are ___10m-0.2m=9.8m___ shares remaining.

Selling shareholders will receive _____$8m_______ in cash.

Remaining shareholders will have shares worth _($378m+$22m-$8m)/9.8m=$40_.

Ignoring taxes, is there an economic difference between dividends and repurchases? Why isthe share price different under the two scenarios?

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Number of shares reduces after share repurchases

Dividends and share repurchasesInvestors may have a preference for dividends or share repurchases depending ontax laws.

Dividends apply to all shareholders. All shareholders pay taxes.

Australia: Uses an imputation tax system. Franking credits ensure total taxpaid by a shareholder is equal to the personal tax rate.

U.S.: Uses a classical tax system. Earnings first taxed at corporate level and

then taxed as income on personal level.Share repurchases only go to shareholders that want to sell. Only selling

shareholders pay taxes on capital gain.

Australia: Capital gains taxed as income.

U.S.: Long-term capital gains taxed at a lower rate than income.

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Dividends and share repurchasesOver time, firms choose to pay back earnings in a tax efficient manner forshareholders.

Australian firms favour dividends as investors prefer to receivecorresponding tax credit.

U.S. firms have moved from dividends to share repurchases over time asinvestors prefer to pay lower tax rate.

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Total payoutThe total amount paid by the firm to shareholders through dividends andshare repurchases. Total payout is expressed as a dollar amount for the firmand NOT normalised by the number of shares outstanding.

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As share repurchases changes the number of equity shares outstanding, totalpayout per share would not be a meaningful measure.

Total Payout ModelThe dividend discount model can be easily adapted to allow for share repurchases:

Estimate total payouts (dividends + share repurchases) to equity. Do not

normalise by the number of shares.

Use total payouts as cash flows to equity in valuation model.

Discount payouts at the cost of equity to the market value of equity.

Divide market value by current number of shares outstanding to find current

share price.

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Example: Total Payout ModelAssume the following for a firm...

Expected earnings at the end of this year is $520 million.

200 million shares outstandingThe firm expects to pay 30% of earnings in dividends and 15% in share repurchases.

Earnings are expected to grow by 6.6% per year and the p ayout rates remain constant

Equity cost of capital is 10%

What is the price of the stock using a constant growth total payout model?

Assuming constant payout rates, the total payout amount would grow at the same rate as

earnings.

=

=

0.3 0.15 ×$520

0.1 0.066= $6.882

=

# ℎ =

$6.882

200= $34.41

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4. Conclusion

80

Summary of formulae

81

Bonds

Coupon bonds: =

1

+

+

Zero-coupon bonds: =

+

Fisher effect: 1 = 1 × (1 )

Equity

Dividend discount model: PV of all future dividends

Total payout model: PV of all future dividends & repurchases

ℎ = (1 )×

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Topic2 Valuation 6PG