Week 3_Valuation of Shares and Bonds-2

8/2/2019 Week 3_Valuation of Shares and Bonds-2

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Week 3

Valuation of

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. a u ng a company

1.1 Asset side approach. a y s e approac

2. Characteristics of Debt and Equity

. a ua on o corpora e e4. Valuation of shares4.1 Constant v en va uat on mo e s

4.2 Constant growth dividend valuation models

. ,

4.4 Price to Earnings ratios

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.

The cash flows generated by the asset, and T e appropriate discount rate e ective Interest

rate) applied to these cash flows

E.g. 4 year ordinary annuity paying $1000 2 3 41

100 100 100PV = $316.99 100100/(1+r) = 90.91

100/(1+r)2 = 82.64

3

+r = .

100/(1+r)4 = 68.30


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1. Valuing a company

rm can e va ue y : Calculating the present value of the cash flows generated by the

firms real assets

Calculating the present value of the firms individual securities

(i.e. equity and debt securities)

Assets

Real

Equity

Debt

Non-Tangible

securities

PV of Capital = Discounted sum ofPV of Assets = Discounted sum of

future cash flows of assets

future dividend flows

+

PV of Debt = Discounted sum of=

uture cas out ows

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.

ShareholdersDividendsFIGURE 3.1

Real assets

Interest

Netcash flow

e t o ersReinvested

+

Principal

Cash flows generated by a firms real assets ultimately

flow throu h to the shareholders and debt holders ofthe firm as dividends and interest

Hence the resent value of cash flows enerated must

be equal to the value of cash flows received 5


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1. Valuing a company - 1.1 Asset side approach

The net cash flows from real assets, afterreinvestment costs, are known asfree cash flows

If the firm is assumed to have an infinite life thevalue of the firm is given by:

V = tt (3.2)

where:

F = free cash flow enerated b the com an in eriod t

t=

r = required rate of return (i.e. appropriate discount rate for thecompany)

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. erna ve y e va ue o a company can e

determined using the following equation:

V = D + E (3.1)

where:

= e presen va ue o cas ows genera e y e rm

D = the present value of cash flows generated by debt securities

E = the value of cash flows enerated b e uit securities

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. arac er s cs o e an qu y e a ternat ve approac to va u ng a rm

involves calculating the present value of then v ua e t an equ ty secur t es t at ma e

up the firms capital structure, and adding them

toget er There is a wide variet of debt, e uit and h brid

securities currently available in capital markets

We will focus on a simplified capital structure

based on debt and equity only

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Return Fixed (interest) Variable (Dividend)

Holding period (life) Fixed (redeemed) Indefinite

Securit eckin order First Residual

ExamplesBonds, Debentures, Bank

loans

Ordinary and Preferential

shares

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. a u ng a company

1.1 Asset side approach. a y s e approac


. a ua on o corpora e e4. Valuation of shares4.1 Constant dividend valuation models


. s ma ng e grow ra e, g


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. a ua on o corpora e e

the issuer (borrower) and

the investor lender

stipulating the issuers obligations to makespecified payments (coupon payment) on

specified future dates has a value e ual to the resent value of all

cash flows associated with holding the bond

Cash flows consist of periodic interestpayments and the repayment of the facevalue upon maturity

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3. Valuation of corporate debt

Example 1. ANZs 3 year bond pays 5% pa coupon on with a

$1,000 face value.

Fixed cou on interest a ment is 5% of FV = $50 is aidat the end of each period

Face value (or Par Value) is repaid at the end of maturity

We need to price this bond

50PV = Price = ?

5050

131,000


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The required information to work out the

rice of bond is Face (or Par) value

. .

Term to maturity (no. of interest paying period), n

Required rate of return or discount rate for the

interest paying period.

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To calculate the bond price, both coupon payments

required (compounding) rate of return, rd, say

,

0 2 31

50PV = $875.65 5050

50/(1+(rd=10%)) = 45.4550/(1+rd)2 = 41.3250/(1+rd)3 = 37.57

1,000

151000/(1+rd)3 = 751.31


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Often the discount rate will need to be worked out

from the iven market rice

then the discount rate rd that equates the PV of cash

flows and the market price is called the yieldto maturity(or simply yield) or the cost of debtfor the bond

return currently required to induce investors to

The bond is traded Below Par: PV < Par value coupon rate < rd

Above Par: PV > Par value coupon rate > rd

At Par: PV = Par value coupon rate = rd 16


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Formally, bond valuation can be done via the

following equation:

D =F

1+ rt

=

n

+ B1+ r

n (3.3)

where:

n = t e rema n ng e o t e on

F = the coupon interest payments

B = the face value of the bondrd = the cost of debt capital

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Since the interest a ment F is an annuit the

value of a debt security whose interest payments

can be ex ressed as an annuit is iven bsubstituting the formula for the present value of

an annuit E uation 2.7 into E uation 3.3:

D = F1 1+ rd( )

n

+B

rd 1+ rd( )n

(3.4)

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Example 2

-

p.a. coupon rate and a face value of $100 when similar

securities have ield to maturit of 8% .a._______________________________________________

FV = $100

Coupon (Interest) payment = 0.08 $100 = $8 per annum Term to maturity is 10 years and there are 10 annual

payments, n = 10

The required rate of return is rd = 8.0% p.a. (given) which

compounding.

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Example 2 (cont)

What is the market value of a 10-year bond with a 8% p.a. coupon rate

and a face value of $100 when similar securities have yield to maturity of

8% p.a.

_______________________________________________

( ) ( )ndd

n

d

rB

rrFD

++

+=

111

( )10

1010008.11

8 +

=

100$319.46$681.53$ =+=

..

In this example the bond is traded at Par

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_______________________________________________


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xamp e .What is the market value of a semi-annualcoupon paying 10-year bond

with a 8% .a. cou on rate and a face value of 100 when similar

securities have yield to maturity of 8% p.a.

_______________________________________________ FV = 100

Coupon (interest) payment

= =. ,

But this is spread over two payments of $8/2 = $4 at the end of each 6month period

erm o ma ur y s s years an u are sem -annua paymen s.

So number of periods, n = 20.

Yield = 8.0% p.a. is now equivalent to nominal interest of 8% pacompounding semi-annually

so the discount rate for the half yearly interest paying period is nominal rate

divided b no. of com oundin eriods

= 8%/2 = 4% per half year 21


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Example 2.1

What is the market value of a semi-annual coupon paying 10-

year bond with a 8% p.a. coupon rate and a face value of $100when similar securities have yield to maturity of 8% p.a.

_______________________________________________

n

( )ndd rrFD

++

=1

2004.1

100

04.0

04.114 +

=

100$638.45$361.54$ =+=

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Important Note: Bonds are priced to yields.

That is, bond prices are determined by discounting cash flows by

Thus, the required rate per annum or annual yield is quoted

in the same manner as com oundin interest rate

nominal interest rate with m compounding periods per annum

So, the yield for a coupon paying period to use in the

calculations is

Annual yield quoted/no. of coupon payment period

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Example 3On 12 March 2008, Timbercorp Ltd issued debentures carrying a

. ., ,

maturing in December 2010. Assuming that the notes were issued at a

yield of 8.05% p.a., what was the value of these securities?______________________________________________

FV = $100

Coupon (Interest) payment = coupon rate

face value = 0.09/4 $100 = $2.25 per quarter

There are n = 11 quarterly payments staring from end of March 2008

DDD MMM J S J S J S

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12 MarPV at 31 Mar


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Example 3 (cont)

Yield = 8.05% p.a. and this is equivalent to nominal interest

with uarterl com oundin the required discount rate for the interest paying period is

8.05%pa/4 = 2.0125% per quarter.

This is theeffective

yield or interest for the quarter

( ) n Br + 11

11

( )ndd rr +=

1

11

.2.25

0.020125 1.020125

= +

32.102$=

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.

Bonds are priced to given yields.

.g. r ce o year on w e

stated coupon (semi annual) and the

yield, produces the PV of $110.23

A yield curve is a plot of annual

bond yields of various terms to

ma ur es a a g ven po n n

time A positive sloping yield curve is

shown

Also possible to have flat or

negatively sloping yield curves

26Source: http://bloomberg.com/markets/rates-bonds/government-bonds/asustralia/


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3. Valuation of corporate debt - 3.1 Yield curve and interest rate risk

The sensitivity of bond prices

At coupon rate = yield,

Price_1y = Price_5Y = Price_10Y

1300

1400

1500o n eres ra e uc ua ons s

the interest rate risk for bond

holders

At coupon rate < yield,

Price_1y > Price_5Y > Price_10Y

1000

1100

1200

Price_1Y

e.g. 1, 5 and 10 year bonds with

PV=$1,000, coupon rate = 10%

Interest rate risk is higher

800

900

_

Price_5Y

Price_10Y

ondP

rice,

$ The longer the term to maturity

The smaller the coupon rate

At coupon rate > yield,

600

5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15%

Interest rate, %

B,

The further the main cash flows

(i.e. principal) are into the

future, the higher the interest

r ce_ y < r ce_ < r ce_

rate risk

There is an inverse relationship

between bond prices and

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interest rates


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. a u ng a company

1.1 Asset side approach

. a y s e approac


. a ua on o corpora e e

4. Valuation of shares4.1 Constant dividend valuation models


. s ma ng e grow ra e, g


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. qu y secur es are s m ar y va ue

by calculating the present value of all cash flows generated

1. Dividends

2. Cash roceeds from future sale of the share

The current value of a share is, in part, influenced byits future value.

However, the future share price is also based on the

value of future dividends

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4.1 Constant ivi en va uation mo e s

-

Assumes that companies pay a constant dividend

0 2 31

P =d

3.6re

where:Pt = current value of share

d = (constant) dividend per period

re = the required return on the share

31 This is the PV of perpetual cash flows of a fixed amount


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4. Valuation of shares - 4.1 Constant dividend valuation models

Example 4

Boral Ltd traded at $5.79 on 12 March 2008. The cash dividend by Boral in

the previous year was around 49 cents per share. What discount rate was

being applied by Borals investors?_______________________________________________

e

trP =

49.079.5 =

e

==

32

..e


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4.2 Constant growth dividend valuation models Constant-growth model

Assumes that dividends grow at a constant rate

0 2 31

g

d1 =d0x(1+g)

d0 d2 =d1x(1+g)

2 d3 = d2x(1+g)3

(3.7)Pt = 1r g

where:

= =1 0 re = the equity cost of capital

g = the constant growth rate (g must be < re)

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4 V l i f h 4 2 C h di id d l i d l


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Exam le 5

4. Valuation of shares - 4.2 Constant growth dividend valuation models

Shares in James Hardie Industries (JHX) were trading for $5.81 on 12March 2008.

JHX paid a total dividend of around 32 cents per share in the prior year.

Assuming that the required return is 8.0%, what perpetual future dividend

growth rate is being used by the market to price JHX?

0 2 31

g = ?

d1 =0.32x(1+g)

d0=$0.32

d2 =0.32x(1+g)2

d3 =0.32x(1+g)3

( )

g

g

+=

08.0

132.081.5Pt =

1

r ( )

%4.2024.081.532.0

32.008.081.5==

+

=g

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. ,

the application of the perpetual growth model

,the earnings of a company

-

For the year ended December 2007: =

Dividends per share (DPS) = 136 cents

Return on equity (ROE) = 19.6%

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4 Valuation of shares 4 3 Estimating the growth rate g


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4. Valuation of shares - 4.3 Estimating the growth rate g

EPS 224c

FIGURE 3.3

management must decide whether to pay this out as

dividends and/or retain it in the firm

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4 Valuation of shares - 4 3 Estimating the growth rate g


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EPS 224c DPS 136cPayout 61%

FIGURE 3.3

In 2007, ANZ paid out 136c (61% of its EPS) as a dividend The proportion of EPS paid out as dividends is called the

payout ratio

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4 Valuation of shares - 4 3 Estimating the growth rate g


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4. Valuation of shares 4.3 Estimating the growth rate g


FIGURE 3.3

Retain

88c

39%

the firm to finance future growth

This is sometimes called the ploughback ratio

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FIGURE 3.3

Retain

88c

39%

Reinvested @ROE 19.6%

The 39% in retained profit is reinvested within the firm,

and it is assumed that it will generate earnings at the

rm s curren o .

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FIGURE 3.3

Retain

88c

39%

grow17.25c

Reinvested @ROE 19.6%

This yields 17.25c in increased EPS in the future, which

will in turn be available for distribution as dividends or

ploughed back into the firm40



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f g g g

Using this model, the dividend growth rate can be expressed

g = 1 payout ratio( )ROE (3.8)

Assumptions:

The a out ratio is stable The estimated ROE is stable In this exam le = 1-0.61 *19.6% = 7.46%

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f g g g

Example 6

n e year en e ecem er , a ona us ra a an genera e

of 269 cents, paid a dividend of 182 cents per share, and its ROE was

estimated at 17%. What is the expected future earnings and dividendgrowth rate?

_______________________________________________

68.0269182 ==ratioPayout

ROEg = ratiopayout1

%5.5055.017.068.01 ===

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4.4 Price to Earnin s ratios

r ce- arn ngs ra o The price of a share divided by its earnings per share

Used to determine whether a stock is overpriced or

underpriced

t =

where:

=

t+1 e

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4. Valuation of shares - 4.4 Price to Earnings ratios


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Note that the left-hand side of this equation represents the

prospect ve rat oecause t e current s are pr ce s

divided by the one-year-ahead (not historical) EPS

This model demonstrates that the prospective P E ratio is:

Positively related to the payout ratio

Positively related to the dividend growth rate

differ because of these factors

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Example 7 TABLE 3.3

ra os or an , -

ANZ NAB

2007 224.1 29.70 13.25 269.0 39.71 14.76

. . . . . .

2005 160.9 14.92 14.92 252.0 33.05 13.12

comparable their P/E ratios were similar in 2006 but not in 2005 and

2007.

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Shareholders were paying too much for one of the stocks,

and/or The other was relatively underpriced by the market

For example, the 2007 P/E ratios indicate that:

NAB shares were relatively overpriced, and/or

ANZ was relatively underpriced by the market

The question arises: are the differences in the P/E ratios

economically justifiable?

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Week 3_Valuation of Shares and Bonds-2

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Transcript of Week 3_Valuation of Shares and Bonds-2