10 pdfsam edited uol fm topic 9 posted
TRANSCRIPT
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Earnings-Based Approach This method requires us to estimate the
earning power of a company.
Typically, we use the price-to-earning ratio(PER) as an indication of the growth potential
Historic PER =
Current market price of share
Last year's earnings per share
=pt
Et 1
PER = = = 1XgooglePrice per share $100
EPS $1000
PER = = = 100XPrice per share $50
EPS $0.50facebook
Example:
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Earnings-Based Approach
How many times of earnings are investorswilling to pay for the shares?
PER = $10 / $1 = 10 times
For PER of 10x, it could also be argued that
you are buying 20 years of constant profits.
1
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For a company with a high PER, the marketisexpecting it to show a faster growth in earnings in thefuture.
P = D1 [Gordons Model: to be explained later]
rg
Dividing both sides by EPS,
P / E = [ D/E] / ( rg )
= Payout ratio / ( rg )
Earnings-Based Approach
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PER has 3 determinants
1. Growth potential
2. Risk level
3. Payout ratio
Investors can analyse the historic PER of acompany and determine the future price.
Earnings-Based Approach
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Earnings-Based Approach
SG p. 101, Example 9.1
The following data relates to Company A plc:
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Earnings-Based Approach
Use of PER in business valuation:
How many times of earnings are you willingto pay for the stock?
Est. share price = PER x Est. EPS
As Average PER (2007-2010)=10.425 times
Estimated (prospective) EPS = 0.75
Estimated share price (historic PER)
= 10.425 x 0.75 = 7.82 (TP, target price).
one way is EPS x (1+g) = 0.750
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Earnings-Based Approach
Shortcomings of PER approach
i. SG:We assume that the PER of acompany stays constant over time. Buthistory tells us that PER fluctuates
Practice: Analysts use the historic high / lowPER and average PER to derive three
estimates of fair values
OR use industry PER as benchmark
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Refer to Handout 9.2on valuation
approaches (UOB Limited)
Here, we are using historical ranges (band) of
UOBs price-multiples to estimate the high and low
values of UOB.
Approaches used are:
1. PER approach
Example: UOBs highest (lowest) value
= Forecasted EPS x Highest (lowest) PER
2. Price-Book Multiple
3. Price-Net tangible asset (NTA) Multiple
(not given)
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Earnings-Based Approach
ii. We assume that the stock market knowshow to value companies correctly in the pastand that the PER has been correctlycomputed
This assumption that stock market analystshave a view of an appropriate PER for eachcompany seems to be unfounded.
A good example of this is the internet bubblebetween 1998 and 2000. Prices for someinternet companies were too high relative to
their earnings.
Shortcomings of PER approach
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Priceearnings ratio approach
to Value a Target FirmValue Target
= P/E ratio Prospective EPS of target firm
Problem here is which P/E ratio to use.
If prospective EPS is not available, use the
current EPS
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Priceearnings ratio approach
to Value a Target Firm
If acquirer believes performance of targetcompany will be similar to its own, it can apply
its own PER
Value of Target plc using Acq.s PER:
= Acq.s PER x Targets Current Earnings
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Find the estimated price of Stock A (unquoted)
Step 1: Compute the Price-earnings ratio (PER) of a
similar firm (Stock B)
If Bs PER = 10 x, investors are willing to pay a stock
price that is 10 times of Bs earnings
If A and B are similar firms, then investors should alsobe willing to pay a price that is 10 times of Asearnings
Priceearnings ratio approach(Unquoted shares)
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Step 2: Estimate Stock As value using its
own EPS and Stock Bs PER
Stock s A value = As EPS x Bs PER
Priceearnings ratio approach(Unquoted shares)
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Discounted Cash Flow Approach
A company is typically engaged in a number
of investments or activities that are financedby, roughly speaking, debt and equity
PV
$$
$$$$
$$
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Treat valuation of firm as a complex capital budgetingproject
DCF value of target
= PV of incremental cash flows gained by acquirer
Problems
Difficult to quantify expected benefits from operating and
financial synergies
Difficult to choose appropriate time horizon and terminalvalue for target
Which discount rate should be used?
Discounted Cash Flow Approach
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Example: Targets data
Current cash flows = 38m Cash flow growth rate = 4% per year
Surplus assets sold in two years = 60m
WACC of Acquirer = 7% per year
(38 1.04) = 1317.3
(0.070.04)60/1.072 = 52.4
DCF value = 1369.7
Discounted Cash Flow Approach
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DEBT
Why do firms borrow?
4 forms of debt
Irredeemable Debt (Bonds / Loan Stock)
Redeemable Debt (Bonds / Loan Stock)
- Bond Characteristics
- Interest Rates and Bond Prices- Yield to Maturity
Zero coupon bonds
Bank loans
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Why do firms borrow?
A. Cost of debt lower than cost of equity becausedebtholders face lower risk than shareholders
Cost of debt is fixed; any excess return belongs toshareholders
B. Interest payments are tax deductible
The after-tax cost of debt is lower than the pre-taxcost of debt (either bank interest rate or a bondsYTM)
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Income Statement: Tax shield
effect Sales
Less Cost of Goods Sold
Gross Profit Less: Operating Expenses
Less Depreciation Expense
Earnings Before Int. and Tax (EBIT)
Less Interest Expense
Net Profit Before Tax
Less Taxes
Net Profit After Tax
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Bonds / Loan Stock / Debentures
These represent loans extended by investors tocorporations and/or the government.
These are issued by the borrower, andpurchased by the lender.
$
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Bond Issue: $100m
Bonds issued: 100,000 units
12 units:
Loan =
$12,000
1 units
par
value =$1,000
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Irredeemable Debt:
These bonds involve a constant annual payment inperpetuity.
No principal repayment
Use perpetuity equation
Note: Interest is before tax
Rd is also before taxcost of debt
hence,
recall: Topic 2 Slide 64
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Irredeemable bonds/loan stock
KdAT Kd
Kd= cost of debt (before tax)
KdAT= cost of debt (after tax)
PMT = annual interest payment in $$
P0= value of bond
note that interest is tax-deductible.
PMT (1-T)Po =PMT
=
recall: Topic 2 Slide 64
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Irredeemable bonds/loan stock
What is the after-tax cost of debt?
(same answer)
Kd= cost of debt (before tax) = PMT / Po
KdAT= cost of debt (after tax)
PMT = annual interest payment in $$
P0= current ex-interest market price
0P
PMT (1-T)KdAT= Kd(1-T)or KdAT=
K =dPMT
P
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Irredeemable bonds/loan stock
Calculating the (current) cost
10% irredeemable bonds (par value = 100)
Ex-interest market price: 72Corporation tax: 30%
Kid(before tax) = PMT/Po =10/ 72 = 13.9%Kid(after tax) = 13.9% (10.3) = 9.7%
OR: Kid(after tax)= 10x(10.3)/72 = 9.7%
(same)
T
method 1
method 2
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Key Features The par (or face or matur i ty) valueis the amount
repaid (excluding interest) by the borrower to the lender(bondholder) at the end of the bonds life. The par valuefor U.S. corporate bonds is $1000.
The coupon rate (pa) determines the interestpayments. Total annual amount = coupon rate x parvalue. Bonds can pay coupons, annual, semi-annuallyor quarterly
A bonds matur i tyis its remaining life, which decreasesover time. Original maturity is its maturity when itsissued. The firm promises to repay the par value at theend of the bonds life (also called maturity).
Redeemable bonds/loan stock
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Treasury Bond: Example
Temasek Financials Bond
Listed: 27 Oct 2009
Tenure: 10 years
Size : SGD1.5 bn (application: USD4 bn) Rating: AAA (S&P); Aaa (Moodys)
Coupon: 4.3% (
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The bonds fair value is the present value of thepromised future coupon and principal payments.
At issue, the coupon rate is set such that the fairvalue of the bonds is very close to its par value.
Later, as market conditions change, the fairvalue may deviate from the par value.
Redeemable bonds: Valuation
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The price of a bond= Present Value of all cash flows
generated by the bond
i.e. coupons and redemption value (RV)discounted at the cost of debt, rd
tr
RVcpnInt
r
cpnInt
r
cpnIntPV
)1(
)(....
)1()1( 21
=
Redeemable bonds: Valuation
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SG:
Value of a bond is accurately
determined because all figures arepre-determined
Redeemable bonds: Valuation
, except Rd.
Bond traders act on interest rate
forecasts on the bond
R can be known as the required return on bondd
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nn
n
r)(1
RV
r)(1(r)
1r)(1PMTPV
=
Bond Value:
PV = PV(coupon payments) + PV(RV)
= PV (Annuity) + PV (Single sum)
Redeemable bonds: Valuation
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Note: $10 is ____________ interest expense
15 percent is the __________ cost of debt
SG example:Rd =cost of debt = 15%
before
before
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Semi-annual coupon payment
= [coupon rate / 2] x par value
= [0.09 / 2] x $1,000 = $45 Number of payments = 12 x 2 = 24
Semiannual required rate of return = 3%
Find the fair value of a bond with a $1,000 par value,a remaining life of 12 years, and a coupon rate of 9%
per year paid semi-annually. The required return on
bonds like this one is currently 6%.
Redeemable bonds: Example
left
^
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$1,254.03
(1.03)
$1,000
(1.03)(0.03)
1(1.03)45$B 2424
24
0
=
=
Bond Value: B0= PV(coupon payments) + PV(par value)
= PV (Annuity) + PV (Single sum)
Redeemable bonds: Example
> 1000 (par value)
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Bond Values and Discount Rate
(Required Return)
Required Return Bond Value
6.0 %9.0 %
12.0 %
$ 1, 254.03$ 1,000.00
$ 811.74
premium bond
par bond
discount bond
Coupon rate = 9% per year.
Coupon = $90 per year ($45 per 6 months)
So, the higher the required return, the lower
the present value of the bond (bond price)
Yi ld T M i
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Yield To Maturity(YTM always on per annum basis)
The Yield to Maturity is the investors return ifthe bond is held till maturity
It is equivalent to the IRR in capital budgeting
-1000 +1000
$45 $45 $45
t = 24
return ytm = 9% p.a
$45 $45 $45
t = 24-1254 +1000
return ytm = 6% p.a
before tax
R d bl b d
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Redeemable bonds The before-tax cost of redeemable bonds is the
YTM of the bond.
Is after-tax cost of debt =YTM (1-T)? No.
Applying the tax effect of (1-T) to the coupon
payment [Coupon$(1-T)] is more accurate thanmultiplying the before-tax cost of debt by (1T),since the redemption value is not tax-
deductible.
The cost of debt can be found using linearinterpolation.
YTM; return ytm include capital item which do not have tax shield effect
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Redeemable Debt:
After-tax cost of debt
Find the Yield to Maturity (YTM) of a bond with:
Par value = $1,000
Remaining life = 12 years. Tax rate = 30%
Coupon rate = 9% per year paid semi-annually.
The bond is currently selling for $1,076.23.
After-tax PMT = $45(1-0.3) = $31.50
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Using a financial calculator,
after-tax cost of debt
= 2.71% per 6-months
= 5.42% per year
2424
24
YTM/2)(1
1,000
YTM/2)+(1(YTM/2)
1YTM/2)+(131.51,076.23
=
Redeemable Debt:
After-tax cost of debt
Redeemable Debt:
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Using interpolation (similar to IRR interpolation)
Try YTM/2 (after tax) = 2% => LHS = + 141
Try YTM/2 (after tax) = 5% => LHS = - 332
Interpolate: Estimated YTM/2 (after tax)
= 2% + [141 / (332+141)] x [ 5 - 2 ] = 2.89%
Est. YTM (after tax) = 2.89 x 2= 5.78%
2424
24
YTM/2)(1
1,000
YTM/2)+(1(YTM/2)
1YTM/2)+(131.51,076.230
=
Redeemable Debt:After-tax cost of debt
Zero Co pon Bonds (ZCB)
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Zero Coupon Bonds (ZCB) No interest payments to bondholder
Issued at deep discount and traded at a discount
TVM: Single sum problem
What is the price of a ZCB with a par value
$1,000 yielding 3 percent p.a. for 6 years?
PV = FV / (1+r)^t= 1,000 / (1.03)^6
= $837.48
PV < FV
Zero Coupon Bonds (ZCB)
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Zero Coupon Bonds (ZCB)
What is the YTM of the same ZCB is theinvestor bought the bond at $700?
r = (FV/PV)^ 1/n - 1= (1000/700)^ 1/6 - 1
= 0.061 (6.1%)cannot be done for UOL examSlide: 54
Bank loan $1.0m $0.8mInterest paid $80000 $60000
Year 1 Year 2
[60K + 80K]/2
[1.0m + 0.8m]/2
=
= =7.7%
formula for
cost of debtAverage interest
Average LoanCost of Bank loan
for year 2 [before tax]
After-tax debt cost = 7.7% x (1 - T)
Bank borrowings
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Bank borrowings Bank borrowings are not traded and have no
market value that interest can be related to.
Cost of bank borrowings can be found by dividingaverage interest paid by average borrowings for
a given period.
Alternatively, the cost of traded debt may be used
as the best approximation.
Appropriate adjustment for taxation is needed.
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Preferred Stock (Preferred Shares)
Claims of preferred stockholders are juniorto claims of debtholders, but senior tothose of common stockholders.
Limited voting rights compared to commonstock.
Preferred stock has a par value and a
dividend rate.
Failure to pay the dividend does not forcethe issuing firm into bankruptcy.
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Irredeemable Preferred Stock:
Valuation
Consider a $100 par value share ofpreferred stock with an 8% dividend rate
(paid quarterly). The required return is12% pa.
Find the preferred shares fair valuetoday.
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Preferred Stock: Irredeemable
This preferred stock is a perpetuity
Then the value would be:
PV = C / i
= $2 per quarter / 0.03 per quarter= $66.67
P f d h I d bl
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Preferred shares: Irredeemable
The cost of preference shares (constant
annual payment in perpetuity) can be foundby dividing the preference dividend by the edividend market price:
Kps = cost of preference shares
P0 = current ex div preference share price
Dp = preference dividend.
0PDK
pps=
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Preferred shares: Irredeemable
Calculating the cost of preference shares:
9% preference shares, nominal value: 100p
Current ex dividend market price: 67p
Kp= (0.09 100)/67 = 0.134Kp= 13.4%.
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Preferred Stock: Redeemable
If the preferred stock is redeemable afterx years, the valuation follows that of abond:
PV = PV (Annuity of Pref Dividends)
+ PV (Par value)
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Preferred shares: Redeemable
The cost of this is found in the samemanner as redeemable bonds EXCEPTthat there is no tax adjustment.
nr)(1
ParPVIFA*DivPrefPV
=
C t f R d bl
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Cost of Redeemable
Preference Shares
Use interpolation as per redeemblebonds except do not apply (1-T) tothe preference dividends
Sh V l ti
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Share Valuation
PER Approach (covered)
Dividend Discount ModelEarnings Yield ApproachDividend Yield Approach
Market Value Approach
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Dividend Discount Model (DDM)
The value of a share of stock is thepresent value of the expected dividendsover the holding period plus the
expected sale priceat the end of theholding period.
n
n
n
n
r
P
r
D
r
DP )1()1()1(
1
10
=
Po on LHS = Fair Value
P on RHS = Market price
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Example
Current forecasts are for XYZ Company to pay div idendsof $3, $3.24, and $3.50 over the next three years,respectively.
At the end of three years you antic ipate sel l ing you rs tock at a market price of $94.48.
The required return on this stock = 12%
How much would you be prepared to pay for th is stock?
That is, what is the intr ins ic (fair) pr ice of the stock?
Dividend Discount Model (DDM)
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PV
PV
=
=
300
1 12
324
1 12
350 94 48
1 1200
1 2 3
.
( . )
.
( . )
. .
( . )$75.
Dividend Discount Model (DDM)
DDM SG p 103
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DDM - SG, p. 103
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DDM - SG, p. 103
The value of a share is the present
value of all future dividends
Th Di id d Di t M d l
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The Dividend Discount Model
....
)1()1()1(2
2
1
10
=n
n
r
D
r
D
r
DP
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The company may pay dividends tocommon stockholders.
However, it is not required to do so.Moreover, there is no pre-set dividend rate.
Future dividends are uncertain.
We need a way to forecast future dividends.
Dividend Discount Model (DDM)
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Gordons Model(Constant Growth)
11
3
14
2
1123
12
1
1
11111
=
=
====
t
t gDD
gDD
gDggDgDD
gDD
Assume dividends are growing at a constant
percentage rate of gper year.
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Constant Growth (Gordons Model)
For a stock with with constant growth forever
after time t:
grD
P t
t
=1
Dt = first constant growth dividend
Given any combination of variables in the
equation, you can solve for the unknown variable.
P Div
r g0
1=
r = cost of equity
Important Features of the Constant
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po ta t eatu es o t e Co sta t
Growth Model
stocks total return
0
1
P
D dividend yield ( = ) plus
capital gains yield ( =g)
0
1
P
D+ gr =
Under Gordons Model, g is also the
growth rate in the stock price
g =[P1- P0]
P0
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Constant dividends where g=0
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Cost of equity
Cost of equity (rate of return required bystockholders) can be derived in two ways:
*Gordons Model: r = (D1/Po) + g
*CAPM (SML equation): Rf + (RmRf) x Beta
Earnings yield approach (to be discussed laterunder business valuation)
Refer to Handout 9.1 on UOLs preference
equity
*
in the past
*
Stock Valuation: Example
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Stock Valuation: Example
The per share annual dividend on a common
stock is expected to be $3.00 one year fromtoday. Stockholders require a 12% rate ofreturn. Find the fair value of the stock for each ofthe following cases:
1. Zero Growth: dividends are constant every year.
2. Five-Percent Growth: dividends are growing at aconstant rate of 5% per year forever
3. Supernormal growth
Div1
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1. Zero Growth (g = 0)
$25.000.12
3.00$
r
DP 10 ===
With g = 0, the dividends of $3.00 per share form a
perpetuity.
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2. Five-Percent Constant Growth
86.42$
05.012.0
00.3$0 =
=P
Recall that D1= $3.00; r = 12%; and g = 5%
3 Supernormal Growth
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3. Supernormal GrowthAn analyst forecasts Stock Xs dividends to grow at 15%
per year for the next 2 years. Thereafter, dividends areexpected to grow constantly at 10%. The last paid DPSwas $1. The cost of equity is 12%. What is the stocksfair value?
D1 = 1 (1.15) = 1.15
D2 = 1 (1.15)^2 = 1.32
D3 = 1.32 (1.1) = 1.45
Fair value = PV (D1) + PV(D2) + PV(P2)
= 1.15/1.12^1 + 1.32/1.12^2
+ [1.45 / (0.120.10)]/1.12^2
= $59.88
t = 0 1 2 3
D1= D0x (1 + gs)P2
P0 = PVC (future dividends) = PV (D1,D2...Dinfinity)D3
r - g
gs = 15% gc = 10%
P2
= PV(D1) + PVC(D2) + PV [P2+ ]
Gordon's growth
D0= $1 D2= D0(1 + gs) D3
S f Di id d G h
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Source of Dividend Growth If the Payout Ratio (POR) is constant, growth
in dividends depends on the growth inearnings.
The growth in earnings depends on: the plowback ratio or retention ratio(1 - POR),
and
the return on investment, i ( = ROA)
i also can be Return on Equity (ROE)
Sustainable growth rate
g = (1 - POR) i
g = (1 - POR) x ROE
ROA = ROE
note:
BMA textbook
uses ROE
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ExampleOur company forecasts to pay a $3.00dividend next year, which represents 100%of its earnings. This will provide investors
with a 12% expected return.
Instead, we decide to plow back 40% ofthe earnings at the firms current return on
equity of 20%. What is the value of thestock before and after the plowbackdecision?
Source of Dividend Growth
S f Di id d G thTested in UOL finals May 2013
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00.25$12.
30 ==P
No Growth With Growth
00.75$08.12.
3
08.40.20.
0 ==
==
P
g
A firm with more growth prospects is worth more!
g = (1 - POR) x ROE
Source of Dividend Growth
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Stock Valuation: Other methods
Earnings Yield Approach
Dividend Yield App roach
Market Value Appro ach
Earnings Yield Approach
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Earnings Yield Approach
IGNORING GROWTH,
Value of Target = Annual maintainable earnings
Earnings Yield
OR
Targets share price = EPS
Earnings yield
EPS =[NPAT - Pref Divi]
number of shares outstanding
Earnings Yield Approach
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Earnings Yield Approach
ExampleTarget plc Acquirers earnings yield
= EPS/share price
=(25p/250p) 100 = 10%
Assume Target plc enjoys same yield.
Targets earnings yield value
= Targets Earnings/Acq.s earnings yield
= 10m/0.10
= 100m.
Earnings Yield Approach
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WITH GROWTH = 2%
Growth can be included by adapting the dividendgrowth (Gordons) model.
P = D1 / (kg)
Earnings yield value
= (10m 1.02) = 127.5m.(0.100.02)
Earnings Yield Approach
Earnings Yield
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Earnings Yield
Earnings yield is also used as a proxy for cost of equity:
Eg. Cost of equity = 10%
Cost of equity (to firm) = Return to shareholders
Return (%) = Return in $ / Price paid to earn the return
So, 10% = EPS /market price
This is the earnings yield equation
Earnings Yield Approach
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g pp
The PER approach is the mirror image
of the Earnings yield approach
Since PER = Market price / EPS,
Then, PER = 1/ 0.1 = 10X
[Investors are willing to pay a multiple of 10
times for the firms earnings]
So, Cost of Equity
= Earnings Yield
= 1 / PER
Price EPS
EPS PricePER inversely proportional to Earnings Yield
how many times of
dividends willing to pay
Price DPS
DPS Priceinversely proportional to Earnings Yield
Dividend Yield Approach: (comparative approach):
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pp
- Price paid as a multiple of gross dividends
(how many times of dividends are investors willing to pay?)Price / dividends = 10 times
Find the estimated price of Stock A
Step 1: Compute the dividend yield of a similar firm (Stock B)
Gross dividendsMarket price
If A and B are similar firms, then the two firms shouldhave similar dividend yields (Dividends/price)
(unquoted)
Dividend Yield Approach:
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Dividend Yield Approach:
Step 2: Estimate Stock As value
Stock s A value
= As Gross dividend per share
Bs Dividend yield
= As Gross DPS * Number of times of DPS
Dividend Yield Approach:
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Dividend Yield
Find Allenby Ltds (unquoted firm) valueusing a quoted firms Dividend Yield.
Tax rate= 20%
Allenbys value per share
= Allenbys Gross Div per share / Quoted Stocks Div Yield
= [Allenbys Net DPS / (1-Tax rate)] / Dividend Yield
= ($0.80/ 0.8) / 0.10
= $10 [ or $1 * 10times = $10]
Market Price Approach
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Market Price Approach
Value = Number of shares x market price
Fair price if market is efficient, but not fixed
Quoted price reflects marginal trading
Cannot be used for unquoted shares
Useful starting point in negotiations
Market Value does not reflect acquirerintentions
Homework
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Homework
Cost of capital components Attempt FM 2009 Prelim Exam, Question 1
(Alpha plc)
Valuation Methods
Attempt FM 2008 Prelim Exam, Question 3(Sources of financing and valuation)
Attempt FM 2009 Prelim Exam, Question 8(Essay on valuation methods in a takeover)
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Session 16 Topics 8 and 9: Past Exam Questions
Session 17- Class test 2
Scope: Topics 6 to 9