Recap of notations
β’ Ξ²π΄- Beta of assets
β’ Ξ²πΈ- Beta of equity
β’ Ξ²π· - Beta of debt
β’ Ξ²π - Beta of equity in an unlevered firm
β’ Ξ²πΏ - Beta of equity in a levered firm
β’ And the corresponding r notations indicating the required rates of return
β’ V β Value of the firm
β’ ππ- Value of unlevered firm
β’ ππΏ - Value of levered firm
β’ ππΌππ - Value of interest tax shelter
β’ ππππ΅ - Value of subsidy
09/03/2013 Beta Rem Series 2
What have we learned?
Learned how to calculate WACC and what different values of Ξ² mean. These have been briefly explained below.
Ξ²π΄ is the risk associated with the operations of the business. This is related to the industry the firm is in.
When a firm is unlevered, right side has only equity and hence assets = equity and so are the risks associated with them.
So, Ξ²π΄ = Ξ²π as per the notations in slide 2.
For finding Ξ²πΈ in a levered firm (Ξ²πΏ), use MM propositions as shown in last presentation.
Once Ξ²πΈ and Ξ²π· are obtained, use them to find WACC.
In addition, ππ΄ = ππ· Γ π·
π+ ππΈ Γ
πΈ
π when D/E is constant or there are no taxes (refer to CF
rem I)
WACC is only meaningful if D/V is constant, otherwise WACC changes every year.
09/03/2013 Beta Rem Series 3
Key equations used
β’ ππΏ = ππ + ππΌππ
β’ Ξ²π΄ Γππ
ππΏ+ Ξ²πΌππ Γ
ππΌππ
ππΏ= Ξ²π· Γ
π·
ππΏ+ Ξ²πΈ Γ
πΈ
ππΏ
β’ When D/E is constant:
β’ Ξ²πΌππ = Ξ²π΄
β’ Ξ²π΄ = Ξ²π· Γ π·
π+ Ξ²πΈ Γ
πΈ
π
β’ ππ΄ = ππ· Γ π·
π+ ππΈ Γ
πΈ
π
β’ When D is constant:
β’ Ξ²πΌππ = Ξ²π·
β’ ππΌππ = DT
β’ Ξ²π΄ = Ξ²π· Γ π·Γ(1βπ)
π+ Ξ²πΈ Γ
πΈ
π
β’ ππ΄ = ππ· Γ π·Γ(1βπ)
π+ ππΈ Γ
πΈ
π
09/03/2013 Beta Rem Series 4
Coming to valuation
β’ Companies are valued for their assets as well as their future cash flows.
β’ ππΏ is the value of the company.
β’ As we already know, ππΏ = ππ + ππΌππ =π· + πΈ
β’ If the firm is unlevered, no interest tax shelter and no debt, hence ππΏ = ππ = πΈ
β’ But, if the firm is levered, then the value increases by the amount interest provides a tax shelter. Let us see how this translates into an equation like below in case of constant D/E ratio
β’ When D/E is constant:
β’ ππΏ =πΉπΆπΉ1
(1+ππ΄πΆπΆ)+
πΉπΆπΉ2
(1+ππ΄πΆπΆ)2+β― Equation for value of the firm
β’ How?
β’ Before we go there, a couple of notations
β’ ππΏ,0 - Value of the levered firm at t=0, ππΏ,1 - Value of the levered firm at t=1
5 Beta Rem Series 09/03/2013
Valuation contdβ¦
β’ Capital cash flow to the firm = Free cash flow + Interest tax shelter
β’ πΆπΆπΉ1 = πΉπΆπΉ1 + ππ· Γ π·0 Γ π
β’ When the Capital cash flow is known which combines all the effects of the capital structure (Capital structure only means how much debt you are taking), then the risk of this cash flow is only reflective of how the business is.
β’ It means that this CCF can be discounted at ππ΄ which would mean
β’ ππΏ,0 =πΆπΆπΉ1+ππΏ,1
(1+ππ΄) =
πΉπΆπΉ1+ππ·Γπ·0Γπ +ππΏ,1(1+ππ΄)
β’ Let π·
π= π and
πΈ
π= π
β’ When π· πΈ is constant, π·0 = π Γ ππΏ,0
β’ Then ππΏ,0 =πΉπΆπΉ1+ππ·ΓπΓππΏ,0Γπ +ππΏ,1
(1+ππ΄)
β’ Rearranging, we end up with ππΏ,0 =πΉπΆπΉ1+ππΏ,1
1+ππ΄βππ·ΓπΓπ
6 Beta Rem Series 09/03/2013
Valuation contdβ¦
7
β’ For constant π· πΈ , ππ΄ = ππ· Γ π·
π+ ππΈ Γ
πΈ
π = ππ· Γ π + ππΈ Γ π
β’ Substituting, we get ππΏ,0 =πΉπΆπΉ1+ππΏ,1
1+ππΈΓπ+ππ·Γ(1βπ)Γπ
β’ Hence, it can be clearly seen that WACC can be used to discount the free cash flows directly to arrive at the firm value.
β’ Simply put, ππΏ =πΉπΆπΉ1
(1+ππ΄πΆπΆ)+
πΉπΆπΉ2
(1+ππ΄πΆπΆ)2+β―+ ππΏ,π
β’ The simple procedure for the valuation of the company levered with constant π· πΈ is discussed in the next slide
Beta Rem Series
WACC
09/03/2013
Valuation procedure for constant D/E
8
β’ Do you know the cash flows of the firm till infinity?
β’ Then just use, ππΏ =πΉπΆπΉ1
(1+ππ΄πΆπΆ)+
πΉπΆπΉ2
(1+ππ΄πΆπΆ)2+β―β
β’ The growth rates and numbers are given only till first N years and after that a constant growth rate is given for FCF?
β’ Then we need to use ππΏ =πΉπΆπΉ1
(1+ππ΄πΆπΆ)+
πΉπΆπΉ2
(1+ππ΄πΆπΆ)2+β―+ ππΏ,π
Where ππΏ,π is the value of the firm at time N after which firm will have constant growth rate. This is also called the continuing value of the firm.
β’ ππΏ,π = πΉπΆπΉπ+1
(1+ππ΄πΆπΆ)+
πΉπΆπΉπ+2
(1+ππ΄πΆπΆ)2+β―β =
πΉπΆπΉπΓ(1+π)
ππ΄πΆπΆβπ
β’ Note: Make sure that cash flows are growing from Nth year. It means that the cash flow in the N+1th year is πΉπΆπΉπ Γ (1 + π).
Beta Rem Series 09/03/2013
Valuation for constant D
9
β’ ππΏ = ππ + ππΌππ
β’ In case of constant debt, ππΌππ = DT
β’ Hence, ππΏ = ππ + π·π.
β’ How to find π½πΌ?
β’ ππ’is nothing but the value of the firm if it is run by full equity. Then ππ΄ = ππ = ππ΄πΆπΆ ππ π’ππππ£ππππ ππππ
β’ So, discount the cash flows by ππ΄.
β’ ππ =πΉπΆπΉ1
(1+ππ΄)+
πΉπΆπΉ2
(1+ππ΄)2 +β―+ ππ,π
β’ ππ,π same as how ππΏ,π is found in the previous slide
Beta Rem Series 09/03/2013
Value added from other financial distortions
10
β’ To reiterate, the value of a levered firm increases from that of an unlevered firm from the financial distortions caused by adding debt to the firm
β’ The distortions we see in this course are
β Interest tax shelter
β Subsidized loans
β’ Lets see how this works
β’ What if there are there are two different debts π«π and π«π?
β’ Then it also matters what are the risk levels associated with these debts
β’ If both the debts are guarded by different security levels, like lets say π·1 gets first rights to assets, then both the debts are facing different risk levels and so are their interest tax shields.
Beta Rem Series 09/03/2013
Value added from other financial distortions
11
β’ But these are the rates decided by the markets. In that case, the only distortion will be the interest tax shelter
β’ It is correct to use the interest rates they are borrowed at, as discounting rates to find the respective values of ππΌππ.
β’ Then ππΌππ1 = ππ·1Γπ·1Γπ
ππ·1= π·1 Γ π and ππΌππ2 =
ππ·2Γπ·2Γπ
ππ·2= π·2 Γ π
β’ So, the value of the firm ππΏ = ππ + ππΌππ1+ππΌππ2 = ππ + π·1π + π·2π
β’ But, if both the debts are facing same risk level but different interest rates, then the cash flows or interest tax shelter should be discounted at the r that reflects the actual risk level which is the market rate. This means that we are getting a loan at a subsidy.
β’ Here, lets say if the firm goes to market, it faces an interest rate π2 and it borrows π·2 at π2
Beta Rem Series 09/03/2013
Value added from other financial distortions
12
β’ If Govt. or someone subsidizes the loan and provides loan at π1, and the firm borrows π·1at π1, this interest tax shield should still be discounted using π2as that is the rate reflecting the actual risk level
β’ Hence ππΌππ1 = π1Γπ·1Γπ
π2 and ππΌππ2 =
π2Γπ·2Γπ
π2 = π·2 Γ π
β’ But then if we assume that the firm value ππΏ = ππ + ππΌππ1+ππΌππ2, we end up
with ππΏ = ππ + π·1ππ1π2 + π·2π which is less than the earlier value as
π1 < π2. But this does not make sense!! We got loan at subsidy!!
β’ This is because here we are ignoring the value of subsidy itself that requires us to actually pay lesser amounts than if we had got it from the market for the same risk level
β’ The difference comes in the actual interest and principal payments made in the case of two loans.
Beta Rem Series 09/03/2013
Value added from other financial distortions
13
β’ How much is this value addition?
β’ If the repayment schedule for the subsidized loan π·1 is as below,
β’ These payments actually face a risk level corresponding to π2 even if the interest payment made is π1. So, if we use π2to find the effective present value of the loan by discounting these payments, we get
β’ π·1β² =
πΌ1
(1+π2)+
πΌ2
(1+π2)2 +β―+
πΌπ
(1+π2)π +
π1
(1+π2)+
π2
(1+π2)2 +β―+
ππ
(1+π2)π
β’ This π·1β² is effectively how much we are repaying.
Beta Rem Series 09/03/2013
Interest π°π π°π π°π
Principal π·π π·π π·π
1 2 n
Value added from other financial distortions
14
β’ So the difference between π·1 and π·1β² is a value addition to the firm and is
called the value of subsidy.
β’ Hence ππΏ = ππ + ππππ’π ππππ πππ π‘πππ‘ππππ
β’ Value from distortions will include value from interest tax shelter plus subsidies if any.
β’ These are called the adjustments and the final value obtained (ππΏ) is called the Adjusted Present Value (APV).
Beta Rem Series 09/03/2013
Illustrations
15
β’ To start with, let us say a firm has the following properties (perpetual CF)
β’ So, the value of unlevered firm, ππ =πΉπΆπΉπΉ
ππ΄
β’ FCFF = PBIT (1-T) = 360 Γ .5 = 180
β’ Hence, ππ =180
12%= 1500
β’ Now, let us assume that instead of funding this firm fully by equity, there is a constant debt funding of 1000 @ 10%.
β’ The only distortion added for the firmβs value is the interest tax shelter.
Beta Rem Series 09/03/2013
ππ¨ Tax PBIT
12% 50% 360
Illustrations
16
β’ In case of constant perpetual debt, interest tax shelter = DT
β’ Hence, ππΌππ = π·π = 1000 Γ 50% = 500
β’ ππΏ = ππ + ππΌππ = 1000 + 500 = 1500
β’ But, let us say in the debt of 1000, 500 actually came at a subsidized interest rate of 8%.
β’ In this case there would be both interest tax shelter distortion and the Subsidy distortion.
β’ ππΌππ =πΌππ ππ 500@10% πππ πππ’ππ‘ππ ππ‘ 10% +πΌππ ππ 500@8% πππ πππ’ππ‘ππ ππ‘ 10%
β’ ππΌππ =500Γ10%Γ50%
10%+
500Γ8%Γ50%
10%= 450
Beta Rem Series 09/03/2013
Illustrations
17
β’ ππππ΅ = D β Dβ² where D = 500 is the subsidized loan and π·β² is the effective value paid to the subsidizer.
β’ π·β² =πΌππ‘ππππ π‘ πππ¦ππππ‘π πππ 500@8% π‘πππ πππππππ‘π¦ πππ πππ’ππ‘ππ ππ‘ 10% =500Γ8%
10%= 400
β’ Hence ππππ΅ = 500 β 400 = 100
β’ ππΏ = ππ + ππΌππ + ππππ΅ = 1000 + 450 + 100 = 2050
Beta Rem Series 09/03/2013
Illustrations
18
β’ ππππ΅ = D β Dβ² where D = 500 is the subsidized loan and π·β² is the effective
Beta Rem Series 09/03/2013
Illustrations
19
β’ We have seen this problem already once last time. So, it will be short now
β’ If the value is calculated by completely ignoring the financial distortions, it is nothing but ππ which is -90 in this problem
β’ The distortions for the two debts is ππΌππ for loan A and ππππ΅ for loan B(as it does not have interest)
β’ For loan A:
β’ Discounting these ITS values at 10%, we get ππΌππ = 80.37
Beta Rem Series 09/03/2013
ITS π.12 9.12 π. ππ
1 2 20
Illustrations
20
β’ For loan B: ππππ΅ = D β Dβ² where D = 55 is the subsidized loan and π·β² is the effective value paid to the subsidizer.
β’ π·β² =πΌ1
(1+π2)+
πΌ2
(1+π2)2 +β―+
πΌπ
(1+π2)π +
π1
(1+π2)+
π2
(1+π2)2 +β―+
ππ
(1+π2)π
β’ = 55
1.09510= 22.19328
β’ Hence ππππ΅ = D β Dβ² = 55 β 22.19328 = 32.80672
β’ APV = ππΏ = ππ + ππΌππ + ππππ΅ = β90 + 80.37 + 32.81 = 23.18 > 0
Beta Rem Series 09/03/2013
Interest π π π
Principal 0 0 55
1 2 10
Acquisitions & Mergers
21
β’ Main point β Synergies and how can the synergies be split?
β Revenue synergies
β Cost synergies
β’ Let the acquirer be A, target be T, synergy be S and the combined firm be C.
β’ Then A+T+S = C
β’ To find S, find the independent values of A, T and find the value of C using the valuation principles learnt till now and find S
β’ Then the decisions has to be how much to pay to the target to acquire it and how to pay?
Beta Rem Series 09/03/2013
Notations
22
β’ πΊπ΄ - Gains to the acquirer
β’ πΊπ - Gains to the target = Acquisition premium
β’ ππ - Number of shares of Target outstanding
β’ ππ΄ - Number of shares of Acquirer outstanding
β’ π β Number of shares of Acquirer issued to target per target share outstanding = Exchange ratio
β’ ππ - Price of the target share
β’ ππ΄ - Price of the acquirer share
β’ π β share of Acquirer in Combined firm
β’ π‘ β share of Target in Combined firm
Beta Rem Series 09/03/2013
Cash acquisition
23
β’ An acquisition opportunity has the following properties
β’ Let us say, if the acquirer decides to pay 250 to the target for the acquisition.
β’ πΊπ = π΄πππ’ππ ππ‘πππ ππππππ’π = Price paid β Target value = 250-200 = 50
β’ πΊπ΄= Synergy β Acquisition premium
β’ This means acquirer will have the remaining part of the synergy which he is not paying as a premium
β’ Hence πΊπ΄= 100 β 50 = 50
Beta Rem Series 09/03/2013
A T S
Value 40 Γ 10 20 Γ 10 100
Shares 40 20
Price 10 10
Cash acquisition
24
β’ What will happen to the share prices of the acquirer and target shares once the announcement of acquisition is made?
β’ Acquirer pays π + πΊπ for the acquisition. This value goes to the ππ outstanding shares of the target. So, the price becomes
β’ ππ =π+πΊπ
ππ=
200+50
20= 12.5
β’ Acquirers final value will be π΄ + πΊπ΄. This will be owned by ππ΄ shares. So, the price becomes
β’ ππ΄ =π΄+πΊπ΄
ππ΄=
400+50
40= 11.25
Beta Rem Series 09/03/2013
All stock acquisition
25
β’ If the firm decides to go with all-stock acquisition and decides to pay 250 by issuing 25 more shares of A to T.
β’ Then, the total number of share of combined firm = 40+25 = 65
β’ In this 65, A has 40 and T has 25.
β’ Total value of combined firm, C = 700
β’ Hence Aβs ratio = 40
65Γ 700 = 430.76
β’ Bβs ratio = 25
65Γ 700 = 269.23
β’ Hence, πΊπ΄ = 430.76 πππππ π£πππ’π β 400(ππππππ ππππ’ππ ππ‘πππ) = 30.76
β’ πΊπ = 269.23 πππππ π£πππ’π β 200(ππππππ ππππ’ππ ππ‘πππ) = 69.23
Beta Rem Series 09/03/2013
All stock acquisition
26
β’ This can also be looked at in this way.
β’ Acquirer gets π of targetβs firm T and loses π‘ of his own firm A, but in addition he gets π of the synergy as well.
β’ Hence the total gain to the acquirer, πΊπ΄ = π Γ π β π‘ Γ π΄ + π Γ π
β’ Here, π =40
65 , π‘ =
25
65
β’ πΊπ΄ =40
65Γ 200 β
25
65Γ 400 +
40
65Γ 100
β’ Similarly, πΊπ = π‘ Γ π΄ β π Γ π + π‘ Γ π
Beta Rem Series 09/03/2013
Stock Acquisition
27
β’ So, to generalize if r acquirer shares are issued for every target share outstanding, then total number of shares in the combined firm = ππ΄ + π Γ ππ, where acquirer has ππ΄ shares and target has π Γ ππ shares
β’ Hence, π =ππ΄
ππ΄+πΓππ and π‘ =
πΓππ
ππ΄+πΓππ
β’ What will happen to the prices of the stocks soon after the announcement is made. Everyone knows combined value of the firm is A+T+S and the total number of shares would be ππ΄ + π Γ ππ . So, the combined share
price should be π΄+π+π
ππ΄+πΓππ
β’ As the acquirers shares are the same as combined firm shares, price of
share of acquirer would become this value. ππ΄ = π΄+π+π
ππ΄+πΓππ
β’ For the target, every one of its current shares represent π shares in the combined firm.
Beta Rem Series 09/03/2013
Stock Acquisition
28
β’ Hence, its share price should reflect the same thing. So, its price moves to
β’ ππ =π΄+π+π
ππ΄+πΓππΓ π = ππ΄ Γ π
β’ So, we know that the prices depend on the value of π. How to decide the value of π?
β’ In addition to the sharing of synergy, another important criterion generally used would be not to dilute the EPS as this is considered important from shareholderβs point of view.
β’ Let us say πΈπππ΄ is the EPS of acquirer and πΈπππ is the EPS of target.
β’ Let πΈπππ΄ = 1 and πΈπππ = 2. Then the total earnings of A = 1 Γ ππ΄ and total earnings of T = 2 Γ ππ. Earnings of combined firm = ππ΄ + 2ππ
β’ Total number of shares of combined firm = ππ΄ + π Γ ππ.
β’ Hence the total EPS of the combined firm = ππ΄+2ππ
ππ΄+πΓππ
Beta Rem Series 09/03/2013
Stock Acquisition
29
β’ If the acquirer does not want the EPS to get diluted, then
β’ππ΄+2ππ
ππ΄+πΓππβ₯ 1
β’ If ππ΄ = ππ , this would give π β€ 2 which means the acquirer would not be willing to give more than 2 of his shares per target share
β’ If the share in synergy demands more pay, the rest he might choose to pay in cash
β’ In such cases, both cash and stock components should be used to measure the gains as well as new prices.
Beta Rem Series 09/03/2013
LBOs and CCF method
30
β’ Leveraged Buy-Out is nothing but taking huge debt and buying out all the equity holders to take the firm private
β’ It is mandatory to value the equity(not the firm) here as it involves specifically buying out equity holders
β’ Methods
β FCFF
β FCFE
β CCF (refer to slide 6)
β’ FCFF and CCF methods of valuation is discussed already
β’ When WACC is changing continuously, CCF method is preferred as ππ΄ is used for discounting in this case which depends on the business does not change with the capital structure
Beta Rem Series 09/03/2013
LBOs and CCF method
31
β’ FCFF and CCF methods both give the value of the firm. Value of debt and other liabilities should be subtracted from the value of the firm to give the value of the equity
β’ FCFE β This is the direct measure of the cash flows to the equity. This can be broadly written as πΉπΆπΉπΈ = πΉπΆπΉπΉ β πΌ Γ (1 β π)
β’ This FCFE can be discounted at ππΈ to directly give the value of equity
Beta Rem Series 09/03/2013
Illustrations
33
ππ΄πΆπΆ = 12% Γ 0.5 + 10% Γ 1 β 0.4 Γ 0.5 = 9%
ππ΄ = 12% Γ 0.5 + 10% Γ 0.5 = 11%
FCFF:
ππ΅πΌπ Γ 1 β π = 90
Firm value = 90/WACC = 1000
Equity value = Firm value β Debt = 1000-500 = 500
CCF:
PAT + Interest = (150-50)Γ 0.6 + 50 = 110
Firm value = 110/ππ΄ = 1000
ππ¬ ππ« π«π¬ π» PBIT D
12% 10% 1 40% 150 500
Beta Rem Series 09/03/2013
Illustrations
34
Value of equity = Firm value β Debt = 1000-500 = 500
FCFE:
PAT = (150-50)Γ .6 = 60
Equity value = 60/ππΈ = 6012% = 500
Beta Rem Series 09/03/2013