capital structure and cost of capital - 23&25-nov-2011
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Capital Structure and Cost of Capital
Dr. M.ThiripalrajuIndian Institute of Capital Markets
Financial ManagementFinancial Management
Capital StructureCapital Structure
bsw zRRzRWACC )1(
Where z = B / (S+B) is the proportion of debt finance and (1-z) = S / (S+B) is the proportion of equity finance. Rw is known as the weighted average cost of capital, WACC.
Capital StructureCapital Structure
The WACC is a weighted average of the cost of equity / share finance and the cost of debt/bond finance
WACCYV $
The value of the firm is:
Capital StructureCapital Structure
Minimising the WACC will also maximise the value of the firm
Capital StructureCapital Structure
The capital structure question merely asks whether it makes any difference to the market value of the firm V if the firm is financed by all equity (z = 0), all debt (z = 1) or a mixture of equity and debt (0<z<1).
The crucial question is whether an increase in leverage z leads to a fall in Rw and hence an increase in the value of the firm.
Traditional View: Cost of CapitalTraditional View: Cost of Capital
Debt-to-equity ratio (B/S)(B/S)*
Cost
of c
apita
l
Debt, Rb
WACC
Equity, Rs
Capital StructureCapital Structure
Franco Modigliani and Merton Miller, in a landmark 1958 paper, argued against the traditional view They stated that (under certain conditions) the value of the firm is independent of the mix of debt-to-equity finance).
WACC and LeverageWACC and Leverage
Let us see how the WACC varies as we alter the level of leverage z. Suppose Rb = 10% p.a. To start the ball rolling, if leverage z = 20%, let us assume shareholders require Rs = 15% p.a. Hence:
Rw = (1 – z) Rs + zRb = 0.8 (15%) + 0.2 (10%) = 14%
If we increase leverage to z = 50% and Rs remains unchanged at 15% then:
WACC Rw = 0.5 (15%) + 0.5 (10%) – 12.5%
The value of the firm V = Y / WACC will increase as the debt level initially increases.
WACC and LeverageWACC and Leverage
The Modigliani-Miller assumption is that as leverage z increases from z0 = 0.2 to z1 = 0.5 then Rs will rise, but it rises just enough so that Rw remains constant. For example, in a Modigliani – Miller world the required return by shareholders Rs would rise to 18% p.a. as leverage increased to 50%, so that Rw remains unchanged at 14%.
Rw = 0.5 (18%) + 0.5 (10%) = 14%
Leverage and the Return on EquityLeverage and the Return on EquityCapital raised = $10m = S + B = shares + debt (bonds)
Cost of debt = 10%1. Poor 2. Average 3. Good
Earnings before interest Yi (equal probability) 0.5 2 4
A. 100% equity (0% leverage)
(S = $10m equity)
Debt interest rB 0 0 0
Earnings/dividends for shareholders $0.5 $200 $4
Return on shares Ri = Div / S 0.5/10 = 5% 2/10 = 20% 4/10 = 40%
Expected return (standard deviation) 21.7% (14.3)
B. 20% levered (z = B/V = 2/10)
(B = $2m debt, S = $8m equity)
Debt interest rB $0.2 $0.2 $0.2
Earnings/dividends for shareholders $0.3 $1.8 $3.8
Return on shares Ri = Div / S 0.3/8 = 3.75%, 1.8/8 = 22.5%, 3.8/8 = 47.5%
Expected return (standard deviation) 24.6% (17.9)
Leverage and the Return on EquityLeverage and the Return on Equity
1. Poor 2. Average 3. Good
Earnings before interest Yi (equal probability)C. 50% levered (z = 5/10)
(B = $5m debt, S =$5m equity)
Debt interest rB $0.5 $0.5 $0.5
Earnings/dividends for shareholders $0.0 $1.5 $3.5
Return on shares Ri = Div / S 0.5 = 0% 1.5/5 = 30% 3.5/5 = 70%
Expected return (standard deviation) 33.3% (21.2)
How Leverage Affects Equity ReturnsHow Leverage Affects Equity Returns
As earnings Yi change from 1m to 4m, the equity return Rs for the all equity financed firm moves from 10% to 40% (A to B) but for the 50% levered firm the equity return changes much more, from 10% to 70% (A’ to C).
Earnings, Yi
Equity return, Rs 50% equity (50% debt)
100% equity (0% debt)
70%
40%
30%
20%
10%A
B
C
A’
0.5 1m 4m
Traditional ViewTraditional View
Consider an initial all equity financed company. The traditional view is that as the firm acquires increasing amounts of debt, then the WACC first falls but eventually rises, thus leading to an optimal debt-to-equity ratio at (B/S)*. The reason for the initial fall in the overall cost of capital is:
• The cost of debt Rb is less than the cost of equity Rs
• The cost of equity initially remains constant.
Hence, as you increase the proportion of debt, Rw falls. However, as more debt is added the cost of equity capital Rs begins to rise because:
The variability of future earnings (after deduction of interest payments) increases with leverage (as interest must be paid to bondholders regardless of the gross earnings of the company);
The risk of bankruptcy increases (and bondholders are ‘paid’ before equity holders).
Traditional ViewTraditional View
TRADITIONAL VIEW
There is a debt-to-equity mix which minimises the WACC and hence maximises the firm’s market value
Modigliani – Miller – No Corporate TaxesModigliani – Miller – No Corporate Taxes
Merton Miller put forward the following analogy to explain the MM Proposition I. Suppose the firm is a giant tub of whole milk. You could sell the ‘whole milk’. Alternatively you could separate out the cream and the remainder would be skimmed milk. The cream would sell at a high price but the skimmed milk would sell at a low price.
More formally, the MM view is also based on the idea that the value of a company is ultimately determined by the capitalised value (i.e. PV) of the future income stream from its activities in production, sales marketing and investment in ‘plant and machinery’.
Modigliani – Miller – No Corporate TaxesModigliani – Miller – No Corporate Taxes
Suppose firm A and firm B both have a PV of future (net) income of $100m. Firm A has 80% debt finance and 20% equity finance, while for firm B the proportions are 20% debt and 80% equity. The MM view implies that the market value should be the same for both firms (and equal to $100m). Basically the idea is this. If two firms X and Y are identical except for their capital structure, yet you can purchase the securities of X for less than the securities of Y, then an arbitrageur should short sell the securities of Y and buy the securities of X, thus making an immediate cash profit. Since the future cash flows from the identical firms X and Y are the same (in PV terms) then there are zero net cash flows in future periods, from the long and short positions in X and Y.
The value of the firm. MM Proposition I (no taxes)The value of the firm. MM Proposition I (no taxes)
V is independent of B/S
Debt-to equity ratio (B/S)
Value of firm, V
V
Modigliani – Miller – No Corporate TaxesModigliani – Miller – No Corporate Taxes
MODIGLIANI – MILLER ‘PROPOSITION I’
The WACC and the value of the firm are both independent of the debt-to-equity mix used in financing the firm’s
activities
Modigliani – Miller – No Corporate TaxesModigliani – Miller – No Corporate Taxes
ASSUMPTIONS: MODIGLIANI – MILLER APPROACH
• Perfect capital markets with borrowing and lending rates equal and the same for companies and persons.
• No corporate or personal taxes or transactions costs.
• Other firms exist with the same business (systematic) risk but different leverage.
• Net cash flows from physical investment projects can be regarded as perpetuities and are independent of the debt-to-equity mix
Modigliani – Miller – No Corporate TaxesModigliani – Miller – No Corporate TaxesV = S + B
Value of levered firm VL = value of unlevered firm VU
Capital StructureUnlevered LeveredVU = $1000 VL = ?
BU = $0 BL= $200
SL = ?
RB= 0.05
Note: Future cash flow from both firms is Y = $800
Modigliani – Miller – No Corporate TaxesModigliani – Miller – No Corporate TaxesLevered and unlevered company
Transaction $ Investment $ Return(a) Case U: buy 10% of unlevered company Buy 0.10 of VU $100 = 0.10 VU 0.10 Y
(b) Case L: buy 10% of levered company Buy 0.10 of VL 0.10SL = 0.10 (VL – BL) 0.10 [Y - 0.05 x 200]
= 0.10 (Y – Rb BL)
Modigliani – Miller – No Corporate TaxesModigliani – Miller – No Corporate Taxes
Cost of L = Cost of SL
0.10 (VL – BL) = 0.10 (VU – BL)
Hence:
VL = VU
We can now fill in the gaps in the preceding table.
VL = VU = $1000 and SL = VL – BL=$1000 - $200 = $800
Profitable ArbitrageProfitable Arbitrage
To show that home-made leverage and arbitrage ensures that VL = VU, consider starting with SL
*= $1300 so that we are in equilibrium:
VL* = SL
* + BL = $1500 > VU = $1000
Synthetic Leveraged CompanySynthetic Leveraged Company
Transaction $ Investment $ Return
Case SL: synthetic leverage = borrow and invest in levered companyBorrow 0.10 of BL -0.10 BL -0.10 Rb BL + 0.10 Y
Buy 0.10 of VU +0.10 VU
Net inv. = 0.10 (VU – BL) Return = 0.10 (Y – RbBL)
Direct Investment in Levered CompanyDirect Investment in Levered Company
Transaction $ Investment $ Return
Case L*: buy 10% of levered companyBuy 0.10 of SL
* (0.10) SL*=(0.10)$1300 0.10 (Y – RbBL)
=$130 =0.10 ($800 – 0.05 ($200))
=$79
Cost of home-made leverageCost of home-made leverage
Transaction $ Investment $ Return
Case SL*: borrow and invest in unlevered companyBorrow 0.10 of BL -0.10 BL= 0.10 ($200) = 20 -0.10 Rb BL = -1
Buy 0.10 of VU +0.10 VU = 0.10 ($1000) = 100 +0.10 Y = 80
Net inv. = $80 Net return = $79 =0.10 (VU – BL) =0.10 (Y – Rb BL)
Leverage and the Required Rate of Return on Leverage and the Required Rate of Return on EquityEquity
We have noted that the MM proposition implies that the overall cost of capital Rw is independent of the degree of leverage. One implication of this is that the WACC formula can be rearranged to show that the equilibrium expected return on equity (shares) Rs is positively related to leverage.
In equation WACC = Rw = (1-z) Rs + zRb, substitute z = B/V = B/(S+B) and rearrange to give:
SBRRRR bwws )(
Leverage and the Required Rate of Return on Leverage and the Required Rate of Return on EquityEquity
MODIGLIANI – MILLER ‘PROPOSITION II’
Since the WACC is independent of the debt-to-equity ratio, this implies that the cost of equity capital Rs rises with the
debt-to-equity ratio B/S
Modigliani – Miller with Corporate TaxesModigliani – Miller with Corporate TaxesThe cost of equity finance. MM proposition II (no taxes)
Cost of equity rises with rising debt-to-equity ratioDebt-to-equity ratio (B/S)(B/S)*
Cost
of c
apita
l
Rb
WACC, Rw
Rs= Rw + (Rw– Rb) (B/S)
Debtholders share some of the business risk
Modigliani – Miller with Corporate TaxesModigliani – Miller with Corporate Taxes
For two firms with the same business risk, then with corporate taxes the optimal debt ratio that maximises the
value of the firm involves 100% leverage (i.e. all debt financed)!
To develop this argument a little further note that, with corporate taxes, the value of an unlevered firm VU (i.e. 100% equity financed) equals the constant after-tax earnings Y(1 – t) discounted at the risk adjusted discount rate for an unlevered (i.e. all equity firm :
us
UtYV
)1(
us
The Value of an Unlevered and Levered FirmThe Value of an Unlevered and Levered Firm
For an unlevered (i.e. 100% equity financed) firm, after-tax earnings are Y(1-t) and the value of the firm is:
Where su = risk adjusted discount rate for an all equity financed
firm. For the levered firm, corporate taxes are calculated after deduction of interest payments. Hence, interest income paid to bondholders and the earnings available to shareholders are:
Interest income of bondholders = RbBL
Shareholder earnings = (Y – RbBL) (1 – t)
us
UtYV
)1(
The Value of an Unlevered and Levered FirmThe Value of an Unlevered and Levered Firm
Therefore, the total income accruing to both stakeholders in a levered firm is:
Total income of levered firm = (Y – RbBL)(1 – t) + RbBL=Y(1 – t) + t(RbBL)
= income of unlevered firm + ‘tax shield’
The Value of an Unlevered and Levered FirmThe Value of an Unlevered and Levered Firm
Note that Y(1 - t) equals the income accuring to an equivalent unlevered firm and hence should be discounted at s
u the risk adjusted discount rate for an all equity firm. The income from the tax shield arises because the firm holds debt of BL. If the tax shield is riskless it should be discounted at the rate Rb. Therefore, from equation the value of the levered firm VL is:
LUb
Lbus
L tBVRtBRtYV
)1(
The Value of an Unlevered and Levered FirmThe Value of an Unlevered and Levered Firm
MM PROPOSITION I (WITH CORPORATE TAXES)
Value of levered firm = value of unlevered firm + value of tax shield
)1/()1()/(*b
usLL
us RTVBWACC
Modigliani – Miller with Corporate TaxesModigliani – Miller with Corporate Taxes
MM PROPOSITION I (WITH CORPORATE TAXES)
Value of a levered firm VL = value of an unlevered firm VU +
value of the ‘tax shield’, tB
VL = VU + tB
Modigliani – Miller with Corporate TaxesModigliani – Miller with Corporate Taxes
It follows from the above equation that as the amount of debt B increases then the value of the levered firm increases and is maximised at 100% debt finance.
L
Lb
us
us
L
SBRtR
s))(1(
Modigliani – Miller with Corporate TaxesModigliani – Miller with Corporate Taxes
MM PROPOSITION II (WITH CORPORATE TAXES)
There is a positive relationship between the required return on equity in a levered firm Rs
L and the debt-to-equity ratio BL / SL
Return on Equity of a Levered Firm, RReturn on Equity of a Levered Firm, RssLL and the and the
Debt-to-Equity Ratio, BDebt-to-Equity Ratio, BLL/ S/ SLL
The relationship between the cost of equity in a levered firm RsL
and the debt-to-equity ratio BL/SL is a little involved. First, consider the balance sheet of the levered firm (paying corporate taxes):
Assets LiabilitiesValue unlevered firm VU Debt (bonds) BL
Value tax shield tBL Equity SL
Total VU + tBL BL + SL
Return on Equity of a Levered Firm, RReturn on Equity of a Levered Firm, RssLL and the and the
Debt-to-Equity Ratio, BDebt-to-Equity Ratio, BLL/ S/ SLL
The expected cash flow (perpetuity) per annum from VU and the tax shield tBL is:
Expected cash flow from assets = su VU
+ Rb (tBL)
The expected cash flow to equity and bondholders is:
RsL SL + Rb BL
Since there are no retained earnings, the two cash flows in equations and must be equal, which gives after rearrangement:
bL
L
L
us
ULs R
SBt
SVR )1(
Return on Equity of a Levered Firm, RReturn on Equity of a Levered Firm, RssLL and the and the
Debt-to-Equity Ratio, BDebt-to-Equity Ratio, BLL/ S/ SLL
But from equation and the fact that in an efficient market the value of the firm VL is equal to the market value of equity plus debt:
VL=VU + tBL =SL + BL
Hence:
VU = SL – (1 – t) BL_
Substituting equation in equation for VU:
bL
LLL
L
usL
s RSBtBtS
SR
)1(])1([
Return on Equity of a Levered Firm, RReturn on Equity of a Levered Firm, RssLL and the and the
Debt-to-Equity Ratio, BDebt-to-Equity Ratio, BLL/ S/ SLL
Note that for each unit increase in BL/SL the required return on equity Rs
L increases by (1 - t)(s
u – Rb), which is less than under the no tax case (I.e. t = 0). This concludes our proof of MM Proposition II.
bus
L
Lb
us
us
Ls Rwhere
SBRtR ))(1(
MM PROPOSITION II (WITH CORPORATE TAXES)
The required return on equity in a levered firm RsL increases
with the debt-to-equity ratio BL/SL
Cost of EquityCost of Equity
The APT requires estimates of the factor loadings bij and the price of risk I for each of these factors. It is then straightforward to calculate the cost of equity for firm i:
Ers = 1bs1 + 2bs2 + …
Either of these measures can be used as a measure of the cost of equity finance.
smss rERrER 83)(
Cost of DebtCost of Debt
bb RtR )1(*
Retained EarningsRetained Earnings
Weighted Average Cost of CapitalWeighted Average Cost of CapitalBtRSRC bs )1(
BSV
)1(cos)( tRBSBR
BSS
valuetotalttotalWACCR bsw
)1()1( tzRRz bs
Where z = B / (B + S) is the degree of leverage. With no corporate taxes we simply set t = 0 in the above equation. The WACC should be used as the discount rate in the NPV formula to discount after-tax earnings Y(1-t) for the marginal capital investment project as long as the following conditions hold.
Incentives and Economic Value AddedIncentives and Economic Value Added
EVA (or residual income) = earnings after tax, EAT – capital used
= EAT – (WACC x KC)
Return on capital ROC = EAT / KC = $100m / $1000m = 10%
The investment decision is then:
Invest in project if ROC > WACC
Economic profit EP = (ROC – WACC) x KC = (0.10 – 0.09) x $1000m = $10m
Incentives and Economic Value AddedIncentives and Economic Value Added
Economists will recognise this ‘average value’ as being the annuity value of the PV of the future earnings, sometimes called ‘permanent earnings/income’. The PV of the annuity flow EAT is, PV = EAT / WACC and the NPV criterion is:
Invest in the project if PV (earnings) > KC where PV = EAT/WACC
Or EAT – WACC x KC > 0
Incentives and Economic Value AddedIncentives and Economic Value Added
Fortune magazine (of 10th November 1997) provided figures for the EVA ($m) of companies, from which the following have been extracted:
EVA Capital ROC WACCGeneral Electric 2515 51017 17.7 12.7
General Motors -3527 94268 5.9 9.7
Johnson & Johnson 1327 15603 21.8 13.3
Incentives and Economic Value AddedIncentives and Economic Value Added
Capital at risk = loan exposure x LGD x ( L x percentile level)
EVA = ‘earnings’ – capital at risk x WACC > 0
RISK ADJUSTED RETURN ON CAPITAL: RAROC
RAROC = ‘earnings’ / ‘capital at risk’
Leverage and the Return on Equity (No Leverage and the Return on Equity (No Corporate Taxes)Corporate Taxes)
Y = earnings (cash flow, profits) before interest, tax and depreciation for either a levered L or unlevered U firm
SL = $-value of equity in a levered firm
BL = $-value of debt (bonds) in a levered firm
Vi = $-value of the firm ( i = U or L)
Rb = interest cost of debt
Rs = return on equity in levered firm
RsL = return on equity in levered firm
Z BL / VL = degree of leverage (and 1 – z SL / VL)
Div = total dividends paid to all shareholders
Leverage and the Return on Equity (No Leverage and the Return on Equity (No Corporate Taxes)Corporate Taxes)
The return on equity is defined as:
RsL = (Div) / SL
Using SL (1 – z) VL and Div = Y – Rb BL = Y – Rb (zBL) then:
Clearly, RsL depends on Y and leverage z.
)1()1()1()(
zzR
zVY
VzzVRYR b
LL
LbLs
Leverage and the Return on Equity (No Corporate Taxes)Leverage and the Return on Equity (No Corporate Taxes)
Rs = Y / VL
Where we have dropped the ‘L’ in the notation. The value of Y for which the all equity and a levered firm give an equal value for Rs is given from which we obtain:
Y* = RbV
Y* = 0.1 ($10m) = $1m which can be seen as the ‘cross-over point’. You might also note that equation can also be obtained by rearranging VL = Y / WACC to solve for Rs
L where WACC = (1 – z)RsL + zRb. This is perfectly
consistent as long as we realise that VL is held constant and only the proportions of S and B are being altered (I.e. leverage), which then has a direct effect on Rs
L. The overall result and equation is that the expected return on equity and the volatility of equity returns, are both higher the greater the degree of leverage z.
Modigliani – Miller with Corporate TaxesModigliani – Miller with Corporate Taxes
We show how Modigliani – Miller Proposition I is altered in the presence of corporate taxes. The relationship between the value of a levered firm and an unlevered firm is:
VL = VU + tBL
The value of the levered firm increases with the amount of debt BL
Therefore our original ‘no tax’ MM Proposition I that VL is independent of debt BL does not hold in the presence of
corporate taxes
Modigliani – Miller with Corporate TaxesModigliani – Miller with Corporate Taxes
We demonstrate that the cost of equity capital RsL in a levered
firm is given by:
Where su is the cost of equity capital in an unlevered firm (I.e.
100% equity financed), hence:
Our original MM Proposition II that RsL rises with the degree
of leverage (BL / SL) still holds in the presence of corporate taxes
L
Lb
us
us
Ls S
BRtR ))(1(
The Return on Equity in an Unlevered Firm and The Return on Equity in an Unlevered Firm and Adjusted Present ValueAdjusted Present Value
We derive an expression for the return on equity in an unlevered firm s
u in terms of the return on equity in a levered firm RsL and
the bond return Rb. This enables us to calculate su in terms of
the observables RsL and Rb.
)( rERr muu
s
We can then use our ‘calculated’ su as the discount rate in
the adjusted NPV technique
To apply the APV technique of project appraisal, we need a measure of the discount rate on an unlevered firm s
u . This can be obtained from the CAPM/SML:
The Return on Equity in an Unlevered Firm and The Return on Equity in an Unlevered Firm and Adjusted Present ValueAdjusted Present Value
However, we now require u, the beta of an unlevered firm. Unfortunately, (nearly) all firms are levered, so what we observe in the data is the beta of a levered firm L. Can we link Uyp L? the answer is yes. But the method is rather involved. We therefore consider the no tax case, before moving on to the case where we have corporate taxes.
Case A: No Corporate TaxesCase A: No Corporate Taxes
We begin with the fact that the beta of a levered firm is a weighted average of the debt b
L and equity sL betas (and the ‘weights’
sum to unity):
bL and s
L are observable/measurable from the SML, using data on returns on debt and equity for levered firms. MM Proposition I implies that the beta of an unlevered firm u (with equal business risk) equals that of a levered firm, hence:
Ls
L
LLb
L
LL
VS
V
Case A: No Corporate TaxesCase A: No Corporate Taxes
Where z = BL / VL. Equation allows us to calculate u from the observed b
L and sL. Now b
L < sL because debt is less risky than
equity, so equation implies:
u < sL
Hence, the beta of an all equity firm is less than the equity beta of a levered company. This also fits with MM-II where we found that the equity of a levered firm has higher risk than an ‘equivalent’ unlevered (100% equity) firm. If b
L 0 then equation becomes:
And it is easy in this case to see that u < sL.
Ls
Lb
Ls
L
LLb
L
L zzVS
Vu )1(
Ls
L
Lu
VS
Case B: With Corporate TaxesCase B: With Corporate Taxes
Again we want to obtain an expression for the unobservable in u terms of the observable/measurable values b
L and sL. The
derivation is a little involved so we immediately present the equation we are looking for, which is:
Ls
LL
LLb
LL
L
SBtS
StBtBu
)1()1()1(
Case B: With Corporate TaxesCase B: With Corporate Taxes
This is very similar to equation since in both equation and equation u is a weighted average of b
L and sL with the weights summing
to unity. In equation the ‘weights’ contain the tax rate t, as we might expect. Of course, if you set t = 0 in equation it ‘collapses’ to equation, the ‘no tax’ form of the equation. To prove equation we begin with the value of a levered firm, given by MM-I (with taxes):
VL=VU + tBL
Case B: With Corporate TaxesCase B: With Corporate Taxes
By definition, the value of the levered firm is equal to the market value of its debt and equity:
VL=BL + SL
From equations:
VU= (1- t) BL + SL
The definition of the beta of a levered firm is:
Ls
L
LLb
L
LL
VS
VB
Case B: With Corporate TaxesCase B: With Corporate Taxes
The next point holds the key to the derivation. From MM-I with taxes we have VL = VU + tBL. Hence, the beta of a levered firm can also be viewed as a weighted average of the beta of an unlevered (100% equity financed) firm and the beta of the tax shield (tB). Hence:
The beta of the cash flow from the tax shield is the ‘debt beta’, since here we assume the tax shield is riskless. We are now nearly there. Equating and rearranging:
Ls
U
LLb
U
Lu
VS
VtB
)1(
Lb
L
Lu
L
UL
VtB
VV
Case B: With Corporate TaxesCase B: With Corporate Taxes
Substituting for VU from equation ( )gives the expression required:
Ls
LL
LLb
LL
Lu
SBtS
SBttB
)1()1()1(
Case B: With Corporate TaxesCase B: With Corporate Taxes
The ‘unobservable’ beta of an unlevered firm is equal to a weighted average of the ‘observable’ betas on debt and
equity of the levered firm
Case B: With Corporate TaxesCase B: With Corporate Taxes
The ‘weights’ on bL and s
L in equation sum to unity. Again, note that since b
L < sL then from equation the beta of the equity
of an unlevered (100% equity financed) firm is less than the beta of the equity of a levered firm:
u < sL
This again fits with our MM-II (with taxes), which implies that levered equity is more risky than unlevered equity. If we set b
L = 0 in equation then it is easy to see that in this case u < s
L.
Assumptions when Using WACCAssumptions when Using WACC
Dollar amount of debt = KC and Dollar amount of equity = KC
The total dollar cost per annum of the debt and equity is:
Total dollar cost of finance p.a. = (1 – t) Rb KC + RsL KC
L
L
VB
L
L
VB
L
L
VB
L
L
VB
Assumptions when Using WACCAssumptions when Using WACCA variable investment project requires perpetual earnings Y p.a. from the project to exceed the dollar cost p.a., that is:
or
Note that the Y / KC is the project’s annual rate of return. Hence, a viable project exceeds the WACC, where the latter assumes the debt ratio BL / VL for the project, is the same as for the firm as a whole.
KCVSRKC
VBRtY
L
LLs
L
Lb
)1(
WACCVSR
VBRt
KCY
L
LLs
L
Lb
)1(
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