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Risk-Adjusted Rates of ReturnCorporate Finance 101
Alan White
Rotman School of Management
University of Toronto
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Overview
What does corporate finance tell us about required
rates of return? Weighted average cost of capital
Capital structure theory Modigliani and Miller
Application to pension plans
Defined benefit plan Defined contribution plan
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Corporate Model
AssetsEarn rate k
DebtInterest rate r
EquityCost of equity ke
A market value balance sheet
Assets = Debt + Equity
Assume no taxes
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Investment Rule - WACC
Borrow $60 (D) at 5% interest (r) Annual cost is $3 (D r)
Raise $40 equity (E) Investors require a 10%return (ke) Annual cost is $4 (E ke)
Invest the assets (A = $100 = D + E) at rate k Annual income is $100 k
Investment rule is income should exceed costs
A k D kd + E r
0.6 5% 0.4 10% 7%e
D Ek r k
D E D E + = + =
+ +
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Levering Up Traditional View
Lower WACC implies makes it easier to attain our
objective Debt is cheap so use more debt. For example, use
90% debt financing
If assets earn 7% ($7 per year) we earn enough topay interest ($4) plus shareholders required return
($2) and have $1 residual The residual accrues to the shareholders
increasing the stock price
WACC 0.8 5% 0.2 10% 6%= + =
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Leverage and the Cost of Capital -Traditional View
WACC
Traditional View
0%
2%
4%
6%
8%
10%
12%
0% 20% 40% 60% 80% 100%
Debt / Debt + Equity
WACC r ke
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Changing Capital StructureModigliani and Miller
Procedure:
Start with our $60 debt, $40 equity firm Borrow an additional $20 (D*)
Repurchase $20 of equity or pay a $20 dividend
Result:
Debt is now worth $80 (D + D*)
Equity is now E* Shareholders have $20 in cash
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Are Shareholders Better Off? part 1
Formerly earned
100 k 60 r Now earn
100 k 80 r and have $20
If shareholders invest the cash in bonds theywould earn
(100 k 80 r) + (20 r) = 100 k 60 r
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Are Shareholders Better Off? part 2
Now earn
100 k 80 r and have $20 in cash
Before the capital structure change shareholderscould have borrowed $20.
In this case they would earn
(100 k 60 r) 20 r = 100 k 80 r
and have $20 in cash
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MM Conclusion
Capital structure changes can be replicated or
undone by homemade leverage As a result there is no value to a capital structure
change
Value of equity after the change plus the cash(E* + cash) equals the value of equity before the
change (E) In our example E = $40, cash = $20 so E* = $20
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MM: Implications for Cost of Equity
If assets earn 7% ($7 per year) we earn enough to
pay interest ($4 = 5% of $80) and to pay theshareholders $3
The equity value is $20 (E*)
Shareholders require and earn a rate of returnof 15%
As the firm levers up from 60% debt to 80% debtshareholders increase their required rate of returnfrom 10% to 15%
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MM: Implications for Cost of Capital
Cost of capital is independent of capital structure
Cost of debt is assumed constant Cost of equity rises as we lever up
where keU
is the cost of equity when there is nodebt, in our example 7%
( )U Ue e eD
k k k r A D
= +
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Leverage and the Cost of Capital -MM View
WACC
MM View
0%
5%
10%
15%
20%
0% 20% 40% 60% 80% 100%
Debt / Debt + Equity
WACC r ke
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MM: Implications for Equity Risk
Cost of equity rises as we lever up
Similar relation holds for both systematic and firmspecific risk measures. If debt is riskless
( )U Ue e eDk k k r A D
= +
ande A e A
A A
A D A D = =
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Application to DB Plan
The balance sheet of a DB plan looks quite a bit
like a corporate balance sheet Assets are a portfolio of 60% equity, 40% debt
Asset beta is about 0.6, asset volatility is about 12%
Pension liabilities are lot like debt
What are the characteristics of the surplus?
Translating this into the corporate modelsurplus = A D
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Risk of Surplus
Surplus Risk
Typical DB Plan
0
10
20
30
40
50
60
0% 5% 10% 15% 20% 25%
Surplus / Assets
Beta
Volatility
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Required Return on Surplus(Riskfree rate 4%, Risk Premium 4%)
Required Return on Surplus
Typical DB Plan
0%
50%
100%
150%
200%
250%
0% 5% 10% 15% 20% 25%
Surplus / Assets
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DB Plan
The risks of the surplus are substantial
Betas and volatilities apply to rates of return The dollar volume of risk is the return based risk
measure times the size of the surplus
Are these the types of risks that a corporationwants on its balance sheet?
$ $or 0.12AA A = =
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Impact on Corporate Balance Sheet(Assume no taxes, Risk premium = 4%)
6.0%6.0%6.0%6.0%WACC
8.4%6.7%6.3%6.8%ke4.0%4.0%4.0%4.0%kd
1.100.690.580.70Equity beta
0.500.500.500.50Asset beta
5.98.642.630.9Equity
7.13.26.812.3Debt1311.849.443.2Assets
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Impact on Corporate Balance Sheet(continued part 2)
0.60.5-0.91.1Surplus
3.97.418.832.7Liabilities
4.57.917.933.8Assets
Pension
5.98.642.630.9Equity
7.13.26.812.3Debt1311.849.443.2Assets
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Impact on Corporate Balance Sheet(continued part 3)
6.1%6.2%6.1%6.2%WACC
9.7%8.7%7.4%9.2%ke4.0%4.0%4.0%4.0%kd
1.421.170.851.31Equity beta
0.530.540.530.54Asset beta
6.59.141.732Equity
1110.625.645Debt17.519.767.377Assets
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Application to DC Plan
The balance sheet of a DC plan is different from a
corporate balance sheet Assets are a portfolio of 60% equity, 40% debt
Asset beta is about 0.6, asset volatility is about 12%
There is no surplus
Pension liabilities act like equity absorbing all risks
and returns This is like an all equity firm
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DC Plan Pension Risk
Pension risks are the same as the asset risks
The value of pension assets has an annual
volatility of about 12% Over a 25-year horizon the standard deviation of
asset returns and the standard deviation of
pension values is about 60% Are these the risks that pensioners are likely to
prefer?
pension pension0.6 and 12%A A = = = =
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Conclusions
Pensions that invest in risky assets create great
risk for the sponsor For DB plans the shareholders absorb a high level
of risk
For DC plans the pensioners absorb the risk
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